Relativistic Binaries in Globular Clusters
Matthew J.\ Benacquista
1500 N.\ 30th
Billings
Montana 59101
http://www.msubillings.edu/ScienceFaculty/Benacquista
The galactic population of globular clusters are old, dense star systems, with a typical cluster containing $10^4 - 10^7$ stars. As an old population of stars, globular clusters contain many collapsed and degenerate objects. As a dense population of stars, globular clusters are the scene of many interesting close dynamical interactions between stars. These dynamical interactions can alter the evolution of individual stars and can produce tight binary systems containing one or two compact objects. In this review, we discuss the theoretical models of globular cluster evolution and binary evolution, techniques for simulating this evolution which lead to relativistic binaries, and current and possible future observational evidence for this population. Globular cluster evolution will focus on the properties that boost the production of hard binary systems and on the tidal interactions of the galaxy with the cluster, which tend to alter the structure of the globular cluster with time. The interaction of the components of hard binary systems alters the evolution of both bodies and can lead to exotic objects. Direct $N$-body integrations and Fokker--Planck simulations of the evolution of globular clusters that incorporate tidal interactions and lead to predictions of relativistic binary populations are also discussed. We discuss the current observational evidence for cataclysmic variables, millisecond pulsars, and low-mass X-ray binaries as well as possible future detection of relativistic binaries with gravitational radiation.
article.tex
\documentclass[11pt]{livrev}
\bibliographystyle{livrev97}

\usepackage{epsf}

\newcommand{\mathbold}[1]{\mbox{\boldmath $#1$}}

\newlength{\zerolength}
\settowidth{\zerolength}{0}
\newcommand{\blankzero}{\hspace{\zerolength}}

\newlength{\dotlength}
\settowidth{\dotlength}{.}
\newcommand{\blankdot}{\hspace{\dotlength}}

\newlength{\gtlength}
\settowidth{\gtlength}{$ > $\,}
\newcommand{\blankgt}{\hspace{\gtlength}}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}

\title{Relativistic Binaries in Globular Clusters}

\author{Matthew  J.\ Benacquista \\
		Montana State University-Billings \\
		1500 N.\ 30th \\
		Billings, Montana 59101 \\
		e-mail: benacquista@msubillings.edu \\
		http://www.msubillings.edu/ScienceFaculty/Benacquista}

\date{}

\maketitle



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{abstract}
  The galactic population of globular clusters are old, dense star
  systems, with a typical cluster containing $10^4 - 10^7$ stars. As
  an old population of stars, globular clusters contain many collapsed
  and degenerate objects. As a dense population of stars, globular
  clusters are the scene of many interesting close dynamical
  interactions between stars. These dynamical interactions can alter
  the evolution of individual stars and can produce tight binary
  systems containing one or two compact objects. In this review, we
  discuss the theoretical models of globular cluster evolution and
  binary evolution, techniques for simulating this evolution which
  lead to relativistic binaries, and current and possible future
  observational evidence for this population. Globular cluster
  evolution will focus on the properties that boost the production of
  hard binary systems and on the tidal interactions of the galaxy with
  the cluster, which tend to alter the structure of the globular
  cluster with time. The interaction of the components of hard binary
  systems alters the evolution of both bodies and can lead to exotic
  objects. Direct $N$-body integrations and Fokker--Planck simulations
  of the evolution of globular clusters that incorporate tidal
  interactions and lead to predictions of relativistic binary
  populations are also discussed. We discuss the current observational
  evidence for cataclysmic variables, millisecond pulsars, and
  low-mass X-ray binaries as well as possible future detection of
  relativistic binaries with gravitational radiation.
\end{abstract}

\keywords{accretion, accretion disks, astronomical observations,
astronomy, astrophysics, binary systems, black holes, dynamical systems,
gravitational wave sources, neutron stars, pulsars, radio astronomy,
stars, white dwarfs}

\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Introduction}
\label{section:introduction}

Relativistic binaries containing white dwarfs, neutron stars, and black holes in compact orbits are over-represented in globular clusters compared with their population in the galactic field. Observations of this population reveal a host of exotic objects such as ultracompact cataclysmic variables, non-flickering X-ray and UV sources, low-mass X-ray binaries, and millisecond pulsars. These objects and their dark counterparts in the population of relativistic binaries are also likely to be observable sources of gravitational radiation for low-frequency gravitational wave detectors such as the planned space-borne interferometer, LISA. In the field, a relativistic binary is a product of the interplay between stellar evolution and the gravitational interaction of a tight binary. In globular clusters, the population of tight binaries is also a product of the dynamical evolution of an $N$-body gravitational system. Thus, relativistic binaries result from a combination of several of the more interesting processes in astrophysics. In keeping with the focus of this review article on relativistic binaries in globular clusters, we shall only touch on the aspects of globular clusters, observations, binary evolution, and $N$-body dynamics as they relate to populations of this specific class of binaries in globular clusters.

We begin by looking at the physical structure and general history of
the galactic globular cluster system that leads to the concentration
of evolved stars, stellar remnants, and binary systems in the cores of
the clusters. Current observations of globular clusters
that have revealed numerous populations of relativistic
binaries and their tracers are also presented. We also look at the prospects for future
observations in this rapidly changing area. Many of these relativistic
binaries are the product of stellar evolution in compact binaries. We
will look at how mass transfer from one star in the presence of a
nearby companion can dramatically alter the evolution of both stars in
the process of binary evolution. The enhanced production of
relativistic binaries in globular clusters results from dynamical
processes that drive binaries toward tighter orbits and that
preferentially exchange more massive and degenerate objects into
binary systems. Numerical simulations of globular cluster evolution,
which can be used to predict the rate at which relativistic binaries
are formed, are discussed. These models are compared with the
observable members of the population of relativistic
binaries. Finally, we conclude with a brief discussion of the
prospects for observing these systems in gravitational radiation.

Readers interested in further studies of the structure and evolution
of globular clusters are invited to look at Binney and Tremaine~\cite{binney87}, Spitzer~\cite{spitzer87}, and Volumes I and
II of Padmanabhan's {\it Theoretical Astrophysics}~\cite{padmanabhan00, padmanabhan01} for a good introduction to the physical processes involved. Review articles of Meylan \& Heggie~\cite{meylan97} and Meylan~\cite{meylan99} also provide a comprehensive look at the internal dynamics of globular clusters. Although our focus is solely on the Galactic globular cluster system, the physics of globular cluster systems associated with other galaxies is well covered in the review article by Harris~\cite{harris91} as well as his lecture notes from the Saas-Fee course on star clusters~\cite{harris01}. Carney has a thorough introduction to evolution of stars in globular clusters~\cite{carney01}. An observational perspective on the role of binaries in globular clusters is presented in an excellent review by Bailyn~\cite{bailyn95}, while a good introduction to the details of observing binary systems in general can be found in {\it An Introduction to Close Binary Stars}~\cite{hilditch01}. Although slightly out of date, the review of binaries in globular clusters by Hut {\it et al.}~\cite{hut92a} is an excellent introduction to the interaction between globular cluster dynamics and binary evolution, as is a short article on globular cluster binaries by McMillan, Pryor, and Phinney~\cite{mcmillan98}. Rappaport {\it  et al.}~\cite{rappaport01} and Rasio {\it et al.}~\cite{rasio01} have written reviews of numerical simulations of binary populations in globular clusters. An excellent introduction to the astrophysics and numerical techniques relevant to globular cluster dynamics can be found in the book by Heggie and Hut~\cite{heggie03}.
\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Globular Clusters}
\label{section:globular_clusters}

Globular clusters comprising $10^4$ to $10^7$ stars were formed early
in the history of the Milky Way, and are scattered throughout the
halo. The age of the clusters is about 13~Gyr, with an age spread of
less than 5~Gyr~\cite{carretta00}. According to the frequently updated
catalog of globular cluster properties maintained on the web by
Harris~\cite{harris96}, the globular cluster system numbers roughly
150 clusters. Although the list is fairly complete, new globular
clusters have been recently discovered at very low galactic
latitudes~\cite{hurt00, kobulnicky05}, and there is the prospect for a few more clusters to be hidden behind the bulge or out in the far reaches of the galaxy. The distribution of globular clusters in galacto-centric coordinates is shown in Figure~\ref{GC_coordinates}.

\begin{figure}[htb]
  \def\epsfsize#1#2{0.7#1}
  \centerline{\epsfbox{GC_coordinates.eps}}
  \caption{\it Globular cluster distribution about the galaxy. Positions
    are from Harris\protect~\protect\cite{harris96} and are plotted as
    black circles on top of the COBE FIRAS 2.2 micron map of the
    Galaxy using a Mollweide projection. Figure taken from Brian
    Chaboyer's website\protect~\protect\cite{chaboyerweb}.}
\label{GC_coordinates}
\end{figure}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Globular cluster stars}
\label{subsection:globular_cluster_stars}

\begin{figure}[htb]
  \def\epsfsize#1#2{1.0#2}
  \centerline{\epsfbox{M80.epsf}}
  \caption{\it Hubble Space Telescope photograph of the dense globular
    cluster M80 (NGC 6093).}
  \label{M80}
\end{figure}

Because the clusters are of great age, most of the stars above about
$0.8 M_{\odot}$ have already evolved off the main sequence. Thus, a
large number of red giants are readily visible in most pictures of
globular clusters (see Figure~\ref{M80}).
When viewing the color--magnitude diagram (CMD) for a globular cluster,
one can clearly see the red giant branch lifting up away from the main
sequence. The horizontal branch of evolved stars is also seen in the
CMD for M80 shown in Figure~\ref{M80_CMD}. 

\begin{figure}[htb]
  \def\epsfsize#1#2{0.6#1}
  \centerline{\epsfbox{M80_CMD.eps}}
  \caption{\it Color--magnitude diagram for M80. Figure taken from the catalog of 52 globular clusters~\cite{rosenberg00}. The entire catalog is available at the Padova Globular Cluster Group website (http://dipastro.pd.astro.it/globulars/).}
  \label{M80_CMD}
\end{figure}

The clearly visible turn-off point in the CMD for globular
clusters is evidence for the roughly coeval nature of the stars in the
cluster. During the early stages of the evolution of a globular
cluster, most of the gas and dust has been swept away. Subsequent
replenishment of the intercluster gas by stellar winds from evolved
stars is removed during periodic passages of the cluster through the
plane of the galaxy. The remaining gas is generally too hot for any
star formation to take place~\cite{freire01a}. Thus globular clusters
are made up of old, population II stars.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Globular cluster structure}
\label{subsection:globular_cluster_structure}

The overall structure of a globular cluster can be described in terms
of a roughly spherical $N$-body system with central densities in the range $10^{-1}$ to
$10^6 M_{\odot}/{\rm pc}^3$, and an average of
$10^4 M_{\odot}/{\rm pc}^3$. The important characteristic radii of a
globular cluster are the core radius $r_{\rm c}$, the half-light
radius $r_{\rm h}$, and the tidal radius $r_{\rm t}$. The core radius
is defined to be the radius at which the surface brightness has
dropped to half the central value. The half-light radius is the radius
that contains half of the light of the cluster and the tidal radius is
defined as the radius beyond which the external gravitational field of
the galaxy dominates the dynamics. Theorists define $r_{\rm h}$ to be
the radius containing half the mass of the cluster. The half-mass
radius is a three-dimensional theoretical construct, while the half-light radius
is a two-dimensional observational construct. The tidal radius is always determined by some
theoretical model. Typical values of these radii are 1.5~pc, 10~pc,
and 50~pc, respectively~\cite{binney87, padmanabhan01}.

There are also important characteristic time scales that govern the
dynamics of globular clusters. These are the crossing time
$t_{\rm cross}$, the relaxation time $t_{\rm relax}$, and the
evaporation time $t_{\rm evap}$. The crossing time is the typical time required for a star in the cluster to travel the characteristic size
$R$ of the cluster (typically taken to be the half-mass
radius). Thus, $t_{\rm cross} \sim R/v$, where $v$ is a typical
velocity ($\sim$\,10~km/s). The relaxation time is the typical
time for gravitational interactions with other stars in the cluster to
remove the history of a star's original velocity. This amounts to the
time required for gravitational encounters to alter the star's velocity
by an amount comparable to its original velocity. Since the relaxation
time is related to the number and strength of the gravitational
encounters of a typical cluster star, it is related to the number of
stars in the cluster and the average energy of the stars in the
cluster. Thus, it can be shown that the mean relaxation time for a
cluster is~\cite{binney87, padmanabhan00}
%
\begin{equation}
  t_{\rm relax} \simeq \frac{0.1 N}{\ln{N}} t_{\rm cross}.
  \label{relaxation_time}
\end{equation}
%
For a globular cluster with $N = 10^5$, a characteristic size of $R \sim r_h \sim 10~{\rm pc}$, and a typical velocity of $v \sim 10~{\rm km/s}$, the crossing time and relaxation time are $t_{\rm cross} \sim 10^6~{\rm yr}$ and $t_{\rm relax} \sim 10^9~{\rm yr}$, although Binney and Tremaine use $t_{\rm cross} \sim 10^5~{\rm yr}$ and consequently $t_{\rm relax} ~ 10^8~{\rm yr}$~\cite{binney87}. In real globular clusters, the relaxation time varies throughout the cluster and the median value is closer to $10^9~{\rm yr}$~\cite{binney87} as found in  Figure~1.3 of Spitzer~\cite{spitzer87} and Padmanabhan~\cite{padmanabhan01}.

The evaporation time for a cluster is the time required for the
cluster to dissolve through the gradual loss of stars that gain
sufficient velocity through encounters to escape its gravitational
potential. In the absence of stellar evolution and tidal interactions
with the galaxy, the evaporation time can be estimated by assuming
that a fraction $\gamma$ of the stars in the cluster are evaporated
every relaxation time. Thus, the rate of loss is
$dN/dt = -\gamma N/t_{\rm relax} = -N/t_{\rm evap}$. The value of
$\gamma$ can be determined by noting that the escape speed
$v_{\rm e}$ at a point $\mathbold{x}$ is related to the gravitational
potential $\Phi(\mathbold{x})$ at that point by
$v_{\rm e}^2 = -2\Phi(\mathbold{x})$. Consequently, the mean-square
escape speed in a cluster with density $\rho(\mathbold{x})$ is
%
\begin{equation}
  \langle{v^2_{\rm e}}\rangle = \frac{\int{\rho(\mathbold{x})
  v^2_{\rm e} d^3x}}{\int{\rho(\mathbold{x}) d^3x}} = -2
  \frac{\int{\rho(\mathbold{x}) \Phi(\mathbold{x}) d^3x}}{M} =
  -\frac{4W}{M},
  \label{escape_speed_1}
\end{equation}
%
where $W$ is the total potential energy of the cluster and $M$ is its
total mass. If the system is virialized (as we would expect after a
relaxation time), then $-W = 2K = M\langle{v^2}\rangle$, where $K$ is
the total kinetic energy of the cluster, and
%
\begin{equation}
  \langle{v^2_{\rm e}}\rangle = 4\langle{v^2}\rangle.
  \label{escape_speed_2}
\end{equation}
%
Thus, stars with speeds above twice the RMS speed will
evaporate. Assuming a Maxwellian distribution of speeds, the fraction
of stars with
$v > 2 v_{\rm rms}$ is $\gamma = 7.38 \times 10^{-3}$. Therefore, the
evaporation time is
%
\begin{equation}
  t_{\rm evap} = \frac{t_{\rm relax}}{\gamma} = 136 \, t_{\rm relax}.
  \label{evaporation_time}
\end{equation}
%
Stellar evolution and tidal interactions tend to shorten the
evaporation time. See Gnedin and Ostriker~\cite{gnedin97} and
references therein for a thorough discussion of these effects. Using a typical $t_{\rm relax}$ for a
globular cluster, we see that $t_{\rm evap} \sim 10^{10} {\rm\ yr}$, which is
comparable to the observed age of globular clusters.

The characteristic time scales of globular clusters differ significantly from each other:
$t_{\rm cross} \ll t_{\rm relax} \ll t_{\rm evap}$.

When discussing
stellar interactions during a given epoch of globular cluster
evolution, it is possible to describe the background structure of the
globular cluster in terms of a static model. These models describe the
structure of the cluster in terms of a distribution function $f$ that
can be thought of as providing a probability of finding a star at a
particular location in phase-space. The static models are valid over
time scales which are shorter than the relaxation time so that
gravitational interactions do not have time to significantly alter the
distribution function. We can therefore assume
$\partial f/\partial t \sim 0$. The structure of the globular cluster
is then determined by the collisionless Boltzmann equation,
%
\begin{equation}
  \mathbold{v} \cdot \mathbold{\nabla} f - \mathbold{\nabla} \phi
  \cdot \frac{\partial f}{\partial \mathbold{v}} = 0,
  \label{collisionless_boltzmann}
\end{equation}
%
where the gravitational potential $\phi$ is found from $f$ with
%
\begin{equation}
  \nabla^2\phi = 4\pi\int f(\mathbold{x}, \mathbold{v}, m) \, d^3v \,
dm.
  \label{static_potential}
\end{equation}

The solutions to Equation~(\ref{collisionless_boltzmann}) are often
described in terms of the relative energy per unit mass
${\cal E} \equiv \Psi - v^2/2$ with the relative potential defined as
$\Psi \equiv -\phi + \phi_0$. The constant $\phi_0$ is chosen so that
there are no stars with relative energy less than 0 (i.e.\ $f > 0$ for
${\cal E} > 0$ and $f = 0$ for ${\cal E} < 0$). A simple class of
solutions to Equation~(\ref{collisionless_boltzmann}),
%
\begin{equation}
  f({\cal E}) = F {\cal E}^{7/2},
  \label{plummer}
\end{equation}
%
generate what are known as Plummer models. A convenient class of
models which admit anisotropy and a distribution in angular momenta
$L$ are known as King--Michie models. The King--Michie distribution
function is:
%
\begin{equation}
  f({\cal E}, L) = \rho_1(2\pi \sigma^2)^{-3/2}
  \exp \left( \frac{-L^2}{2r_{\rm a}^2\sigma^2} \right)
  \left[e^{{\cal E}/{\sigma^2}}-1\right],
  \qquad {\cal E} > 0,
  \label{king-michie}
\end{equation}
%
with $f = 0$ for ${\cal E} \leq 0$ and $\rho_1$ a constant. The
velocity dispersion is determined by $\sigma$ and the anisotropy
radius $r_{\rm a}$ is defined so that the velocity distribution
changes from nearly isotropic at the center to nearly radial at
$r_{\rm a}$. The King--Michie distribution can be generalized to multi-mass systems, and although not dynamically correct, they can be used for mass estimates. A good description of the construction of a multi-mass King--Michie model can be found in the appendix of Miocchi~\cite{miocchi05}.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Globular cluster evolution}
\label{subsection:globular_cluster_evolution}

An overview of the evolution of globular clusters can be found in Hut
{\it et al.}~\cite{hut92a}, Meylan \& Heggie~\cite{meylan97}, and
Meylan~\cite{meylan99}. We summarize here the aspects of globular
cluster evolution that are relevant to the formation and concentration
of relativistic binaries. The formation of globular clusters is not
well understood~\cite{geyer02} and the details of the initial mass
function (IMF) are an ongoing field of star cluster studies. The Kroupa mass function~\cite{kroupa01d} is the most common IMF currently used (see~\cite{kroupa01a} for a discussion of the local IMF). It has the form:
%
\begin{equation}
  dN \propto m^{-\alpha_i} dm.
  \label{imf}
\end{equation}
%
where
%
\begin{equation}
          \begin{array}{l@{\quad\quad,\quad}l}
\alpha_0 = +0.3\pm0.7   &0.01 \le m/M_\odot < 0.08, \\
\alpha_1 = +1.3\pm0.5   &0.08 \le m/M_\odot < 0.50, \\
\alpha_2 = +2.3\pm0.3   &0.50 \le m/M_\odot < 1.00, \\
\alpha_3 = +2.3\pm0.7   &1.00 \le m/M_\odot,\\
          \end{array}
\label{alphas}
\end{equation}
%
Some older work uses the Salpeter IMF which assumes a single value of $\alpha$ in Equation~(\ref{imf}) for all masses.
Once the stars form out of the initial molecular cloud the system is not virialized (i.e. it does not satisfy Equation~(\ref{collisionless_boltzmann}), and it
will undergo what is known as violent relaxation as the protocluster first begins to
collapse. During violent relaxation, the total energy of individual stars can change as the local gravitational potential changes. The process of violent relaxation is a collisionless process and it occurs rapidly over a timescale given by a few crossing times. During violent relaxation, the energy per mass of a given star changes in a way that is independent of the mass of the star~\cite{binney87}. Thus, the more massive stars will have more kinetic
energy. These stars will then lose their kinetic energy to the less
massive stars through stellar encounters, which leads towards
equipartition of energy. Through virialization, this tends to
concentrate the more massive stars in the center of the cluster---a process known as mass segregation. The
process of mass segregation for stars of mass $m_i$ occurs on a
timescale given by $t_i \sim t_{\rm relax} \langle{m}\rangle/m_i$.

The higher concentration of stars in the center of the cluster
increases the probability of an encounter, which, in turn, decreases
the relaxation time. Thus, the relaxation time given in
Equation~(\ref{relaxation_time}) is an average over the whole
cluster. The local relaxation time of the cluster is given in Meylan
\& Heggie~\cite{meylan97} and can be described by:
%
\begin{equation}
  t_{\rm r} = \frac{0.065{\langle{v^2}\rangle}^{3/2}}
  {\rho \langle{m}\rangle G^2 \ln{\Lambda}},
  \label{local_relaxation_time}
\end{equation}
%
where $\rho$ is the local mass density, $\langle{v^2}\rangle$ is the
mass-weighted mean square velocity of the stars, $\langle{m}\rangle$
is the mean stellar mass. The Coulomb logarithm, $\ln{\Lambda}$, is the logarithm of the ratio of the maximum to minimum expected impact parameters in the cluster. Typical values of $\Lambda$ range between $0.4 N$~\cite{meylan97,padmanabhan01} and $0.1 N$~\cite{giersz96}. Binney and Tremaine provide a range of values for $\ln{\Lambda}$ from 10.1 in the center of the cluster to 12 at $r_{h}$. Note that in the
central regions of the cluster, the value of $t_{\rm r}$ is much lower
than the average relaxation time. This means that in the core of the
cluster, where the more massive stars have concentrated, there are
more encounters between these stars.

The concentration of massive stars in the core of the cluster will
occur within a few relaxation times,
$t \sim t_{\rm relax} \sim 10^9 {\rm\ yr}$. This time is longer than
the lifetime of low metallicity stars with
$M \geq 2 M_{\odot}$~\cite{schaller92}. Consequently, these stars will
have evolved into carbon-oxygen (CO) and oxygen-neon (ONe) white
dwarfs, neutron stars, and black holes. After a few more
relaxation times, the average mass of a star in the globular cluster
will be around $0.5 M_{\odot}$ and these degenerate objects will once
again be the more massive objects in the cluster, despite having lost
most of their mass during their evolution. Thus, the population in the
core of the cluster will be enhanced in degenerate objects. Any
binaries in the cluster that have a gravitational binding energy
significantly greater than the average kinetic energy of a cluster
star will act effectively as single objects with masses equal to their
total mass. These objects, too, will segregate to the central regions
of the globular cluster~\cite{vesperini97}. The core will then be
overabundant in binaries and degenerate objects.

The core would undergo what is known as core collapse within a few
tens of relaxation times unless these binaries release some of their
binding energy to the cluster. In core collapse, the central density
increases to infinity as the core radius shrinks to zero. An example
of core collapse can be seen in the comparison of two cluster
evolution simulations shown in
Figure~\ref{GC_evolution}~\cite{joshi00}. Note the core collapse when
the inner radius containing 1\% of the total mass dramatically shrinks
after $t \sim 15 \, t_{\rm relax}$. Since these evolution syntheses are
single-mass, Plummer models without binary interactions, the actual
time of core collapse is not representative of a real globular
cluster.

\begin{figure}[htbp]
  \def\epsfsize#1#2{0.6#1}
  \centerline{\epsfbox{GC_evolution.ps}}
  \caption{\it Lagrange radii indicating the evolution of a Plummer
	model globular cluster for an $N$-body simulation and a Monte Carlo
    simulation. The radii correspond to radii containing 0.35, 1, 3.5,
    5, 7, 10, 14, 20, 30, 40, 50, 60, 70, and 80\protect\% of the total
    mass. Figure taken from Joshi {\it et
     al.}\protect~\protect\cite{joshi00}.}
    \label{GC_evolution}
\end{figure}

The static description of the structure of globular clusters using
King--Michie or Plummer models provides a framework for describing the
environment of relativistic binaries and their progenitors in globular
clusters. The short-term interactions between stars and degenerate
objects can be analyzed in the presence of this background. Over
longer time scales (comparable to $t_{\rm relax}$), the dynamical
evolution of the distribution function as well as population changes
due to stellar evolution can alter the overall structure of the
globular cluster. We will discuss the dynamical evolution and its
impact on relativistic binaries in
Section~\ref{section:dynamical_evolution}.

Before moving on to the dynamical models and population syntheses of
relativistic binaries, we will first look at the observational
evidence for these objects in globular clusters.

\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Observations}
\label{section:tables}

Observational evidence for relativistic binaries in globular clusters has undergone an explosion in recent years, thanks to concentrated pulsar searches, improved X-ray source positions from Chandra, and optical follow-ups with HST and ground-based telescopes. There are challenges to detecting most binaries since they have generally segregated to the cores of the clusters where crowding can be a problem. Nonetheless, numerous observations of both binaries and their tracer populations have been made in several globular clusters.

One tracer population of the dynamical processes that may lead to the formation of relativistic binaries is the population of blue stragglers. These are stars that appear on the main sequence above and to the left of the turn-off in the CMD of a globular cluster (see Figure~\ref{M3BSS}). These stars are hot and massive enough that they should have already evolved off the main sequence. Consequently, these objects are thought to arise from stellar coalescences either through the gradual merger of the components of binaries or through direct collisions~\cite{fregeau04,piotto04}. Blue stragglers are some of the most visible and populous evidence of the dynamical interactions that can also give rise to relativistic binaries. For a good description of the use of far-ultraviolet surveys in detecting these objects, see Knigge~\cite{knigge04}. For somewhat older but still valuable reviews on the implications of blue stragglers on the dynamics of globular clusters, see Hut~\cite{hut93} and Bailyn~\cite{bailyn95}.

\begin{figure}[htbp]
  \def\epsfsize#1#2{0.3#1}
  \centerline{\epsfbox{M3HSTBSS.epsf}}
  \caption{\it CMD of M3 from the Hubble Space Telescope WFPC2. Note the stars above and to the left of the turn-off. These are the blue stragglers. Figure taken from Zhao and Bailyn \protect~\protect\cite{zhao05}.}
    \label{M3BSS}
\end{figure}


The globular cluster population of white dwarfs can be used to determine the ages of globular clusters~\cite{moehler04}, and so they have been the focus of targeted searches despite the fact that they are arguably the faintest objects in a globular cluster. These searches have yielded large numbers of globular cluster white dwarfs. For example, a recent search of $\omega$ Centauri has revealed over 2000 white dwarfs~\cite{monelli05}, while Hansen {\it et al.}~\cite{hansen04} have detected 222 white dwarfs in M4. In general, however, these searches uncover single white dwarfs. Optical detection of white dwarfs in binary systems tends to rely on properties of the accretion process related to the binary type. Therefore, searches for cataclysmic variables
generally focus on low-luminosity X-ray sources~\cite{johnston96,
grindlay01a, verbunt01} and on ultraviolet-excess
stars~\cite{grindlay99, knigge02a, margon81}, but these systems are
usually a white dwarf accreting from a low mass star. The class of
``non-flickerers'' which have been detected recently~\cite{cool98,
taylor01} have been explained as He white dwarfs in binaries
containing dark CO white dwarfs~\cite{edmonds99, grindlay01b, hansen03}.

Pulsars, although easily seen in radio, are difficult to detect when
they occur in hard binaries, due to the Doppler shift of the pulse
intervals. Thanks to an improved technique known as an ``acceleration
search''~\cite{middleditch84}, which assumes a constant acceleration
of the pulsar during the observation period, more short orbital period
binary pulsars are being discovered~\cite{camilo00, camilo01,
damico01a, damico01b, freire01b, fruchter00, ransom01}. For a good
review and description of this technique, see
Lorimer~\cite{lorimer01}. The progenitors of the ultracompact
millisecond pulsars are thought to pass through a low-mass X-ray
binary (LMXB) phase~\cite{deutsch00, grindlay01a, rappaport87,
rasio00a}. These systems are very bright and all of them in the
globular cluster system are known. There are, however, several
additional LMXBs that are currently quiescent~\cite{grindlay01a,verbunt04}.

Although there are many theoretical predictions of the existence of black holes in globular clusters (e.g.~\cite{miller02, portegieszwart00b, miller04, dantona04}), there are very few observational hints of them. Measurements of the kinematics of the cores of M15~\cite{gebhardt00,guhathakurta96} and NGC 6752~\cite{drukier03} provide some suggestions of a large, compact mass. However, these observations can also be explained without requiring an intermediate mass black hole~\cite{macnamara03, pasquali04}. The unusual millisecond pulsar in the outskirts of NGC 6752 has also been argued to be the result of a dynamical interaction with a possible binary intermediate mass black hole in the core~\cite{colpi02}. If the velocity dispersion in globular clusters follows the same correlation to black hole mass as in galactic bulges, then there may be black holes with masses in the range $1 - 10^3 M_{\odot}$ in many globular clusters~\cite{zheng01}. Stellar mass black hole binaries may also be visible as low luminosity X-ray sources, but if they are formed in exchange interactions, they will have very low duty cycles and hence are unlikely to be seen~\cite{kalogera04}.

Recent observations and catalogs of known binaries are presented in
the following sections.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Cataclysmic variables}
\label{subsection:cataclysmic_variables}

Cataclysmic variables (CVs) are white dwarfs accreting matter from a
companion that is usually a dwarf star or another white dwarf. They have been detected in globular clusters through
identification of the white dwarf itself or through evidence of the
accretion process. White dwarfs managed to avoid detection until
observations with the Hubble Space Telescope revealed
photometric sequences in several globular clusters~\cite{cool96,
cool98, paresce95, renzini96, richer95, richer97, taylor01,hansen04}. Spectral identification of white dwarfs in globular clusters has begun both from the ground with the VLT~\cite{moehler00,moehler04} and in space with the Hubble Space Telescope~\cite{cool98, edmonds99, taylor01,monelli05}. With spectral identification, it will be possible to identify those white dwarfs in hard binaries through Doppler shifts in the ${\rm H}\beta$ line. This approach has promise for detecting a large number of the expected double white dwarf binaries in globular clusters. Photometry has also begun to reveal orbital periods~\cite{neill02,edmonds03b,kaluzny03} of CVs in globular clusters.

Accretion onto the white dwarf may eventually lead to a dwarf nova
outburst. Identifications of globular cluster CVs have been made
through such outbursts in the cores of M5~\cite{margon81}, 47
Tuc~\cite{paresce94}, NGC 6624~\cite{shara96b}, M15~\cite{shara04}, and M22~\cite{anderson03,bond05}. With the exception
of V101 in M5~\cite{margon81}, original searches for dwarf novae
performed with ground based telescopes proved unsuccessful. This is
primarily due to the fact that crowding obscured potential dwarf novae
up to several core radii outside the center of the
cluster~\cite{shara94, shara95a}. Since binaries tend to settle into
the core, it is not surprising that none were found significantly
outside of the core. Subsequent searches using the improved resolution
of the Hubble Space Telescope eventually revealed a few dwarf novae
close to the cores of selected globular clusters~\cite{shara96a,
shara95b, shara96b,shara04,anderson03}.

A more productive approach has been to look for direct evidence of the
accretion around the white dwarf. This can be in the form of excess UV
emission and strong ${\rm H}\alpha$ emission~\cite{ferraro01,
grindlay91, knigge02a, knigge02b, dieball05} from the accretion disk. This technique has
resulted in the discovery of candidate CVs in 47~Tuc~\cite{ferraro01,
knigge02a}, M92~\cite{ferraro00a}, NGC 2808~\cite{dieball05}, NGC 6397~\cite{cool98, edmonds99,
taylor01}, and NGC 6712~\cite{ferraro00b}. The accretion disk can
also be discerned by very soft X-ray emissions. These low luminosity
X-ray binaries are characterized by a luminosity
$L_{\rm X} < 10^{34.5} {\rm\ erg/s}$, which distinguishes them from
the low-mass X-ray binaries with
$L_{\rm X} > 10^{36} {\rm\ erg/s}$. Initial explanations of these
objects focused on accreting white dwarfs~\cite{bailyn91}, and a
significant fraction of them are probably CVs~\cite{verbunt04, webb05}. There have been 10 identified candidate CVs in 6752~\cite{pooley02a}, 19 in 6440~\cite{ pooley02b}, 2 in $\omega$ Cen~\cite{gendre03}, 5 in Terzan 5~\cite{heinke03a}, 22 in 47 Tuc~\cite{edmonds03a}, 5 in M80~\cite{heinke03b}, and 1 in M4~\cite{bassa04}. However, some of the
more energetic sources may be LMXBs in quiescence~\cite{verbunt04}, or even candidate QSO sources~\cite{bassa04}.

The state of the field at this time is one of rapid change as Chandra
results come in and optical counterparts are found for the new X-ray
sources. A living catalog of CVs has been created by Downes {\it et
al.}~\cite{downes01} and may be the best source for confirmed CVs in
globular clusters.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Low-mass X-ray binaries}
\label{subsection:lmxbs}

The X-ray luminosities of low-mass X-ray binaries are in the range
$L_{\rm X} \sim 10^{36} - 10^{38} {\rm\ erg/s}$. The upper limit is
close to the Eddington limit for accretion onto a neutron star, so
these systems must contain an accreting neutron star or black
hole. All of the LMXBs in globular clusters contain an accreting
neutron star as they also exhibit X-ray bursts, indicating
thermonuclear flashes on the surface of the neutron
star~\cite{johnston96}. Compared with $\sim 100$ such systems in the
galaxy, there are 13 LMXBs known in globular clusters. The globular
cluster system contains roughly 0.1\% of the mass of the galaxy and
roughly 10\% of the LMXBs. Thus, LMXBs are substantially
over-represented in globular clusters.

Because these systems are so bright in X-rays, the globular cluster
population is completely known -- we expect no new LMXBs to be
discovered in the globular cluster system (unless more multiple
sources are resolved from these 13 sources). The 13 sources are in 12
separate clusters. Three have orbital periods greater than a few
hours, four ultracompact systems have measured orbital periods less
than 1 hour, and six have undetermined orbital periods. The period of X1746-370 in NGC 6441 has recently been measured at $P_{\rm orb} = 5.16~{\rm h}$ using the Rossi X-ray Timing Explorer (RXTE)~\cite{balucinska04}. A member of
the ultracompact group, 4U 1820-30 (X1820-303) in the globular cluster
NGC 6624, has an orbital period of 11 minutes~\cite{stella87}. This is
the shortest known orbital period of any binary and most certainly
indicates a degenerate companion. The orbital period, X-ray
luminosity, and host globular clusters for these systems are given in
Table~\ref{LMXB_Properties}.

\vspace{1 em} \hrule \vspace{0.05 cm} \hrule \vspace{0.2 cm}

\noindent \, \hfill
\begin{minipage}[t]{2.5 cm}
\centering{LMXB Name} \\
\centering{~}
\end{minipage}
\begin{minipage}[t]{2.5 cm}
\centering{Cluster} \\
\centering{~}
\end{minipage}
\begin{minipage}[t]{2.5 cm}
\centering{$ L_{\rm X} $} \\
\centering{($ \times 10^{36} {\rm\ erg/s} $)}
\end{minipage}
\begin{minipage}[t]{1.2 cm}
\centering{$ P_{\rm orb} $} \\
\centering{(hr)}
\end{minipage}
\begin{minipage}[t]{2.5 cm}
\centering{Ref.} \\
\centering{~}
\end{minipage}
\hfill \,

\vspace{0.2 cm} \hrule \vspace{0.2 cm}

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X0512--401~\end{minipage}
\begin{minipage}{2.5 cm}~~~NGC 1851~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{1.9~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{$ < 0.85 $~}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1724--307\footnotemark~\end{minipage}%
\footnotetext{Sidoli {\it et al.}~\cite{sidoli01} give X1724--304.}
\begin{minipage}{2.5 cm}~~~Terzan 2~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{4.3~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\centerline{~~---}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1730--335~\end{minipage}
\begin{minipage}{2.5 cm}~~~Liller 1~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{2.2~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\centerline{~~---}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1732--304~\end{minipage}
\begin{minipage}{2.5 cm}~~~Terzan 1~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{0.5~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\centerline{~~---}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1745--203~\end{minipage}
\begin{minipage}{2.5 cm}~~~NGC 6440~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{0.9~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\centerline{~~---}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1745--248~\end{minipage}
\begin{minipage}{2.5 cm}~~~Terzan 5~\end{minipage}
\begin{minipage}{2.5 cm}\centerline{~~---}\end{minipage}
\begin{minipage}{1.2 cm}\centerline{~~---}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1746--370~\end{minipage}
\begin{minipage}{2.5 cm}~~~NGC 6441~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{7.6~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{5.70~}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00, podsiadlowski02,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1747--313~\end{minipage}
\begin{minipage}{2.5 cm}~~~Terzan 6~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{3.4~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{12.36~}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00, podsiadlowski02,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1820--303~\end{minipage}
\begin{minipage}{2.5 cm}~~~NGC 6624~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{40.6~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.19~}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00, podsiadlowski02,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1832--330~\end{minipage}
\begin{minipage}{2.5 cm}~~~NGC 6652~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{2.2~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.73~}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00,
podsiadlowski02}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X1850--087~\end{minipage}
\begin{minipage}{2.5 cm}~~~NGC 6712~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{0.8~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.33~}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00, podsiadlowski02,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X2127+119-1~\end{minipage}
\begin{minipage}{2.5 cm}~~~NGC 7078~\end{minipage}
\begin{minipage}{2.5 cm}\rightline{3.5~~~~~~~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{17.10~}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00, podsiadlowski02,
sidoli01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}~~X2127+119-2~\end{minipage}
\begin{minipage}{2.5 cm}~~~NGC 7078~\end{minipage}
\begin{minipage}{2.5 cm}\centerline{~~---}\end{minipage}
\begin{minipage}{1.2 cm}\centerline{~~---}\end{minipage}
\begin{minipage}{2.5 cm}\rightline{\cite{deutsch00, podsiadlowski02,nwhite01}}\end{minipage}
\hfill \,

\vspace{0.2 cm} \hrule \vspace{0.05 cm} \hrule \vspace{- 0.5 cm}

\begin{table}[hptb]
  \caption{\it Low-mass X-ray binaries in globular clusters: Host
    clusters and LMXB properties.}
  \label{LMXB_Properties}
\end{table}

The improved resolution of Chandra allows for the possibility of
identifying optical counterparts to LMXBs. If an optical counterpart
can be found, a number of additional properties and constraints for
these objects can be determined through observations in other
wavelengths. In particular, the orbital parameters and the nature of
the secondary can be determined. So far, optical counterparts have
been found for X0512--401 in NGC 1851~\cite{homer01b}, X1745--203 in
NGC 6440~\cite{verbunt00}, X1746--370 in NGC 6441~\cite{deutsch98},
X1830--303 in NGC 6624~\cite{king93}, X1832--330 in NGC
6652~\cite{deutsch00, heinke01}, X1850--087 in NGC
6712~\cite{cudworth88, bailyn88, nieto90}, X1745-248 in Terzan 5~\cite{heinke03a}, and both LMXBs in NGC
7078~\cite{auriere84,nwhite01}. Continued X-ray observations will also further
elucidate the nature of these systems~\cite{mukai00}.

The 13 bright LMXBs are thought to be active members of a larger population of lower luminosity quiescent low mass X-ray binaries (qLMXBs)~\cite{wijnands05}. Early searches performed with ROSAT data (which had a detection limit
of $10^{31} {\rm\ erg/s}$) revealed roughly 30 sources in 19 globular
clusters~\cite{johnston96}. A more recent census of the ROSAT low
luminosity X-ray sources, published by Verbunt~\cite{verbunt01}, lists
26 such sources that are probably related to globular clusters. Recent
observations with the improved angular resolution of Chandra have
begun to uncover numerous low luminosity X-ray candidates for
CVs~\cite{grindlay01a, grindlay01b, heinke01, homer01a, heinke03a, heinke03b, edmonds03a, edmonds03b, gendre03, pooley02a, pooley02b}. For a reasonbly complete discussion of recent observations of qLMXBs in globular clusters, see Verbunt and Lewin~\cite{verbunt04} or Webb and Barret~\cite{webb05} and references therein.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Millisecond pulsars}
\label{subsection:millisecond_pulsars}

The population of known millisecond pulsars (MSPs) is one of the fastest growing populations of relativistic binaries in globular clusters. Several ongoing searches are continuing to reveal millisecond pulsars in a number of globular clusters. Previous searches have used deep
multifrequency imaging to estimate the population of pulsars in
globular clusters~\cite{fruchter00}. In this approach, the expected number of pulsars
beaming toward the earth, $N_{\rm puls}$, is determined by the total
radio luminosity observed when the radio beam width is comparable in
diameter to the core of the cluster. If the minimum pulsar luminosity
is $L_{\rm min}$ and the total luminosity observed is $L_{\rm tot}$,
then, with simple assumptions on the neutron star luminosity function,
%
\begin{equation}
  N_{\rm puls} = \frac{L_{\rm tot}}{L_{\rm min}
  \ln{\left(L_{\rm tot}/L_{\rm min}\right)}}.
  \label{luminosity_number}
\end{equation}
%
In their observations of 7 globular clusters, Fruchter and Goss have
recovered previously known pulsars in NGC 6440, NGC 6539, NGC 6624,
and 47~Tuc~\cite{fruchter00}. Their estimates based on
Equation~(\ref{luminosity_number}) give evidence of a population of
between 60 and 200 previously unknown pulsars in Terzan~5, and about
15 each in Liller~1 and NGC 6544~\cite{fruchter00}.

Current searches include: Arecibo, which is searching over 22 globular clusters~\cite{hessels04}; Green Bank Telescope (GBT), which is working alone and in conjunction with Arecibo~\cite{jacoby02, hessels04}; the Giant Metrewave Radio Telescope (GMRT), which is searching over about 10 globular clusters~\cite{freire04}; and Parkes, which is searching over 60 globular clusters~\cite{damico03}. Although these searches have been quite successful, they are still subject to certain selection effects such as distance, dispersion measure, and acceleration in compact binaries~\cite{camilo05}. For an excellent review of the properties of all pulsars in globular clusters, see the review by Camilo and Rasio~\cite{camilo05} and references therein. The properties of known pulsars in binary systems with orbital period less than one day are listed in Table~\ref{MSP_Properties}, which is a subset of Table~1 in Camilo and Rasio~\cite{camilo05}.

\vspace{1 em} \hrule \vspace{0.05 cm} \hrule \vspace{0.2 cm}

\noindent \, \hfill
\begin{minipage}[t]{2.5 cm}
\centering{Pulsar} \\
\centering{~}
\end{minipage}
\begin{minipage}[t]{1.5 cm}
\centering{$ P_{\rm spin} $} \\
\centering{(ms)}
\end{minipage}
\begin{minipage}[t]{2.0 cm}
\centering{Cluster} \\
\centering{~}
\end{minipage}
\begin{minipage}[t]{1.2 cm}
\centering{$ P_{\rm orb} $} \\
\centering{(days)}
\end{minipage}
\begin{minipage}[t]{1.6 cm}
\centering{$ e $} \\
\centering{~}
\end{minipage}
\begin{minipage}[t]{1.2 cm}
\centering{$ M_2 $} \\
\centering{($ M_{\odot} $)}
\end{minipage}
\begin{minipage}[t]{1.6 cm}
\centering{Ref.} \\
\centering{~}
\end{minipage}
\hfill \,

\vspace{0.2 cm} \hrule \vspace{0.2 cm}

\noindent \, \hfill
\begin{minipage}{2.5 cm}J0024--7204I~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.484~}\end{minipage}
\begin{minipage}{2.0 cm}~47~Tuc~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.229~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\,0.0004~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.013~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{freire03}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J0023--7203J~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{2.100~}\end{minipage}
\begin{minipage}{2.0 cm}~47~Tuc\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.120~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\,0.00004~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.021~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{freire03}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J0024--7204LO~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{2.643~}\end{minipage}
\begin{minipage}{2.0 cm}~47~Tuc\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.135~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\,0.00016~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.022~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{freire03}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J0024--72P~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.643~}\end{minipage}
\begin{minipage}{2.0 cm}~47~Tuc\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.147~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.017~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{camilo00}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J0024--72R~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.480~}\end{minipage}
\begin{minipage}{2.0 cm}~47~Tuc\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.066~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.026~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{camilo00}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J0024--7203U~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{4.342~}\end{minipage}
\begin{minipage}{2.0 cm}~47~Tuc~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.429~}\end{minipage}
\begin{minipage}{1.6 cm}~\blankgt 0.000014~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.12~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{freire03}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J0024--72V~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{4.810~}\end{minipage}
\begin{minipage}{2.0 cm}~47~Tuc\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.2~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.34~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{camilo00}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J0024--7204W~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{2.352~}\end{minipage}
\begin{minipage}{2.0 cm}~47~Tuc~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.133~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.12~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{edmonds02}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J0024--72Y~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{2.196~}\end{minipage}
\begin{minipage}{2.0 cm}~47~Tuc\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.521~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.013~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{lorimer03}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}B1516+02C~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{2.484~}\end{minipage}
\begin{minipage}{2.0 cm}~M5\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.087~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.037~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{camilo05}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}B1639+36D~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.118~}\end{minipage}
\begin{minipage}{2.0 cm}~M13\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.591~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.17~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{camilo05}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}B1639+36E~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{2.487~}\end{minipage}
\begin{minipage}{2.0 cm}~M13\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.213~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.061~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{camilo05}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1701--3006B~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.593~}\end{minipage}
\begin{minipage}{2.0 cm}~M62\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.144~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\,0.00007~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.12~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{possenti03}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1701--3006C~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.806~}\end{minipage}
\begin{minipage}{2.0 cm}~M62\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.215~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\,0.00006~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.069~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{possenti03}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1701--3006E~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.234~}\end{minipage}
\begin{minipage}{2.0 cm}~M62\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.16~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.03~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{chandler03}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1701--3006F~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{2.295~}\end{minipage}
\begin{minipage}{2.0 cm}~M62\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.20~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.018~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{chandler03}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}B1718--19~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{1004.03~}\end{minipage}
\begin{minipage}{2.0 cm}~NGC 6342~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.258~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\,0.005~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.11~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{vankerkwijk00}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1748--2446A~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{11.563~}\end{minipage}
\begin{minipage}{2.0 cm}~Terzan 5~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.075~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\,0.0012~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.087~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{lyne00}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1748--2446AM\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.569~}\end{minipage}
\begin{minipage}{2.0 cm}~Terzan 5~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.443~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.13~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{ransom05}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1748--2446N~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{8.666~}\end{minipage}
\begin{minipage}{2.0 cm}~Terzan 5~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.385~}\end{minipage}
\begin{minipage}{1.6 cm}~0.000045~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.46~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{ransom05}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1748--2446O~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{1.676~}\end{minipage}
\begin{minipage}{2.0 cm}~Terzan 5~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.259~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.035~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{ransom05}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1748--2446P~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{1.728~}\end{minipage}
\begin{minipage}{2.0 cm}~Terzan 5~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.362~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.36~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{ransom05}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1748--2446V~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{2.072~}\end{minipage}
\begin{minipage}{2.0 cm}~Terzan 5~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.503~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.11~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{ransom05}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1807--24A~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.059~}\end{minipage}
\begin{minipage}{2.0 cm}~NGC 6544~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.071~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{---~}\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.0089~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{damico01a,
ransom01}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1911--5958A~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.266~}\end{minipage}
\begin{minipage}{2.0 cm}~NGC 6752~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.837~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\,0.00001~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.18~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{damico02}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J1911+0102A~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{3.618~}\end{minipage}
\begin{minipage}{2.0 cm}~NGC 6760~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.140~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\,0.00013~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.017~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{freire05}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}B2127+11C~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{30.529~}\end{minipage}
\begin{minipage}{2.0 cm}~M 15~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.335~}\end{minipage}
\begin{minipage}{1.6 cm}~\blankgt 0.681~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.92~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{anderson90}}\end{minipage}
\hfill \,

\noindent \, \hfill
\begin{minipage}{2.5 cm}J2140--2310A~\end{minipage}
\begin{minipage}{1.5 cm}\rightline{11.019~}\end{minipage}
\begin{minipage}{2.0 cm}~M30~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.173~}\end{minipage}
\begin{minipage}{1.6 cm}~$ < $\, 0.00012~\end{minipage}
\begin{minipage}{1.2 cm}\rightline{0.01~}\end{minipage}
\begin{minipage}{1.6 cm}\rightline{\cite{ransom04}}\end{minipage}
\hfill \,

\vspace{0.2 cm} \hrule \vspace{0.05 cm} \hrule \vspace{- 0.5 cm}

\begin{table}[hptb]
  \caption{\it Short orbital period binary millisecond pulsars in
    globular clusters. Host clusters and orbital properties.}
  \label{MSP_Properties}
\end{table}

With the ongoing searches, it can be reasonably expected that the number of millisecond pulsars in binary systems in globular clusters will continue to grow in the coming years.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Black holes}
\label{subsection:black_holes}

There have been very few observations of black hole binaries in
globular clusters. Although there have been hints of possible black
hole binaries in extragalactic globular cluster
systems~\cite{angelini01, distefano02}, there are no known black hole
binaries in the galactic globular cluster system. All of the globular
cluster high luminosity LMXBs exhibit the X-ray variability that is indicative of
nuclear burning on the surface of a neutron star. It is possible that some of the recently discovered low luminosity LMXBs may house black holes instead of neutron stars~\cite{verbunt04}, it is more likely that they are simply unusual neutron star LMXBs in quiesence~\cite{wijnands05}. Finally, there is very circumstantial evidence for the possible existence of an intermediate mass black hole (IMBH) binary in NGC 6752 based upon an analysis of the MSP binary PSR A~\cite{colpi03,colpi02}.

\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Relativistic Binaries}
\label{section:relativistic_binaries}

Relativistic binaries are binary systems with at least one degenerate
or collapsed object and an orbital period such that they will be
brought into contact within a Hubble time. (Note that this definition
also includes binaries which are already in contact.) Outside of dense
stellar clusters, most relativistic binary systems arise from
primordial binary systems whose evolution drives them to tight,
ultracompact orbits. The dynamical processes in globular clusters can
drive wide binary systems toward short orbital periods and can also
insert degenerate or collapsed stars into relativistic orbits with
other stars. Before addressing specific evolutionary scenarios, we
will present the generic features of binary evolution that lead to the
formation of relativistic binaries.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Binary evolution}
\label{subsection:binary_evolution}

The evolution of a binary system of two main-sequence (MS) stars can 
significantly affect the evolution of both component stars if the
orbital separation is sufficiently small. If the orbital period is less than about 10 days, tidal interactions will have circularized the orbit during the pre- and early main-sequence phase.~\cite{goldman91, zahn89a, zahn89b} Both stars start in the main sequence with the mass of the primary $M_{\rm p}$, and the mass of the secondary $M_{\rm s}$, defined such that $M_{\rm p} \geq M_{\rm s}$. The binary system is described by the orbital separation $a$, and the mass ratio of the components $q \equiv M_{\rm s}/M_{\rm p}$. The gravitational potential of the binary system is described by the Roche model where each star dominates the gravitational potential inside regions called Roche lobes. The two Roche lobes meet at the inner Lagrange point along the line joining the two stars. Figure~\ref{roche_lobe} shows equipotential surfaces in the orbital plane for a binary with $q = 0.4$. If either star fills its Roche lobe, matter will stream from the Roche lobe filling star through the inner Lagrange point to the other star in a process known as Roche lobe overflow (RLOF). This mass transfer affects both the evolution of the components of the binary as well as the binary properties such as orbital period and eccentricity.

\begin{figure}[htb]
  \def\epsfsize#1#2{0.6#1}
  \centerline{\epsfbox{roche_lobe.eps}}
  \caption{\it Cross section of equipotential surfaces in the orbital
    plane of a binary with $q = 0.4$. The values of the potential
    surfaces are 5.0, 3.9075, 3.8, 3.559, 3.2, 3.0, and 2.8. The units
    have been normalized to the orbital separation, so $a = 1$.}
  \label{roche_lobe}
\end{figure}

Roche lobe overflow can be triggered by the evolution of the binary 
properties or by evolution of the component stars. On the one hand,
the orbital separation of the binary can change so that the Roche lobe
can shrink to within the surface of one of the stars. On the other
hand, stellar evolution may eventually cause one of the stars to
expand to fill its Roche lobe. When both stars in the binary are
main-sequence stars, the latter process is more common. Since the more
massive star will evolve first, it will be the first to expand and
fill its Roche lobe. At this stage, the mass exchange can be
conservative (no mass is lost from the binary) or non-conservative
(mass is lost). Depending on the details of the mass exchange and the
evolutionary stage of the mass-losing star there are several outcomes
that will lead to the formation of a relativistic binary. The primary
star can lose its envelope, revealing its degenerate core as either a
helium, carbon-oxygen, or oxygen-neon white dwarf; it can explode as a
supernova, leaving behind a neutron star or a black hole; or it can
simply lose mass to the secondary so that they change roles. Barring
disruption of the binary, its evolution will then continue. In most
outcomes, the secondary is now the more massive of the two stars and
it may evolve off the main sequence to fill its Roche lobe. The
secondary can then initiate mass transfer or mass loss with the result
that the secondary also can become a white dwarf, neutron star, or
black hole.

The relativistic binaries that result from this process fall into a
number of observable categories. A WD--MS or WD--WD binary may
eventually become a cataclysmic variable once the white dwarf begins
to accrete material from its companion. If the companion is a
main-sequence star, RLOF can be triggered by the evolution of the
companion. If the companion is another white dwarf, then RLOF is
triggered by the gradual shrinking of the orbit through the emission
of gravitational radiation. Some WD--WD cataclysmic variables are also
known as AM CVn stars. If the total mass of the WD--WD binary is above
the Chandrasekhar mass, the system may be a progenitor to a type I
supernova.

The orbit of a NS--MS or NS--WD binary will shrink due to the emission
of gravitational radiation. At the onset of RLOF, the binary will become 
either a low-mass X-ray binary (if the donor star is a WD or MS with
$M \leq 2 M_{\odot}$), or a high-mass X-ray binary (if the donor is a
more massive main-sequence star). These objects may further evolve to
become millisecond pulsars if the NS is spun up during the X-ray
binary phase~\cite{davies98, rasio00a}. A NS--NS binary will remain
virtually invisible unless one of the neutron stars is observable as a
pulsar. A BH--MS or BH--WD binary may also become a low- or high-mass
X-ray binary. If the neutron star is observable as a pulsar, a BH--NS
binary will appear as a binary pulsar. BH--BH binaries will be
invisible unless they accrete matter from the interstellar medium. A
comprehensive table of close binary types that can be observed in
electromagnetic radiation can be found in Hilditch~\cite{hilditch01}.

The type of binary that emerges depends upon the orbital separation
and the masses of the component stars. During the evolution of a
$10 M_{\odot}$ star, the radius will slowly increase by a factor of
about two as the star progresses from zero age main sequence to
terminal age main sequence. The radius will then increase by about
another factor of 50 as the star transitions to the red giant phase,
and an additional factor of 10 during the transition to the red
supergiant phase. These last two increases in size occur very quickly
compared with the slow increase during the main-sequence evolution. Depending upon the orbital separation, the onset of RLOF can occur any time during the evolution of the star. Mass transfer can be divided into three cases related to the timing of the onset of RLOF.

\begin{description}
%
\item[Case A:] If the orbital separation is small enough (usually a
  few days), the star can fill its Roche lobe during its slow
  expansion through the main-sequence phase while still burning
  hydrogen in its core.
%
\item[Case B:] If the orbital period is less than about 100 days, but
  longer than a few days, the star will fill its Roche lobe during the
  rapid expansion to a red giant with a helium core. If the helium
  core ignites during this phase and the transfer is interrupted, the
  mass transfer is case BB.
%
\item[Case C:] If the orbital period is above 100 days, the star can
  evolve to the red supergiant phase before it fills its Roche
  lobe. In this case, the star may have a CO or ONe core.
%
\end{description}

The typical evolution of the radius for a low metallicity star is
shown in Figure~\ref{radial_evolution}. Case A mass transfer occurs
during the slow growth, case B during the first rapid expansion, and
case C during the final expansion phase. The nature of the remnant
depends upon the state of the primary during the onset of RLOF and the
orbital properties of the resultant binary depend upon the details of
the mass transfer.

\begin{figure}[htb]
  \def\epsfsize#1#2{0.5#1}
  \centerline{\epsfbox{radial_evolution.eps}}
  \caption{\it Evolution of the radius for a $10 M_{\odot}$ star with
    $Z = 0.001$. Figure taken from Pfahl {\it et
    al.}\protect~\protect\cite{pfahl02a}.}
  \label{radial_evolution}
\end{figure}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Mass transfer}
\label{subsection:mass_transfer}

Although there are still many unanswered theoretical questions about
the nature of the mass transfer phase, the basic properties of the
evolution of a binary due to mass transfer can easily be
described. The rate at which a star can adjust to changes in its mass
is governed by three time scales. The dynamical time scale results
from the adiabatic response of the star to restore hydrostatic
equilibrium, and can be approximated by the free fall time across the
radius of the star
%
\begin{equation}
  t_{\rm dyn} \simeq \left(\frac{2 R^3}{G M}\right)^{1/2} \sim
  40\left[ \left( \frac{R}{R_{\odot}} \right)^3
  \frac{M_{\odot}}{M}\right]^{1/2} \!\!\!\!\!\! {\rm\ min},
  \label{dynamical_time}
\end{equation}
%
where $M$ and $R$ are the mass and radius of the star. The thermal
equilibrium of the star is restored over a longer period given by the
thermal time scale
%
\begin{equation}
  t_{\rm th} \simeq \frac{G M^2}{R L} \sim 3 \times 10^7 
  \left(\frac{M}{M_{\odot}}\right)^2
  \frac{R_{\odot}}{R}\frac{L_{\odot}}{L} {\rm\ yr},
  \label{thermal_time}
\end{equation}
%
where $L$ is the luminosity of the star. Finally, the main-sequence
lifetime of the star itself provides a third time scale, which is also
known as the nuclear time scale:
%
\begin{equation}
  t_{\rm nuc} \sim 7 \times 10^9
  \frac{M}{M_{\odot}}\frac{L_{\odot}}{L} {\rm yr}.
  \label{nuclear_time}
\end{equation}

The rate of mass transfer/loss from the Roche lobe filling star is
governed by how the star's radius changes in response to changes in
its mass. Hjellming and Webbink~\cite{hjellming87} describe these
changes and the response of the Roche lobe to mass changes in the
binary using the radius-mass exponents,
$\zeta \equiv d \ln{R}/d \ln{M}$, for each of the three processes
described in Equations~(\ref{dynamical_time}, \ref{thermal_time},
\ref{nuclear_time}) and defining
%
\begin{equation}
  \zeta_{\rm L} = (1 + q)\frac{d \ln{R_{\rm L}}}{d \ln{q}}
  \label{roche_lobe_exponent}
\end{equation}
%
for the Roche lobe radius-mass exponent. If $\zeta_{\rm L} > \zeta_{\rm dyn}$, the star cannot adjust to the Roche lobe, then the mass transfer takes place on a dynamical time scale and is limited only by the rate at which material can stream through the inner Lagrange point. If $\zeta_{\rm dyn} > \zeta_{\rm L} > \zeta_{\rm th}$, then the mass transfer rate is governed by the slow expansion of the star as it relaxes toward thermal equilibrium, and it occurs on a thermal time scale. If both $\zeta_{\rm dyn}$ and $\zeta_{\rm th}$ are greater than $\zeta_{\rm L}$, then the mass loss is driven either by stellar
evolution processes or by the gradual shrinkage of the orbit due to
the emission of gravitational radiation. The time scale for both of
these processes is comparable to the nuclear time scale. A good
analysis of mass transfer in cataclysmic variables can be found in
King {\it et al.}~\cite{king96}.

Conservative mass transfer occurs when there is no mass loss from the
system. During conservative mass transfer, the orbital elements of the
binary can change. Consider a system with total mass $M = M_1 + M_2$
and semi-major axis $a$. The total orbital angular momentum
%
\begin{equation}
  J = \left[\frac{GM_1^2M_2^2 a}{M}\right]^{1/2}
  \label{orbital_J}
\end{equation}
%
is a constant, and we can write $a \propto (M_1 M_2)^{-2}$. Using
Kepler's third law and denoting the initial values by a subscript $i$,
we find:
%
\begin{equation}
  \frac{P}{P_i} = \left[\frac{M_{1i} M_{2i}}{M_1 M_2}\right]^3.
  \label{period_change}
\end{equation}
%
Differentiating Equation~(\ref{period_change}) and noting that
conservative mass transfer requires $\dot{M}_1 = - \dot{M}_2$ gives:
%
\begin{equation}
  \frac{\dot{P}}{P} = \frac{3\dot{M}_1\left(M_1-M_2\right)}{M_1M_2}.
  \label{Pdot}
\end{equation}
%
Note that if the more massive star loses mass, then the orbital period
decreases and the orbit shrinks. If the less massive star is the
donor, then the orbit expands. Usually, the initial phase of RLOF
takes place as the more massive star evolves. As a consequence, the
orbit of the binary will shrink, driving the binary to a more compact
orbit.

In non-conservative mass transfer, both mass and angular momentum can
be removed from the system. There are two basic non-conservative
processes which are important to the formation of relativistic
binaries -- the common-envelope process and the supernova explosion of
one component of the binary. The result of the first process is often
a short-period, circularized binary containing a white dwarf. Although
the most common outcome of the second process is the disruption of the
binary, occasionally this process will result in an eccentric binary
containing a neutron star.

Common envelope scenarios result when one component of the binary
expands so rapidly that the mass transfer is unstable and the
companion becomes engulfed by the donor star. The companion then
ejects the envelope of the donor star. The energy required to eject
the envelope comes from the orbital energy of the binary and thus the
orbit shrinks. The efficiency of this process determines the final
orbital period after the common envelope phase. This is described by
the efficiency parameter
%
\begin{equation}
  \alpha_{\rm CE} = \frac{\Delta E_{\rm bind}}{\Delta E_{\rm orb}},
  \label{CE_efficiency}
\end{equation}
%
where $\Delta E_{\rm bind}$ is the binding energy of the mass stripped
from the envelope and $\Delta E_{\rm orb}$ is the change in the
orbital energy of the binary. The result of the process is the exposed
degenerate core of the donor star in a tight, circular orbit with the
companion. This process can result in a double degenerate binary if
the process is repeated twice or if the companion has already evolved
to a white dwarf through some other process. A brief description of
the process is outlined by Webbink~\cite{webbink84}, and a discussion
of the factors involved in determining $\alpha_{\rm CE}$ is presented
in Sandquist {\it et al.}~\cite{sandquist00}.

The effect on a binary of mass loss due to a supernova can be quite
drastic. Following Padmanabhan~\cite{padmanabhan01}, this process is
outlined using the example of a binary in a circular orbit with radius
$a$. Let $v$ be the velocity of one component of the binary relative
to the other component. The initial energy of the binary is given by
%
\begin{equation}
  E = \frac{1}{2} \left(\frac{M_1 M_2}{M_1 + M_2}\right) v^2 -
  \frac{G M_1 M_2}{a} = - \frac{G M_1 M_2}{2a}.
  \label{initial_energy}
\end{equation}
%
Following the supernova explosion of $M_1$, the expanding mass shell
will quickly cross the orbit of $M_2$, decreasing the gravitational
force acting on the secondary. The new energy of the binary is then
%
\begin{equation}
  E^{\prime} = \frac{1}{2} \frac{M_{\rm NS} M_2}{M_{\rm NS} + M_2}
  v^2 - \frac{G M_{\rm NS} M_2}{a},
  \label{final_energy_1}
\end{equation}
%
where $M_{\rm NS}$ is the mass of the remnant neutron star. We have
assumed here that the passage of the mass shell by the secondary has
negligible effect on its velocity (a safe assumption, see Pfahl
{\it et al.}~\cite{pfahl02a} for a discussion), and that the primary
has received no kick from the supernova (not necessarily a safe
assumption, but see Davies and Hansen~\cite{davies98} or Pfahl {\it et al.}~\cite{pfahl02b} for an
application to globular cluster binaries). Since we have assumed that
the instantaneous velocities of both components have not been
affected, we can replace them by $v^2 = G\left(M_1 + M_2\right)/a$,
and so
%
\begin{equation}
  E^{\prime} = \frac{G M_{\rm NS} M_2}{2a}\left(\frac{M_1+M_2}
  {M_{\rm NS} + M_2} -2\right).
  \label{final_energy_2}
\end{equation}
%
Note that the final energy will be positive and the binary will be
disrupted if $M_{\rm NS} < (1/2)(M_1 + M_2)$. This condition occurs
when the mass ejected from the system is greater than half of the
initial total mass:
%
\begin{equation}
  \Delta M > \frac{1}{2}\left(M_1 + M_2\right),
  \label{deltaM}
\end{equation}
%
where $\Delta M = M_1 - M_{\rm NS}$. If the binary is not disrupted,
the new orbit becomes eccentric and expands to a new semi-major axis
given by
%
\begin{equation}
  a^{\prime} = a\left(\frac{M_1 + M_2 - \Delta M}
  {M_1 + M_2 - 2\Delta M}\right),
  \label{final_a}
\end{equation}
%
and orbital period
%
\begin{equation}
  P^{\prime} = P\left(\frac{a^{\prime}}{a}\right)^{3/2}
  \left(\frac{2a^{\prime}-a}{a^{\prime}}\right)^{1/2}.
  \label{final_P}
\end{equation}

We have seen that conservative mass transfer can result in a tighter
binary if the more massive star is the donor. Non-conservative mass
transfer can also drive the components of a binary together during a
common envelope phase when mass and angular momentum are lost from the
system. Direct mass loss through a supernova explosion can also alter
the properties of a binary, but this process generally drives the
system toward larger orbital separation and can disrupt the binary
entirely. With this exception, the important result of all of these
processes is the generation of tight binaries with at least one
degenerate object.

The processes discussed so far apply to the generation of
relativistic binaries anywhere. They occur whenever the orbital
separation of a progenitor binary is sufficiently small to allow for
mass transfer or common envelope evolution. Population distributions
for relativistic binaries are derived from an initial mass function, a
distribution in mass ratios, and a distribution in binary
separations. These initial distributions are then fed into models for
binary evolution such as StarTrack~\cite{belczynski02} or SeBa~\cite{portegieszwart96, nelemans01a} in order to determine rates of production of
relativistic binaries. The evolution of the binary is often determined
by the application of some simple operational formulae such as those
described by Tout {\it et al.}~\cite{tout97} or Hurley {\it et al.}~\cite{hurley00}. For example, Hils,
Bender, and Webbink~\cite{hils90} estimated a population of close
white dwarf binaries in the disk of the galaxy using a Salpeter mass
function, a mass ratio distribution strongly peaked at 1, and a
separation distribution that was flat in $\ln(a)$. Other estimates
of relativistic binaries differ mostly by using different
distributions~\cite{belczynski01, iben97, nelemans01a, nelemans01b}.




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Globular cluster processes}
\label{subsection:globular_cluster_processes}

When the above evolutionary scenarios are played out in the
environment of a globular cluster, additional mechanisms arise that
enhance the production of relativistic binaries. New binary systems
can be formed by dynamical interaction among three or more single
stars or through tidal capture, and the period distribution and
binary components of existing binary systems can be altered by
interactions with other stars in the cluster. We will discuss here the
broad features of these interactions and how they affect the evolution
of binary systems toward relativistic binaries.

The formation of binaries during the dynamical evolution of globular
clusters can occur either through tidal capture or through $N$-body
interactions. Tidal capture occurs when an encounter between two stars
is close enough that significant tides are raised on each. The tides
excite non-radial oscillations in the stars. If the energy absorbed in
these oscillations is great enough to leave the two stars with
negative total energy, then the system will form a binary. This
process was originally thought to be the dominant channel through
which binaries were formed in globular clusters~\cite{binney87,
fabian75}. It is now thought to be quite rare, as detailed
calculations have shown that the final result is more likely to be
coalescence of the two stars~\cite{bailyn95, hut92a,
rasio00a}. Although $N$-body interactions are less likely to occur
than tidally significant two-body interactions, they are now thought
to be the dominant channel for the formation of binaries during the
evolution of a globular cluster. This process, however, is not likely
to produce more than a few binaries during the lifetime of a
cluster~\cite{binney87, padmanabhan01}.

\begin{figure}[htb]
  \def\epsfsize#1#2{1.0#1}
  \centerline{\epsfbox{three_body.eps}}
  \caption{\it Example of a binary-field star exchange interaction. The
    binary comes in from the right (red-white), while the field star
    (green) enters from the left. After a complicated interaction, the
    white star is ejected and the newly formed red-green binary is in
    a more tightly bound orbit. Figure taken from
    McMillan\protect~\protect\cite{mcmillanweb}.}
  \label{three_body}
\end{figure}

Observations of present binary fractions in globular clusters combined with evolutionary and dynamical simulations indicate initial binary fractions as large as 100\% are not unreasonable~\cite{ivanova05a}. The existence of such a population of primordial binaries provides a much
more efficient channel for the transformation of the initial
distribution in component masses and orbital periods towards higher
mass components and shorter orbital periods. This process follows from
the interaction of primordial binaries with single stars and other
binaries. Three results of the interaction are possible: complete
disruption of the binary, an exchange of energy between the binary and
the field star, or a replacement of one of the binary components by
the field star. When a binary interacts with either a field star or
with another binary, the energy of the interaction is shared among all
stars in the interaction. The result is that the lowest mass object in
the interaction will receive the largest velocity and be more likely
to escape the interaction. In general, these interactions are quite
complex, and must be studied numerically. A typical exchange
interaction between a binary and a field star is shown in
Figure~\ref{three_body}.

If the initial binding energy of the binary is large, the result of
these interactions is to shrink the orbit of the new binary as the
gravitational energy of the binary is used to bring the field star up
to the speeds of the binary components. However, if the binding energy
is low, the field star contributes energy to the components of the
binary, thereby widening the orbit. This is an example of ``Heggie's
Law''~\cite{heggie75}, which can be summarized as {\it hard binaries
get harder and soft binaries get softer}. For roughly equal mass
stars, a binary is considered ``hard'' if its binding energy is
greater than the average kinetic energy of a field star in the cluster
and ``soft'' if its binding energy is less.  For unequal mass
encounters, Hills~\cite{hills90} has shown that the ratio of the
orbital speeds of the binary components to the speed of the impactor
is a better indicator of whether the binding energy will increase or
decrease.

The average kinetic energy of a field star in the cluster is sometimes
related to an effective temperature of the cluster~\cite{heggie75,
mcmillan98, portegieszwart00b} so that
$\langle{m v^2}\rangle = 3kT$. Numerical studies of the outcome of
hard binary interactions indicate that the binding energy of the
binary will increase by about 20\% with each encounter~\cite{hut92b,
  portegieszwart00b}. Since the encounter rate is proportional to the
semi-major axis (or $1/E$) and the energy increase per encounter is
proportional to $E$, the rate of hardening per relaxation time is
independent of the energy and is
$\langle{\Delta E_{\rm bind}}\rangle \sim - 0.6 \,kT/t_{\rm
relax}$~\cite{binney87}.
A common feature of numerical studies of hard binary interactions is
the preferential exchange of high-mass stars and stellar remnants with
the least massive member of the binary~\cite{sigurdsson95}. Thus, the
dynamical interactions in a globular cluster drive the initial orbital
period distribution toward shorter periods by hardening the short
period binaries while disrupting the softer binaries. Through exchange
interactions, the mass distribution of the binary components is also
driven toward higher mass stars, which further enhances the number of
mass-transferring systems that can evolve to become relativistic
binaries. A very useful numerical simulation of multiple star interactions is Fewbody~\cite{fregeau04}.

Because stellar remnants can also be exchanged into hard binaries,
globular cluster evolution opens up a new channel for the formation of
relativistic binaries by introducing evolved components into binary
systems that have not yet undergone a mass transfer phase. A
particularly promising channel involves the exchange of a neutron star
into a binary with a main-sequence star. The binary then undergoes
case B or case C mass transfer with a common envelope phase, resulting
in a NS--WD binary~\cite{rasio00a}. Podsiadlowski {\it et al.}\
describe a similar process without requiring the common envelope
phase~\cite{podsiadlowski02}. Similar interactions can occur to
produce WD--WD binaries if a massive CO or ONe white dwarf is
exchanged into a hard binary. A collaboration of various groups working in stellar dynamics maintains a page at {\tt http://manybody.org/modest/projects.html} that provides a number of useful computational tools for comparing how dynamical interactions can affect different binary evolution codes~\cite{modestweb}.

Black hole binaries can also form as a result of exchange
interactions, but the process is different because black hole
progenitors will evolve so quickly in relation to the relaxation time
of most globular clusters~\cite{kulkarni93, sigurdsson93}. One
scenario that generates black hole binaries in globular clusters is
described by Portegies Zwart and
McMillan~\cite{portegieszwart00b}. Stellar mass black holes of mass
$M \sim 10 M_{\odot}$ will be born early in the life of a globular
cluster and, through mass segregation, they will quickly sink to the
core. Once in the core, these black holes will be so much more massive
than the field stars that they will effectively form their own cluster
and interact solely with themselves. Single black holes will form
binaries with other black holes through three-body encounters; any
black holes which are in binaries with other stars will team up with
another black hole through exchange encounters. This population of
black holes and black hole binaries will then evolve separately from
the rest of the cluster as no other stars will be massive enough to
affect its dynamics.

Current intermediate mass black hole (IMBH) formation scenarios that involve globular clusters can also affect the dynamics of the globular cluster evolution, and therefore, can affect the evolution of binaries within the cluster. In the two most common scenarios, an IMBH is either formed early in the life of the globular cluster through runaway mergers of massive stars~\cite{portegieszwart04b,freitag05,gurkan04} or it is formed through the gradual accumulation of black holes throughout the lifetime of the globular cluster~\cite{miller04}. The existence of an IMBH in a globular cluster can also alter its density profile, and this can have an affect on the rest of the dynamics of the cluster~\cite{baumgardt05}.

We have seen how the dynamics of globular clusters can enhance the
population of progenitors to relativistic binaries, making the
standard channels of mass-transfer more likely to occur. In addition,
globular cluster dynamics can open up new channels for the formation
of relativistic binaries by inserting evolved, stellar remnants such
as neutron stars or white dwarfs into binary systems and by shrinking
the orbits of binary systems to enhance the likelihood of mass
exchange. Finally, binary-single star encounters can simply create
relativistic binaries by inserting two evolved objects into a binary
and then shrinking the orbit to ultracompact periods. We next discuss
the probable rates for the formation of such systems and the dynamical
simulations that are used to synthesize globular cluster populations
of relativistic binaries.

\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Dynamical Evolution}
\label{section:dynamical_evolution}

Simulations of the populations of relativistic binaries in globular
clusters rely on the interplay between the evolution of individual
stars in the progenitor systems and the evolution of globular
clusters. The evolution of stars in the progenitor systems has been
discussed in the previous section and we now turn to techniques for
simulating the evolution of globular clusters.

The evolution of a globular cluster is dominated by the gravitational
interaction between the component stars in the cluster. The overall
structure of the cluster as well as the dynamics of most of the stars
in the cluster are determined by simple $N$-body gravitational
dynamics. However, the evolutionary time scales of stellar evolution
are comparable to the relaxation time and core collapse time of the
cluster. Consequently, stellar evolution affects the masses of the
component stars of the cluster, which affects the dynamical state of
the cluster. Thus, the dynamical evolution of the cluster is coupled
to the evolutionary state of the stars. Also, as we have seen in the
previous section, stellar evolution governs the state of the binary
evolution and binaries may provide a means of support against core
collapse. Thus, the details of binary evolution as coupled with
stellar evolution must also be incorporated into any realistic model
of the dynamical evolution of globular clusters. To close the loop,
the dynamical evolution of the globular cluster affects the
distribution and population of the binary systems in the cluster. In
our case, we are interested in the end products of binary evolution,
which are tied both to stellar evolution and to the dynamical
evolution of the globular cluster. To synthesize the population of
relativistic binaries, we need to look at the dynamical evolution of
the globular cluster as well as the evolution of the binaries in the
cluster. MODEST (MOdeling DEnse STellar systems), a collaboration of various groups working stellar dynamics, maintains a website that provides the latest information about efforts to combine simulations of both the dynamical evolution of $N$-body systems and stellar evolution~\cite{modestweb}.

General approaches to this problem involve solving the $N$-body
problem for the component stars in the cluster and introducing binary
and stellar evolution when appropriate to modify the $N$-body
evolution. There are two fundamental approaches to tackling this
problem -- direct integration of the equations of motion for all $N$
bodies in the system and large-$N$ techniques, such as Fokker--Planck
approximations coupled with Monte Carlo treatments of binaries (see
Heggie {\it et al.}~\cite{heggie98} for a comparison of these
techniques). For a recent review of progress in implementing these techniques, see the summary of the MODEST-2 meeting~\cite{sills03}. In the next two subsections, we discuss the basics of
each approach and their successes and shortfalls. We conclude this
section with a discussion of the recent relativistic binary population
syntheses generated by dynamical simulations.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{{\it N}-body}
\label{subsection:N-body}

The $N$-body approach to modeling globular cluster dynamics involves
direct calculations of the gravitational interactions between all $N$
bodies in the simulation. In principle this is a very straightforward
approach. The positions of the $N$ objects in the cluster are
determined by direct integration of the $3N$ equations of motion:
%
\begin{equation}
  {\ddot{\bf r}}_i = -\sum_{j\neq i}{\frac{GM_j({\bf r}_i -
  {\bf r}_j)}{|{\bf r}_j - {\bf r}_i|^3}}.
  \label{equations_of_motion}
\end{equation}
%
When the positions indicate that objects are sufficiently close to
each other, then the interaction is modeled to determine the
outcome. In order to achieve realistic simulations with tidal
interactions, possible mass transfer, and a mass spectrum of bodies,
detailed stellar evolution and stellar collision models must be
included and calculated.

The two main codes for performing $N$-body simulations are Kira and
NBODYx. The Kira integrator is part of the Starlab environment which
also includes stellar evolution codes and other modules for doing
$N$-body simulations~\cite{starlabweb}. The NBODYx codes have been
developed and improved by Aarseth since the early 1960's. He has two
excellent summmaries of the general properties and development of the
NBODYx codes~\cite{aarseth99b, aarseth99a}. For further details, see Aarseth's book on $N$-body simulations~\cite{aarseth03}. A good summmary of general
$N$-body applications can also be found at the NEMO
website~\cite{nemoweb}. NBODY6++ is a parallelization of the NBODY6 code for use on large computer clusters~\cite{spurzem99}, and a parallel version of Kira is under development~\cite{modestweb}. Most large $N$-body calculations are done with
a special purpose computer called the GRAPE (GRAvity PipE) invented by
Makino~\cite{makino98}. The most recent incarnation of the GRAPE is
the GRAPE 6, which has a theoretical peak speed of 100
Tflops~\cite{grapeweb}. There is also a PCI card version (GRAPE-6A) which is designed for use in PC clusters~\cite{fukushige05}. The GRAPE calculates the accelerations and
jerks for the interaction between each star in the cluster. The next generation GRAPE-DR, which could reach $\sim 1$ Pflops, should be operational in about three years.

The main advantage of $N$-body simulations is the small number of
simplifying assumptions which must be made concerning the dynamical
interactions within the cluster. The specific stars and trajectories
involved in any interactions during the simulation are
known. Therefore, the details for those specific interactions can be
calculated during the simulation. Within the limits of the numerical
errors that accumulate during the calculation~\cite{goodman93}, one
can have great confidence in the results of $N$-body simulations.

Obviously, one of the main computational difficulties is simply the
CPU cost necessary to integrate the equations of motion for $N$
bodies. This scales roughly as $N^3$~\cite{heggie03}. The other
computational difficulty of the direct $N$-body method is the wide
range of precision required~\cite{hut93, heggie03}. Consider the range
of distances, from the size of neutron stars ($\sim 10 {\rm\ km}$) to
the size of the globular cluster
($\sim 50 {\rm\ pc} \sim 10^{15} {\rm\ km}$), spanning 14 orders of
magnitude. If the intent of the calculations is to determine the
frequency of interactions with neutron stars, we have to know the
relative position of every star to within 1 part in $10^{14}$. The
range of time scales is worse yet. Considering that the time for a
close passage of two neutron stars is on the order of milliseconds and
that the age of a globular cluster is $10^{10} {\rm\ yr} \sim 10^{20} {\rm\ ms}$, we find that the time scales span 20 orders of magnitude. These computational requirements coupled with hardware limitations mean that the number of bodies which can be included in a reasonable simulation is no more than $\sim 10^5$. This is about an order of magnitude less than the number of stars in a typical globular cluster.

Although one has great confidence in the results of an $N$-body
simulation, these simulations are generally for systems that are
smaller than globular clusters. Consequently, applications of $N$-body
simulations to globular cluster dynamics involve scaling lower $N$
simulations up to the globular cluster regime. Although many processes
scale with $N$, they do so in different ways. Thus, one scales the
results of an $N$-body simulation based upon the assumption of a
dominant process. However, one can never be certain that the
extrapolation is smooth and that there are no critical points in the
scaling with $N$. One can also scale other quantities in the model, so
that the quantity of interest is correctly
scaled~\cite{portegieszwart99}. An understanding of the nature of the
scaling is crucial to understanding the applicability of $N$-body
simulations to globular cluster dynamics (see
Baumgardt~\cite{baumgardt00} for an example). The scaling problem is
one of the fundamental shortcomings of the $N$-body approach.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Fokker--Planck}
\label{subsection:fokker-planck}

The computational limitations of $N$-body simulations can be
sidestepped by describing the system in terms of distribution
functions $f_m(\mathbold{x},\mathbold{v},t)$ with the number of stars
of mass $m$ at time $t$ in the range
$(\mathbold{x},\mathbold{x} + d^3x)$ and
$(\mathbold{v},\mathbold{v} + d^3v)$ given by $dN = f_md^3xd^3v$. This
description requires that either the phase-space element $d^3xd^3v$ be
small enough to be infinitesimal yet large enough to be statistically
meaningful, or that $f_m$ be interpreted as the probability
distribution for finding a star of mass $m$ at a location in phase
space. The evolution of the cluster is then described by the evolution
of $f_m$. The gravitational interaction is provided by a smoothed
gravitational potential $\phi$, which is determined by
%
\begin{equation}
  \nabla^2\phi = 4 \pi \sum_i{\left[
  m_i\int{f_{m_i}({\bf x}, {\bf v}, t) d^3{\bf v}}\right]}.
  \label{smoothed_potential}
\end{equation}
%
The effect of gravitational interactions is modeled by a collision
term $\Gamma\left[{f}\right]$ (see~\cite{binney87, padmanabhan01} for
specific descriptions of $\Gamma$). The dynamics of the globular
cluster are then governed by the Fokker--Planck equation:
%
\begin{equation}
  \frac{\partial f}{\partial t} + {\bf v}\cdot{\bf \nabla}f -
  {\bf \nabla}\phi\cdot\frac{\partial f}{\partial {\bf v}} =
  \Gamma\left[f\right].
  \label{fokker-planck}
\end{equation}

In the Fokker--Planck approach, the mass spectrum of stars is binned,
with a separate $f_m$ for each bin. Increasing the resolution of the
mass spectrum requires increasing the number of distribution functions
and thus increasing the complexity of the problem. Consequently, Fokker--Planck codes can handle at most a few dozen different $f_m$. The inclusion of
additional physical variables such as binaries adds sufficient further
complexity that the codes are taxed beyond their capacity. Methods for numerically solving the Fokker--Planck
equation use either an orbit-averaged form of
Equation~(\ref{fokker-planck})~\cite{cohn79}, or a Monte Carlo
approach~\cite{freitag01, giersz98, giersz01, joshi00, fregeau03}.

The two time scales involved in the evolution of $f_m$ are
$t_{\rm cross}$ (which governs changes in position) and
$t_{\rm relax}$ (which governs changes in energy). The orbit-averaged
form of Equation~(\ref{fokker-planck}) derives from the realization
that changes in position are essentially periodic with orbital period
$T \sim t_{\rm cross} \ll t_{\rm relax}$. Thus, one can average over
the rapid changes in position and retain the slow changes in the phase
space coordinates that occur over relaxation times. Given suitable assumptions on the symmetry of the potential and the velocity distribution, when one does this the Fokker--Planck equation is reduced to an equation involving the energy and the magnitude of the angular momentum. The orbit-averaged solutions of
the Fokker--Planck equation cannot easily handle the effect of
binaries and the binary interactions that occur during the evolution
of a globular cluster~\cite{gao91}. These effects are usually inserted
by hand using statistical methods. The advantages of the
orbit-averaged approach are that one can generalize it to handle
anisotropy in velocity, thus allowing study of the effects of the
galactic gravitational field and tidal stripping. One can also include
the rotation of the cluster~\cite{kim02}.

The more recent Monte Carlo simulations~\cite{giersz98,joshi00,freitag01} do not actually deal with the distribution functions, but rather treat the cluster as a collection of particles that represent a spherical shell of similar stars. Based on the pioneering work of H\'enon~\cite{henon71a,henon71b}, they are able to represent an arbitrary number of species and can follow binary evolution and other effects. The underlying treatment of relaxation throughout the simulation is done in the Fokker-Planck approximation, but the interactions and evolution of the stars are handled on a particle by particle basis. Consequently, these codes are significantly more robust in their ability to handle realistic populations of stars. A nearly continuous mass spectrum can be used and stellar evolution and binarity can be included with relative ease. In addition, both stellar collisions and large-angle scatterings can also be tracked. The primary disadvantages of these Monte Carlo codes are that they require spherical symmetry and that they suffer from statistical noise despite the large number of particles being tracked. For an excellent overview of the implementations and history of the Monte Carlo methods based on H\'enon's work, see Marc Freitag's link on the Working Group 3 page at the MODEST website~\cite{modestweb}.

Another approach to solving the Fokker-Planck equation makes use of the analogy between a globular cluster and a self-gravitating gaseous sphere~\cite{louis91, giersz94}. The most effective use of the gaseous models are in a hybrid code that treats the single stars in a gaseous model while treating the relaxation of binary, three- and four-body interactions using a Monte Carlo code~\cite{giersz00, giersz03}. This approach shows promise for its flexibility in adding new physics.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Population syntheses}
\label{subsection:population_syntheses}

Over the last ten years, there have been several works addressing binary populations in
globular clusters~\cite{benacquista99, benacquista01c, davies95a,
davies95b, davies97, davies98, giersz03, hurley03, ivanova05a, miller02, pfahl02a, popov02,
portegieszwart00b, rappaport01, rasio00a, schneider01, shara02, sigurdsson95,
takahashi00}. These have been derived from both dynamical
simulations and static models. Although the motivations have been
varied, it is often possible to extract information about the
resulting populations of relativistic binaries. Despite the differing
models and population synthesis techniques, the predicted populations
are in rough agreement. Here, we summarize the different techniques
and their predictions for relativistic binaries in globular clusters.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsubsection{{\it N}-body simulations}
\label{subsubsection:n-body_simulations}

Although $N$-body simulations have the potential to provide the most
detailed population syntheses of relativistic binaries in globular
clusters, there are very few actual populations described in the
literature. Most of the current work that treats binaries in a
consistent and detailed way is limited to open
clusters~\cite{portegieszwart01,hurley01,hurley03,kroupa01b,madsen03} and is focused on
a particular outcome of the binary population, such as blue stragglers~\cite{hurley01}, brown dwarfs~\cite{kroupa01b}, initial binary distributions~\cite{kroupa01c}, or white dwarf CMD sequences~\cite{hurley03}. Portegies Zwart {\it
et al.} focus on photometric observations of open clusters~\cite{portegieszwart01} and on spectroscopy~\cite{portegieszwart04a}. In their comparison of
$N$-body and Fokker--Planck simulations of the evolution of globular
clusters, Takahashi and Portegies Zwart~\cite{takahashi00} followed
the evolution of $N = 1{\rm\ K}, 16{\rm\ K}$, and $32{\rm\ K}$ systems
with initial mass functions given by Equation~(\ref{imf}) and initial
density profiles set up from King models. Although they allowed for
realistic stellar binary evolution in their comparisons, their focus
was on the structural evolution of globular clusters. Consequently
there is no binary population provided. Other $N$-body simulations
suffer from this same problem~\cite{portegieszwart02}. On the other hand, recent work by Shara and Hurley has focused specifically on white dwarf binary populations in globular clusters and has produced a detailed table of close white dwarf binaries that were generated in their simulation~\cite{shara02}.

It is possible to generate a population distribution for black hole
binaries in globular clusters using the $N$-body simulations of
Portegies Zwart and McMillan~\cite{portegieszwart00b} that were
intended to describe the population of black hole binaries that were
{\it ejected} from globular clusters. Their scenario for black hole
binary ejection describes a population of massive stars that evolves
into black holes. The black holes then rapidly segregate to the core
and begin to form binaries. As the black holes are significantly more
massive than the other stars, they effectively form a separate
sub-system, which interacts solely with itself. The black holes form
binaries and then harden through binary-single black hole interactions
that occasionally eject either the binary, the single black hole, or
both.

They simulated this scenario using $N = 2048$ and $N = 4096$ systems
with 1\% massive stars. The results of their simulations roughly
confirm a theoretical argument based on the recoil velocity that a
binary receives during an interaction. Noting that each encounter
increases the binding energy by about 20\% and that roughly $1/3$ of
this energy goes into binary recoil, the minimum binding energy
$E_{\rm b\, min}$ of an ejected black hole binary is
%
\begin{equation}
  E_{\rm b\,min} \sim 36 W_0 \frac{M_{\rm bh}}{\langle M\rangle} kT,
  \label{binding_energy}
\end{equation}
%
where $\langle{M}\rangle$ is the average mass of a globular cluster
star and $W_0 = \langle M\rangle |\phi_0|/kT$ is the dimensionless
central potential. After most binaries are ejected,
$\langle{M}\rangle \sim 0.4 M_{\odot}$. After a few gigayears, nearly
all of the black holes were ejected.

At the end of this phase of black hole binary ejection, there is a
50\% chance that a binary remains in the cluster with no other black
hole to eject it. Thus, there should be a stellar mass black hole
binary remaining in about half of the galactic globular clusters. The
maximum binding energy of the remaining black hole binary is
$E_{\rm b\,min}$ and is also given by
Equation~(\ref{binding_energy}). We can then approximate the
distribution in energies of the remaining black hole binaries as being
flat in $\log (E_{\rm b})$. The eccentricities of this population will
follow a thermal distribution with $P(e) = 2e$.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsubsection{Monte Carlo simulations}
\label{subsubsection:monte-carlo_simulations}

Dynamical Monte Carlo simulations can be used to study the evolution
of binary populations within evolving globular cluster models. Rasio
{\it et al.}~\cite{rasio00a} have used a Monte Carlo approach
(described in Joshi {\it et al.}~\cite{joshi01, joshi00}) to study the
formation and evolution of NS--WD binaries, which may be progenitors of
the large population of millisecond pulsars being discovered in
globular clusters (see
Section~\ref{subsection:millisecond_pulsars}). In addition to
producing the appropriate population of binary millisecond pulsars to
match observations, the simulations also indicate the existence of a
population of NS--WD binaries (see Figure~\ref{WD-NS_in_47Tuc}).

\begin{figure}[htb]
  \def\epsfsize#1#2{0.5#1}
  \centerline{\epsfbox{WD-NS_in_47Tuc.ps}}
  \caption{\it Results of the Monte Carlo simulation of NS--WD binary
    generation and evolution in 47\protect~Tuc. Each small dot
	represents a binary system. The circles and error bars are the 10
	binary pulsars in 47\protect~Tuc with well measured orbits. Systems 
	in A have evolved through mass transfer from the WD to the NS.
	Systems in B have not yet evolved through gravitational radiation to 
	begin RLOF from the WD to the NS. Systems in C will not undergo a 
	common envelope phase. Figure taken from Rasio {\it et 
	al.}\protect~\protect\cite{rasio00a}.}
  \label{WD-NS_in_47Tuc}
\end{figure}

The tail end of the systems in group B of Figure~\ref{WD-NS_in_47Tuc}
represents the NS--WD binaries that are in very short period orbits and
are undergoing a slow inspiral due to gravitational radiation. These
few binaries can be used to infer an order of magnitude estimate on
the population of such objects in the galactic globular cluster
system. If we consider that there are two binaries with orbital period
less than 2000~s out of $\sim 10^6 M_{\odot}$ in 47~Tuc, and assume
that this rate is consistent throughout the globular cluster system as
a whole, we find a total of $\sim 60$ such binaries. Although this
estimate is quite crude, it compares favorably with estimates arrived
at through the encounter rate population syntheses, which are
discussed in Section~\ref{subsubsection:encounter_rates}.

More recent applications of the Monte Carlo simulations that have focused on the properties of binaries include Fregeau {\it et al.}~\cite{fregeau04} who look at the production of blue stragglers and other collision products as a result of binary interactions in globular clusters and Ivanova {\it et al.}~\cite{ivanova05a} who have studied the evolution of binary fractions in globular clusters. The latter work demonstrates the gradual burning of binaries in the core that delays the collapse of the core. In addition, they have also shown the build-up of short period white dwarf binaries in the core through dynamical interactions (see Figure~\ref{ivanova47tuc}).

\begin{figure}[htb]
  \def\epsfsize#1#2{0.5#1}
  \centerline{\epsfbox{ivanova47tuc.eps}}
  \caption{\it Binary period distributions from the Monte Carlo simulation of binary
    fraction evolution in 47\protect~Tuc. The bottom panel indicates the period distribution for binaries containing at least one white dwarf. $N_{\rm b}$ is the total number of binaries and $N_{\rm b,p}$ is the number of binaries per bin. Figure taken from Ivanova {\it et 
	al.}\protect~\protect\cite{ivanova05a}.}
  \label{ivanova47tuc}
\end{figure}

There is also great promise for the hybrid gas/Monte Carlo method
being developed by Spurzem and Giersz~\cite{spurzem96}. Their recent
simulation of the evolution of a cluster of 300,000 equal point-mass
stars and 30,000 binaries yields a wealth of detail about the position
and energy distribution of binaries in the
cluster~\cite{giersz00}. Further improvements on their code have resulted in direct integration of the binary-binary and binary-single interactions~\cite{giersz03}. As a result, they have been able to produce empirical cross-sections for eccentricity variations during interactions.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsubsection{Encounter rate techniques}
\label{subsubsection:encounter_rates}

One method for exploring the production of relativistic binary populations in globular clusters involves determining the encounter rate expected between different classes of objects in a globular cluster. Sigurdsson and Phinney~\cite{sigurdsson95} use Monte Carlo
simulations of binary encounters to infer populations using a static
background cluster described by an isotropic King--Michie model. Their
results are focused toward predicting the observable end products of
binary evolution such as millisecond pulsars, cataclysmic variables,
and blue stragglers. Therefore, there are no clear descriptions of
relativistic binary populations provided. The work of Ivanova {\it et al.}~\cite{ivanova05a} also uses this technique to determine the evolution of binary fractions, but they also do not provide sufficient detail of the population to distinguish the relativistic binaries from other binaries in the simulation. There is promise to produce a more detailed description of ultracompact X-ray binaries consisting of a white dwarf and a neutron star using encounter rates~\cite{ivanova05b}.

Davies and collaborators use the technique of calculating encounter rates (based on
calculations of cross-sections for various binary interactions and
number densities of stars using King--Michie static models) to
determine the production of end products of binary
evolution~\cite{davies95a, davies95b}. Although they also do not
provide a clear description of a population of relativistic binaries,
their results allow the estimation of such a population.

Using the encounter rates of Davies and collaborators~\cite{davies95a,
davies95b}, one can follow the evolution of binaries injected into
the core of a cluster. A fraction of these binaries will evolve into
compact binaries which will then be brought into contact through the
emission of gravitational radiation. By following the evolution of
these binaries from their emergence from common envelope to contact,
we can construct a population and period distribution for present day
globular clusters~\cite{benacquista99}. For a globular cluster with
dimensionless central potential $W_0 = 12$, Davies~\cite{davies95b}
followed the evolution of 1000 binaries over two runs. The binaries
were chosen from a Salpeter IMF with exponent $\alpha = 2.35$, and the
common envelope evolution used an efficiency parameter
$\alpha_{\rm CE} = 0.4$. One run was terminated after 15~Gyr and the
population of relativistic binaries which had been brought into
contact through gravitational radiation emission was noted. The second
run was allowed to continue until all binaries were either in merged
or contact systems. There are four classes of relativistic binaries
that are brought into contact by gravitational radiation: low mass
white dwarf--white dwarf binaries (${\rm WD}^2_a$) with total mass below
the Chandrasekhar mass; high mass white dwarf--white dwarf binaries
(${\rm WD}^2_b$) with total mass above the Chandrasekhar mass; neutron
star-white dwarf binaries (${\rm NW}$); and neutron star-neutron star
binaries ${\rm NS}^2$. The number of systems brought into contact at the
end of each run is given in Table~\ref{contact_numbers}.

\begin{table}[h]
  \begin{center}
    \begin{tabular}{|c|c|c|c|c|}
      \hline
      $T_{\rm evol}$ & ${\rm WD}_a^2$ & ${\rm WD}_b^2$ & ${\rm NW}$ &
      ${\rm NS}^2$\rule{0 em}{1 em} \\
      \hline
      15 Gyr & 11 & 0 & 10 & \blankzero 1 \\
      $\infty$ & 57 & 0 & 74 & 18 \\
      \hline
    \end{tabular}
  \end{center}
  \caption{\it Number of relativistic binaries brought into contact
    through binary interactions.}
  \label{contact_numbers}
\end{table}

In the second run, the relativistic binaries had all been brought into
contact. In similar runs, this occurs after another 15~Gyr. An
estimate of the present-day period distribution can be made by
assuming a constant merger rate over the second 15~Gyr. Consider the
total number of binaries that will merge to be described by
$n(t)$. Thus, the merger rate is $\eta = -dn/dt$. Assuming that the
mergers are driven solely by gravitational radiation, we can relate
$n(t)$ to the present-day period distribution. We define $n(P)$ to be
the number of binaries with period less than P, and thus
%
\begin{equation}
  \eta = -\frac{dn}{dt} = -\frac{dn}{dP}\frac{dP}{dt},
  \label{merger_rate}
\end{equation}
%
so
%
\begin{equation}
  \frac{dn}{dP} = \frac{-\eta}{dP/dt}.
  \label{period_distribution}
\end{equation}

The merger rate is given by the number of mergers of each binary type
per 1000 primordial binaries per 15~Gyr. If the orbits have been
circularized (which is quite likely if the binaries have been formed
through a common envelope), the evolution of the period due to
gravitational radiation losses is given by~\cite{hils90}
%
\begin{equation}
  \frac{dP}{dt} = -k_0P^{-5/3},
  \label{gr_period_evolution}
\end{equation}
%
where $k_0$ is given by
%
\begin{equation}
  k_0 = \frac{96}{5} (2\pi)^{8/3}\frac{G^{5/3}}{c^5}{\cal M}^{5/3},
  \label{knaught}
\end{equation}
%
with the ``chirp mass'' ${\cal M}^{5/3} \equiv M_1M_2(M_1 +M_2)^{-1/3}$. 

Following this reasoning and using the numbers in
Table~\ref{contact_numbers}, we can determine the present day
population of relativistic binaries per 1000 primordial binaries. To
find the population for a typical cluster, we need to determine the
primordial binary fraction for globular clusters. Estimates of the
binary fraction in globular clusters range from 13\% up to about 40\%
based on observations of either eclipsing binaries~\cite{albrow01,
yan94, yan96} or luminosity functions~\cite{rubenstein97,
rubenstein99}. Assuming a binary fraction of 30\%, we can determine
the number of relativistic binaries with short orbital period
$(P_{\rm orb} < P_{\rm max})$ for a typical cluster with
$10^6 M_{\odot}$ and the galactic globular cluster system with
$10^{7.5} M_{\odot}$~\cite{sigurdsson95} by simply integrating the
period distribution from contact $P_{\rm c}$ up to $P_{\rm max}$
%
\begin{equation}
  N = \int_{P_{\rm c}}^{P_{\rm max}}{\frac{\eta}{k_0}P^{5/3}dP}.
  \label{encounter_number}
\end{equation}
%
The value of $P_{\rm c}$ can be determined by using the Roche lobe
radius of Eggleton~\cite{eggleton83},
%
\begin{equation}
  R_{\rm L} = \frac{0.49 q^{2/3}}{0.6 q^{2/3} +
  \ln{\left(1 + q^{1/3}\right)}}a,
  \label{eggleton_roche_lobe}
\end{equation}
%
and stellar radii as determined by Lynden-Bell and
O'Dwyer~\cite{lyndenbell01}.

The expected populations for an individual cluster and the galactic
cluster system are shown in Table~\ref{encounter_populations} using
neutron star masses of $1.4 M_{\odot}$, white dwarf masses of $0.6
M_{\odot}$ and $0.3 M_{\odot}$, and $P_{\rm max} = 2000 {\rm\ s}$.

\begin{table}[h]
  \begin{center}
    \begin{tabular}{|c|c|c|c|}
      \hline
      Object & ${\rm WD}_a^2$ & ${\rm NW}$ &
      ${\rm NS}^2$\rule{0 em}{1 em} \\
      \hline
      Cluster & \blankzero \blankzero 5.6 & \blankzero \blankzero 4.0 &
0.5 \\
      System  & 176.5 & 125.2 & \blankdot 16 \\
      \hline
    \end{tabular}
  \end{center}
  \caption{\it Encounter rate estimates of the population of
    relativistic binaries in a typical globular cluster and the
    galactic globular cluster system.}
  \label{encounter_populations}
\end{table}

Although we have assumed the orbits of these binaries will be
circularized, there is the possible exception of ${\rm NS}^2$
binaries, which may have a thermal distribution of eccentricities if
they have been formed through exchange interactions rather than
through a common envelope. In this case,
Equations~(\ref{gr_period_evolution}) and~(\ref{knaught}) are no
longer valid. An integration over both period and eccentricity, using
the formulae of Pierro and Pinto~\cite{pierro96}, would be required.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsubsection{Semi-empirical methods}
\label{subsubsection:semi-empirical_methods}

The small number of observed relativistic binaries can be used to
infer the population of dark progenitor
systems~\cite{benacquista01c}. For example, the low-mass X-ray binary
systems are bright enough that we see essentially all of those that
are in the galactic globular cluster system. If we assume that the
ultracompact ones originate from detached WD--NS systems, then we can
estimate the number of progenitor systems by looking at the time spent
by the system in both phases. Let $N_{\rm X}$ be the number of
ultracompact LMXBs and $T_{\rm X}$ be their typical lifetime. Also,
let $N_{\rm det}$ be the number of detached WD--NS systems that will
evolve to become LMXBs, and $T_{\rm det}$ be the time spent during the
inspiral due to the emission of gravitational radiation until the
companion white dwarf fills its Roche lobe. If the process is
stationary, we must have
%
\begin{equation}
  \frac{N_{\rm X}}{T_{\rm X}} = \frac{N_{\rm det}}{T_{\rm det}}.
  \label{population_ratio}
\end{equation}
%
The time spent in the inspiral phase can be found from integrating
Equation~(\ref{gr_period_evolution}) to get
%
\begin{equation}
  T_{\rm det} = \frac{3}{8k_0}\left(P_0^{8/3}-P_{\rm c}^{8/3}\right)
  \label{detached_time}
\end{equation}
%
where $P_0$ is the period at which the progenitor emerges from the
common envelope and $P_{\rm c}$ is the period at which RLOF from the
white dwarf to the neutron star begins. Thus, the number of detached
progenitors can be estimated from
%
\begin{equation}
  N_{\rm det} = \frac{N_{\rm X}}{T_{\rm X}}
  \frac{3}{8k_0}\left(P_0^{8/3}-P_{\rm c}^{8/3}\right).
  \label{detached_number}
\end{equation}

There are four known ultracompact LMXBs~\cite{deutsch00} with orbital 
periods small enough to require a degenerate white dwarf companion to
the neutron star. There are six other LMXBs with unknown orbital
periods. Thus, $4 \leq N_{\rm X} \leq 10$. The lifetime $T_{\rm X}$
is rather uncertain, depending upon the nature of the mass transfer
and the timing when the mass transfer would cease. A standard
treatment of mass transfer driven by gravitational radiation alone
gives an upper bound of $T_{\rm X} \sim 10^9 {\rm\ yr}$~\cite{rappaport87}, but other effects such as tidal heating or irradiation may shorten this to $T_{\rm X} \sim 10^7 {\rm\ yr}$~\cite{applegate94,rasio00a}. The value of $P_0$ depends critically upon the evolution of the neutron star--main-sequence binary, and is very uncertain. Both $k_0$ and $P_{\rm c}$ depend upon the masses of the WD secondary and the NS primary. For a rough estimate, we take the mass of the secondary to be a typical He WD of mass $0.4 M_{\odot}$ and the mass of the primary to be $1.4 M_{\odot}$. Rather than estimate the typical period of emergence from the common envelope, we arbitrarily choose $P_0 = 2000 {\rm\ s}$. We can be certain that all progenitors have emerged from the common envelope by the time the orbital period is this low. The value of $P_c$ can be determined by using
Equation~(\ref{eggleton_roche_lobe}) and the radius of the white dwarf
as determined by Lynden-Bell and O'Dwyer~\cite{lyndenbell01}. Adopting
the optimistic values of $N_{\rm X} = 10$ and $T_{\rm X} = 10^7 {\rm\ yr}$, and evaluating Equation~(\ref{detached_time}) gives $T_{\rm det} \sim 10^7 {\rm\ yr}$. Thus, we find $N_{\rm det} \sim 1 - 10$, which is within an order of magnitude of the numbers found through dynamical simulations (Section~\ref{subsubsection:monte-carlo_simulations}) and encounter rate estimations (Section~\ref{subsubsection:encounter_rates}).

Current production of ultracompact WD-NS binaries is more likely to arise through collisions of neutron stars with lower mass red giant stars near the current turn-off mass. The result of such a collision is a common envelope that will quickly eject the envelope of the red giant and leave behind the core in an eccentric orbit. The result of the eccentric orbit is to hasten the inspiral of the degenerate core into the neutron star due to gravitational radiation~\cite{peters63}. Consequently, $T_{\rm det}$ can be significantly shorter~\cite{ivanova05b}. Adopting a value of $T_{\rm det} \sim 10^6$ gives $N_{\rm det} < 100$.

Continuing in the spirit of small number statistics, we note that
there is one known radio pulsar in a globular cluster NS--NS binary
(B2127+11C) and about 50 known radio pulsars in the globular cluster
system as a whole (although this number may continue to
grow)~\cite{lorimer01}. We may estimate that NS--NS binaries make up
roughly $1/50$ of the total number of neutron stars in the globular
cluster system. A lower limit on the number of neutron stars comes
from estimates of the total number of active radio pulsars in
clusters, giving $N_{\rm NS^2} \sim 10^5$~\cite{kulkarni90}. Thus, we
can estimate the total number of NS--NS binaries to be $\sim 2000$. Not
all of these will be in compact orbits, but we can again estimate the
number of systems in compact orbits by assuming that the systems
gradually decay through gravitational radiation and thus
%
\begin{equation}
  \frac{N_{\rm compact}}{N_{\rm NS^2}} =
  \frac{T_{\rm compact}}{T_{\rm coalesce}}
  \label{NS_binary_ratio}
\end{equation}
%
where $N_{\rm compact}$ is the number of systems in compact orbits
($P_{\rm orb} < 2000 {\rm\ s}$), $T_{\rm compact}$ is the time spent
as a compact system, and $T_{\rm coalesce}$ is the typical time for a
globular cluster NS--NS binary to coalesce due to gravitational
radiation inspiral. Adopting the coalescence time of B2127+11C as
typical, $T_{\rm coalesce} = 2 \times 10^8 {\rm\ yr}$~\cite{prince91},
and integrating Equation~(\ref{detached_time}) for two $1.4 M_{\odot}$
neutron stars, we find $N_{\rm compact} \sim 25$. Again this value
compares favorably with the values found from encounter rate
estimations.

\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Prospects of Gravitational Radiation}
\label{section:gravitational_radiation}

A very exciting prospect for the observation of relativistic binaries
in globular clusters lies in the fact that they will be sources of
gravitational radiation. There is a phase in the evolution of most
relativistic binaries during which the orbital period is slowly
shrinking due to the emission of gravitational radiation. If the
binary is in a circularized orbit, the gravitational radiation will be
peaked strongly in the second harmonic of the orbital period, so
$f_{\rm gw} = 2f_{\rm orb}$. Gravitational radiation can be described
by the dimensionless strain amplitude $h_o$. Although the strength of
the gravitational radiation varies with the orientation of the binary,
an angle-averaged estimate of the signal strength is~\cite{lisa96}
%
\begin{equation}
  h_0 = 1.5 \times 10^{-21} \left(\frac{f_{\rm gw}}{10^{-3}
  {\rm\ Hz}}\right)^{2/3} \left(\frac{1 {\rm\ kpc}}{r}\right)
  \left(\frac{{\cal M}}{M_{\odot}}\right)^{5/3}.
\end{equation}
%
At a typical globular cluster distance of $r \sim 10 {\rm\ kpc}$ and
typical chirp mass of ${\cal M} \sim 0.5 M_{\odot}$, a relativistic
WD--WD or WD--NS binary with $P_{\rm orb} = 400 {\rm\ s}$ will have a
gravitational wave amplitude of $10^{-22}$. This value is within the
range of the proposed space-based gravitational wave observatory
LISA~\cite{lisa96}.

Many globular clusters lie off the plane of the galaxy and are
relatively isolated systems with known positions. The angular
resolution of LISA improves with signal strength. By focusing the
search for gravitational radiation using known positions of suspected
sources, it is possible to increase the signal-to-noise ratio for the
detected signal. Thus, the angular resolution of LISA for globular
cluster sources can be on the order of the angular size of the
globular cluster itself at $f_{\rm gw} > 1 {\rm\ mHz}$. Consequently,
the orbital period distribution of a globular cluster's population of
relativistic binaries can be determined through observations in
gravitational radiation. We will discuss the prospects for observing
each class of relativistic binaries covered in this review.

White dwarf--white dwarf binaries that are formed from a common
envelope phase will be briefly visible while the recently revealed hot
core of the secondary cools. These objects are most likely the
``non-flickerers'' of Cool {\it et al.}~\cite{cool98} and  Edmonds
{\it et al.}~\cite{edmonds99}. WD--WD binaries formed through exchange
interactions may very well harbor white dwarfs which are too cool to
be observed.  In either case, hardening through dynamical interactions
will become less likely as the orbit shrinks and the effective cross
section of the binary becomes too small. These objects will then be
effectively invisible in electromagnetic radiation until they are
brought into contact and RLOF can begin. During this invisible phase,
the orbital period is ground down through the emission of
gravitational radiation until the orbital period is a few hundred
seconds~\cite{benacquista99}. With a frequency of 1 to 10 mHz,
gravitational radiation from such a binary will be in the band of
LISA~\cite{lisa96}. There are $\sim 175$ such systems predicted from
encounter rates (see Table~\ref{encounter_populations}).

White dwarf--neutron star binaries that are expected to be progenitors
of the millisecond pulsars must pass through a phase of gravitational
radiation after the degenerate core of the donor star emerges from the
common envelope phase and before the spin-up phase begins with the
onset of mass transfer from the WD to the neutron star. The orbital
period at the onset of RLOF will be on the order of 1 to 2 minutes and
the gravitational wave signal will be received at LISA with a
signal-to-noise of $50-100$ at a frequency of around $20 {\rm\ mHz}$
for a globular cluster binary. Estimates of the number of such systems
range from $1 - 10$ for semi-empirical methods
(Section~\ref{subsubsection:semi-empirical_methods}) to $\sim 125$
from encounter rates (Table~\ref{encounter_populations}).

Binaries with significant eccentricity will have a spectrum of
harmonics of the orbital frequency, with the relative strength of the
$n$th harmonic for eccentricity $e$ given by~\cite{peters63}
%
{\arraycolsep 0.14 em
\begin{eqnarray}
  g(n, e) & = & \frac{n^4}{32}\bigg\{\left[J_{n-2}(ne) -
  J_{n-1}(ne) + \frac{2}{n}J_n(ne) + J_{n+1}(ne) -
  J_{n+2}(ne)\right]^2
  \nonumber \\
  & & \qquad + (1-e^2)\left[J_{n-2}(ne) \!-\! 2J_n(ne) \!+\!
  J_{n+2}(ne)\right]^2 \!+\! \frac{4}{3n^2}\left[J_n(ne)\right]^2
  \!\!\bigg\}, \nonumber \\
\end{eqnarray}}%
%
where $J_n$ is the Bessel function. The higher harmonics of
sufficiently eccentric binaries ($e > 0.7$) can be detected by LISA
even though the fundamental orbital frequency is well below its
sensitivity band of $1 - 100 {\rm\ mHz}$~\cite{benacquista02}.

Although the globular cluster population of NS--NS binaries is
expected to be quite small ($\sim 10$), they may have high
eccentricities. The binary pulsar B2127+11Cis an example of a NS--NS
binary in a globular cluster. In terms of the unknown angle of
inclination $i$, the companion mass to the pulsar is
$M_2\sin{i} \sim 1 M_{\odot}$ and its eccentricity is
$e = 0.68$~\cite{lorimer01}. These binaries may also be detectable by
LISA. If the globular cluster systems of other galaxies follow similar
evolution as the Milky Way population, these binaries may be potential
sources for LIGO as gravitational radiation grinds them down to
coalescence. With their high eccentricities and large chirp mass,
black hole binaries will also be good potential sources for
gravitational radiation from the galactic globular cluster
system~\cite{benacquista01b, benacquista02}.

The relatively close proximity of the galactic globular cluster system
and the separations between individual globular clusters allows for
the identification of gravitational radiation sources with their
individual host clusters. Although the expected angular resolution of
LISA is not small enough to allow for the identification of individual
sources, knowledge of the positions of the clusters will allow for
focused searches of the relativistic binary populations of the
majority of the galactic globular clusters. Armed with a knowledge of
the orbital periods of any detected binaries, concentrated searches in
electromagnetic radiation can be successful in identifying
relativistic binaries that may have otherwise been missed.

\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Summary}
\label{section:summary}

Relativistic binaries are tracers for the rich dynamical evolution of
globular clusters. The populations of these objects are the result of
an interplay between the gravitational dynamics of large $N$-body
systems, the dynamics of mass transfer, the details of stellar
evolution, and the effect of the gravitational field of the
galaxy. The gravitational dynamics of globular clusters can enhance
the population of short period binaries of main-sequence stars as well
as inject compact objects such as white dwarfs and neutron stars into
stellar binary systems. Once they are in such systems, the details of
stellar evolution and mass transfer in close binary systems govern the
likely end products of the dynamical interaction between the two
stars. Furthermore, most models of the evolution of the core of a
globular cluster rely on the gradual hardening and ejection of binary
systems to delay the onset of core collapse. The hardening of binaries
in the core of globular clusters will produce relativistic binaries,
but it will also eventually eject these systems as they gain larger
and larger recoil velocities in each subsequent encounter. The
threshold for ejection from a globular cluster depends both upon the
gravitational potential of the cluster itself and the gravitational
potential of its environment generated by the Milky Way. As the
globular cluster orbits the Milky Way, its local environment
changes. Consequently, if other dynamical processes (such as
gravothermal oscillations) do not dominate, the globular cluster's
population of relativistic binaries may also reflect the past orbital
history of the globular cluster.

Over the last decade, observational techniques and technology have
improved to the extent that significant discoveries are being made
regularly. At this point, the bottleneck in observations of binary
millisecond pulsars, low-mass X-ray binaries, and cataclysmic
variables is time, not technology. As these observational techniques
are brought to bear on more clusters, more discoveries are bound to be
made. In the next decade, the possibility of using gravitational wave
astronomy to detect relativistic binaries brings the exciting
possibility of identifying the populations of electromagnetically
invisible objects such as detached WD and NS binaries and black hole
binaries in globular clusters. These observations can only help to
improve the understanding of the complex and interesting  evolution of
these objects and their host globular clusters.

\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Acknowledgements}
\label{section:acknowledgements}

I would like to acknowledge the kind hospitality of the Aspen Center for Physics, and the anonymous referees whose extensive knowledge of the subject has helped fill in the gaps in my understanding. Extensive use was made of both the arXiv pre-print server and the ADS system. This work has been supported by NASA EPSCoR grant NCCW-0058, Montana EPSCoR grant NCC5-240, NASA Cooperative Agreement NCC5-579, and NASA APRA grant NNG04GD52G.

\newpage



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\bibliography{newrefs}

\end{document}

article.bbl
\begin{thebibliography}{100}

\bibitem{aarseth99b}\comment{article}
\comment{author}Aarseth, S.~J., \comment{title}``From NBODY1 to NBODY6: The
  growth of an industry'', \comment{journal}{\em Publ. Astron. Soc. Pac.},
  \comment{volume}{\bf 111}, \comment{pages}1333--1346, (\comment{year}1999).
  \keywords{numerical methods}

\bibitem{aarseth99a}\comment{article}
\comment{author}Aarseth, S.~J., \comment{title}``Star cluster simulations: The
  state of the art'', \comment{journal}{\em Celest. Mech. Dyn. Astr.},
  \comment{volume}{\bf 73}, \comment{pages}127--137, (\comment{year}1999). For
  a related online version see: \comment{author}S.~J. Aarseth,
  \comment{onlinetitle}``Star cluster simulations: The state of the art'',
  (\comment{onlineyear}1999), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}7 January 1999,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/9901069.
  \keywords{numerical methods}

\bibitem{aarseth03}\comment{book}
\comment{author}Aarseth, S.~J., \comment{title}{\em Gravitational N-Body
  Simulations: Tools and Algorithms}, (\comment{publisher}Cambridge University
  Press, \comment{address}Cambridge, \comment{year}2003). \keywords{numerical
  methods, dynamical systems}

\bibitem{albrow01}\comment{article}
\comment{author}Albrow, M.~D., Gilliland, R.~L., Brown, T.~M., Edmonds, P.~D.,
  Guhathakurta, P., and Sarajedini, A., \comment{title}``The frequency of
  binary stars in the core of 47 Tucanae'', \comment{journal}{\em Astrophys.
  J.}, \comment{volume}{\bf 559}, \comment{pages}1060--1081,
  (\comment{year}2001). For a related online version see: \comment{author}M.~D.
  Albrow, et al., \comment{onlinetitle}``The frequency of binary stars in the
  core of 47 Tucanae'', (\comment{onlinemonth}May, \comment{onlineyear}2001),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}24 May 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0105441.
  \keywords{globular clusters, binary systems}

\bibitem{anderson03}\comment{article}
\comment{author}Anderson, J., Cool, A.~M., and King, I.~R., \comment{title}``A
  probable dwarf nova outburst in the core of the globular cluster M22'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 597},
  \comment{pages}137--140, (\comment{year}2003). \keywords{globular clusters,
  binary systems, white dwarfs}

\bibitem{anderson90}\comment{article}
\comment{author}Anderson, S.~B., Gorham, P.~W., Kulkarni, S.~R., Prince, T.~A.,
  and Wolszczan, A., \comment{title}``Discovery of two radio pulsars in the
  globular cluster M15'', \comment{journal}{\em Nature}, \comment{volume}{\bf
  346}, \comment{pages}42--44, (\comment{year}1990). \keywords{pulsars,
  globular clusters}

\bibitem{angelini01}\comment{article}
\comment{author}Angelini, L., Loewenstein, M., and Mushotzky, R.~F.,
  \comment{title}``The X-ray globular cluster population in NGC 1399'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 557},
  \comment{pages}L35--L38, (\comment{year}2001). For a related online version
  see: \comment{author}L.~Angelini, et al., \comment{onlinetitle}``The X-ray
  globular cluster population in NGC 1399'', (\comment{onlinemonth}July,
  \comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}19 July 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0107362.
  \keywords{globular clusters, binary systems, galaxies, X-ray astronomy}

\bibitem{applegate94}\comment{article}
\comment{author}Applegate, J.~H., and Shaham, J., \comment{title}``Orbital
  period variability in the eclipsing pulsar binary PSR B1957+20: Evidence for
  a tidally powered star'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 436}, \comment{pages}312--318, (\comment{year}1994).
  \keywords{binary systems, neutron stars, pulsars, white dwarfs}

\bibitem{auriere84}\comment{article}
\comment{author}Auriere, M., Le~Fevre, O., and Terzan, A., \comment{title}``A
  possible optical counterpart for the M15 globular cluster X-ray source'',
  \comment{journal}{\em Astron. Astrophys.}, \comment{volume}{\bf 138},
  \comment{pages}415--420, (\comment{year}1984). \keywords{globular clusters,
  X-ray astronomy, binary systems}

\bibitem{bailyn91}\comment{inproceedings}
\comment{author}Bailyn, C.~D., \comment{title}``Compact objects in globular
  clusters'', in \comment{editor}Janes, K., ed., \comment{booktitle}{\em ASP
  Conf. Ser. 13: The Formation and Evolution of Star Clusters}, \comment{pages}
  307--323, (\comment{publisher}ASP, \comment{address}San Francisco,
  \comment{year}1991). \keywords{globular clusters, white dwarfs, pulsars,
  neutron stars, X-ray astronomy, binary systems}

\bibitem{bailyn95}\comment{article}
\comment{author}Bailyn, C.~D., \comment{title}``Blue stragglers and other
  stellar anomalies: Implications for the dynamics of globular clusters'',
  \comment{journal}{\em Annu. Rev. Astron. Astrophys.}, \comment{volume}{\bf
  33}, \comment{pages}133--162, (\comment{year}1995). \keywords{globular
  clusters, binary systems, white dwarfs, pulsars, neutron stars}

\bibitem{bailyn88}\comment{article}
\comment{author}Bailyn, C.~D., Grindlay, J.~E., Cohn, H., and Lugger, P.,
  \comment{title}``Color maps of X-ray globular clusters'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 331},
  \comment{pages}303--312, (\comment{year}1988). \keywords{globular clusters,
  X-ray astronomy}

\bibitem{balucinska04}\comment{article}
\comment{author}Balucinska-Church, M., Church, M.~J., and Smale, A.~P.,
  \comment{title}``The orbital period of the dipping, bursting, globular
  cluster X-ray source XB 1746-371 from {\it Rossi X-ray Timing Explorer}
  observations'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 347}, \comment{pages}334--338, (\comment{year}2004).
  \keywords{}

\bibitem{bassa04}\comment{article}
\comment{author}Bassa, C., Pooley, D., Homer, L., Verbunt, F., Gaensler, B.~M.,
  Lewin, W.~H~.G., Anderson, S.~F., Margon, B., Kaspi, V.~M., and van~der Klis,
  M., \comment{title}``X-ray sources and their optical counterparts in the
  globular cluster M4'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 609}, \comment{pages}755--765, (\comment{year}2004).
  \keywords{globular clusters, X-ray astronomy, neutron stars, white dwarfs,
  binary systems, novae}

\bibitem{baumgardt00}\comment{article}
\comment{author}Baumgardt, H., \comment{title}``Scaling of $N$-body
  calculations'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 325}, \comment{pages}1323--1331, (\comment{year}2001).
  For a related online version see: \comment{author}H.~Baumgardt,
  \comment{onlinetitle}``Scaling of $N$-body calculations'',
  (\comment{onlinemonth}December, \comment{onlineyear}2000),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}14 December 2000,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0012330.
  \keywords{numerical methods}

\bibitem{baumgardt05}\comment{article}
\comment{author}Baumgardt, H., Makino, J., and Hut, P., \comment{title}``Which
  globular clusters contain intermediate-mass black holes?'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 620},
  \comment{pages}238--243, (\comment{year}2005). \keywords{globular clusters,
  numerical methods, black holes, dynamical systems}

\bibitem{belczynski01}\comment{article}
\comment{author}Belczynski, K., and Kalogera, V., \comment{title}``A new
  formation channel for double neutron stars without recycling, implications
  for gravitational wave detection'', \comment{journal}{\em Astrophys. J.
  Lett.}, \comment{volume}{\bf 550}, \comment{pages}L183--L187,
  (\comment{year}2001). \keywords{binary systems, gravitational wave sources,
  neutron stars}

\bibitem{belczynski02}\comment{article}
\comment{author}Belczynski, K., Kalogera, V., and Bulik, T., \comment{title}``A
  comprehensive study of binary compact objects as gravitational wave sources:
  Evolutionary channels, rates, and physical properties'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 572},
  \comment{pages}407--431, (\comment{year}2002). \keywords{binary systems,
  neutron stars, gravitational wave sources, black holes}

\bibitem{benacquista99}\comment{article}
\comment{author}Benacquista, M., \comment{title}``Gravitational radiation from
  globular clusters'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 520}, \comment{pages}233--238, (\comment{year}1999).
  \keywords{binary systems, globular clusters, gravitational radiation}

\bibitem{benacquista01b}\comment{inproceedings}
\comment{author}Benacquista, M., \comment{title}``Detecting eccentric globular
  cluster binaries with LISA'', in \comment{editor}Wheeler, J.C., and Martel,
  H., eds., \comment{booktitle}{\em Relativistic Astrophysics: 20th Texas
  Symposium}, volume 586, \comment{pages} 793--795, (\comment{publisher}AIP,
  \comment{address}Melville, NY, \comment{year}2001). For a related online
  version see: \comment{author}M.~Benacquista, \comment{onlinetitle}``Detecting
  eccentric globular cluster binaries with LISA'', (\comment{onlinemonth}June,
  \comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}6 June 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0106086.
  \keywords{gravitational radiation, globular clusters, binary systems, black
  holes}

\bibitem{benacquista02}\comment{article}
\comment{author}Benacquista, M., \comment{title}``Gravitational Radiation from
  Black Hole Binaries in Globular Clusters'', \comment{journal}{\em Class.
  Quantum Grav.}, \comment{volume}{\bf 19}, \comment{pages}1297--1302,
  (\comment{year}2002). For a related online version see:
  \comment{author}M.~Benacquista, \comment{onlinetitle}``Gravitational
  radiation from black hole binaries in globular clusters'',
  (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}1 October 2001,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0110016.
  \keywords{globular clusters, black holes, gravitational radiation}

\bibitem{benacquista01c}\comment{article}
\comment{author}Benacquista, M.~J., Portegies~Zwart, S., and Rasio, F.~A.,
  \comment{title}``LISA sources in globular clusters'', \comment{journal}{\em
  Class. Quantum Grav.}, \comment{volume}{\bf 18}, \comment{pages}4025--4031,
  (\comment{year}2001). For a related online version see: \comment{author}M.~J.
  Benacquista, et al., \comment{onlinetitle}``LISA sources in globular
  clusters'', (\comment{onlinemonth}October, \comment{onlineyear}2000),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}9 October 2000,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/gr-qc/0010020.
  \keywords{gravitational wave detectors, gravitational radiation, globular
  clusters, binary systems}

\bibitem{binney87}\comment{book}
\comment{author}Binney, J., and Tremaine, S., \comment{title}{\em Galactic
  Dynamics}, (\comment{publisher}Princeton University Press,
  \comment{address}Princeton, \comment{year}1987). \keywords{astrophysics,
  dynamical systems}

\bibitem{bond05}\comment{article}
\comment{author}Bond, I.~A., Abe, F., Eguchi, S., Furuta, Y., Hearnshaw, J.~B.,
  Kamiya, K., Kilmartin, P.~M., Kurata, Y., Masuda, K., Matsubara, Y., Muraki,
  Y., Noda, S., Okajima, K., Rattenbury, N.~J., Sako, T., Sekiguchi, T.,
  Sullivan, D.~J., Sumi, T., Tristram, P.~J., Yanagisawa, T., and Yock,
  P.~C.~M, \comment{title}``Multiple outbursts of a cataclysmic variable in the
  globular cluster M22'', \comment{journal}{\em Astrophys. J. Lett.},
  \comment{volume}{\bf 620}, \comment{pages}103--106, (\comment{year}2005).
  \keywords{globular clusters, binary systems, novae, white dwarfs}

\bibitem{camilo00}\comment{article}
\comment{author}Camilo, F., Lorimer, D.~R., Freire, P., Lyne, A.~G., and
  Manchester, R.~N., \comment{title}``Observations of 20 millisecond pulsars in
  47 Tucanae at 20 centimeters'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 535}, \comment{pages}975--990, (\comment{year}2000).
  \keywords{binary systems, globular clusters, pulsars}

\bibitem{camilo01}\comment{article}
\comment{author}Camilo, F., Lyne, A.~G., Manchester, R.~N., Bell, J.~F.,
  Stairs, I.~H., D'Amico, N., Kaspi, V.~M., Possenti, A., Crawford, F., and
  McKay, N.~P.~F., \comment{title}``Discovery of five binary radio pulsars'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 548},
  \comment{pages}L187--L191, (\comment{year}2001). \keywords{binary systems,
  pulsars}

\bibitem{camilo05}\comment{online}
\comment{author}Camilo, F., and Rasio, F.~A., \comment{onlinetitle}``Pulsars in
  globular clusters'', (\comment{onlineyear}2005), \comment{fileformat}[Online
  ArXiv Preprint]: cited on \comment{cited}12 January 2005,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0501226.
  \keywords{globular clusters, radio astronomy, neutron stars, pulsars}

\bibitem{carney01}\comment{inbook}
\comment{author}Carney, B.~W., \comment{title}``Globular cluster systems'', in
  \comment{editor}Labhardt, L., and Binggeli, B., eds., \comment{booktitle}{\em
  Star Clusters: Saas-Fee Advanced Course 28}, \comment{pages} 223--408,
  (\comment{publisher}Springer-Verlag, \comment{address}Berlin,
  \comment{year}2001). \keywords{globular clusters, astronomy}

\bibitem{carretta00}\comment{article}
\comment{author}Carretta, E., Gratton, R.~G., Clementini, G., and Fusi~Pecci,
  F., \comment{title}``Distance, ages, and epoch of formation of globular
  clusters'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 533},
  \comment{pages}215--235, (\comment{year}2000). \keywords{galaxies, globular
  clusters, stars}

\bibitem{chaboyerweb}\comment{lr_url}
\comment{author}\comment{author}Chaboyer, B., \comment{onlinetitle}``Milky Way
  Globular Clusters'', (\comment{onlineyear}2001), \comment{fileformat}[Online
  HTML Document]: cited on \comment{cited}31 December 2001,
  \comment{onlineaddress}http://www.dartmouth.edu/\~{}chaboyer/mwgc.html.
  \keywords{globular clusters}

\bibitem{chandler03}\comment{misc}
\comment{author}Chandler, A.~M., \comment{title}``Pulsar searches: From radio
  to gamma-rays'', (\comment{year}2003). \keywords{pulsars}

\bibitem{cohn79}\comment{article}
\comment{author}Cohn, H., \comment{title}``Numerical integration of the
  Fokker-Planck equation and the evolution of star clusters'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 234},
  \comment{pages}1036--1053, (\comment{year}1979). \keywords{globular clusters,
  numerical methods, dynamical systems}

\bibitem{colpi03}\comment{article}
\comment{author}Colpi, M., Mapelli, M., and Possenti, A.,
  \comment{title}``Probing the presence of a single or binary black hole in the
  globular cluster NGC 6752 with pulsar dynamics'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 599}, \comment{pages}1260--1271,
  (\comment{year}2003). \keywords{globular clusters, pulsars, neutron stars,
  black holes, binary systems}

\bibitem{colpi02}\comment{article}
\comment{author}Colpi, M., Possenti, A., and Gualandris, A.,
  \comment{title}``The case of PSR J1911-5958A in the outskirts of NGC 6752:
  Signature of a black hole binary in the cluster core?'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 570},
  \comment{pages}85--88, (\comment{year}2002). \keywords{globular clusters,
  pulsars, neutron stars, black holes, binary systems}

\bibitem{cool98}\comment{article}
\comment{author}Cool, A.~M., Grindlay, J.~E., Cohn, H.~N., Lugger, P.~M., and
  Bailyn, C.~D., \comment{title}``Cataclysmic variables and a new class of
  faint ultraviolet stars in the globular cluster NGC 6397'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 508},
  \comment{pages}L75--L79, (\comment{year}1998). \keywords{binary systems,
  globular clusters, white dwarfs}

\bibitem{cool96}\comment{article}
\comment{author}Cool, A.~M., Piotto, G., and King, I.~R., \comment{title}``The
  main sequence and a white dwarf sequence in the globular cluster NGC 6397'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 468},
  \comment{pages}655--662, (\comment{year}1996). \keywords{globular clusters,
  white dwarfs}

\bibitem{cudworth88}\comment{article}
\comment{author}Cudworth, K.~M., \comment{title}``Astrometry and photometry in
  the gloublar cluster NGC 6712'', \comment{journal}{\em Astron. J.},
  \comment{volume}{\bf 96}, \comment{pages}105--115, (\comment{year}1988).
  \keywords{globular clusters, binary systems, X-ray astronomy}

\bibitem{damico01a}\comment{article}
\comment{author}D'Amico, N., Lyne, A.~G., Manchester, R.~N., Possenti, A., and
  Camilo, F., \comment{title}``Discovery of short-period binary millisecond
  pulsars in four globular clusters'', \comment{journal}{\em Astrophys. J.
  Lett.}, \comment{volume}{\bf 548}, \comment{pages}L171--L174,
  (\comment{year}2001). \keywords{binary systems, globular clusters, pulsars}

\bibitem{damico02}\comment{article}
\comment{author}D'Amico, N., Possenti, A., Fici, L., Manchester, R.~N., Lyne,
  A.~G, and Camilo, F., \comment{title}``Timing of millisecond pulsars in NGC
  6752: Evidence for a high mass-to-light ratio in the core'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 570},
  \comment{pages}89--92, (\comment{year}2002). \keywords{globular clusters,
  pulsars}

\bibitem{damico03}\comment{inproceedings}
\comment{author}D'Amico, N., Possenti, A., Manchester, R.~N., Lyne, A.~G.,
  Camilo, F., and Sarkissian, J., \comment{title}``Searching for millisecond
  pulsars in globular clusters with Parkes'', in \comment{editor}Bailes, M.,
  Nice, D.~J., and Thorsett, S.~E., eds., \comment{booktitle}{\em Radio
  Pulsars}, volume 302, \comment{pages} 375--+,
  (\comment{publisher}Astronomical Society of the Pacific, \comment{address}San
  Francisco, \comment{year}2003). \keywords{globular clusters, pulsars, neutron
  stars, radio astronomy}

\bibitem{damico01b}\comment{inproceedings}
\comment{author}D'Amico, N., Possenti, A., Manchester, R.~N., Sarkissian, J.,
  Lyne, A.~G., and Camilo, F., \comment{title}``New millisecond pulsars in
  globular clusters'', in \comment{editor}Wheeler, J.C., and Martel, H., eds.,
  \comment{booktitle}{\em Relativistic Astrophysics: 20th Texas Symposium},
  volume 586, \comment{pages} 526--531, (\comment{publisher}AIP,
  \comment{address}Melville, NY, \comment{year}2001). For a related online
  version see: \comment{author}N.~D'Amico, et al., \comment{onlinetitle}``New
  millisecond pulsars in globular clusters'', (\comment{onlineyear}2001),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}8 May 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0105122.
  \keywords{binary system, globular clusters, pulsars}

\bibitem{dantona04}\comment{article}
\comment{author}D'Antona, F., and Caloi, V., \comment{title}``The early
  evolution of globular clusters: the case of NGC 2808'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 611}, \comment{pages}871--880,
  (\comment{year}2004). \keywords{globular clusters, stellar evolution}

\bibitem{davies95b}\comment{article}
\comment{author}Davies, M.~B., \comment{title}``The binary zoo: the calculation
  of production rates of binaries through 2~+~1 encounters in globular
  clusters'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 276}, \comment{pages}887--905, (\comment{year}1995).
  \keywords{binary systems, stars, dynamical systems, globular clusters}

\bibitem{davies97}\comment{article}
\comment{author}Davies, M.~B., \comment{title}``Cataclysmic variable production
  in globular clusters'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 288}, \comment{pages}117--128, (\comment{year}1997).
  \keywords{binary systems, globular clusters}

\bibitem{davies95a}\comment{article}
\comment{author}Davies, M.~B., and Benz, W., \comment{title}``A stellar audit:
  the computation of encounter rates for 47 Tucanae and $\omega$ Centauri'',
  \comment{journal}{\em Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 276},
  \comment{pages}876--886, (\comment{year}1995). \keywords{binary system,
  dynamical systems, globular clusters}

\bibitem{davies98}\comment{article}
\comment{author}Davies, M.~B., and Hansen, B.~M.~S., \comment{title}``Neutron
  star retention and millisecond pulsar production in globular clusters'',
  \comment{journal}{\em Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 301},
  \comment{pages}15--24, (\comment{year}1998). \keywords{dynamical systems,
  pulsars, neutron stars, globular clusters}

\bibitem{deutsch98}\comment{article}
\comment{author}Deutsch, E.~W., Anderson, S.~F., Margon, B., and Downes, R.~A.,
  \comment{title}``The probable optical counterpart of the luminous X-ray
  source in NGC 6441'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 493}, \comment{pages}775--780, (\comment{year}1998).
  \keywords{globular clusters, neutron stars, X-ray astronomy}

\bibitem{deutsch00}\comment{article}
\comment{author}Deutsch, E.~W., Margon, B., and Anderson, S.~F.,
  \comment{title}``Ultracompact X-ray binaries in globular clusters:
  variability of the optical counterpart of X1832-330 in NGC 6652'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 530},
  \comment{pages}L21--L24, (\comment{year}2000). \keywords{globular clusters,
  neutron stars}

\bibitem{distefano02}\comment{article}
\comment{author}Di~Stefano, R., Kong, A.~K.~H., Garcia, M.~R., Barmby, P.,
  Greiner, J., Murray, S.~S., and Primini, F.~A., \comment{title}``Bright X-ray
  sources in M31 globular clusters'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 570}, \comment{pages}618--636, (\comment{year}2002). For
  a related online version see: \comment{author}R.~Di~Stefano, et al.,
  \comment{onlinetitle}``Bright X-ray sources in M31 globular clusters'',
  (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}14 June 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0106254.
  \keywords{galaxies, globular clusters, X-ray astronomy}

\bibitem{dieball05}\comment{article}
\comment{author}Dieball, A., Knigge, C., Zurek, D.~R., Shara, M.~M., and Long,
  K.~S., \comment{title}``Far-ultraviolet observations of the globular cluster
  NGC 2808 revisited: Blue stragglers, white dwarfs, and cataclysmic
  variables'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 625},
  \comment{pages}156--166, (\comment{year}2005). \keywords{globular clusters,
  binary stars, white dwarfs}

\bibitem{downes01}\comment{article}
\comment{author}Downes, R.~A., Webbink, R.~F., Shara, M.~M., Ritter, H., Kolb,
  U., and Duerbeck, H.~W., \comment{title}``A catalog and atlas of catclysmic
  variables: The living edition'', \comment{journal}{\em Publ. Astron. Soc.
  Pac.}, \comment{volume}{\bf 113}, \comment{pages}764--768,
  (\comment{year}2001). For a related online version see: \comment{author}R.~A.
  Downes, et al., \comment{onlinetitle}``A catalog and atlas of cataclysmic
  variables -- The living edition'', (\comment{onlineyear}2001),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}16 February 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0102302.
  \keywords{binary systems}

\bibitem{drukier03}\comment{article}
\comment{author}Drukier, G.~A., Bailyn, C.~D., Van~Altena, W.~F., and Girard,
  T.~M., \comment{title}``Central proper-motion kinematics of NGC 6752'',
  \comment{journal}{\em Astron. J.}, \comment{volume}{\bf 125},
  \comment{pages}2559--2567, (\comment{year}2003). \keywords{globular clusters}

\bibitem{edmonds02}\comment{article}
\comment{author}Edmonds, P.~D., Gilliland, R.~L., Camilo, F., Heinke, C.~O.,
  and Grindlay, J.~E., \comment{title}``A millisecond optical counterpart with
  large-amplitude variability in the globular cluster 47 Tucanae'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 579},
  \comment{pages}741--751, (\comment{year}2002). \keywords{globular clusters,
  binary systems, pulsars, neutron stars}

\bibitem{edmonds03a}\comment{article}
\comment{author}Edmonds, P.~D., Gilliland, R.~L., Heinke, C.~O., and Grindlay,
  J.~E., \comment{title}``An extensive census of {\it Hubble Space Telescope}
  counterparts to {\it Chandra} X-ray sources in the globular cluster 47
  Tucanae. I. Astrometry and photometry'', \comment{journal}{\em Astrophys.
  J.}, \comment{volume}{\bf 596}, \comment{pages}1177--1196,
  (\comment{year}2003). \keywords{globular clusters, binary systems, novae,
  X-ray astronomy, white dwarfs, neutron stars}

\bibitem{edmonds03b}\comment{article}
\comment{author}Edmonds, P.~D., Gilliland, R.~L., Heinke, C.~O., and Grindlay,
  J.~E., \comment{title}``An extensive census of {\it Hubble Space Telescope}
  counterparts to {\it Chandra} X-ray sources in the globular cluster 47
  Tucanae. II. Time series and analysis'', \comment{journal}{\em Astrophys.
  J.}, \comment{volume}{\bf 596}, \comment{pages}1197--1219,
  (\comment{year}2003). \keywords{binary systems, globular clusters, white
  dwarfs, X-ray astronomy}

\bibitem{edmonds99}\comment{article}
\comment{author}Edmonds, P.~D., Grindlay, J.~E., Cool, A., Cohn, H., Lugger,
  P., and Bailyn, C., \comment{title}``Cataclysmic variables and a candidate
  helium white dwarf in the globular cluster NGC 6397'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 516}, \comment{pages}250--262,
  (\comment{year}1999). \keywords{globular clusters, binary systems, white
  dwarfs}

\bibitem{eggleton83}\comment{article}
\comment{author}Eggleton, P.~P., \comment{title}``Approximations to the radii
  of Roche lobes'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf
  268}, \comment{pages}368--369, (\comment{year}1983). \keywords{binary
  systems}

\bibitem{fabian75}\comment{article}
\comment{author}Fabian, A.~C., Pringle, J.~E., and Rees, M.~J.,
  \comment{title}``Tidal capture formation of binary systems and X-ray sources
  in globular clusters'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 172}, \comment{pages}15--18, (\comment{year}1975).
  \keywords{binary systems, X-ray astronomy, globular clusters}

\bibitem{ferraro01}\comment{article}
\comment{author}Ferraro, F.~R., D'Amico, N., Possenti, A., Mignani, R.~P., and
  Paltrinieri, B., \comment{title}``Blue stragglers, young white dwarfs and
  UV-excess stars in the core of 47 Tuc'', \comment{journal}{\em Astrophys.
  J.}, \comment{volume}{\bf 561}, \comment{pages}337--345,
  (\comment{year}2001). For a related online version see: \comment{author}F.~R.
  Ferraro, et al., \comment{onlinetitle}``Blue stragglers, young white dwarfs
  and UV-excess stars in the core of 47 Tuc'', (\comment{onlineyear}2001),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}3 July 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0107056.
  \keywords{globular clusters, neutron stars, pulsars, white dwarfs, binary
  systems}

\bibitem{ferraro00b}\comment{article}
\comment{author}Ferraro, F.~R., Paltrinieri, B., Paresce, F., and De~Marchi,
  G., \comment{title}``Very Large Telescope observations of the peculiar
  globular cluster NGC 6712: Discovery of a UV, H$\alpha$-excess star in the
  core'', \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf
  542}, \comment{pages}L29--L32, (\comment{year}2000). \keywords{binary
  systems, white dwarfs, globular clusters}

\bibitem{ferraro00a}\comment{article}
\comment{author}Ferraro, F.~R., Paltrinieri, B., Rood, R.~T., Fusi~Pecci, F.,
  and Buananno, R., \comment{title}``Another faint ultraviolet object
  associated with a globular cluster X-ray source: The case of M92'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 537},
  \comment{pages}312--318, (\comment{year}2000). \keywords{binary systems,
  globular clusters, astronomy}

\bibitem{fregeau04}\comment{article}
\comment{author}Fregeau, J.~M., Cheung, P., Portegies~Zwart, S.~F., and Rasio,
  F.~A., \comment{title}``Stellar collisions during binary-binary and
  binary-single star interactions'', \comment{journal}{\em Mon. Not. R. Astron.
  Soc.}, \comment{volume}{\bf 352}, \comment{pages}1--19, (\comment{year}2004).
  \keywords{globular clusters, binary systems, numerical methods}

\bibitem{fregeau03}\comment{article}
\comment{author}Fregeau, J.~M., G\"{u}rkan, M.~A., Joshi, K.~J., and Rasio,
  F.~A., \comment{title}``Monte Carlo simulations of globular cluster
  evolution. III. Primordial binary interactions'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 593}, \comment{pages}772--787,
  (\comment{year}2003). \keywords{globular clusters, stellar dynamics, binary
  systems}

\bibitem{freire03}\comment{article}
\comment{author}Freire, P.~C., Camilo, F., Kramer, M., Lorimer, D.~R., Lyne,
  A.~G., Manchester, R.~N., and D'Amico, N., \comment{title}``Further results
  from the timing of the millisecond pulsars in 47 Tucanae'',
  \comment{journal}{\em Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 340},
  \comment{pages}1359--1374, (\comment{year}2003). \keywords{globular clusters,
  binary systems, neutron stars, pulsars}

\bibitem{freire01b}\comment{article}
\comment{author}Freire, P.~C., Camilo, F., Lorimer, D.~R., Lyne, A.~G.,
  Manchester, R.~N., and D'Amico, N., \comment{title}``Timing the millisecond
  pulsars in 47 Tucanae'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 326}, \comment{pages}901--915, (\comment{year}2001). For
  a related online version see: \comment{author}P.~C. Freire, et al.,
  \comment{onlinetitle}``Timing the millisecond pulsars in 47 Tucanae'',
  (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}22 March 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0103372.
  \keywords{binary systems, globular clusters, pulsars}

\bibitem{freire04}\comment{article}
\comment{author}Freire, P.~C., Gupta, Y., Ransom, S.~M., and Ishwara-Chandra,
  C.~H., \comment{title}``Giant Metrewave Radio Telescope discovery of a
  millisecond pulsar in a very eccentric binary system'', \comment{journal}{\em
  Astrophys. J. Lett.}, \comment{volume}{\bf 606}, \comment{pages}53--56,
  (\comment{year}2004). \keywords{globular clusters, radio astronomy, pulsars,
  binary systems}

\bibitem{freire05}\comment{article}
\comment{author}Freire, P.~C., Hessels, J.~W.~T, Nie, D.~J., Ransom, S.~M.,
  Lorimer, D.~R., and Stairs, I.~H., \comment{title}``The millisecond pulsars
  in NGC 6760'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf
  621}, \comment{pages}959--965, (\comment{year}2005). \keywords{globular
  clusters, binary systems, pulsars}

\bibitem{freire01a}\comment{article}
\comment{author}Freire, P.~C., Kramer, M., Lyne, A.~G., Camilo, F., Manchester,
  R.~N., and D'Amico, N., \comment{title}``Detection of ionized gas in the
  globular cluster 47 Tucanae'', \comment{journal}{\em Astrophys. J. Lett.},
  \comment{volume}{\bf 557}, \comment{pages}L105--L108, (\comment{year}2001).
  For a related online version see: \comment{author}P.~C. Freire, et al.,
  \comment{onlinetitle}``Detection of ionized gas in the globular cluster 47
  Tucanae'', (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos
  Archive Preprint]: cited on \comment{cited}11 July 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0107206.
  \keywords{globular clusters, pulsars}

\bibitem{freitag01}\comment{article}
\comment{author}Freitag, M., and Benz, W., \comment{title}``A new Monte Carlo
  code for star cluster simulations: I. Relaxation'', \comment{journal}{\em
  Astron. Astrophys.}, \comment{volume}{\bf 375}, \comment{pages}711--738,
  (\comment{year}2001). \keywords{galaxies, numerical methods, globular
  clusters}

\bibitem{freitag05}\comment{online}
\comment{author}Freitag, M., Gurkan, M.~A., and Rasio, F.~A.,
  \comment{onlinetitle}``Runaway collisions in young star clusters. II.
  Numerical results'', (\comment{onlineyear}2005), \comment{fileformat}[Online
  arXiv preprint]: cited on \comment{cited}4 May 2005,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0503130.
  \keywords{dynamical systems, globular clusters, black holes}

\bibitem{fruchter00}\comment{article}
\comment{author}Fruchter, A.~S., and Goss, W.~M., \comment{title}``Deep radio
  imaging of globular clusters and the cluster pulsar population'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 536},
  \comment{pages}865--874, (\comment{year}2000). \keywords{globular clusters,
  astronomy}

\bibitem{fukushige05}\comment{online}
\comment{author}Fukushige, T., Makino, J., and Kawai, A.,
  \comment{onlinetitle}``GRAPE-6A: A single-card GRAPE-6 for parallel PC-GRAPE
  cluster system'', (\comment{onlineyear}2005), \comment{fileformat}[Online
  arXiv preprint]: cited on \comment{cited}19 April 2005,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0504407.
  \keywords{numerical methods}

\bibitem{gao91}\comment{article}
\comment{author}Gao, B., Goodman, J., Cohn, H., and Murphy, B.,
  \comment{title}``Fokker-Planck calculations of star clusters with primordial
  binaries'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 370},
  \comment{pages}567--582, (\comment{year}1991). \keywords{globular clusters,
  binary systems, numerical methods}

\bibitem{gebhardt00}\comment{article}
\comment{author}Gebhardt, K., Pryor, C., O'Connell, R.~D., Williams, T.~B., and
  Hesser, J.~E., \comment{title}``Canada-France-Hawaii Telescope adaptive
  optics observations of the central kinematics in M15'', \comment{journal}{\em
  Astron. J.}, \comment{volume}{\bf 119}, \comment{pages}1268--1281,
  (\comment{year}2000). \keywords{black holes, dynamical systems, globular
  clusters, galaxies}

\bibitem{gendre03}\comment{article}
\comment{author}Gendre, B., Barret, D., and Webb, N.~A., \comment{title}``An
  XMM-Newton observation of the globular cluster Omega Centauri'',
  \comment{journal}{\em Astron. Astrophys.}, \comment{volume}{\bf 400},
  \comment{pages}521--531, (\comment{year}2003). \keywords{globular clusters,
  X-ray astronomy, binary systems, novae, white dwarfs, neutron stars}

\bibitem{geyer02}\comment{inproceedings}
\comment{author}Geyer, M.~P., and Burkert, A., \comment{title}``Formation of
  Globular Clusters in Turbulent Molecular Clouds'', in
  \comment{editor}Geisler, D., Grebel, E.K., and Minniti, D., eds.,
  \comment{booktitle}{\em Extragalactic Star Clusters}, \comment{pages} 678--+,
  (\comment{publisher}ASP, \comment{address}San Francisco, \comment{year}2002).
  For a related online version see: \comment{author}M.~P. Geyer, et al.,
  \comment{onlinetitle}``Formation of globular clusters in turbulent molecular
  clouds'', (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos
  Archive Preprint]: cited on \comment{cited}26 July 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0106016. To be
  published in {\it Extragalactic Star Clusters}, IAU Symposium Series, Vol.
  207. \keywords{globular clusters, galaxies}

\bibitem{giersz98}\comment{article}
\comment{author}Giersz, M., \comment{title}``Monte Carlo simulations of star
  clusters - I. First results'', \comment{journal}{\em Mon. Not. R. Astron.
  Soc.}, \comment{volume}{\bf 298}, \comment{pages}1239--1248,
  (\comment{year}1998). \keywords{globular clusters, numerical methods}

\bibitem{giersz01}\comment{article}
\comment{author}Giersz, M., \comment{title}``Monte Carlo simulations of star
  clusters - II. Tidally limited, multi-mass systems with stellar evolution'',
  \comment{journal}{\em Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 324},
  \comment{pages}218--230, (\comment{year}2001). \keywords{globular clusters,
  numerical methods}

\bibitem{giersz96}\comment{article}
\comment{author}Giersz, M., and Heggie, D.C., \comment{title}``Statistics of
  $N$-body simulations - III. Unequal masses'', \comment{journal}{\em Mon. Not.
  R. Astron. Soc.}, \comment{volume}{\bf 279}, \comment{pages}1037--1056,
  (\comment{year}1996). \keywords{globular clusters, numerical methods, binary
  systems}

\bibitem{giersz94}\comment{article}
\comment{author}Giersz, M., and Spurzem, R., \comment{title}``Comparing direct
  N-body integration with anisotropic gaseous models of star clusters'',
  \comment{journal}{\em Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 269},
  \comment{pages}241--256, (\comment{year}1994). \keywords{numerical methods,
  globular clusters}

\bibitem{giersz00}\comment{article}
\comment{author}Giersz, M., and Spurzem, R., \comment{title}``A stochastic
  Monte Carlo approach to model real star cluster evolution, II.
  Self-consistent models and primordial binaries'', \comment{journal}{\em Mon.
  Not. R. Astron. Soc.}, \comment{volume}{\bf 317}, \comment{pages}581--606,
  (\comment{year}2000). \keywords{numerical methods, globular clusters, binary
  systems}

\bibitem{giersz03}\comment{article}
\comment{author}Giersz, M., and Spurzem, R., \comment{title}``A stochastic
  Monte Carlo approach to model real star cluster evolution, III. Direct
  integration of three- and four-body interactions'', \comment{journal}{\em
  Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 343},
  \comment{pages}781--795, (\comment{year}2003). \keywords{binary systems,
  globular clusters, numerical methods}

\bibitem{gnedin97}\comment{article}
\comment{author}Gnedin, O.~Y., and Ostriker, J.~P.,
  \comment{title}``Destruction of the galactic globular cluster system'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 474},
  \comment{pages}223--255, (\comment{year}1997). \keywords{globular clusters}

\bibitem{goldman91}\comment{article}
\comment{author}Goldman, I., and Mazeh, T., \comment{title}``On the orbital
  circularization of close binaries'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 376}, \comment{pages}260--265, (\comment{year}1991).
  \keywords{binary systems, stellar evolution}

\bibitem{goodman93}\comment{article}
\comment{author}Goodman, J., Heggie, D.~C., and Hut, P., \comment{title}``On
  the exponential instability of $N$-body systems'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 415}, \comment{pages}715--733,
  (\comment{year}1993). \keywords{numerical methods}

\bibitem{grindlay99}\comment{inproceedings}
\comment{author}Grindlay, J.~E., \comment{title}``Magnetic CVs in globular
  clusters'', in \comment{editor}Hellier, C., and Mukai, K., eds.,
  \comment{booktitle}{\em ASP Conf. Ser. 157: Annapolis Workshop on Magnetic
  Cataclysmic Variables}, \comment{pages} 377+, (\comment{publisher}ASP,
  \comment{address}San Francisco, \comment{year}1999). \keywords{globular
  clusters, binary systems}

\bibitem{grindlay91}\comment{inproceedings}
\comment{author}Grindlay, J.~E., Cool, A.~M., and Bailyn, C.~D.,
  \comment{title}``CVs and millisecond pulsar progenitors in globular
  clusters'', in \comment{editor}Janes, K., ed., \comment{booktitle}{\em ASP
  Conf. Ser. 13: The Formation and Evolution of Star Clusters}, \comment{pages}
  396--400, (\comment{publisher}ASP, \comment{address}San Francisco,
  \comment{year}1991). \keywords{binary systems, globular clusters}

\bibitem{grindlay01a}\comment{article}
\comment{author}Grindlay, J.~E., Heinke, C., Edmonds, P.~D., and Murray, S.~S.,
  \comment{title}``High-resolution X-ray imaging of a globular cluster core:
  Compact binaries in 47 Tuc'', \comment{journal}{\em Science},
  \comment{volume}{\bf 292}, \comment{pages}2290--2295, (\comment{year}2001).
  \keywords{globular clusters, binary systems, X-ray astronomy}

\bibitem{grindlay01b}\comment{article}
\comment{author}Grindlay, J.~E., Heinke, C.~O., Edmonds, P.~D., Murray, S.~S.,
  and Cool, A.~M., \comment{title}``Chandra exposes the core collapsed globular
  cluster NGC 6397'', \comment{journal}{\em Astrophys. J. Lett.},
  \comment{volume}{\bf 563}, \comment{pages}L53--L56, (\comment{year}2001). For
  a related online version see: \comment{author}J.~E. Grindlay, et al.,
  \comment{onlinetitle}``Chandra exposes the core collapsed globular cluster
  NGC 6397'', (\comment{onlineyear}2001), \comment{fileformat}[Online Los
  Alamos Archive Preprint]: cited on \comment{cited}15 August 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0108265.
  \keywords{globular clusters, neutron stars, white dwarfs, binary systems,
  pulsars}

\bibitem{guhathakurta96}\comment{article}
\comment{author}Guhathakurta, P., Yanny, B., Schneider, D.~P., and Bahcall,
  J.~N., \comment{title}``Globular cluster photometry with the {\it Hubble
  Space Telescope}. V. WFPC2 study of M15's central density cusp'',
  \comment{journal}{\em Astron. J.}, \comment{volume}{\bf 111},
  \comment{pages}267--282, (\comment{year}1996). \keywords{globular clusters,
  photometry, black holes}

\bibitem{gurkan04}\comment{article}
\comment{author}Gurkan, M.~A., Freitag, M., and Rasio, F.~A.,
  \comment{title}``Formation of massive black holes in dense star clusters. I.
  Mass segregation and core collapse'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 604}, \comment{pages}632--652, (\comment{year}2004).
  \keywords{globular clusters, dynamical systems, black holes}

\bibitem{hansen03}\comment{article}
\comment{author}Hansen, B.~M.~S., Kalogera, V., and Rasio, F.~A.,
  \comment{title}``Helium core white dwarfs in globular clusters'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 586},
  \comment{pages}1364--1373, (\comment{year}2003). \keywords{globular clusters,
  binary systems, white dwarfs}

\bibitem{hansen04}\comment{article}
\comment{author}Hansen, B.~M.~S., Richer, H.~B., Fahlman, G.~G., Stetson,
  P.~B., Brewer, J., Currie, T., Gibson, B.~K., Ibata, R., Rich, R.~M., and
  Shara, M.~M., \comment{title}``{\it Hubble Space Telescope} observations of
  the white dwarf cooling sequence of M4'', \comment{journal}{\em Astrophys. J.
  Suppl. S.}, \comment{volume}{\bf 155}, \comment{pages}551--576,
  (\comment{year}2004). \keywords{globular clusters, binary systems, white
  dwarfs}

\bibitem{harris91}\comment{article}
\comment{author}Harris, W.~E., \comment{title}``Globular cluster systems in
  galaxies beyond the local group'', \comment{journal}{\em Annu. Rev. Astron.
  Astrophys.}, \comment{volume}{\bf 29}, \comment{pages}543--579,
  (\comment{year}1991). \keywords{galaxies, globular clusters}

\bibitem{harris96}\comment{article}
\comment{author}Harris, W.~E., \comment{title}``A catalog of parameters for
  globular clusters in the Milky Way'', \comment{journal}{\em Astron. J.},
  \comment{volume}{\bf 112}, \comment{pages}1487--1488, (\comment{year}1996).
  For a related online version see: \comment{author}W.~E. Harris,
  \comment{onlinetitle}``Catalog of parameters for Milky Way globular
  clusters'', (\comment{onlinemonth}June, \comment{onlineyear}1999),
  \comment{fileformat}[Online HTML Document]: cited on \comment{cited}June
  1999, \comment{onlineaddress}http://physun.physics.mcmaster.ca/Globular.html.
  \keywords{globular clusters}

\bibitem{harris01}\comment{inbook}
\comment{author}Harris, W.~E., \comment{title}``Globular cluster systems'', in
  \comment{editor}Labhardt, L., and Binggeli, B., eds., \comment{booktitle}{\em
  Star Clusters: Saas-Fee Advanced Course 28}, \comment{pages} 223--408,
  (\comment{publisher}Springer-Verlag, \comment{address}Berlin,
  \comment{year}2001). \keywords{globular clusters, dynamical systems}

\bibitem{heggie75}\comment{article}
\comment{author}Heggie, D.~C., \comment{title}``Binary evolution in stellar
  dynamics'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 173}, \comment{pages}729--787, (\comment{year}1975).
  \keywords{globular clusters, binary systems, dynamical systems}

\bibitem{heggie98}\comment{inproceedings}
\comment{author}Heggie, D.~C., Giersz, M., Spurzem, R., and Takahashi, K.,
  \comment{title}``Dynamical simulations: Methods and comparisons'', in
  \comment{editor}Andersen, J., ed., \comment{booktitle}{\em Highlights of
  Astronomy}, volume~11 of {\em Joint Discussions and Special Session held at
  the XXIIIth IAU General Assembly}, \comment{pages} 591+,
  (\comment{publisher}Kluwer Acad. Publ., \comment{address}Dordrecht,
  \comment{year}1998), IAU. \keywords{globular clusters, numerical methods,
  dynamical systems}

\bibitem{heggie03}\comment{book}
\comment{author}Heggie, D.~C., and Hut, P., \comment{title}{\em The
  Gravitational Million-Body Problem: A Multidisciplinary Approach to Star
  Cluster Dynamics}, (\comment{publisher}Campridge University Press,
  \comment{address}Cambridge, \comment{year}2003). For a related online version
  see: \comment{author}D.~C. Heggie, et al.,
  \comment{onlinetitle}``Computational Physics Introduction'',
  (\comment{onlineyear}2001), \comment{fileformat}[Postscript Document]: cited
  on \comment{cited}12 August 2001,
  \comment{onlineaddress}http://www.sns.ias.edu/\~{}piet/publ/gmbp/chapter03.p%
s. \keywords{astrophysics, numerical methods, dynamical systems}

\bibitem{heinke01}\comment{article}
\comment{author}Heinke, C.~O., Edmonds, P.~D., and Grindlay, J.~E.,
  \comment{title}``Identification of the LMXB and faint X-ray sources in NGC
  6652'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 562},
  \comment{pages}363--367, (\comment{year}2001). For a related online version
  see: \comment{author}C.~O. Heinke, et al.,
  \comment{onlinetitle}``Identification of the LMXB and faint X-ray sources in
  NGC 6652'', (\comment{onlineyear}2001), \comment{fileformat}[Online Los
  Alamos Archive Preprint]: cited on \comment{cited}26 July 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0107513.
  \keywords{binary systems, neutron stars, dynamical systems, globular
  clusters}

\bibitem{heinke03a}\comment{article}
\comment{author}Heinke, C.~O., Edmonds, P.~D., Grindlay, J.~E., Lloyd, D.~A.,
  Cohn, H.~N., and Lugger, P.~M., \comment{title}``A {\it Chandra} X-ray study
  of the dense globular cluster Terzan 5'', \comment{journal}{\em Astrophys.
  J.}, \comment{volume}{\bf 590}, \comment{pages}809--821,
  (\comment{year}2003). \keywords{globular clusters, X-ray astronomy, neutron
  stars, white dwarfs, binary systems, novae}

\bibitem{heinke03b}\comment{article}
\comment{author}Heinke, C.~O., Grindlay, J.~E., Edmonds, P.~D., Lloyd, D.~A.,
  Murray, S.~S., Cohn, H.~N., and Lugger, P.~M., \comment{title}``A {\it
  Chandra} X-ray study of the globular cluster M80'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 598}, \comment{pages}516--526,
  (\comment{year}2003). \keywords{globular clusters, X-ray astronomy, neutron
  stars, white dwarfs, binary systems, novae}

\bibitem{henon71b}\comment{article}
\comment{author}H\'enon, M., \comment{title}``The Monte Carlo method'',
  \comment{journal}{\em Astrophys. \& S. S.}, \comment{volume}{\bf 14},
  \comment{pages}151--167, (\comment{year}1971). \keywords{numerical methods,
  dynamical systems}

\bibitem{henon71a}\comment{article}
\comment{author}H\'enon, M., \comment{title}``Monte Carlo models of star
  clusters'', \comment{journal}{\em Astrophys. \& S. S.}, \comment{volume}{\bf
  13}, \comment{pages}284--299, (\comment{year}1971). \keywords{numerical
  methods, dynamical systems}

\bibitem{hessels04}\comment{inproceedings}
\comment{author}Hessels, J.~W.~T, Ransom, S.~M., Stairs, I.~H., Kaspi, V.~M.,
  Freire, P.~C.~C., Backer, D.~C., and Lorimer, D.~R., \comment{title}``A 20 cm
  search for pulsars in globular clusters with Arecibo and the GBT'', in
  \comment{editor}Camilo, F., and Gaensler, B.~M., eds.,
  \comment{booktitle}{\em IAU Sump. 218: Young Neutron Stars and Their
  Environments}, (\comment{publisher}Astronomical Society of the Pacific,
  \comment{address}San Francisco, \comment{year}2004). \keywords{globular
  clusters, radio astronomy, pulsars}

\bibitem{hilditch01}\comment{book}
\comment{author}Hilditch, R.~W., \comment{title}{\em An Introduction to Close
  Binary Stars}, (\comment{publisher}Cambridge University Press,
  \comment{address}Cambridge, U.K., \comment{year}2001). \keywords{binary
  systems}

\bibitem{hills90}\comment{article}
\comment{author}Hills, J.~G., \comment{title}``Encounters between single and
  binary stars: The effect of intruder mass on the maximum impact velocity for
  which the mean change in binding energy is positive'', \comment{journal}{\em
  Astron. J.}, \comment{volume}{\bf 99}, \comment{pages}979--982,
  (\comment{year}1990). \keywords{celestial mechanics, binary systems}

\bibitem{hils90}\comment{article}
\comment{author}Hils, D., Bender, P.~L., and Webbink, R.~F.,
  \comment{title}``Gravitational radiation from the galaxy'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 360},
  \comment{pages}75--94, (\comment{year}1990). \keywords{galaxies, binary
  systems, white dwarfs}

\bibitem{hjellming87}\comment{article}
\comment{author}Hjellming, M.~S., and Webbink, R.~F.,
  \comment{title}``Thresholds for rapid mass transfer in binary systems. I.
  Polytropic models'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 318}, \comment{pages}794--808, (\comment{year}1987).
  \keywords{binary systems, computational fluid dynamics}

\bibitem{homer01b}\comment{article}
\comment{author}Homer, L., Anderson, S.~F., Margon, B., and Deutsch, E.~W.,
  \comment{title}``Optical identification of the X-ray burster in the globular
  cluster NGC 1851'', \comment{journal}{\em Astrophys. J. Lett.},
  \comment{volume}{\bf 550}, \comment{pages}L155--L157, (\comment{year}2001).
  \keywords{globular clusters, neutron stars}

\bibitem{homer01a}\comment{article}
\comment{author}Homer, L., Deutsch, E.~W., Anderson, S.~F., and Margon, B.,
  \comment{title}``The rapid burster in Liller 1: the {\it Chandra} X-ray
  position and a search for an IR counterpart'', \comment{journal}{\em Astron.
  J.}, \comment{volume}{\bf 122}, \comment{pages}2627--2633,
  (\comment{year}2001). For a related online version see:
  \comment{author}L.~Homer, et al., \comment{onlinetitle}``The rapid burster in
  Liller 1: the {\it Chandra} X-ray position and a search for an IR
  counterpart'', (\comment{onlineyear}2001), \comment{fileformat}[Online Los
  Alamos Archive Preprint]: cited on \comment{cited}18 July 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0106140.
  \keywords{globular clusters, neutron stars, binary systems}

\bibitem{hurley00}\comment{article}
\comment{author}Hurley, J.~R., Pols, O.~R., and Tout, C.~A.,
  \comment{title}``Comprehensive analytic formulae for stellar evolution as a
  function of mass and metallicity'', \comment{journal}{\em Mon. Not. R.
  Astron. Soc.}, \comment{volume}{\bf 315}, \comment{pages}543--569,
  (\comment{year}2000). \keywords{stellar evolution}

\bibitem{hurley03}\comment{article}
\comment{author}Hurley, J.~R., and Shara, M.~M., \comment{title}``White dwarf
  sequences in dense star clusters'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 589}, \comment{pages}179--198, (\comment{year}2003).
  \keywords{globular clusters, binary systems, white dwarfs, numerical methods}

\bibitem{hurley01}\comment{article}
\comment{author}Hurley, J.~R., Tout, C.~A., Aarseth, S.~J., and Pols, O.~R.,
  \comment{title}``Direct $N$-body modelling of stellar populations: Blue
  stragglers in M67'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 323}, \comment{pages}630--650, (\comment{year}2001).
  \keywords{numerical methods, binary systems, globular clusters}

\bibitem{hurt00}\comment{article}
\comment{author}Hurt, R.~L., Jarrett, T.~H., Kirkpatrick, J.~D., and Cutri,
  R.~M., \comment{title}``Serendipitous 2MASS discoveries near the galactic
  plane: a spiral galaxy and two globular clusters'', \comment{journal}{\em
  Astron. J.}, \comment{volume}{\bf 120}, \comment{pages}1876--1883,
  (\comment{year}2000). \keywords{galaxies, globular clusters, astronomy}

\bibitem{hut93}\comment{inproceedings}
\comment{author}Hut, P., \comment{title}``Blue stragglers as tracers of
  globular cluster evolution'', in \comment{editor}Saffer, R.E., ed.,
  \comment{booktitle}{\em ASP Conf. Ser. 53: Blue Stragglers},
  (\comment{publisher}ASP, \comment{address}San Francisco, \comment{year}1993).
  \keywords{globular clusters, numerical methods, dynamical systems}

\bibitem{hut92a}\comment{article}
\comment{author}Hut, P., McMillan, S., Goodman, J., Mateo, M., Phinney, E.~S.,
  Pryor, C., Richer, H.~B., Verbunt, F., and Weinberg, M.,
  \comment{title}``Binaries in globular clusters'', \comment{journal}{\em Publ.
  Astron. Soc. Pac.}, \comment{volume}{\bf 104}, \comment{pages}981--1034,
  (\comment{year}1992). \keywords{binary systems, dynamical systems, globular
  clusters}

\bibitem{starlabweb}\comment{lr_url}
\comment{author}\comment{author}Hut, P., McMillan, S., Makino, J., and
  Portegies~Zwart, S.~F., \comment{onlinetitle}``Starlab: A Software
  Environment for Collisional Stellar Dynamics'', (\comment{onlineyear}2001),
  \comment{fileformat}[Online HTML Document]: cited on \comment{cited}12 August
  2001, \comment{onlineaddress}http://www.sns.ias.edu/\~{}starlab/starlab.html.
  \keywords{numerical methods, dynamical systems}

\bibitem{hut92b}\comment{article}
\comment{author}Hut, P., McMillan, S., and Romain, R.~W., \comment{title}``The
  evolution of a primordial binary population in a globular cluster'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 389},
  \comment{pages}527--545, (\comment{year}1992). \keywords{binary systems,
  globular clusters, numerical methods, dynamical systems}

\bibitem{iben97}\comment{article}
\comment{author}Iben~Jr., I., Tutukov, A.~V., and Yungelson, L.~R.,
  \comment{title}``Helium and carbon-oxygen white dwarfs in close binaries'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 475},
  \comment{pages}291--299, (\comment{year}1997). \keywords{binary systems,
  dynamical systems, white dwarfs}

\bibitem{ivanova05a}\comment{article}
\comment{author}Ivanova, N., Belczynski, K., Fregeau, J.~M., and Rasio, F.~A.,
  \comment{title}``The evolution of binary fractions in globular clusters'',
  \comment{journal}{\em Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 358},
  \comment{pages}572--584, (\comment{year}2005). \keywords{binary systems,
  globular clusters, N-body systems}

\bibitem{ivanova05b}\comment{article}
\comment{author}Ivanova, N., Rasio, F.~A., Lombardi~Jr., J.~C., Dooley, K.~L.,
  and Proulx, Z.~F., \comment{title}``Formation of ultracompact X-ray binaries
  in dense star clusters'', \comment{journal}{\em Astrophys. J. Lett.},
  \comment{volume}{\bf 621}, \comment{pages}109--112, (\comment{year}2005).
  \keywords{globular clusters, binary systems, X-ray astronomy, neutron stars}

\bibitem{jacoby02}\comment{article}
\comment{author}Jacoby, B.~A., Chandler, A.~M., Backer, D.~C., Anderson, S.~B,
  and Kulkarni, S.~R., \comment{title}``Pulsars in M62'', \comment{journal}{\em
  IAUC}, \comment{volume}{\bf 7783}, \comment{pages}1--+, (\comment{year}2002).
  \keywords{globular clusters, pulsars, radio astronomy}

\bibitem{johnston96}\comment{article}
\comment{author}Johnston, H.~M., and Verbunt, F., \comment{title}``The globular
  cluster population of low-luminosity X-ray sources'', \comment{journal}{\em
  Astron. Astrophys.}, \comment{volume}{\bf 312}, \comment{pages}80--87,
  (\comment{year}1996). \keywords{globular clusters, X-ray astronomy}

\bibitem{joshi01}\comment{article}
\comment{author}Joshi, K.~J., Nave, C.~P., and Rasio, F.~A.,
  \comment{title}``Monte Carlo simulations of globular cluster evolution. II.
  Mass spectra, stellar evolution, and lifetimes in the galaxy'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 550},
  \comment{pages}691--702, (\comment{year}2001). \keywords{dynamical systems,
  globular clusters, numerical methods}

\bibitem{joshi00}\comment{article}
\comment{author}Joshi, K.~J., Rasio, F.~A., and Portegies~Zwart, S.,
  \comment{title}``Monte Carlo simulations of globular cluster evolution. I.
  Method and test calculations'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 540}, \comment{pages}969--982, (\comment{year}2000).
  \keywords{dynamical systems, globular clusters, numerical methods}

\bibitem{kalogera04}\comment{article}
\comment{author}Kalogera, V., King, A.~R., and Rasio, F.~A.,
  \comment{title}``Could black hole X-ray binaries be detected in globular
  clusters?'', \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf
  601}, \comment{pages}171--174, (\comment{year}2004). \keywords{globular
  clusters, black holes, X-ray astronomy, binary systems}

\bibitem{kaluzny03}\comment{article}
\comment{author}Kaluzny, J., and Thompson, I.~B., \comment{title}``Time series
  photometry of variable stars in the globular cluster NGC 6397'',
  \comment{journal}{\em Astron. J.}, \comment{volume}{\bf 125},
  \comment{pages}2534--2542, (\comment{year}2003). \keywords{globular clusters,
  binary systems, white dwarfs, novae}

\bibitem{kim02}\comment{article}
\comment{author}Kim, E., Einsel, C., Lee, H.~M., Spurzem, R., and Lee, M.~G.,
  \comment{title}``Dynamical evolution of rotating stellar systems - II.
  Post-collapse, equal mass system'', \comment{journal}{\em Mon. Not. R.
  Astron. Soc.}, \comment{volume}{\bf 334}, \comment{pages}310--322,
  (\comment{year}2002). For a related online version see:
  \comment{author}E.~Kim, et al., \comment{onlinetitle}``Dynamical evolution of
  rotating stellar systems - II. Post-collapse, equal mass system'',
  (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}5 September 2001,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0109062.
  \keywords{numerical methods, globular clusters}

\bibitem{king96}\comment{article}
\comment{author}King, A.~R., Frank, J., Kolb, U., and Ritter, H.,
  \comment{title}``Global analysis of mass transfer cycles in cataclysmic
  variables'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 467},
  \comment{pages}761--772, (\comment{year}1996). \keywords{accretion, binary
  systems}

\bibitem{king93}\comment{article}
\comment{author}King, I.~R., Stanford, S.~A., Albrecht, R., Barbieri, C.,
  Blades, J.~C., Boksenberg, A., Crane, P., Disney, M.~J., Deharveng, J.~M.,
  Jakobsen, P., Kamperman, T.~M., Macchetto, F., Mackay, C.~D., Paresce, F.,
  Weigelt, G., Baxter, D., Greenfield, P., Jedrzejewski, R., Nota, A., Sparks,
  W.~B., and Sosin, C., \comment{title}``Detection of an ultraviolet and
  visible counterpart of the NGC 6624 X-ray burster'', \comment{journal}{\em
  Astrophys. J. Lett.}, \comment{volume}{\bf 413}, \comment{pages}L117--L120,
  (\comment{year}1993). \keywords{globular clusters, neutron stars, X-ray
  astronomy}

\bibitem{knigge04}\comment{article}
\comment{author}Knigge, C., \comment{title}``Far-ultraviolet surveys of
  globualr clusters: Hunting for the products of stellar collisions and near
  misses'', \comment{journal}{\em Mod. Phys. Lett. A}, \comment{volume}{\bf
  19}, \comment{pages}2013--+, (\comment{year}2004). For a related online
  version see: \comment{author}C.~Knigge,
  \comment{onlinetitle}``Far-ultraviolet surveys of globular clusters: Hunting
  for the products of stellar collisions and near misses'',
  (\comment{onlineyear}2004), \comment{fileformat}[Online ArXiv Preprint]:
  cited on \comment{cited}2 July 2004,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0407054.
  \keywords{globular clusters, astronomy, binary systems}

\bibitem{knigge02a}\comment{inproceedings}
\comment{author}Knigge, C., Shara, M.~M., Zurek, D.~R., Long, K.~S., and
  Gilliland, R.~L., \comment{title}``A far-ultraviolet spectroscopic survey of
  the globular cluster 47 Tuc'', in \comment{editor}Shara, M., ed.,
  \comment{booktitle}{\em Stellar Collisions, Mergers and their Consequences},
  volume 263, \comment{pages} 137--+, (\comment{publisher}ASP,
  \comment{address}San Francisco, \comment{year}2002). For a related online
  version see: \comment{author}C.~Knigge, et al., \comment{onlinetitle}``A
  far-ultraviolet spectroscopic survey of the globular cluster 47 Tuc'',
  (\comment{onlineyear}2000), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}8 December 2000,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0012187.
  \keywords{globular clusters, binary systems, astronomy}

\bibitem{knigge02b}\comment{article}
\comment{author}Knigge, C., Zurek, D.~R., Shara, M.~M., and Long, K.~S.,
  \comment{title}``A far-ultraviolet survey of 47 Tucanae. I. Imaging'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 579},
  \comment{pages}752--759, (\comment{year}2002). \keywords{globular clusters,
  binary systems, novae, white dwarfs}

\bibitem{kobulnicky05}\comment{article}
\comment{author}Kobulnicky, H.~A., Monson, A.~J., Buckalew, A., B., Darnel,
  J.~M., Uzpen, B., Meade, M.~R., Babler, B.~L., Indebetouw, R., Whitney,
  B.~A., Watson, C., Churchwell, E., Wolfire, M.~G., Wolff, M.~J., Clemens,
  D.~P., Shah, R., Bania, T.~M., Benjamin, R.~A., Cohen, M., Dickey, J.~M.,
  Jackson, J.~M., Marston, A.~P., Mathis, J.~S., Mercer, E.~P., Stauffer,
  J.~R., Stolovy, S.~R., Norris, J.~P., Kutyrev, A., Canterna, R., and Pierce,
  M.~J., \comment{title}``Discovery of a New Low-Latitude Milky Way Globular
  Cluster using GLIMPSE'', \comment{journal}{\em Astron. J},
  \comment{volume}{\bf 129}, \comment{pages}239--250, (\comment{year}2005). For
  a related online version see: \comment{author}H.~A. Kobulnicky, et al.,
  \comment{onlinetitle}``Discovery of a New Low-Latitude Milky Way Globular
  Cluster using GLIMPSE'', (\comment{onlineyear}2004),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}16 October 2004,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0410400.
  \keywords{globular clusters, infra-red astronomy}

\bibitem{kroupa01a}\comment{inproceedings}
\comment{author}Kroupa, P., \comment{title}``The local stellar initial mass
  function'', in \comment{editor}Deiters, S., Fuchs, B., Just, A., Spurzem, R.,
  and Wielen, R., eds., \comment{booktitle}{\em STAR2000: Dynamics of Star
  Clusters and the Milky Way}, volume 228, \comment{pages} 187+,
  (\comment{publisher}Astronomical Society of the Pacific, \comment{address}San
  Francisco, \comment{year}2001a). For a related online version see:
  \comment{author}P.~Kroupa, \comment{onlinetitle}``The local stellar initial
  mass function'', (\comment{onlineyear}2000), \comment{fileformat}[Online Los
  Alamos Archive Preprint]: cited on \comment{cited}17 November 2000,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0011328.
  \keywords{astronomy, mass functions}

\bibitem{kroupa01d}\comment{article}
\comment{author}Kroupa, P., \comment{title}``On the variation of the initial
  mass function'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 322}, \comment{pages}231--246, (\comment{year}2001d).
  \keywords{astronomy, mass functions}

\bibitem{kroupa01b}\comment{article}
\comment{author}Kroupa, P., Aarseth, S., and Hurley, J., \comment{title}``The
  formation of a bound star cluster: From the Orion Nebula Cluster to the
  Pleiades'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 321}, \comment{pages}699--712, (\comment{year}2001b).
  \keywords{numerical methods, binary systems, open clusters}

\bibitem{kroupa01c}\comment{article}
\comment{author}Kroupa, P., and Burkert, A., \comment{title}``On the origin of
  the distribution of binary star periods'', \comment{journal}{\em Astrophys.
  J.}, \comment{volume}{\bf 555}, \comment{pages}945--949,
  (\comment{year}2001c). \keywords{open clusters, binary systems, numerical
  methods}

\bibitem{kulkarni93}\comment{article}
\comment{author}Kulkarni, S.~R., Hut, P., and McMillan, S.,
  \comment{title}``Stellar black holes in globular clusters'',
  \comment{journal}{\em Nature}, \comment{volume}{\bf 364},
  \comment{pages}421--423, (\comment{year}1993). \keywords{black holes,
  globular clusters, binary systems}

\bibitem{kulkarni90}\comment{article}
\comment{author}Kulkarni, S.~R., Narayan, R., and Romani, R.~W.,
  \comment{title}``The pulsar content of globular clusters'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 356},
  \comment{pages}174--183, (\comment{year}1990). \keywords{globular clusters,
  neutron stars, pulsars, X-ray astronomy}

\bibitem{lisa96}\comment{techreport}
\comment{title}{\em LISA: Pre-phase A report, December 1995},
  (\comment{institution}Max-Planck-Institut f{\"u}r Quantenoptik,
  \comment{address}Garching, Germany, \comment{year}1996),
  \comment{number}Report no. MPQ 28. \keywords{gravitational wave detectors}

\bibitem{lorimer01}\comment{misc}
\comment{author}Lorimer, D.~R., \comment{title}``Binary and millisecond pulsars
  at the new millennium''. \keywords{binary systems, pulsars}

\bibitem{lorimer03}\comment{inproceedings}
\comment{author}Lorimer, D.~R., Camilo, F., Freire, P., Kramer, M., lyne,
  A.~G., Manchester, R.~N., and D'Amico, N., \comment{title}``Millisecond
  pulsars of 47 Tucanae'', in \comment{editor}Bailes, M., Nice, D.~J., and
  Thorsett, S.~E., eds., \comment{booktitle}{\em Radio Pulsars}, volume 302,
  \comment{pages} 363--+, (\comment{publisher}Astronomical Society of the
  Pacific, \comment{address}San Francisco, \comment{year}2003).
  \keywords{globular clusters, pulsars, binary systems}

\bibitem{louis91}\comment{article}
\comment{author}Louis, P.~D., and Spurzem, R., \comment{title}``Anisotropic
  gaseous models for the evolution of star clusters'', \comment{journal}{\em
  Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 251},
  \comment{pages}408--426, (\comment{year}1991). \keywords{numerical methods,
  globular clusters}

\bibitem{lyndenbell01}\comment{online}
\comment{author}Lynden-Bell, D., and O'Dwyer, J.~P., \comment{onlinetitle}``One
  mass-radius relation for planets, white dwarfs and neutron stars'',
  (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}27 April 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0104450.
  \keywords{white dwarfs, neutron stars}

\bibitem{lyne00}\comment{article}
\comment{author}Lyne, A.~G., Mankelow, S.~H., Bell, J.~F., and Manchester,
  R.~N., \comment{title}``Radio pulsars in Terzan 5'', \comment{journal}{\em
  Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 316},
  \comment{pages}491--493, (\comment{year}2000). \keywords{globular clusters,
  pulsars}

\bibitem{macnamara03}\comment{article}
\comment{author}MacNamara, B.~J., Harrison, T.~E., and Anderson, J.,
  \comment{title}``Does M15 possess and intermediate-mass black hole in its
  core?'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 595},
  \comment{pages}187--194, (\comment{year}2003). \keywords{globular clusters,
  black holes}

\bibitem{madsen03}\comment{article}
\comment{author}Madsen, S., \comment{title}``Hyades dynamics from N-body
  simulations: Accuracy of astrometric radial velocities from Hipparcos'',
  \comment{journal}{\em Astron. Astrophys.}, \comment{volume}{\bf 401},
  \comment{pages}565--576, (\comment{year}2003). \keywords{open clusters,
  numerical methods,astrometry}

\bibitem{makino98}\comment{book}
\comment{author}Makino, J., and Taiji, M., \comment{title}{\em Scientific
  Simulations with Special-Purpose Computers: The GRAPE Systems},
  (\comment{publisher}Wiley, \comment{address}Chichester, \comment{year}1998).
  \keywords{Numerical methods}

\bibitem{margon81}\comment{article}
\comment{author}Margon, B., Downes, R.~A., and Gunn, J.~E., \comment{title}``M5
  V101: A close binary system in a globular cluster'', \comment{journal}{\em
  Astrophys. J. Lett.}, \comment{volume}{\bf 247}, \comment{pages}L89--L92,
  (\comment{year}1981). \keywords{globular clusters, stars}

\bibitem{modestweb}\comment{lr_url}
\comment{author}\comment{author}McMillan, S., \comment{onlinetitle}``MODEST'',
  (\comment{onlineyear}2004), \comment{fileformat}[Online HTML Document]: cited
  on \comment{cited}25 May 2005,
  \comment{onlineaddress}http://www.manybody.org/modest/. \keywords{numerical
  methods, dynamical systems}

\bibitem{mcmillanweb}\comment{lr_url}
\comment{author}\comment{author}McMillan, S.~L.~W.,
  \comment{onlinetitle}``Resonant Binary Interactions'',
  (\comment{onlineyear}2001), \comment{fileformat}[Online HTML Document]: cited
  on \comment{cited}11 Aug 2001,
  \comment{onlineaddress}http://www.physics.drexel.edu/\~{}steve/resonance.htm%
l. \keywords{numerical methods, binary systems}

\bibitem{mcmillan98}\comment{inproceedings}
\comment{author}McMillan, S.~L.~W., Pryor, C., and Phinney, E.~S.,
  \comment{title}``Binaries in globular clusters'', in
  \comment{editor}Anderson, J., ed., \comment{booktitle}{\em Highlights of
  Astronomy}, volume 11A, \comment{pages} 616+, (\comment{publisher}Kluwer
  Academic Press, \comment{address}Dordrecht, \comment{year}1998).
  \keywords{globular clusters, binary systems, numerical methods}

\bibitem{meylan99}\comment{online}
\comment{author}Meylan, G., \comment{onlinetitle}``The internal dynamics of
  globular clusters'', (\comment{onlineyear}1999), \comment{fileformat}[Online
  Los Alamos Archive Preprint]: cited on \comment{cited}5 March 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/9912495. Submitted to
  World Scientific. \keywords{globular clusters}

\bibitem{meylan97}\comment{article}
\comment{author}Meylan, G., and Heggie, D.~C., \comment{title}``Internal
  dynamics of globular clusters'', \comment{journal}{\em Astron. Astrophys.
  Rev.}, \comment{volume}{\bf 8}, \comment{pages}1--143, (\comment{year}1997).
  \keywords{dynamical systems, globular clusters}

\bibitem{middleditch84}\comment{article}
\comment{author}Middleditch, J., and Kristian, J., \comment{title}``A search
  for young, luminous optical pulsars in extragalactic supernova remnants'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 279},
  \comment{pages}157--161, (\comment{year}1984). \keywords{pulsars, radio
  astronomy}

\bibitem{miller04}\comment{article}
\comment{author}Miller, M.~C., and Colbert, E.~J.~M.,
  \comment{title}``Intermediate mass black holes'', \comment{journal}{\em Int.
  J. Mod. Phys. D}, \comment{volume}{\bf 13}, \comment{pages}1--64,
  (\comment{year}2004). \keywords{black holes, globular clusters, galaxies,
  cosmology}

\bibitem{miller02}\comment{article}
\comment{author}Miller, M.~C., and Hamilton, D.~P., \comment{title}``Production
  of intermediate-mass black holes in globular clusters'',
  \comment{journal}{\em Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 330},
  \comment{pages}232--240, (\comment{year}2002). For a related online version
  see: \comment{author}M.~C. Miller, et al., \comment{onlinetitle}``Production
  of intermediate-mass black holes in globular clusters'',
  (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}11 June 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0106188.
  \keywords{accretion, binary systems, black holes, globular clusters}

\bibitem{miocchi05}\comment{online}
\comment{author}Miocchi, P., \comment{onlinetitle}``Central energy
  equipartition in multi-mass models of globular clusters'',
  (\comment{onlineyear}2005), \comment{fileformat}[Online ArXiv Preprint]:
  cited on \comment{cited}9 November 2005,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0511263.
  \keywords{globular clusters, dynamical systems}

\bibitem{moehler00}\comment{article}
\comment{author}Moehler, S., Heber, U., Napiwotzki, R., Koester, D., and
  Renzini, A., \comment{title}``First VLT spectra of white dwarfs in a globular
  cluster'', \comment{journal}{\em Astron. Astrophys.}, \comment{volume}{\bf
  354}, \comment{pages}L75--L78, (\comment{year}2000). \keywords{globular
  clusters, white dwarfs}

\bibitem{moehler04}\comment{article}
\comment{author}Moehler, S., Koester, D., Zoccali, M., Ferraro, F.~R., Heber,
  U., Napiwotzki, R., and A., Renzini, \comment{title}``Spectral types and
  masses of white dwarfs in globular clusters'', \comment{journal}{\em Astron.
  Astrophys.}, \comment{volume}{\bf 420}, \comment{pages}515--525,
  (\comment{year}2004). For a related online version see:
  \comment{author}S.~Moehler, et al., \comment{onlinetitle}``Spectral types and
  masses of white dwarfs in globular clusters'', (\comment{onlineyear}2004),
  \comment{fileformat}[Online ArXiv Preprint]: cited on \comment{cited}10 March
  2004, \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0403245.
  \keywords{globular clusters, white dwarfs}

\bibitem{monelli05}\comment{article}
\comment{author}Monelli, M., Corsi, C.~E., Castellani, V., Ferraro, I.,
  Iannicola, G., Prada~Moroni, P.~G., Bono, G., Buonanno, R., Calamida, A.,
  Freyhammer, L.~M., Pulone, L., and Stetson, P.~B., \comment{title}``The
  discovery of more than 2000 white dwarfs in the globular cluster $\omega$
  Centauri'', \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf
  621}, \comment{pages}117--120, (\comment{year}2005). \keywords{globular
  clusters, white dwarfs}

\bibitem{mukai00}\comment{article}
\comment{author}Mukai, K., and Smale, A.~P., \comment{title}``The low-mass
  X-ray binary X1832-330 in the globular cluster NGC 6652: A serendipitous {\it
  ASCA} observation'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 533}, \comment{pages}352--357, (\comment{year}2000).
  \keywords{binary systems, X-ray astronomy}

\bibitem{neill02}\comment{article}
\comment{author}Neill, J.~D., Shara, M.~M., Caulet, A., and Buckley, D.~A.~H.,
  \comment{title}``The first orbital period for a dwarf nova in a globular
  cluster: V101 in M5'', \comment{journal}{\em Astron. J.},
  \comment{volume}{\bf 123}, \comment{pages}3298--3304, (\comment{year}2002).
  \keywords{binary systems, globular clusters, white dwarfs}

\bibitem{nelemans01b}\comment{article}
\comment{author}Nelemans, G., Portegies~Zwart, S.~F., Verbunt, F., and
  Yungelson, L.~R., \comment{title}``Populations synthesis for double white
  dwarfs. II. Semi-detached systems: AM CVn stars'', \comment{journal}{\em
  Astron. Astrophys.}, \comment{volume}{\bf 368}, \comment{pages}939--949,
  (\comment{year}2001). \keywords{stars, binary systems, white dwarfs}

\bibitem{nelemans01a}\comment{article}
\comment{author}Nelemans, G., Yungelson, L.~R., Portegies~Zwart, S.~F., and
  Verbunt, F., \comment{title}``Populations synthesis for double white dwarfs.
  I. Close detached systems'', \comment{journal}{\em Astron. Astrophys.},
  \comment{volume}{\bf 365}, \comment{pages}491--507, (\comment{year}2001).
  \keywords{stars, binary systems, white dwarfs}

\bibitem{nieto90}\comment{article}
\comment{author}Nieto, J.-L., Auriere, M., Sebag, J., Arnaud, J., Lelievre, G.,
  Blazit, A., Foy, R., Bonaldo, S., and Thouvenot, E., \comment{title}``The
  optical counterpart of the X-ray binary in the globular cluster NGC 6712'',
  \comment{journal}{\em Astron. Astrophys.}, \comment{volume}{\bf 239},
  \comment{pages}155--162, (\comment{year}1990). \keywords{globular clusters,
  X-ray astronomy}

\bibitem{padmanabhan00}\comment{book}
\comment{author}Padmanabhan, T., \comment{title}{\em Theoretical Astrophysics,
  Volume I: Astrophysical Processes}, (\comment{publisher}Cambridge University
  Press, \comment{address}Cambridge, U.K., \comment{year}2000).
  \keywords{astrophysics}

\bibitem{padmanabhan01}\comment{book}
\comment{author}Padmanabhan, T., \comment{title}{\em Theoretical Astrophysics,
  Volume II: Stars and Stellar Systems}, (\comment{publisher}Cambridge
  University Press, \comment{address}Cambridge, U.K., \comment{year}2001).
  \keywords{astrophysics}

\bibitem{paresce94}\comment{article}
\comment{author}Paresce, F., and De~Marchi, G., \comment{title}``A dwarf nova
  in the core of 47 Tucanae'', \comment{journal}{\em Astrophys. J. Lett.},
  \comment{volume}{\bf 427}, \comment{pages}L33--L35, (\comment{year}1994).
  \keywords{globular clusters, binary systems, white dwarfs}

\bibitem{paresce95}\comment{article}
\comment{author}Paresce, F., De~Marchi, G., and Romaniello, M.,
  \comment{title}``Very low mass stars and white dwarfs in NGC 6397'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 440},
  \comment{pages}216--226, (\comment{year}1995). \keywords{globular clusters,
  white dwarfs}

\bibitem{pasquali04}\comment{article}
\comment{author}Pasquali, A., De~Marchi, G., Pulone, L., and Brigas, M.~S.,
  \comment{title}``The global mass function of M15'', \comment{journal}{\em
  Astron. Astrophy.}, \comment{volume}{\bf 428}, \comment{pages}469--478,
  (\comment{year}2004). \keywords{globular clusters}

\bibitem{peters63}\comment{article}
\comment{author}Peters, P.~C., and Mathews, J., \comment{title}``Gravitational
  radiation from point masses in a Keplerian orbit'', \comment{journal}{\em
  Phys. Rev.}, \comment{volume}{\bf 131}, \comment{pages}435--440,
  (\comment{year}1963). \keywords{gravitational radiation}

\bibitem{pfahl02a}\comment{article}
\comment{author}Pfahl, E., Rappaport, S., and Podsiadlowski, P.,
  \comment{title}``A comprehensive study of neutron star retention in globular
  clusters'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 573},
  \comment{pages}283--305, (\comment{year}2002). For a related online version
  see: \comment{author}E.~Pfahl, et al., \comment{onlinetitle}``A comprehensive
  study of neutron star retention in globular clusters'',
  (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}7 June 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0106141.
  \keywords{globular clusters, neutron stars}

\bibitem{pfahl02b}\comment{misc}
\comment{author}Pfahl, E., Rappaport, S., Podsiadlowski, P., and Spruit, H.,
  \comment{title}``A new class of high-mass X-ray binaries: Implications for
  core collapse and neutron star recoil'', (\comment{year}2002).
  \keywords{neutron stars, supernovae}

\bibitem{pierro96}\comment{article}
\comment{author}Pierro, V., and Pinto, I.~M., \comment{title}``Steady state
  population statistics of compact binary stars'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 469}, \comment{pages}272--279,
  (\comment{year}1996). \keywords{binary systems, gravitational radiation}

\bibitem{piotto04}\comment{article}
\comment{author}Piotto, G., De~Angelli, F., King, I.~R., Djorgovski, S.~G.,
  Bono, G., Cassisi, S., Meylan, G., Recio-Blanco, A., Rich, R.~M., and Davies,
  M.~B., \comment{title}``Relative frequencies of blue stragglers in galactic
  globular clusters: Constraints for the formation mechanisms'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 604},
  \comment{pages}109--112, (\comment{year}2004). \keywords{globular clusters}

\bibitem{podsiadlowski02}\comment{article}
\comment{author}Podsiadlowski, P., Rappaport, S., and Pfahl, E.,
  \comment{title}``Evolutionary sequences for low- and intermediate-mass X-ray
  binaries'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 565},
  \comment{pages}1107--1133, (\comment{year}2002). For a related online version
  see: \comment{author}P.~Podsiadlowski, et al.,
  \comment{onlinetitle}``Evolutionary binary sequences for low- and
  intermediate-mass X-ray binaries'', (\comment{onlineyear}2001),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}15 July 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0107261.
  \keywords{binary systems, neutron stars, pulsars, X-ray astronomy, white
  dwarfs}

\bibitem{pooley02a}\comment{article}
\comment{author}Pooley, D., Lewin, W.~H.~G, Homer, L., Verbunt, F., Anderson,
  S.~F., Gaensler, B.~M., Margon, B., Miller, J.~M., Fox, D.~W., Kaspi, V.~M.,
  and van~der Klis, M., \comment{title}``Optical identification of multiple
  faint X-ray sources in the globular cluster NGC 6752: Evidence for numerous
  cataclysmic variables'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 569}, \comment{pages}405--417, (\comment{year}2002).
  \keywords{globular clusters, X-ray astronomy, binary systems, white dwarfs,
  novae}

\bibitem{pooley02b}\comment{article}
\comment{author}Pooley, D., Lewin, W.~H.~G, Verbunt, F., Homer, L., Margon, B.,
  Gaensler, B.~M, Kaspi, V.~M., Miller, J.~M., Fox, D.~W., and van~der Klis,
  M., \comment{title}``{\it Chandra} observation of the globular cluster NGC
  6440 and the nature of cluster X-ray luminosity functions'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 573},
  \comment{pages}184--190, (\comment{year}2002). \keywords{globular clusters,
  binary systems, novae, neutron stars, white dwarfs}

\bibitem{popov02}\comment{article}
\comment{author}Popov, S.~B., and Prokhorov, M.~E., \comment{title}``Evolution
  of isolated neutron stars in globular clusters: number of accretors'',
  \comment{journal}{\em Astron. and Astrophys. Trans.}, \comment{volume}{\bf
  21}, \comment{pages}217--221, (\comment{year}2002). For a related online
  version see: \comment{author}S.~B. Popov, et al.,
  \comment{onlinetitle}``Evolution of isolated neutron stars in globular
  clusters: number of accretors'', (\comment{onlineyear}2001),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}12 February 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0102201.
  \keywords{neutron stars, globular clusters}

\bibitem{portegieszwart04b}\comment{article}
\comment{author}Portegies~Zwart, S.~F., Baumgardt, H., Hut, P., Makino, J., and
  McMillan, S.~L.~W., \comment{title}``The formation of massive black holes
  through collision runaway in dense young stellar clusters'',
  \comment{journal}{\em Nature}, \comment{volume}{\bf 428}, \comment{pages}724,
  (\comment{year}2004). \keywords{numerical methods, globular clusters,
  dynamical systems}

\bibitem{portegieszwart04a}\comment{article}
\comment{author}Portegies~Zwart, S.~F., Hut, P., McMillan, S.~L.~W., and
  Makino, J., \comment{title}``Star cluster ecology -- V: Dissection of an open
  star cluster: spectroscopy'', \comment{journal}{\em Mon. Not. R. Astron.
  Soc.}, \comment{volume}{\bf 351}, \comment{pages}473--486,
  (\comment{year}2004). \keywords{open clusters, numerical methods, binary
  systems}

\bibitem{portegieszwart99}\comment{article}
\comment{author}Portegies~Zwart, S.~F., Makino, J., McMillan, S.~L.~W., and
  Hut, P., \comment{title}``Star cluster ecology. III. Runaway collisions in
  young compact star clusters'', \comment{journal}{\em Astron. Astrophys.},
  \comment{volume}{\bf 348}, \comment{pages}117--126, (\comment{year}1999).
  \keywords{binary systems, numerical methods, globular clusters}

\bibitem{portegieszwart02}\comment{inproceedings}
\comment{author}Portegies~Zwart, S.~F., Makino, J., McMillan, S.~L.~W., and
  Hut, P., \comment{title}``Runaway collisions in star clusters'', in
  \comment{editor}Shara, M., ed., \comment{booktitle}{\em Stellar Collisions,
  Mergers and their Consequences}, volume 263, \comment{pages} 95--+,
  (\comment{publisher}ASP, \comment{address}San Francisco, \comment{year}2002).
  For a related online version see: \comment{author}S.~F. Portegies~Zwart, et
  al., \comment{onlinetitle}``Runaway collisions in star clusters'',
  (\comment{onlineyear}2000), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}11 December 2000,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0012237.
  \keywords{dynamical systems, stars, globular clusters}

\bibitem{portegieszwart00b}\comment{article}
\comment{author}Portegies~Zwart, S.~F., and McMillan, S.~L.~W.,
  \comment{title}``Black hole mergers in the universe'', \comment{journal}{\em
  Astrophys. J. Lett.}, \comment{volume}{\bf 528}, \comment{pages}L17--L20,
  (\comment{year}2000). \keywords{binary systems, globular clusters, dynamical
  systems, numerical methods}

\bibitem{portegieszwart01}\comment{article}
\comment{author}Portegies~Zwart, S.~F., McMillan, S.~L.~W., Hut, P., and
  Makino, J., \comment{title}``Star cluster ecology IVa: Dissection of an open
  star cluster -- photometry'', \comment{journal}{\em Mon. Not. R. Astron.
  Soc.}, \comment{volume}{\bf 321}, \comment{pages}199--226,
  (\comment{year}2001). \keywords{numerical methods, binary systems, open
  clusters}

\bibitem{portegieszwart96}\comment{article}
\comment{author}Portegies~Zwart, S.~F., and Verbunt, F.,
  \comment{title}``Population synthesis of high-mass binaries'',
  \comment{journal}{\em Astron. Astrophys.}, \comment{volume}{\bf 309},
  \comment{pages}179--196, (\comment{year}1996). \keywords{binary systems,
  numerical methods}

\bibitem{possenti03}\comment{article}
\comment{author}Possenti, A., D'Amico, N., Manchester, R., Camilo, F., Lyne,
  A.~G., Sarkissian, J., and Corongiu, A., \comment{title}``Three binary
  millisecond pulsars in NGC 6266'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 599}, \comment{pages}475, (\comment{year}2003).
  \keywords{globular clusters, pulsars, binary systems,neutron stars}

\bibitem{prince91}\comment{article}
\comment{author}Prince, T.~A., Anderson, S.~B., Kulkarni, S.~R., and Wolszczan,
  A., \comment{title}``Timing observations of the 8 hour binary pulsar 2127+11C
  in the globular cluster M15'', \comment{journal}{\em Astrophys. J. Lett.},
  \comment{volume}{\bf 374}, \comment{pages}L41--L44, (\comment{year}1991).
  \keywords{pulsars, binary systems, globular clusters, neutron stars}

\bibitem{ransom01}\comment{article}
\comment{author}Ransom, S.~M., Greenhill, L.~J., Herrnstein, J.~R., Manchester,
  R.~N., Camiilo, F., Eikenberry, S.~S., and Lyne, A.~G., \comment{title}``A
  binary millisecond pulsar in globular cluster NGC 6544'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 546},
  \comment{pages}L25--L28, (\comment{year}2001). \keywords{globular clusters,
  pulsars}

\bibitem{ransom05}\comment{article}
\comment{author}Ransom, S.~M., Hessels, J.~W.~T., Stairs, I.~H., Freire, P.~C.,
  Camilo, F., Kaspi, V.~M., and Kaplan, D.~L., \comment{title}``Twenty-one
  millisecond pulsars in Terzan 5 using the Green Bank Telescope'',
  \comment{journal}{\em Science}, \comment{volume}{\bf 307},
  \comment{pages}892--896, (\comment{year}2005). \keywords{globular clusters,
  pulsars, radio astronomy}

\bibitem{ransom04}\comment{article}
\comment{author}Ransom, S.~M., Stairs, I.~H., Backer, D.~C., Greenhill, L.~J.,
  Bassa, C.~G, Hessels, J.~W.~T, and Kaspi, V.~M., \comment{title}``Green Bank
  Telescope discovery of two binary millisecond pulsars in the globular cluster
  M30'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 604},
  \comment{pages}328--338, (\comment{year}2004). \keywords{globular clusters,
  binary systems, pulsars}

\bibitem{rappaport87}\comment{article}
\comment{author}Rappaport, S., Nelson, L.~A., Ma, C.~P., and Joss, P.~C.,
  \comment{title}``The evolutionary status of 4U 1820-30'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 322},
  \comment{pages}842--851, (\comment{year}1987). \keywords{globular clusters,
  binary systems, stars}

\bibitem{rappaport01}\comment{inproceedings}
\comment{author}Rappaport, S., Pfahl, E., Rasio, F., and Podsiadlowski, P.,
  \comment{title}``Formation of compact binaries in globular clusters'', in
  \comment{editor}Podsiadlowski, P., Rappaport, A., King, R., D'Antona, F., and
  Burder, L., eds., \comment{booktitle}{\em Evolution of Binary and Multiple
  Star Systems}, volume 229, \comment{pages} 409+, (\comment{publisher}ASP,
  \comment{address}San Francisco, \comment{year}2001). For a related online
  version see: \comment{author}S.~Rappaport, et al.,
  \comment{onlinetitle}``Formation of compact binaries in globular clusters'',
  (\comment{onlineyear}2001), \comment{fileformat}[Online Los Alamos Archive
  Preprint]: cited on \comment{cited}30 January 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0101535.
  \keywords{Globular clusters, dynamical systems, binary systems, white dwarfs,
  neutron stars}

\bibitem{rasio01}\comment{inproceedings}
\comment{author}Rasio, F.~A., Fregeau, J.~M., and Joshi, K.~J.,
  \comment{title}``Binaries and globular cluster dynamics'', in
  \comment{editor}Vanbeveren, D., ed., \comment{booktitle}{\em The Influence of
  Binaries on Stellar Population Studies}, volume 264, \comment{pages}
  387--401, (\comment{publisher}Kluwer Academic Publishers,
  \comment{address}Dordrecht, \comment{year}2001). For a related online version
  see: \comment{author}F.~A. Rasio, et al., \comment{onlinetitle}``Binaries and
  globular cluster dynamics'', (\comment{onlineyear}2001),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}1 March 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0103001.
  \keywords{globular clusters, binary systems, dynamical systems, numerical
  methods}

\bibitem{rasio00a}\comment{article}
\comment{author}Rasio, F.~A., Pfahl, E.~D., and Rappaport, S.,
  \comment{title}``Formation of short-period binary pulsars in globular
  clusters'', \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf
  532}, \comment{pages}L47--L50, (\comment{year}2000). \keywords{dynamical
  systems, globular clusters, pulsars, neutron stars, binary systems}

\bibitem{renzini96}\comment{article}
\comment{author}Renzini, A., Bragaglia, A., Ferraro, F.~R., Gilmozzi, R.,
  Ortolani, S., Holberg, J.~B., Liebert, J., Wesemael, F., and Bohlin, R.~C.,
  \comment{title}``The white dwarf distance to the globular cluster NGC 6752
  (and its age) with the {\it Hubble Space Telescope}'', \comment{journal}{\em
  Astrophys. J. Lett.}, \comment{volume}{\bf 465}, \comment{pages}L23--L26,
  (\comment{year}1996). \keywords{globular clusters}

\bibitem{richer97}\comment{article}
\comment{author}Richer, H.~B., Fahlman, G.~G., Ibata, R.~A., Pryor, C., Bell,
  R.~A., Bolte, M., Bond, H.~E., Harris, W.~E., Hesser, J.~E., Holland, S.,
  Ivanans, N., Mandushev, G., Stetson, P.~B., and Wood, M.~A.,
  \comment{title}``White dwarfs in globular clusters: {\it Hubble Space
  Telescope} observations of M4'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 484}, \comment{pages}741--760, (\comment{year}1997).
  \keywords{globular clusters, white dwarfs}

\bibitem{richer95}\comment{article}
\comment{author}Richer, H.~B., Fahlman, G.~G., Ibata, R.~A., Stetson, P.~B.,
  Bell, R.~A., Bolte, M., Bond, H.~E., Harris, W.~E., Hesser, J.~E., Mandushev,
  G., Pryor, C., and VandenBerg, D.~A., \comment{title}``{\it Hubble Space
  Telescope} observations of white dwarfs in the globular cluster M4'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 451},
  \comment{pages}L17--L20, (\comment{year}1995). \keywords{globular clusters,
  white dwarfs}

\bibitem{rosenberg00}\comment{article}
\comment{author}Rosenberg, A., Piotto, G., Saviane, I., and Aparicio, A.,
  \comment{title}``Photometric catalog of nearby globular clusters. I. A large
  homogeneous (V,I) color magnitude diagram data-base'', \comment{journal}{\em
  Astron. Astrophys. Suppl. Ser.}, \comment{volume}{\bf 114},
  \comment{pages}5--38, (\comment{year}2000). \keywords{globular clusters,
  photometry}

\bibitem{rubenstein97}\comment{article}
\comment{author}Rubenstein, E.~P., and Bailyn, C.~D., \comment{title}``{\it
  Hubble Space Telescope} observations of the post-core-collapse globular
  cluster NGC 6752. II. A large main-sequence binary population'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 474},
  \comment{pages}701--709, (\comment{year}1997). \keywords{binary systems,
  globular clusters, astronomy, dynamical systems}

\bibitem{rubenstein99}\comment{article}
\comment{author}Rubenstein, E.~P., and Bailyn, C.~D., \comment{title}``{\it
  Hubble Space Telescope} observations of the central-cusp globular cluster NGC
  6752: The effect of binary stars on the luminosity function in the core'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 513},
  \comment{pages}L33--L36, (\comment{year}1999). \keywords{binary systems,
  globular clusters, astronomy, dynamical systems}

\bibitem{sandquist00}\comment{article}
\comment{author}Sandquist, E.~L., Taam, R.~E., and Burkert, A.,
  \comment{title}``On the formation of helium double degenerate stars and
  pre-cataclysmic variables'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 533}, \comment{pages}984--997, (\comment{year}2000).
  \keywords{binary systems, dynamical systems}

\bibitem{schaller92}\comment{article}
\comment{author}Schaller, G., Schaerer, D., Meynet, G., and Maeder, A.,
  \comment{title}``New grids of stellar models from 0.8 to 120 $M_{\odot}$ at
  $Z = 0.020$ and $Z = 0.001$'', \comment{journal}{\em Astron. Astrophys.
  Suppl.}, \comment{volume}{\bf 96}, \comment{pages}269--331,
  (\comment{year}1992). \keywords{stars}

\bibitem{schneider01}\comment{article}
\comment{author}Schneider, R., Ferrari, V., Matarrese, S., and Portegies~Zwart,
  S.~F., \comment{title}``Low-frequency gravitational waves from cosmological
  compact binaries'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 324}, \comment{pages}797--810, (\comment{year}2001). For
  a related online version see: \comment{author}R.~Schneider, et al.,
  \comment{onlinetitle}``Gravitational waves from cosmological compact
  binaries'', (\comment{onlineyear}2000), \comment{fileformat}[Online Los
  Alamos Archive Preprint]: cited on \comment{cited}2 February 2000,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0002055.
  \keywords{gravitational radiation, binary systems}

\bibitem{shara96a}\comment{article}
\comment{author}Shara, M.~M., Bergeron, L.~E., Gilliland, R.~L., Saha, A., and
  Petro, L., \comment{title}``Cataclysmic and close binaries in star clusters.
  IV. The unexpectedly low number of erupting dwarf novae detected by the {\it
  Hubble Space Telescope} in the core of 47 Tuc'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 471}, \comment{pages}804--815,
  (\comment{year}1996). \keywords{binary systems, globular clusters, astronomy}

\bibitem{shara94}\comment{article}
\comment{author}Shara, M.~M., Bergeron, L.~E., and Moffat, A.~F.~J.,
  \comment{title}``Cataclysmic binaries in star clusters. I. A search for
  erupting dwarf novae in the globular cluster M92'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 429}, \comment{pages}767--771,
  (\comment{year}1994). \keywords{binary systems, globular clusters, astronomy}

\bibitem{shara95b}\comment{article}
\comment{author}Shara, M.~M., and Drissen, L., \comment{title}``Cataclysmic and
  close binaries in star clusters. III. Recovery of the quiescent nova 1860
  A.D. (T Scorpii) in the core of the globular cluster M80'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 448},
  \comment{pages}203--206, (\comment{year}1995). \keywords{binary systems,
  globular clusters, astronomy}

\bibitem{shara95a}\comment{article}
\comment{author}Shara, M.~M., Drissen, L., Bergeron, L.~E., and Paresce, F.,
  \comment{title}``Cataclysmic amd close binaries in star clusters. II. Probing
  the core of NGC 6752 with {\it Hubble Space Telescope}'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 441},
  \comment{pages}617--628, (\comment{year}1995). \keywords{binary systems,
  globular clusters, astronomy}

\bibitem{shara04}\comment{article}
\comment{author}Shara, M.~M., Hinkley, S., Zurek, D.~R., Knigge, C., and Bond,
  H.~E., \comment{title}``The luminous erupting dwarf nova CV 1 in the dense
  globular cluster M15'', \comment{journal}{\em Astron. J.},
  \comment{volume}{\bf 128}, \comment{pages}2847--2853, (\comment{year}2004).
  \keywords{globular clusters, novae, white dwarfs}

\bibitem{shara02}\comment{article}
\comment{author}Shara, M.~M., and Hurley, J.~R., \comment{title}``Star clusters
  as type Ia supernova factories'', \comment{journal}{\em Astrophys. J.},
  \comment{volume}{\bf 571}, \comment{pages}830--842, (\comment{year}2002).
  \keywords{globular clusters, numerical methods, binary systems, supernovae}

\bibitem{shara96b}\comment{article}
\comment{author}Shara, M.~M., Zurek, D.~R., and Rich, R.~M.,
  \comment{title}``The discovery of an erupting dwarf nova in NGC 6624'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 473},
  \comment{pages}L35--L36, (\comment{year}1996). \keywords{binary systems,
  globular clusters, astronomy}

\bibitem{sidoli01}\comment{article}
\comment{author}Sidoli, L., Parmar, A.~N., Oosterbroek, T., Stella, L.,
  Verbunt, F., Masetti, N., and Dal~Fiume, D., \comment{title}``BeppoSAX study
  of the broad-band properties of luminous globular cluster X-ray sources'',
  \comment{journal}{\em Astron. Astrophys.}, \comment{volume}{\bf 368},
  \comment{pages}451--463, (\comment{year}2001). \keywords{accretion, accretion
  disks, neutron stars, globular clusters, X-ray astronomy}

\bibitem{sigurdsson93}\comment{article}
\comment{author}Sigurdsson, S., and Hernquist, L., \comment{title}``Primordial
  black holes in globular clusters'', \comment{journal}{\em Nature},
  \comment{volume}{\bf 364}, \comment{pages}423--425, (\comment{year}1993).
  \keywords{binary systems, black holes, globular clusters}

\bibitem{sigurdsson95}\comment{article}
\comment{author}Sigurdsson, S., and Phinney, E.~S., \comment{title}``Dynamics
  and interactions of binaries and neutron stars in globular clusters'',
  \comment{journal}{\em Astrophys. J. Suppl. Ser.}, \comment{volume}{\bf 99},
  \comment{pages}609--635, (\comment{year}1995). \keywords{binary systems,
  dynamical systems, globular clusters, numerical methods, pulsars, neutron
  stars}

\bibitem{sills03}\comment{article}
\comment{author}Sills, A., Deiters, S., Eggleton, P., Freitag, M., Giersz, M.,
  Heggie, D., Hurley, J., Hut, P., Ivanova, N., Klessen, R.~S., Kroupa, P.,
  Lombardi~Jr., J.~C., McMillan, S., Portegies~Zwart, S., and Zinnecker, H.,
  \comment{title}``MODEST-2: A Summary'', \comment{journal}{\em New Astronomy},
  \comment{volume}{\bf 8}, \comment{pages}605--628, (\comment{year}2003). For a
  related online version see: \comment{author}A.~Sills, et al.,
  \comment{onlinetitle}``MODEST-2: A Summary'', (\comment{onlineyear}2003),
  \comment{fileformat}[Online ArXiv Preprint]: cited on \comment{cited}11 March
  2003, \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0301478.
  \keywords{dynamical systems, numerical methods, stellar evolution}

\bibitem{spitzer87}\comment{book}
\comment{author}Spitzer~Jr., L., \comment{title}{\em Dynamical Evolution of
  Globular Clusters}, (\comment{publisher}Princeton University Press,
  \comment{address}Princeton, \comment{year}1987). \keywords{globular clusters,
  dynamical systems}

\bibitem{spurzem99}\comment{article}
\comment{author}Spurzem, R., \comment{title}``Direct $N$-body simulations'',
  \comment{journal}{\em J. Comput. Appl. Math.}, \comment{volume}{\bf 109},
  \comment{pages}407--432, (\comment{year}1999). \keywords{numerical methods,
  dynamical systems}

\bibitem{spurzem96}\comment{article}
\comment{author}Spurzem, R., and Giersz, M., \comment{title}``A stochastic
  Monte Carlo approach to modelling of real star cluster evolution--I. The
  model'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 283}, \comment{pages}805--810, (\comment{year}1996).
  \keywords{numerical methods, globular clusters, binary systems}

\bibitem{stella87}\comment{article}
\comment{author}Stella, L., Priedhorsky, W., and White, N.~E.,
  \comment{title}``The discovery of a 685 second orbital period from the X-ray
  source 4U 1820-30 in the globular cluster NGC 6624'', \comment{journal}{\em
  Astrophys. J. Lett.}, \comment{volume}{\bf 312}, \comment{pages}L17--L21,
  (\comment{year}1987). \keywords{globular clusters, binary systems, X-ray
  astronomy}

\bibitem{takahashi00}\comment{article}
\comment{author}Takahashi, K., and Portegies~Zwart, S.~F., \comment{title}``The
  evolution of globular clusters in the galaxy'', \comment{journal}{\em
  Astrophys. J.}, \comment{volume}{\bf 535}, \comment{pages}759--775,
  (\comment{year}2000). \keywords{galaxies, dynamical systems, globular
  clusters, numerical methods}

\bibitem{taylor01}\comment{article}
\comment{author}Taylor, J.~M., Grindlay, J.~E., and Edmonds, P.~D.,
  \comment{title}``Helium white dwarfs and BY Draconis binaries in the globular
  cluster NGC 6397'', \comment{journal}{\em Astrophys. J. Lett.},
  \comment{volume}{\bf 553}, \comment{pages}L169--L172, (\comment{year}2001).
  \keywords{binary systems, globular clusters, neutron stars, white dwarfs,
  dynamical systems}

\bibitem{nemoweb}\comment{lr_url}
\comment{author}\comment{author}Teuben, P., \comment{onlinetitle}``NEMO Home
  Page'', (\comment{onlineyear}2001), \comment{fileformat}[Online HTML
  Document]: cited on \comment{cited}12 August 2001,
  \comment{onlineaddress}http://bima.astro.umd.edu/nemo/. \keywords{numerical
  methods, dynamical systems}

\bibitem{grapeweb}\comment{lr_url}
\comment{organization}The Grape Project, \comment{onlinetitle}``The Grape
  Project'', (\comment{onlineyear}2001), \comment{fileformat}[Online HTML
  Document]: cited on \comment{cited}11 August 2001,
  \comment{onlineaddress}http://astrogrape.org. \keywords{numerical methods,
  astrophysics, dynamical systems}

\bibitem{tout97}\comment{article}
\comment{author}Tout, C.~A., Aarseth, S.~J., Pols, O.~R., and Eggleton, P.~P.,
  \comment{title}``Rapid binary star evolution for $N$-body simulations and
  population synthesis'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 291}, \comment{pages}732--748, (\comment{year}1997).
  \keywords{binary systems, numerical methods, stellar dynamics}

\bibitem{vankerkwijk00}\comment{article}
\comment{author}van Kerkwijk, M.~H., Kaspi, V.~M., Klemola, A.~R., Kulkarni,
  S.~R., Lyne, A.~G., and Van~Buren, D., \comment{title}``Optical observations
  of the binary pulsar system PSR B1718--19: Implications for tidal
  circularization'', \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf
  529}, \comment{pages}428--434, (\comment{year}2000). \keywords{globular
  clusters, binary systems, pulsars}

\bibitem{verbunt01}\comment{article}
\comment{author}Verbunt, F., \comment{title}``A census with ROSAT of
  low-luminosity X-ray sources in globular clusters'', \comment{journal}{\em
  Astron. Astrophys.}, \comment{volume}{\bf 368}, \comment{pages}137--159,
  (\comment{year}2001). \keywords{globular clusters, X-ray astronomy, binary
  systems}

\bibitem{verbunt04}\comment{inbook}
\comment{author}Verbunt, F., and Lewin, W.~H.~G., \comment{title}``Globular
  Cluster X-ray Sources'', in \comment{editor}Lewin, W.~H.~G., and van~der
  Klis, M., eds., \comment{booktitle}{\em Compact Stellar X-ray Sources},
  chapter~8, (\comment{publisher}Cambridge University Press,
  \comment{address}Cambridge, \comment{year}2004). For a related online version
  see: \comment{author}F.~Verbunt, et al., \comment{onlinetitle}``Globular
  cluster x-ray sources'', (\comment{onlineyear}2004),
  \comment{fileformat}[Online ArXiv Preprint]: cited on \comment{cited}6 April
  2004, \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0404136.
  \keywords{globular clusters, x-ray astronomy, binary systems}

\bibitem{verbunt00}\comment{article}
\comment{author}Verbunt, F., van Kerkwijk, M.~H., in~'t Zand, J.~J.~M., and
  Heise, J., \comment{title}``X-ray and optical follow-up observations of the
  August 1998 X-ray transient in NGC 6440'', \comment{journal}{\em Astron.
  Astrophys.}, \comment{volume}{\bf 359}, \comment{pages}960--966,
  (\comment{year}2000). \keywords{neutron stars, globular clusters, X-ray
  astronomy}

\bibitem{vesperini97}\comment{article}
\comment{author}Vesperini, E., and Heggie, D.~C., \comment{title}``On the
  effects of dynamical evolution on the initial mass function of globular
  clusters'', \comment{journal}{\em Mon. Not. R. Astron. Soc.},
  \comment{volume}{\bf 289}, \comment{pages}898--920, (\comment{year}1997).
  \keywords{globular clusters, numerical methods, stellar dynamics}

\bibitem{webb05}\comment{inproceedings}
\comment{author}Webb, N.~A., and Barret, D., \comment{title}``Faint X-ray
  sources in globular clusters in the XMM-Newton and Chandra era'', in
  \comment{editor}Hameury, J.-M., and Lasota, J.-P, eds.,
  \comment{booktitle}{\em The Astrophysics of Cataclysmic Variables and Related
  Objects}, \comment{pages} 41--+, (\comment{publisher}ASP,
  \comment{address}San Francisco, \comment{year}2005). For a related online
  version see: \comment{author}N.~A. Webb, et al., \comment{onlinetitle}``Faint
  X-ray sources in globular clusters in the XMM-Newton and Chandra era'',
  (\comment{onlineyear}2004), \comment{fileformat}[Online ArXiv Preprint]:
  cited on \comment{cited}17 November 2004,
  \comment{onlineaddress}http://arXiv.org/abs/astro-ph/0411506.
  \keywords{globular clusters, X-ray astronomy, binary systems, novae, neutron
  stars, white dwarfs}

\bibitem{webbink84}\comment{article}
\comment{author}Webbink, R.~F., \comment{title}``Double white dwarfs as
  progenitors of R Coronae Borealis stars and type I supernovae'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 277},
  \comment{pages}355--360, (\comment{year}1984). \keywords{white dwarfs, binary
  systems, supernovae}

\bibitem{nwhite01}\comment{article}
\comment{author}White, N.E., and Angelini, L., \comment{title}``The discovery
  of a second luminous low-mass X-ray binary in the globular cluster M15'',
  \comment{journal}{\em Astrophys. J. Lett.}, \comment{volume}{\bf 561},
  \comment{pages}L101--L105, (\comment{year}2001). \keywords{globular clusters,
  binary systems, x-ray astronomy}

\bibitem{wijnands05}\comment{article}
\comment{author}Wijnands, R., Heinke, C.~O., Pooley, D., Edmonds, P.~D., Lewin,
  W.~H.~G., Grindlay, J.~E., Jonker, P.~G., and Miller, J.~M.,
  \comment{title}``The hard quiescent spectrum of the neutron star X-ray
  transient EXO 1745-248 in the globular cluster Terzan 5'',
  \comment{journal}{\em Astrophys. J.}, \comment{volume}{\bf 618},
  \comment{pages}883--890, (\comment{year}2005). \keywords{globular clusters,
  accretion, neutron stars, X-ray astronomy}

\bibitem{yan94}\comment{article}
\comment{author}Yan, L., and Mateo, M., \comment{title}``Primordial main
  sequence binary stars in the globular cluster M71'', \comment{journal}{\em
  Astron. J.}, \comment{volume}{\bf 108}, \comment{pages}1810--1827,
  (\comment{year}1994). \keywords{binary systems, globular clusters, astronomy}

\bibitem{yan96}\comment{article}
\comment{author}Yan, L., and Reid, I.~N., \comment{title}``Discovery of six
  short-period eclipsing binaries in the globular cluster M5'',
  \comment{journal}{\em Mon. Not. R. Astron. Soc.}, \comment{volume}{\bf 279},
  \comment{pages}751--766, (\comment{year}1996). \keywords{binary systems,
  globular clusters, astronomy}

\bibitem{zahn89a}\comment{article}
\comment{author}Zahn, J.-P., \comment{title}``Tidal evolution of close binary
  stars. I. Revisiting the theory of the equilibrium tide'',
  \comment{journal}{\em Astron. Astrophys.}, \comment{volume}{\bf 220},
  \comment{pages}112--116, (\comment{year}1989). \keywords{binary systems,
  stellar evolution}

\bibitem{zahn89b}\comment{article}
\comment{author}Zahn, J.-P., and Bouchet, L., \comment{title}``Tidal evolution
  of close binary stars. II. Orbital circularization of late-type binaries'',
  \comment{journal}{\em Astron. Astrophys.}, \comment{volume}{\bf 223},
  \comment{pages}112--118, (\comment{year}1989). \keywords{binary systems,
  stellar evolution}

\bibitem{zhao05}\comment{article}
\comment{author}Zhao, B., and Bailyn, C.D., \comment{title}``{\it Hubble Space
  Telescope} WFPC2 photometry of the globular clusters M3 and M13: Binaries and
  intrinsic broadening on the main sequence'', \comment{journal}{\em Astron.
  J.}, \comment{volume}{\bf 129}, \comment{pages}1934--1953,
  (\comment{year}2005). \keywords{binary systems, globular clusters}

\bibitem{zheng01}\comment{online}
\comment{author}Zheng, X.-Z., \comment{onlinetitle}``Do globular clusters
  harbor black holes?'', (\comment{onlineyear}2001),
  \comment{fileformat}[Online Los Alamos Archive Preprint]: cited on
  \comment{cited}22 June 2001,
  \comment{onlineaddress}http://xxx.lanl.gov/abs/astro-ph/0106410.
  \keywords{globular clusters, black holes}

\end{thebibliography}
