Formation of the binary pulsars J1141--6545 and B2023+46
Melvyn B.\ Davies$^1$
Hans Ritter$^2$
and Andrew King$^1$
$^1$ Department Physics \& Astronomy
Leicester LE1 7RH
UK
$^2$ Max--Planck--Institut f\"ur Astrophysik
Karl--Schwarzschild-Str.~1
D--85740 Garching
Germany
The binaries PSR J1141--6545 and PSR B2303+46 each appear to contain a white dwarf which formed before the neutron star. We describe an evolutionary pathway to produce these two systems. In this scenario, the primary transfers its envelope onto the secondary which is then the more massive of the two stars, and indeed sufficiently massive later to produce a neutron star via a supernova. The core of the primary produces a massive white dwarf which enters into a common envelope with the core of the secondary when the latter evolves off the main sequence. During the common envelope phase, the white dwarf and the core of the secondary spiral together as the envelope is ejected. The evolutionary history of PSR J1141--6545 and PSR B2303+46 differ after this phase. In the case of PSR J1141--6545, the secondary (now a helium star) evolves into contact transferring its envelope onto the white dwarf. We propose that the vast majority of this material is in fact ejected from the system. The remains of the secondary then explode as a supernova producing a neutron star. Generally the white dwarf and neutron star will remain bound in tight, often eccentric, systems resembling PSR J1141--6545. These systems will spiral in and merge on a relatively short timescale and may make a significant contribution to the population of gamma ray burst progenitors. In PSR B2303+46, the helium-star secondary and white dwarf never come into contact. Rather the helium star loses its envelope via a wind, which increases the binary separation slightly. Only a small fraction of such systems will remain bound when the neutron star is formed (as the systems are wider). Those systems which are broken up will produce a population of high--velocity white dwarfs and neutron stars.
paper.tex
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\input epsf.sty
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\title{Formation of the binary pulsars J1141--6545 and B2023+46}
\author[M. B. Davies et al.]{Melvyn B.\ Davies$^1$, 
Hans Ritter$^2$, and Andrew King$^1$\\ 
$^1$ Department Physics \& Astronomy, University of Leicester, Leicester LE1
7RH, UK\\
$^2$ Max--Planck--Institut f\"ur Astrophysik,
Karl--Schwarzschild-Str.~1, D--85740 Garching, Germany}

\maketitle            
\begin{abstract}
The binaries PSR J1141--6545 and PSR B2303+46 each appear
to contain a white dwarf which formed before the neutron star.
We describe an evolutionary pathway to produce these two systems. 
In this scenario, the primary transfers its envelope onto the
secondary which is then the more massive of the two stars,
and indeed sufficiently massive later to produce a neutron star
via a supernova. The core of the primary produces a massive
white dwarf which enters into a common envelope with the
core of the secondary when the latter evolves off the main sequence.
During the common envelope phase, the white dwarf and the core
of the secondary spiral together as the envelope is ejected.
The evolutionary history of PSR J1141--6545 and PSR B2303+46 
differ after this phase. In the case of PSR J1141--6545,
the secondary (now a helium star) evolves into contact transferring
its envelope onto the white dwarf. We propose that the vast majority
of this material is in fact ejected from the system. The remains of the
secondary then explode as a supernova producing a neutron star. Generally
 the white dwarf and neutron star will remain bound in tight,
often eccentric, systems resembling PSR J1141--6545.
These systems will spiral in
and merge on a relatively short timescale and may make a significant
contribution to the population of gamma ray burst progenitors.
In PSR B2303+46, the helium-star secondary and white dwarf
never come into contact. Rather the helium star loses its envelope
via a wind, which increases the binary separation slightly. 
Only a small fraction of such systems will remain bound when the neutron
star is formed (as the systems are wider). Those systems which are
broken up will produce a population of high--velocity white dwarfs and
neutron stars. 
\end{abstract}
\begin{keywords}
accretion, accretion discs --- binaries: close
stars: evolution --- stars: stars.
\end{keywords}

\section{introduction}


Observations suggest that in the two binaries PSRs B2303+46 and
J1141--6545, the companions of the observed pulsars are white dwarfs
which appear to have been formed {\it before} the neutron stars
(van Kerkwijk \& Kulkarni 1999; Kaspi et al 2000; Manchester et al
2000). 



If the white dwarf were the remains of a former donor star
of the neutron star, we would expect the white dwarf to be in a circular
orbit. However B2023+46 has an eccentricity of 0.658, so we must conclude
that the white dwarf was made first and the current observed eccentricity
is derived from the kick received when the neutron star was formed.


J1141--6545 is a non-recycled pulsar with a massive companion in an eccentric
orbit (Kaspi et al 2000; Manchester et al 2000). 
If the pulsar had formed first, we would expect it to have
been spun up (ie recycled) when the secondary evolved into contact
and transferred material onto it, ultimately leaving either a second neutron
star or a white dwarf. If the companion produced a white dwarf after 
the birth of the neutron star, we would also expect the orbit
today to be circular, whereas it has a measured eccentricity of 0.172. 
Hence it seems likely that in J1141--6545 the 
 companion is also probably a massive white dwarf which was formed
before the neutron star. It should be noted that although many of the basic properties
of J1141--6545 and B2023+46 are similar, their orbital periods differ by a factor of 60.
Accounting for this fact is one of the problems we are going to address in this paper.


We consider an evolutionary scenario for the production
of such white-dwarf neutron-star (WD--NS) binaries. 
In this scenario, the
original primary transfers its envelope to the secondary conservatively 
leaving only the helium-star core.
This helium star then evolves, filling its Roche lobe, leading to a second
phase of mass transfer where the envelope of the helium star
is transferred to the secondary (which is still on the main sequence).
In the process the primary becomes a white dwarf.
In sufficiently wide binaries,
when the secondary evolves into contact, the ensuing phase of 
mass transfer will produce a common-envelope system in which
the white dwarf and the helium-star core of the secondary
will spiral together as the common envelope of gas is ejected from
the system. The post-common-envelope system will consist of the white
dwarf and the helium star in a tight binary.
Providing sufficient mass has been transferred to the secondary during
earlier phases in the binary evolution, the helium star may be massive
enough to produce a neutron star via a supernova explosion.

This scenario has been considered elsewhere (see for
example Portegies--Zwart \& Yungelson 1999; Brown et al 2000;
Tauris \& Sennels 2000). 
Here we extend the earlier work by considering
the role of the helium star radius in the evolution of the system after
the common envelope phase which will depend on the separation of the binary
and the maximum size of the pre-supernova helium star.
 
Systems similar to B2023+46 will be produced in
relatively wide systems, where the
helium star avoids filling its Roche lobe as it expands. Instead it 
loses mass via a wind. 
For closer binaries (ie those producing
systems similar to J1141--6545), the helium star in the post-common-envelope
system will fill its Roche lobe. In this paper, we propose
that a phase of mass transfer follows where the helium star envelope
is transferred to the white dwarf at highly super-Eddington rates.
Rather than being accreted, we propose that this material is ejected
from the system. 


In Section 2, we begin by describing a simplified version of
the scenario described above where we neglect the radius
of the final helium star. In Section 3 we compute the population of
binaries produced using this simplified scenario.
In Section 4 we consider the role of the helium-star radius on the 
binary evolution. In Section 5 we consider the inferred birthrate of
B2023+46--like and J1141--6545--like systems. We also consider the
timescale for the merger of the tighter systems and the importance
of the kick velocities received by the binaries on formation of
the neutron star.  We summarise our results in Section 6.

\section{evolutionary scenario}

 
The key feature of both J1141--6545 and B2303+46 is that the neutron star
is {\it younger} than the white dwarf. This implies that the star which
produced the neutron star in each system must have originally been the 
secondary. Yet the primary was only massive enough to produce a white
dwarf. Mass transfer from the primary to the secondary must have 
increased its mass sufficiently to yield a supernova. These requirements
greatly restrict the binary parameter space which may produce such
neutron star--white dwarf (WD--NS) systems. The evolutionary sequence
envisaged to produce WD--NS binaries is outlined below:


We consider a binary of initial separation, $a_{\rm i}$,
and total mass contained in the system 
${\cal{M}}_{\rm i} = M_{\rm 1,i} + M_{\rm 2,i}$.


The first phase of mass transfer occurs when the primary fills
its Roche lobe just off the main sequence.
During this phase of conservative, radiative  mass transfer
(early Case B), the primary transfers its entire envelope to the secondary.
Only the helium core of the primary remains. 
The masses of the two stars, $M_{\rm 1,B}$ and $M_{\rm 2,B}$, after this
phase of mass transfer are given by

\begin{equation}
M_{\rm 1,B} = M_{\rm He}(M_{\rm 1,i})= a M_{\rm 1,i}^b
\end{equation}

\begin{equation}
M_{\rm 2,B} = {\cal{M}}_{\rm i} - M_{\rm 1,B}
\end{equation}
where $a=0.125$ and $b=1.4$ (van den Heuvel 1994).
The ratio of the separation after this phase to the initial separation
is given by

\begin{equation}
F_{{\rm i} \rightarrow {\rm B}} = {a_{\rm B} \over a_{\rm i}} =
{M_{1,{\rm i}}^2 M_{2,{\rm i}}^2 \over  M_{1,{\rm B}}^2 M_{2,{\rm B}}^2} 
\end{equation}


This helium star
then evolves filling its Roche lobe leading to the second phase of mass
transfer (Case BB) where the primary transfers the envelope of the helium
star to the secondary (which is still on the main sequence). 
In a  calculation of Case BB evolution by Delgado \& Thomas (1981), a
2 M$_\odot$ helium star initiates mass transfer
when its radius is about 20 R$_\odot$ and terminates mass transfer at a radius of
about 50 R$_\odot$ yet it is stripped down to the CO core.
We therefore assume here that after this phase of mass transfer
the primary becomes a CO or ONeMg white dwarf.
The masses of the two stars, $M_{\rm 1,BB}$ and $M_{\rm 2,BB}$, after this
phase of mass transfer are given by

\begin{equation}
M_{\rm 1,BB} = M_{\rm CO}(M_{\rm 1,B})= M_{\rm WD}
\end{equation}

\begin{equation}
M_{\rm 2,BB} = {\cal{M}}_{\rm i} - M_{\rm 1,BB}
\end{equation}

The ratio of the separation after the Case BB mass transfer to the
initial separation is given by

\begin{equation}
F_{{\rm i} \rightarrow {\rm BB}} = 
{a_{\rm BB} \over a_{\rm i}} = {M_{1,{\rm i}}^2 M_{2,{\rm i}}^2 \over  
M_{1,{\rm BB}}^2 M_{2,{\rm BB}}^2} 
\end{equation}



The secondary will evolve into contact on its nuclear evolutionary
timescale. If the system is sufficiently wide, this third phase of
mass transfer will be convective Case B which will lead to a common--envelope
phase during which the white dwarf and the helium--star core of the secondary
spiral together as the common envelope of gas is ejected from 
the system. Alternatively, the a common--envelope phase will be initiated from
radiative, Case B mass transfer, followed by a delayed dynamical instability (DDI)
if the mass ratio is large enough (Hjellming 1989, Kalogera \& Webbink 1996). 
The masses of the two stars after this phase, $M_{\rm 1,CE}$
and $M_{\rm 2,CE}$, are given by

\begin{equation}
M_{\rm 1,CE} = M_{\rm 1,BB}= M_{\rm WD}
\end{equation}

\begin{equation}
M_{\rm 2,CE} = M_{\rm He}(M_{\rm 2,BB})= a M_{\rm 2,BB}^b
\end{equation}

The inspiral during the common envelope phase may be computed
by equating the change in orbital energy  of the two stars to
the binding energy of the envelope up to an efficiency 
$\alpha_{\rm CE}$, ie $E_{\rm env} = \alpha_{\rm CE} \Delta E$.
Here $E_{\rm env}$ can be written in the following form (Webbink 1984)

\begin{equation}
E_{\rm env} = { G M_{\rm 2,BB} ( M_{\rm 2,BB} - M_{\rm 2,CE})
\over \lambda_{\rm CE} f_2(q_{\rm BB}) a_{\rm BB} }
\end{equation}
where the radius of star 2 when it fills its Roche lobe
is given by $R_{\rm 2,BB} = f_2(q_{\rm BB}) a_{\rm BB}$,
where $q_{\rm BB} = M_{\rm 1,BB} /M_{\rm 2,BB}$ and  
$f_2(q)= { 0.49 q^{2/3} / (0.6 q^{2/3} + {\rm ln}(1+q^{1/3})) }$ 
(Eggleton 1983). 
Combining equation (9) with the expression 
for $\Delta E$, after some rearrangement
we arrive at the following expression for the inspiral during the common
envelope phase

\begin{eqnarray}
F_{{\rm BB} \rightarrow {\rm CE}} = { a_{\rm CE} \over a_{\rm BB} } & = & 
( {2 M_{2,{\rm BB}} ( 
M_{2,{\rm BB}} - M_{2,{\rm CE}}) \over \alpha_{\rm CE} \lambda_{\rm CE} 
f_2(q_{\rm BB}) M_{2,{\rm CE}} M_{1,{\rm BB}} } + \nonumber \\
&& { M_{2,{\rm BB}} \over M_{2,{\rm CE}} } )^{-1} 
\end{eqnarray}


We may combine equations (6) and (10) to produce an expression relating
the initial separation of the binary to that after the common envelope
phase. 

\begin{equation}
F_{{\rm i} \rightarrow {\rm CE}} = { a_{\rm CE} \over a_{\rm i} } =  
F_{{\rm i} \rightarrow {\rm BB}} \cdot F_{{\rm BB} \rightarrow {\rm CE}} 
\end{equation}

The post-common-envelope system will consist of the white dwarf
and the helium star in a tight binary. If the helium star is sufficiently
massive, it will explode as a supernova, producing a neutron star.
The instantaneous mass-loss together with the kick the neutron receives
at birth will unbind some of these binaries, while 
others will remain bound.
By sampling the neutron star kick distribution of Hansen \& Phinney
(1997), and
allowing for the effects of mass-loss during the supernova, we
are able to produce a population of WD--NS binaries and plot their
binary properties and system kick velocities, given a population of 
pre-supernova binaries.


Before we  inspect the population of WD--NS systems produced
in the scenario outlined above, we must consider the
constraints on the properties of the original pre-evolution binaries.

\subsection{Constraints on initial masses}

We require that the mass of the primary should be insufficient to
produce a supernova on its own. In other words the mass of
the compact object produced after the case BB mass transfer
(as given in equation [4]) does not exceed the Chandrasekhar
mass:

\begin{equation}
M_{\rm WD} = M_{\rm CO}(a M_{\rm 1,i}^b) < M_{\rm CH}
\end{equation}
By definition the primary mass exceeds that of the secondary,
ie 

\begin{equation}
M_{\rm 1,i} > M_{\rm 2,i} 
\end{equation}
In order to avoid the onset
of a delayed dynamical instability when mass is transferred from
the primary to the secondary we require 

\begin{equation}
M_{\rm 2,i} \go M_{\rm 1,i}/3
\end{equation}
In addition, we require that the secondary does ultimately produce
a supernova. In other words, $M_{\rm CO}(M_{\rm 2,CE}) > M_{\rm CH}$.
As $M_{\rm 2,CE} = a M_{\rm 2,BB}^b = a (M_{\rm 1,i}+M_{\rm 2,i}-
M_{\rm WD})^b$, rearrangement yields

\begin{equation}
M_{\rm 2,i} >  \left( {M_{\rm He}(M_{\rm CH}) \over a } \right)^{1/b}
+ M_{\rm WD} - M_{\rm 1,i}
\end{equation}


The constraints on the initial masses given in equations (12) -- (15)
are illustrated in Fig. 1. The maximum allowed mass
for the primary is set by equation (12) and is given by  $M_{\rm 1,i}
= 8.3M_\odot$. The upper mass limit for $M_{\rm 2,i}$ is given by
equation (13), while the lower-mass limit is given by equation (15)
for lower values of $M_{\rm 1,i}$ and by equation (14) for larger
values of $M_{\rm 1,i}$.

%\begin{equation}
%M_{\rm 1,i} > M_{\rm 2,i} > {\rm max} \left\{ \begin{array}{l}
%                                      {M_{\rm 1,i} \over 3} \\
%                                      \left( {M_{\rm He}(M_{\rm CH}) \over
%                               a } \right)^{1/b} + M_{\rm WD} - M_{\rm 1,i} 
%                                      \end{array} 
%                                      \right.
%\end{equation}

\begin{figure}
\psboxto(\hsize;0cm){plotinitmass.ps}
\caption{Plot of initial primary mass $M_1$ as a function of secondary mass
$M_2$(both in solar units) showing constraints for the formation of
a WD--NS binary as described in section 3.}
\end{figure}


\subsection{Constraints on initial separations}


The evolutionary pathway described above places a number of
constraints on the initial separation, $a_{\rm i}$, of the binary
if a WD--NS system is to be produced.


For the first phase of mass transfer to be  radiative 
Case B mass transfer, we require that the radius of the primary
when it first fills its Roche lobe, $R_{\rm 1,i}$, is larger
than the minimum radius required for Case B transfer, 
$R_{\rm min,B}(M_{\rm 1,i})$, and smaller than the maximum
radius allowed for radiative case B mass transfer, 
$R_{\rm max,rB}(M_{\rm 1,i})$. In other words

\begin{equation}
{R_{\rm min,B}(M_{\rm 1,i}) \over f_1(q_{\rm i}) } < a_{\rm i} <
{R_{\rm max,rB}(M_{\rm 1,i}) \over f_1(q_{\rm i}) }   
\end{equation}
where $R_{\rm 1,i} = f_1(q_{\rm i}) a_{\rm i}$ with $q_{\rm i} = 
M_{\rm 1,i} /M_{\rm 2,i}$ and 
$f_1(q)= 0.49 q^{-2/3} / (0.6 q^{-2/3} + {\rm ln}(1+q^{-1/3}))$. 
In order for Case BB
mass transfer from the primary to occur, we require the helium star
to fill its Roche lobe. In other words

\begin{equation}
a_{\rm i} < {R_{\rm max,He}(M_{\rm 1,b}) \over 
F_{{\rm i} \rightarrow {\rm B}} f_1(q_{\rm B}) }
\end{equation}
where $q_{\rm B}= M_{\rm 1,B}/ M_{\rm 2,B}$. In order for the late
(convective) Case B mass transfer from the secondary to occur, leading
to the onset of a common envelope phase, we require that the
secondary fill its Roche lobe, but not until it has a radius
larger than the maximum allowed for early (radiative) Case B
mass transfer, ie 

\begin{equation}
{R_{\rm max,rB}(M_{\rm 2,BB}) 
\over F_{{\rm i} \rightarrow {\rm BB}} f_2(q_{\rm BB})}
< a_{\rm i} < {R_{\rm max,B}(M_{\rm 2,BB}) \over 
F_{{\rm i} \rightarrow {\rm BB}}
f_2(q_{\rm BB})}
\end{equation}
where $q_{\rm BB}= M_{\rm 1,BB}/ M_{\rm 2,BB}$ and $R_{\rm max,B}(M_{\rm 2,BB})$
is the maximum radius allowed for Case B mass transfer for a star
of mass $M_{\rm 2,BB}$. 
A CE envelope can also follow from a donor with a radiative envelope
if the mass ratio is big enough for a delayed--dynamical instability 
to occur. The systems of interest here have a white--dwarf primary
mass of 1--1.4 M$_\odot$ and a donor star whose mass is above the 
lower limit for evolving to a supernova, ie $M_2 > 8.3$ M$_\odot$.
This means that the lower limit implied by equation (18) will not
be a restriction to the onset of a CE phase and thus on the formation
of WD--NS binaries.


We require that the helium main-sequence-star
secondary does not fill its Roche lobe at the end of the common
envelope phase. 

\begin{equation}
a_{\rm i} > 
{R_{\rm HeMS}(M_{\rm 2,CE}) \over 
F_{{\rm i} \rightarrow {\rm CE}} f_2(q_{\rm CE})}
\end{equation}
where $R_{\rm HeMS}(M_{\rm 2,CE})$ is the radius of the helium 
main-sequence-star secondary and $q_{\rm CE}= M_{\rm 1,CE}/M_{\rm 2,CE}$.

\section{evolution ignoring the he star radius}

We now consider the evolution of binaries following the scenario
descibed above, applying the constraints given in equations (12) -- (19).
The evolution of the binary separations and stellar masses 
were computed using equations (1) -- (11). 
The functions $R_{\rm min,
B}(M)$, $R_{\rm max, rB}(M)$, and $R_{\rm max, B}(M)$ were
tabulated from Bressan et al. (1993), $R_{\rm max, He}(M)$ from
Paczy\'nski (1971) and Habets (1986), and $M_{\rm CO}(M)$ from
Habets (1986). Linear interpolation was used to
evaluate them for a particular mass, $M$. 
We note that the only information which we draw from Paczy\'nski (1971) is
$R_{\rm max, He}(M)$, and this only to compare with results of Habets (1986), 
on which we mostly rely.
The radius of a zero-age
helium main-sequence star, $R_{\rm HeMS}(M)$, can be approximated
as follows (Habets 1986)


\begin{equation}
{\rm log} {R_{\rm HeMS} \over R_\odot} \simeq -0.68 + 0.67 \ {\rm log}
{M_{\rm He} \over M_\odot}
\end{equation}

For illustration we consider here systems
having an initial primary mass, $M_{\rm 1,i}=7.25 M_\odot$.
We follow the evolution of binaries having a range of initial
separations, $a_{\rm i}$, and secondary masses, $M_{\rm 2,i}$ (within
the range allowed by equations [13] -- [15]). We thus synthesize a population
of binaries containing a white dwarf and a helium star on the verge of
exploding as a supernova. We then apply a random kick to the neutron
star formed in the supernova explosion (drawn from the kick distribution
of Hansen \& Phinney [1997]) and combine it with the dynamical consequences
of the instantaneous ejection of the helium star envelope. A fraction
of the binaries will be broken up by the supernova; those that remain
form our population of WD--NS systems, and should contain systems
resembling both J1141--6554 and B2023+46.

\begin{figure}
%\psboxto(\hsize;0cm){plotas.tauris.ps}
\psboxto(\hsize;0cm){plotas.tauris.new3.ps}
\caption{Plot of initial separation $a_i$ as a function of secondary mass
$M_2$(both in solar units) showing constraints for the formation of
a WD--NS binary as described in section 3.}
\end{figure}

\begin{figure}
\psboxto(\hsize;0cm){ploteccvsd.tauris.new2.ps}
\caption{Plot of eccentricity $e$ as a function of separation, $a_{\rm
psr}$ (in solar
radii) for WD--NS systems produced through the evolutionary
scenario described in section 3. The two open circles are the observed
systems J1141--6545 and B2023+46.}
\end{figure}


The initial parameter space (ie $a_{\rm i}$ and $M_{\rm 2,i}$) 
which produces WD--NS systems is shown as
a dotted region in Fig. 2, where the five lines drawn are the
constraints given in equations (16) -- (19). Here we have
assumed $\alpha_{\rm CE} \lambda_{\rm CE} = 0.5$. The range of values
of $M_2$ is constrained by equations (13) and (14). 
The top line in Fig. 2 is
the upper limit given in equation (17) (labelled U$_{17}$) and the bottom
line is the the lower limit from equation (16) (labelled L$_{16}$) with
other lines being labelled accordingly.
We therefore see from the figure that the lower limit
on initial separations is constrained by the lower limits of equations (16)
and (19),
ie the requirements that the first phase of mass transfer is
Case B, and that the helium main--sequence star secondary  does not
fill its Roche lobe at the end of the common envelope phase.
The upper limit on initial separations is given
by the upper limit from equation (16) for $M_2 \leq 4$ M$_\odot$,
ie by requiring the first phase of mass transfer from the primary to
occur while the star is still radiative. For more massive secondaries,
the upper limit on initial separations is given 
by the upper limit from equation (18), by requiring that the secondary
fill its Roche lobe causing the onset of a common envelope phase.
The lower limit from equation (18) divides systems entering a common envelope phase
via convective mass transfer (above L$_{18}$) and via a delayed dynamical instability
(below L$_{18}$).



 


The resulting population of WD--NS systems is shown in Fig. 3, where
we plot the semi-major axes of the binaries, $a_{\rm psr}$, as  a function
of their eccentricities, $e$. The observed locations of
J1141-6545 and B2303+46 are also shown
as open circles (separations of $1.89$ R$_\odot$ and $31.0$ R$_\odot$
respectively, where we have assumed total masses of $2.3$ M$_\odot$
and $2.64$ M$_\odot$ respectively). 
We see from this plot that under the assumptions
of section 2, we can easily produce J1141--6545, 
but that B2023+46 is wider (by a 
factor of about 2) than any system of a similar eccentricity produced
by our population synthesis code. Wider systems will be produced
if we increase the value of $\alpha_{\rm CE} \lambda_{\rm CE}$ to values
in excess of unity, but then this makes it much harder to produce J1141--6545.
In fact, in this approach, one 
cannot have both systems explained with the same value
of $\alpha_{\rm CE} \lambda_{\rm CE}$. Whether $\alpha_{\rm CE}
\lambda_{\rm CE} \go 1$ implies $\alpha_{\rm CE} > 1$ depends on
the value of $\lambda_{\rm CE}$, which is uncertain, 
although values greater than unity seem to be possible
(see Dewi \& Tauris 2000, and Tauris \& Dewi 2001).


\section{role of the Helium star radius}

\subsection{B2023+46--like evolution}

\begin{figure}
\psboxto(\hsize;0cm){plotas.2303.ps}
\caption{Plot of initial separation $a_i$ as a function of secondary mass
$M_2$(both in solar units) showing constraints for the formation of
a WD--NS binary as described in section 4, where the actual radius
of the pre-supernova helium star is considered.}
\end{figure}

\begin{figure}
\psboxto(\hsize;0cm){ploteccvsd.2303.ps}
\caption{Plot of eccentricity $e$ as a function of separation,  
$a_{\rm psr}$ (in solar
radii) for systems produced without mass transfer
after the common-envelope phase as described in section 4. 
As in Figure 3, the two open circles are the observed systems
J1141--6545 and B2023+46.}
\end{figure}


We consider now the evolution of the
helium main-sequence star after the common envelope phase.
In the previous section we assumed that its mass and radius did
not evolve prior to the supernova explosion. Neither assumption
is correct. In isolation, the helium star will evolve to a radius
$R_{\rm max,He}(M_{\rm 2,CE})$.  If this star is to avoid
filling its Roche lobe and transferring material to the white 
dwarf, we require

\begin{equation}
a_{\rm i} > {R_{\rm max,He}(M_{\rm 2,CE}) \over 
F_{{\rm i} \rightarrow {\rm CE}} f_2(q_{\rm CE})}  
\end{equation}
where $q_{\rm CE} = M_{\rm 1,CE} / M_{\rm 2,CE}$. 
The initial parameter space (ie $a_{\rm i}$ and $M_{\rm 2,i}$) 
which satisfies equations (16) -- (19) and equation (21) is shown in the
 dotted region in Fig. 4, where we have
assumed $\alpha_{\rm CE} \lambda_{\rm CE} = 0.5$. 
Note that the initial phase space is much reduced compared 
to Fig. 2. If equation (21) is satisfied,
the helium star will lose its envelope as a wind before the remaining
core explodes as a supernova, where the pre-supernova core mass is given
by

\begin{equation}
M_{\rm 2,PSN} = M_{\rm CO}(M_{\rm 2,CE})
\end{equation}
This mass loss will also affect the separation of the two stars.
The relative change in separation will be given by 

\begin{equation}
F_{{\rm CE} \rightarrow {\rm PSN}} = {a_{\rm PSN} \over a_{\rm CE}} = 
{ M_{\rm WD} + M_{2,{\rm CE}} \over M_{\rm WD} + M_{2,{\rm PSN}}}
\end{equation}
Hence the mass loss will {\it increase} the separation of the two stars
prior to the supernova. Continuing the evolution of the binaries as before
we produce a population of post-supernova systems, as illustrated
in Fig. 5. Note from this figure that B2023+46-like are on the edge (but within)
the phase space of allowed systems. No systems similar to J1141--6545 
are produced.
It is in fact quite impossible to produce a system resembling J1141--6545
without the helium star filling its Roche lobe in the post-common-envelope
phase. The timescale for a wider, more eccentric system to evolve into
a J1141--6545-like system via the emission of gravitational waves is prohibitively 
long. We therefore conclude that this type of evolution is able to explain
the production of B2023+46 but is unable to explain the origin of J1141--6545.


\subsection{J1141--6545--like evolution}

\begin{figure}
%\psboxto(\hsize;0cm){ploteccvsd.1141.ps}
\psboxto(\hsize;0cm){ploteccvsd.1141.new.ps}
\caption{Plot of eccentricity $e$ as a function of separation (in solar
radii) for WD--NS systems undergoing mass transfer
after the common envelope phase as described in section 4.
As in Figure 3, the two open circles are the observed systems
J1141--6545 and B2023+46.}
\end{figure}



We consider next the case where the helium star fills its Roche lobe
prior to the supernova, ie

\begin{equation}
a_{\rm i} < {R_{\rm max,He}(M_{\rm 2,CE}) \over 
F_{{\rm i} \rightarrow {\rm CE}} f_2(q_{\rm CE})} 
\end{equation}
where $q_{\rm CE}=M_{\rm 1,CE}/M_{\rm 2,CE}$. A number of outcomes are then
possible. If a second common envelope phase were to ensue, the core of the
helium star and the white dwarf would probably merge and we would
be left with a single object rather than a binary. Alternatively, 
one might imagine a phase of mass transfer similar to that envisaged
for Cygnus X-2 (King \& Ritter 1999, Kolb et al. 2000) where material
was transferred rapidly from a donor on to a compact object (in that case,
a neutron star) but rather than being accreted, the vast bulk of the 
material was ejected from the system. 
Taking the data from Habets (1986), we estimate that $\dot M_{\rm KH}
= M/\tau_{\rm KH}$ for He-stars in the mass range of interest
$\sim 2.5 {\rm M_{\odot}} - \sim 4 {\rm M_{\odot}}$ is of the order of
$\sim 10^{-3} {\rm M_{\odot}}{\rm yr}^{-1}$ if the radius of the He-star
is $R_{\rm He} \approx 3 R_{\odot}$.At the same time the Eddington
accretion rate for a WD of mass $M_{\rm WD} = 1.2 {\rm M_{\odot}}$ is
$\dot M_{\rm Edd} \approx 6.4~10^{-6} {\rm M_{\odot}}{\rm yr}^{-1}$;
therefore, $\dot M_{\rm KH}/\dot M_{\rm Edd} \approx 10^2$ for the
situation of interest. Since mass transfer starts from the more
massive component, the actual mass transfer rates are likely to peak
at even higher rates.
Assuming the binary follows this Cygnus X--2 like evolution, 
and that the ejected material carries with it the specific angular
momentum of the white dwarf, we have the following expression
for the relative change in separation due to mass transfer from
the Roche-lobe-filling helium star on to the white dwarf


\begin{eqnarray}
F_{{\rm CE} \rightarrow {\rm PSN}} & = &  \left( { M_{2,{\rm CE}} \over
M_{2,{\rm PSN}}} \right)^2 { M_{\rm WD} + M_{2,{\rm CE}}
\over M_{\rm WD} + M_{2,{\rm PSN}}} \times \nonumber \\
&& {\rm exp}  \left[ {2 ( M_{2,{\rm PSN}} - M_{2,{\rm CE}} ) \over M_{\rm WD}
} \right]
\end{eqnarray}
where $M_{2,{\rm PSN}}$ is evaluated using equation (22). After this
phase of mass transfer the core of the helium star explodes as a supernova.
Again we synthesize a population of post-supernova binaries which is
shown in Fig. 6. It is clear from this figure that J1141--6545--like systems
can be produced via this route but that B2023+46--like systems cannot be
a product of systems which have undergone mass transfer after the common
envelope phase. 


We therefore see two distinct evolutionary paths: systems
undergoing mass transfer after a common envelope phase
produce systems like J1141--6545 whilst those like B2023+46 
are produced when the pre-supernova helium star fails to fill
its Roche lobe.
All computations of He star
evolution agree on the fact that for single He stars
$R_{\rm max, He}(M)$ drops {\em rapidly} from $\approx 10^2$
R$_{\odot}$ to a few $R_{\odot}$ between $M_{\rm He} \approx 2.5 $
M$_{\odot}$ and $\approx 4 $M$_{\odot}$. It is this rapid drop in
$R_{\rm max, He}(M)$ which leads to the clear division between
the evolutionary channels for J1141--type and B2303--type
systems. Where exactly this dividing line is is less important
than that it exists.



\section{discussion}

\subsection{System birthrates}


We now consider the production of J1141--6545--like and B2023+46--like objects
from binaries containing a range of primary masses. As can be seen
from Fig. 1, constraints on the initial masses of the two stars (as decribed
in section 2.1) restrict the primary mass to $4.6 \msun \lo M_1 \lo 
8.3 \msun$. In Fig. 7, we show the
computed fraction of binaries producing J1141--6545--like and 
B2023+46--like objects, assuming the binaries to be distributed uniformly in
log($a_{\rm i}/$R$_\odot$) and $1 \le {\rm log}(a_{\rm i}) \le 3$.
From this figure we note that the further restrictions on the parameter
space produce the two types of binary (as described in section 2.2)
are such that no binaries of either type are produced for $M_1 \lo
6.4 \msun$. This in turn implies that the mass
of white dwarfs generated in this way, $M_{\rm WD} \go 1$ M$_\odot$.
We note also that the fraction of 
binaries producing J1141--6545--like
systems is far higher than that for B2023+46--like systems. As also shown
in Fig. 7, we considered different distributions of secondary masses, 
ie different values of $\alpha$ where $dN_2/dM_2 \propto M_2^{-\alpha}$.
A flat distribution (ie $\alpha=0$) produced a larger fraction of both
types of binary compared to a Salpeter--like distribution (ie $\alpha=2.35$).
This is because larger secondary masses are required to produce
either J1141--6545--like or B2023+46--like systems. 

\begin{figure}
%\psboxto(\hsize;0cm){plotfracvsm1.ps}
\psboxto(\hsize;0cm){plotfracvsm1.new.ps}
\caption{The fraction of binary systems, $f$, 
producing either an J1141--6545--like
system (solid lines) or a B2023+46--like system (dashed lines). In each case
the lower of the two lines assumes a Salpeter--like distribution of
secondary masses, whilst the upper line assumes a flat distribution of
secondary masses.}
\end{figure}

\begin{table}
\begin{tabular}{rrr} \hline\hline
\noalign{\medskip}
%$\alpha$ & J1141--6545--like rate & B2023+46--like rate \\
$\alpha$ & ${\dot N}_{1141}$ & ${\dot N}_{2303}$ \\
\noalign{\medskip}
\hline
\noalign{\medskip}
%2.35 & 6.99 $\times 10^{-5}$ & 2.40 $\times 10^{-6}$  \\
%0.00 & 5.23 $\times 10^{-4}$ & 5.63 $\times 10^{-5}$  \\
%-2.35 & 6.61 $\times 10^{-4}$ & 1.17 $\times 10^{-4}$  \\
2.35 & 8.75 $\times 10^{-5}$ & 2.45 $\times 10^{-6}$  \\
0.00 & 6.20 $\times 10^{-4}$ & 5.70 $\times 10^{-5}$  \\
-2.35 & 7.60 $\times 10^{-4}$ & 1.17 $\times 10^{-4}$  \\
\noalign{\medskip}
\hline
\end{tabular}
\caption{The galactic production rate (in units of systems yr$^{-1}$) 
of J1141--6545--like and B2023+46--like systems
(${\dot N}_{1141}$ and ${\dot N}_{2303}$ respectively)
as a function of distribution of secondary masses, $\alpha$,
where $dN_2/dM_2 \propto M_2^{-\alpha}$.}
\end{table}


We can now compute the galactic formation rate of systems
assuming a primary formation rate $d{\dot N}_1 = M_1^{-2.35} dM_1$ (which
is equivalent to a galactic star formation rate of $\sim 3 \msun$/yr).
We also assume that one quarter of all massive stars are formed in binaries
having the separation range $1 \le {\rm log}(a_{\rm i}) \le 3$.
Hence the formation rate of systems of type X, derived from binaries having
an original primary mass $M_1$, is $d{\dot N}_{1,X} = f_X d{\dot N}_1 /4$,
where $f_X$ is the fraction of binaries, having the separation range 
$1 \le {\rm log}(a_{\rm i}) \le 3$, which produce systems 
of type X (as shown in Fig. 7).
In Table 1 we list the galactic formation rate of systems as a 
function of $\alpha$, for $\alpha_{\rm ce} \lambda = 0.5$.
 We note that for both J1141--6545--like and B2023+46--like
systems, the formation rate increases with decreasing $\alpha$, as
a larger fraction of the original binaries contain more massive secondaries.
The relative formation rates of the two types of systems is also a function
of $\alpha$ as B2023+46--like systems require a secondary of mass similar 
to that of the primary (as shown in Fig. 4) whereas J1141--6545--like systems
are produced for a broader range of secondary masses.
We now consider the effect of changing the value of $\alpha_{\rm ce} 
\lambda$. In Fig. 8 we plot the galactic production rates for
J1141--6545--like and B2023+46--like systems, for the two cases
$\alpha = 2.35$ (ie Salpeter--like distribution of secondary masses)
and $\alpha=0.0$ (ie a flat distribution of secondary masses).
The production rate of J1141--6545--like systems is relatively independent
of $\alpha_{\rm ce} \lambda$ whereas the production rate of B2023+46--like 
systems increases with $\alpha_{\rm ce} \lambda$.
The formation rate of J1141--6545--like systems appears to be larger than 
for B2023+46-like systems for all reasonable values of
$\alpha$ and $\alpha_{\rm ce} \lambda$.

\begin{figure}
\psboxto(\hsize;0cm){plotrates.new2.ps}
\caption{The galactic production rate (in units of systems yr$^{-1}$)
of J1141--6545--like systems (solid lines) and B2023+46--like systems
(dashed lines) as a function of $\alpha_{\rm ce} \lambda$.
In each case
the lower of the two lines assumes a Salpeter--like distribution of
secondary masses, whilst the upper line assumes a flat distribution of
secondary masses.}
\end{figure}

We now consider the formation rates inferred from the two observed
systems. J1141--6545 is at a distance $\simeq$ 3 kpc and has a characteristic
age derived from the pulsar spin-down of 1.4 Myr. The  distance to B2023+46
is less well-known but is thought to lie between 3 -- 10 kpc.
It has a spin-down age of 30 Myr. The beaming of pulsar emission
means that we will only see those which are pointing towards us. We might
only see 1/5 of the actual population.
Including the effect of beaming, the distances to both
systems would suggest that there are currently 50 -- 500 similar systems
thoughout the Galaxy. From the pulsar characteristic ages, this
in turn implies formation rates of $5 \times 10^{-5} - 
5 \times 10^{-4}$ yr$^{-1}$ for J1141--6545--like systems
and $ 2 \times 10^{-6} - 2 \times 10^{-5}$ yr$^{-1}$ for
B2023+46--like systems. These values are consistent with the range seen in 
Table 1. From Figure 8, we note that in addition that the observed
formation rates of B2023+46--like systems would seem to suggest that
$\alpha_{\rm ce} \lambda \ga 0.3$.
We therefore conclude that the scenario described in this paper
is able to account for the two observed systems PSR J1141--6545 and B2023+46.   


\subsection{Kick velocities}


We consider now the system kick received
by J1141--6545--like and B2023+46--like binaries. The system kick of each binary
is a combination of the kick the neutron star receives at birth
with the kick resulting from the mass--loss in the supernova 
explosion of the helium star.  The distribution of system kick velocities 
are shown in Fig. 9. From this figure we note that the kicks span
a large range of values, the largest being likely to remove the system
from the Galaxy entirely (when combined appropriately with the initial
orbital velocity of the pre-supernova binary). In a majority of cases,
such kicks will at least take the binary significantly away from the
plane of the galactic disk (where the systems will have been formed).
The kicks for systems most closely resembling J1141--6545 range between 50 km/s
and 300 km/s. For B2023+46 the equivalent range is 100 km/s to 200 km/s.
These are both consistent with the observed 
positions of J1141--6545 and B2023+46.
J1141--6545 has a galactic latitude of $-3.86$ degrees which, at a distance of
3.2 kpc and assuming an age of 1.4 Myr, implies a velocity out
of the galactic plane $\lo 150$ km/s.   
B2023+46 has a galactic latitude of $-12.02$ degrees which, at a distance
of 3 -- 10 kpc and assuming an age of 30 Myr, implies a velocity out of
the galactic plane of $\sim 20 - 60 $  km/s.

%2303: l = 104.93 b=-12.02, d=3-10kpc, tc=30myr
%1141: l = 295.79 b=-3.86, d=3.2kpc, tc=1.4myr
%NB h=dsintheta= 0.21d for 2303
%h= 0.07 d for 1141




%\begin{figure}
%\psboxto(\hsize;0cm){plotvbinvsdclose.ps}
%\caption{The kick velocity received by the WD--NS binaries $V_{\rm bin}$
%(in km/s) as a function of their semi-major axes $a_{\rm psr}$ (in solar 
%radii). Crosses are for systems resembling J1141--6545, whilst
%the open squares are for systems resembling 2303.}
%\end{figure}

%\begin{figure}
%\psboxto(\hsize;0cm){plotvwdvsd.ps}
%\caption{The kick velocity received by the white dwarfs, $V_{\rm wd}$
%(in km/s) in binaries which are broken up when the neutron
%star forms, as a function of the semi-major axes 
%of the pre-supernova binaries, $a_{\rm psn}$ (in solar 
%radii). Crosses are for systems produced via the 
%J1141--6545--like route, whilst
%the open squares are for systems produced via the B2023+46--like route.}
%\end{figure}

%\begin{figure}
%\psboxto(\hsize;0cm){plotvnsvsd.ps}
%\caption{The kick velocity received by the neutron stars, $V_{\rm ns}$
%(in km/s) in binaries which are broken up when the neutron
%star forms, as a function of the semi-major axes 
%of the pre-supernova binaries, $a_{\rm psn}$ (in solar 
%radii). Crosses are for systems produced via the J1141--6545--like route, whilst
%the open squares are for systems produced via the 2303--like route.}
%\end{figure}

%It is also interesting to note that the components of binaries broken
%up when the helium star exploded as a supernova will also have high 
%velocities. In Fig. 9 we plot the kick received by the white dwarf as
%a function of the pre-supernova separation of the binary. We see that
%those systems evolving along the J1141--6545--like route have smaller
%separations prior to the supernova and thus larger orbital velocities.
%This in turn explains why the unbound white dwarfs tend to receive
%larger kicks compared to those produced via the B2023+46--like route.
%In either case, the white dwarfs often receive kicks $\go 200$ km/s.
%The observation of such high-velocity white dwarfs would provide
%further evidence for the evolutionary scenario offered in this paper
%to explain J1141--6545 and B2023+46. 
%Indeed it is hard to imagine an alternative
%method of producing very high-velocity white dwarfs assuming they were
%produced in the galactic disk.


\begin{figure}
%\psboxto(\hsize;0cm){plotvbinvsd.ps}
\psboxto(\hsize;0cm){plotvbinvsd.new.ps}
\caption{The kick velocity received by the WD--NS binaries $V_{\rm bin}$
(in km/s) as a function of their semi-major axes $a_{\rm psr}$ (in solar 
radii). Crosses are for systems produced via the J1141--6545--like route, whilst
the open squares are for systems produced via the B2023+46--like route.}
\end{figure}


\subsection{Merger rates}


In this section we discuss the subsequent evolution of
the J1141--6545--like objects. As can be seen from Fig. 6, in
these systems, the white dwarf and neutron star have separations
$\sim 1 - 10 \rsun$, and a wide range of eccentricities.
These systems will spiral in as they lose angular momentum and energy
via the emission of gravitational radiation.
One may compute the subsequent evolution of the binary separation, $a$,
and eccentricity, $e$,  using the following expressions (Peters 1964)

%\begin{equation}
%{da \over dt} = - { 64 G^3 M_{\rm WD} M_{\rm NS} (M_{\rm WD} + M_{\rm NS})  
%\over 5 c^5 a^3 (1 - e^2)^{7/2}}
%\times \left( 1 + {73 \over 24} e^2 + {37 \over 96} e^4 \right)
%\end{equation}

\begin{eqnarray}
{da \over dt} & = & - { 64 G^3 M_{\rm WD} M_{\rm NS} (M_{\rm WD} + M_{\rm NS})  
\over 5 c^5 a^3 (1 - e^2)^{7/2}}
\times \nonumber \\
&& \left( 1 + {73 \over 24} e^2 + {37 \over 96} e^4 \right)
\end{eqnarray}

\begin{equation}
%{de \over dt} = - {304 M_1 M_2 (M_1 + M_2) e \over 15 a^4 (1 - e^2)^{5/2}}
{de \over dt} = - {304 G^3 M_{\rm WD} M_{\rm NS} (M_{\rm WD} + M_{\rm NS})
e \over 15 c^5 a^4 (1 - e^2)^{5/2}}
\times \left( 1 + {121 \over 304} e^2 \right)
\end{equation}

We thus computed the time required for the binaries to evolve into contact.
The cumulative distribution for contact times is shown 
in Fig. 10. We see from this figure that over half  of the systems will
merge in a timecale $\lo 10^8$ years, and more than 95\% within a Hubble time. 
These merging systems may make an important contribution to the population
of gamma-ray burst progenitors as will be explored in a later paper.

\begin{figure}
%\psboxto(\hsize;0cm){plotcumtcont.ps}
\psboxto(\hsize;0cm){plotcumtcont.new.ps}
\caption{The cumulative distribution of timescales for 
the population of inspiralling WD--NS binaries to
come in to contact via the emission of gravitational radiation,
$t_{\rm contact}$ (in years).}
\end{figure}


\section{Summary}

We have described an evolutionary pathway for producing white dwarf--neutron
star binaries where the white dwarf is made first. This explains the
observed systems J1141--6545 and B2023+46. In this scenario, the 
original primary transfers its envelope to the secondary conservatively during
a radiative Case B phase of mass transfer leaving only the helium-star core.
This helium star then evolves, filling its Roche lobe and leading to the second
phase of mass transfer (Case BB) where the envelope of the helium star
is transferred to the secondary (which is still on the main sequence).
In the process the primary becomes a CO or ONeMg white dwarf.
The secondary evolves into contact on its nuclear evolutionary
timescale. If the system is sufficiently wide, this third phase of
mass transfer leads to a common-envelope
phase during which the white dwarf and the helium-star core of the secondary
spiral together as the common envelope of gas is ejected from 
the system. The post-common-envelope system consists of the white
dwarf and the helium star in a tight binary. 
Providing sufficient mass has been transferred to the secondary during
earlier phases in the binary evolution, the helium star may be massive
enough to produce a neutron star via a supernova explosion.
The post-common-envelope but pre-supernova evolution depends on
the separation of the binary.



Systems like B2023+46 are produced in
relatively wide systems, where the
helium star avoids filling its Roche lobe as it expands. Rather it 
loses mass via a wind. The core of the helium star eventually
explodes as a supernova producing a neutron star. Assuming the neutron star
receives a kick at birth, the majority of these systems are broken up,
producing high-velocity, single, white dwarfs and neutron stars. In
a minority of cases, the neutron star and white dwarf produce a binary
having a separation $\sim 5 - 50 \rsun$. 



For closer binaries, the helium star in the post-common-envelope
system fills its Roche lobe. In this paper, we have proposed
that a phase of mass transfer follows where the helium star envelope
is transferred to the white dwarf at highly super-Eddington rates.
Rather than being accreted, we propose that this material is ejected
from the system. Subsequently the helium-star core explodes
as a supernova, producing a neutron star. As these binaries
are significantly tighter than those producing B2023+46--like 
systems, the vast majority remain bound, having separations in the 
range $\sim 0.5 - 5 \rsun$. This is the way we believe J1141--6545 was formed.



We have computed the expected formation rates for J1141--6545--like and 
B2023+46--like systems and shown that they are both large and consistent
with the two observed systems.



We have shown that the vast majority of J1141--6545--like binaries
will spiral in and merge in less than a Hubble time due to
the emission of gravitational radiation. Given their relatively high
formation rate ($\sim 10^{-4} - 10^{-5}$ yr$^{-1}$), these systems
may make an important contribution to the population of gamma-ray burst
progenitors.


\bigskip

\paragraph*{Acknowledgments}

MBD gratefully acknowledges the support of a URF from the Royal Society.
Theoretical astrophysics research at Leicester is supported by a rolling grant
from the UK Particle Physics \& Astronomy Research Council.

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\end{document}



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%   TeX \scale commands)
%
\def\psfortextures{%     For TeXtures on the Macintosh
%-----------------
\def\PSspeci@l##1##2{%
\special{illustration ##1\space scaled ##2}%
}}%
\def\psfordvitops{%      For the DVItoPS converter on IBM mainframes
%----------------
\def\PSspeci@l##1##2{%
\special{dvitops: import ##1\space \the\drawingwd \the\drawinght}%
}}%
\def\psfordvips{%      For DVIPS converter on VAX, UNIX and PC's
%--------------
\def\PSspeci@l##1##2{%
%    \special{/@scaleunit 1000 def}% never read dox without trying!
\d@my=0.1bp \d@mx=\drawingwd \divide\d@mx by\d@my% BUG! for large \drawingwd
\special{PSfile=##1\space llx=\psllx\space lly=\pslly\space%
urx=\psurx\space ury=\psury\space rwi=\number\d@mx
}}}%
\def\psforoztex{%        For the OzTeX shareware on the Macintosh
%--------------
\def\PSspeci@l##1##2{%
\special{##1 \space
      ##2 1000 div dup scale
      \number-\psllx\space \number-\pslly\space translate
}}}%
\def\psfordvitps{%       From the UNIX TeXPS package, vers.>3.12
%---------------
% Convert a dimension into the number \psn@sp (in scaled points)
\def\psdimt@n@sp##1{\d@mx=##1\relax\edef\psn@sp{\number\d@mx}}
\def\PSspeci@l##1##2{%
% psfig.psr contains the def of "startTexFig": if you can locate it
% and include the correct pathname, it should work
\special{dvitps: Include0 "psfig.psr"}% contains def of "startTexFig"
\psdimt@n@sp{\drawingwd}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\drawinght}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\psllx bp}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\pslly bp}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\psurx bp}
\special{dvitps: Literal "\psn@sp\space"}
\psdimt@n@sp{\psury bp}
\special{dvitps: Literal "\psn@sp\space startTexFig\space"}
\special{dvitps: Include1 "##1"}
\special{dvitps: Literal "endTexFig\space"}
}}%
\def\psfordvialw{%   Try for dvialw, a UNIX public domain
%---------------
\def\PSspeci@l##1##2{
\special{language "PostScript",
position = "bottom left",
literal "  \psllx\space \pslly\space translate
  ##2 1000 div dup scale
  -\psllx\space -\pslly\space translate",
include "##1"}
}}%
\def\psforptips{%   For MS-DOS; LUOMA@brandeis.bitnet
%---------------
\def\PSspeci@l##1##2{{
\d@mx=\psurx bp
\advance \d@mx by -\psllx bp
\divide \d@mx by 1000\multiply\d@mx by \xscale
\incm{\d@mx}
\let\tmpx\dimincm
\d@my=\psury bp
\advance \d@my by -\pslly bp
\divide \d@my by 1000\multiply\d@my by \xscale
\incm{\d@my}
\let\tmpy\dimincm
\d@mx=-\psllx bp
\divide \d@mx by 1000\multiply\d@mx by \xscale
\d@my=-\pslly bp
\divide \d@my by 1000\multiply\d@my by \xscale
\at(\d@mx;\d@my){\special{ps:##1 x=\tmpx, y=\tmpy}}
}}}%
\def\psonlyboxes{%     Draft-like behaviour if none of the others works
%---------------
\def\PSspeci@l##1##2{%
\at(0cm;0cm){\boxit{\vbox to\drawinght
  {\vss\hbox to\drawingwd{\at(0cm;0cm){\hbox{({\tt##1})}}\hss}}}}
}}%
\def\psloc@lerr#1{%
\let\savedPSspeci@l=\PSspeci@l%
\def\PSspeci@l##1##2{%
\at(0cm;0cm){\boxit{\vbox to\drawinght
  {\vss\hbox to\drawingwd{\at(0cm;0cm){\hbox{({\tt##1}) #1}}\hss}}}}
\let\PSspeci@l=\savedPSspeci@l% restore normal output for other figs!
}}%
%\def\psfor...  add your own!
%
% Some common defs
%
\newread\pst@mpin
\newdimen\drawinght\newdimen\drawingwd
\newdimen\psxoffset\newdimen\psyoffset
\newbox\drawingBox
\newcount\xscale \newcount\yscale \newdimen\pscm\pscm=1cm
\newdimen\d@mx \newdimen\d@my
\newdimen\pswdincr \newdimen\pshtincr
\let\ps@nnotation=\relax
{\catcode`\|=0 |catcode`|\=12 |catcode`|%=12 |catcode`~=12
|catcode`#=12 |catcode`*=14
|xdef|backslashother{\}*
|xdef|percentother{%}*
|xdef|tildeother{~}*
|xdef|sharpother{#}*
}%
% useful to display special chars in \tt; fails for \,#,%
\def\R@moveMeaningHeader#1:->{}%
\def\uncatcode#1{%
\edef#1{\expandafter\R@moveMeaningHeader\meaning#1}}%
%
\def\execute#1{#1}% NOT stupid: cs in #1 are then identified BEFORE execution
\def\psm@keother#1{\catcode`#112\relax}% borrowed from latex
\def\executeinspecs#1{%
\execute{\begingroup\let\do\psm@keother\dospecials\catcode`\^^M=9#1\endgroup}}%
\def\@mpty{}%
% \if\matchin#1#2<=> \iftrue if #1 contains #2, <=>\iffalse otherwise:
% \if\matchexpin: idem, but #1 & #2 are first fully expanded (no \if
% inside!)
% \tmpa & \tmpb contain what's before and after the occurence of #2
\def\matchexpin#1#2{
  \fi%
%\message{(#1>#2)}
  \edef\tmpb{{#2}}%
  \expandafter\makem@tchtmp\tmpb%
  \edef\tmpa{#1}\edef\tmpb{#2}%
  \expandafter\expandafter\expandafter\m@tchtmp\expandafter\tmpa\tmpb\endm@tch%
  \if\match%
}%
\def\matchin#1#2{%
  \fi%
  \makem@tchtmp{#2}%
  \m@tchtmp#1#2\endm@tch%
  \if\match%
}%
\def\makem@tchtmp#1{\def\m@tchtmp##1#1##2\endm@tch{%
  \def\tmpa{##1}\def\tmpb{##2}\let\m@tchtmp=\relax%
  \ifx\tmpb\@mpty\def\match{YN}%
  \else\def\match{YY}\fi%
}}%
% converts any dimen in cm, with 1E-4 cm precision
\def\incm#1{{\psxoffset=1cm\d@my=#1
 \d@mx=\d@my
  \divide\d@mx by \psxoffset
  \xdef\dimincm{\number\d@mx.}
  \advance\d@my by -\number\d@mx cm
  \multiply\d@my by 100
 \d@mx=\d@my
  \divide\d@mx by \psxoffset
  \edef\dimincm{\dimincm\number\d@mx}
  \advance\d@my by -\number\d@mx cm
  \multiply\d@my by 100
 \d@mx=\d@my
  \divide\d@mx by \psxoffset
  \xdef\dimincm{\dimincm\number\d@mx}
}}%
%
%  \ReadPSize{PSfilename} reads the dimensions of a PostScript drawing
%      and stores it in \drawinght(wd)
\newif\ifNotB@undingBox
\newhelp\PShelp{Proceed: you'll have a 5cm square blank box instead of
your graphics (Jean Orloff).}%
\def\s@tsize#1 #2 #3 #4\@ndsize{
  \def\psllx{#1}\def\pslly{#2}%
  \def\psurx{#3}\def\psury{#4}%  needed by a crazyness of dvips!
  \ifx\psurx\@mpty\NotB@undingBoxtrue% this is not a valid one!
  \else
    \drawinght=#4bp\advance\drawinght by-#2bp
    \drawingwd=#3bp\advance\drawingwd by-#1bp
%  !Units related by crazy factors as bp/pt=72.27/72 should be BANNED!
  \fi
  }%
\def\sc@nBBline#1:#2\@ndBBline{\edef\p@rameter{#1}\edef\v@lue{#2}}%
\def\g@bblefirstblank#1#2:{\ifx#1 \else#1\fi#2}%
{\catcode`\%=12
\xdef\B@undingBox{%%BoundingBox}}%
%% is not a true comment in PostScript, even if % is!
\def\ReadPSize#1{
 \readfilename#1\relax
 \let\PSfilename=\lastreadfilename
 \openin\pst@mpin=#1\relax
 \ifeof\pst@mpin \errhelp=\PShelp
   \errmessage{I haven't found your postscript file (\PSfilename)}%
   \psloc@lerr{was not found}%
   \s@tsize 0 0 142 142\@ndsize
   \closein\pst@mpin
 \else
% each entry in \GlobalInputList should be unique
   \if\matchexpin{\GlobalInputList}{, \lastreadfilename}%
   \else\xdef\GlobalInputList{\GlobalInputList, \lastreadfilename}%
     \immediate\write\psbj@inaux{\lastreadfilename,}%
   \fi%
   \loop
     \executeinspecs{\catcode`\ =10\global\read\pst@mpin to\n@xtline}%
     \ifeof\pst@mpin
       \errhelp=\PShelp
       \errmessage{(\PSfilename) is not an Encapsulated PostScript File:
           I could not find any \B@undingBox: line.}%
       \edef\v@lue{0 0 142 142:}%
       \psloc@lerr{is not an EPSFile}%
       \NotB@undingBoxfalse
     \else
       \expandafter\sc@nBBline\n@xtline:\@ndBBline
       \ifx\p@rameter\B@undingBox\NotB@undingBoxfalse
         \edef\t@mp{%
           \expandafter\g@bblefirstblank\v@lue\space\space\space}%
         \expandafter\s@tsize\t@mp\@ndsize
       \else\NotB@undingBoxtrue
       \fi
     \fi
   \ifNotB@undingBox\repeat
   \closein\pst@mpin
 \fi
\message{#1}%
}%
%
% \psboxto(xdim;ydim){psfilename}: you specify the dimensions and
%    TeX uniformly scales to fit the largest one. If xdim=0pt, the
%    scale is fully determined by ydim and vice versa.
%    Notice: psboxes are a real vboxes; couldn't take hbox otherwise all
%    indentation and all cr's would be interpreted as spaces (hugh!).
%
\def\psboxto(#1;#2)#3{\vbox{%
   \ReadPSize{#3}%
   \advance\pswdincr by \drawingwd
   \advance\pshtincr by \drawinght
   \divide\pswdincr by 1000
   \divide\pshtincr by 1000
   \d@mx=#1
   \ifdim\d@mx=0pt\xscale=1000
         \else \xscale=\d@mx \divide \xscale by \pswdincr\fi
   \d@my=#2
   \ifdim\d@my=0pt\yscale=1000
         \else \yscale=\d@my \divide \yscale by \pshtincr\fi
   \ifnum\yscale=1000
         \else\ifnum\xscale=1000\xscale=\yscale
                    \else\ifnum\yscale<\xscale\xscale=\yscale\fi
              \fi
   \fi
   \divide\drawingwd by1000 \multiply\drawingwd by\xscale
   \divide\drawinght by1000 \multiply\drawinght by\xscale
   \divide\psxoffset by1000 \multiply\psxoffset by\xscale
   \divide\psyoffset by1000 \multiply\psyoffset by\xscale
   \global\divide\pscm by 1000
   \global\multiply\pscm by\xscale
   \multiply\pswdincr by\xscale \multiply\pshtincr by\xscale
   \ifdim\d@mx=0pt\d@mx=\pswdincr\fi
   \ifdim\d@my=0pt\d@my=\pshtincr\fi
   \message{scaled \the\xscale}%
 \hbox to\d@mx{\hss\vbox to\d@my{\vss
   \global\setbox\drawingBox=\hbox to 0pt{\kern\psxoffset\vbox to 0pt{%
      \kern-\psyoffset
      \PSspeci@l{\PSfilename}{\the\xscale}%
      \vss}\hss\ps@nnotation}%
   \global\wd\drawingBox=\the\pswdincr
   \global\ht\drawingBox=\the\pshtincr
   \global\drawingwd=\pswdincr
   \global\drawinght=\pshtincr
   \baselineskip=0pt
   \copy\drawingBox
 \vss}\hss}%
  \global\psxoffset=0pt
  \global\psyoffset=0pt
  \global\pswdincr=0pt
  \global\pshtincr=0pt % These are local to one figure
  \global\pscm=1cm %should not be necessary
}}%
%
% \psboxscaled{scalefactor*1000}{PSfilename} allows to bypass the
%   rounding errors of TeX integer divisions for situations where the
%   TeX box should fit the original BoundingBox with a precision
%   better
%   than 1/1000.
%
\def\psboxscaled#1#2{\vbox{%
  \ReadPSize{#2}%
  \xscale=#1
  \message{scaled \the\xscale}%
  \divide\pswdincr by 1000 \multiply\pswdincr by \xscale
  \divide\pshtincr by 1000 \multiply\pshtincr by \xscale
  \divide\psxoffset by1000 \multiply\psxoffset by\xscale
  \divide\psyoffset by1000 \multiply\psyoffset by\xscale
  \divide\drawingwd by1000 \multiply\drawingwd by\xscale
  \divide\drawinght by1000 \multiply\drawinght by\xscale
  \global\divide\pscm by 1000
  \global\multiply\pscm by\xscale
  \global\setbox\drawingBox=\hbox to 0pt{\kern\psxoffset\vbox to 0pt{%
     \kern-\psyoffset
     \PSspeci@l{\PSfilename}{\the\xscale}%
     \vss}\hss\ps@nnotation}%
  \advance\pswdincr by \drawingwd
  \advance\pshtincr by \drawinght
  \global\wd\drawingBox=\the\pswdincr
  \global\ht\drawingBox=\the\pshtincr
  \global\drawingwd=\pswdincr
  \global\drawinght=\pshtincr
  \baselineskip=0pt
  \copy\drawingBox
  \global\psxoffset=0pt
  \global\psyoffset=0pt
  \global\pswdincr=0pt
  \global\pshtincr=0pt % These are local to one figure
  \global\pscm=1cm
}}%
%
%  \psbox{PSfilename} makes a TeX box having the minimal size to
%      enclose the picture
\def\psbox#1{\psboxscaled{1000}{#1}}%
%------------------------------------------------------
%  \joinfiles file1, file2, ...n \into joinedfilename .
%     makes one file out of many
%  \splitfile joinedfilename
%     the opposite
\newif\ifn@teof\n@teoftrue
\newif\ifc@ntrolline
\newif\ifmatch
\newread\j@insplitin
\newwrite\j@insplitout
\newwrite\psbj@inaux
\immediate\openout\psbj@inaux=psbjoin.aux
\immediate\write\psbj@inaux{\string\joinfiles}%
\immediate\write\psbj@inaux{\jobname,}%
%
% INPUT REDEFINITION
%
% works if #1 is a single character
\def\toother#1{\ifcat\relax#1\else\expandafter%
  \toother@ux\meaning#1\endtoother@ux\fi}%
\def\toother@ux#1 #2#3\endtoother@ux{\def\tmp{#3}%
  \ifx\tmp\@mpty\def\tmp{#2}\let\next=\relax%
  \else\def\next{\toother@ux#2#3\endtoother@ux}\fi%
\next}%
%
% \readfilename defs:
%
\let\readfilenamehook=\relax
\def\re@d{\expandafter\re@daux}% spares typing 10 \expandafter's...
\def\re@daux{\futurelet\nextchar\stopre@dtest}%
\def\re@dnext{\xdef\lastreadfilename{\lastreadfilename\nextchar}%
  \afterassignment\re@d\let\nextchar}%
\def\stopre@d{\egroup\readfilenamehook}%
\def\stopre@dtest{%
  \ifcat\nextchar\relax\let\nextread\stopre@d
  \else
    \ifcat\nextchar\space\def\nextread{%
      \afterassignment\stopre@d\chardef\nextchar=`}%
    \else\let\nextread=\re@dnext
      \toother\nextchar
      \edef\nextchar{\tmp}%
    \fi
  \fi\nextread}%
\def\readfilename{\bgroup%
  \let\\=\backslashother \let\%=\percentother \let\~=\tildeother
  \let\#=\sharpother \xdef\lastreadfilename{}%
  \re@d}%
%
% redefines \input using \readfilename
%
\xdef\GlobalInputList{\jobname}%
\def\psnewinput{%
  \def\readfilenamehook{% each entry in \GlobalInputList should be unique
    \if\matchexpin{\GlobalInputList}{, \lastreadfilename}%
    \else\xdef\GlobalInputList{\GlobalInputList, \lastreadfilename}%
      \immediate\write\psbj@inaux{\lastreadfilename,}%
    \fi%
    \ps@ldinput\lastreadfilename\relax%
    \let\readfilenamehook=\relax%
  }\readfilename%
}%
\expandafter\ifx\csname @@input\endcsname\relax    % then Plain
  \immediate\let\ps@ldinput=\input\def\input{\psnewinput}%
\else
  \immediate\let\ps@ldinput=\@@input
  \def\@@input{\psnewinput}%
\fi%
%
\def\nowarnopenout{%
 \def\warnopenout##1##2{%
   \readfilename##2\relax
   \message{\lastreadfilename}%
   \immediate\openout##1=\lastreadfilename\relax}}%
\def\warnopenout#1#2{%
 \readfilename#2\relax
 \def\t@mp{TrashMe,psbjoin.aux,psbjoint.tex,}\uncatcode\t@mp
 \if\matchexpin{\t@mp}{\lastreadfilename,}%
 \else
   \immediate\openin\pst@mpin=\lastreadfilename\relax
   \ifeof\pst@mpin
     \else
     \errhelp{If the content of this file is so precious to you, abort (ie
press x or e) and rename it before retrying.}%
     \errmessage{I'm just about to replace your file named \lastreadfilename}%
   \fi
   \immediate\closein\pst@mpin
 \fi
 \message{\lastreadfilename}%
 \immediate\openout#1=\lastreadfilename\relax}%
% % will have an unusual catcode below; use * instead
%\vbox
{\catcode`\%=12\catcode`\*=14
\gdef\splitfile#1{*
 \readfilename#1\relax
 \immediate\openin\j@insplitin=\lastreadfilename\relax
 \ifeof\j@insplitin
   \message{! I couldn't find and split \lastreadfilename!}*
 \else
   \immediate\openout\j@insplitout=TrashMe
   \message{< Splitting \lastreadfilename\space into}*
   \loop
     \ifeof\j@insplitin
       \immediate\closein\j@insplitin\n@teoffalse
     \else
       \n@teoftrue
       \executeinspecs{\global\read\j@insplitin to\spl@tinline\expandafter
         \ch@ckbeginnewfile\spl@tinline%Beginning-Of-File-Named:%\endcheck}*
       \ifc@ntrolline
       \else
         \toks0=\expandafter{\spl@tinline}*
         \immediate\write\j@insplitout{\the\toks0}*
       \fi
     \fi
   \ifn@teof\repeat
   \immediate\closeout\j@insplitout
 \fi\message{>}*
}*
\gdef\ch@ckbeginnewfile#1%Beginning-Of-File-Named:#2%#3\endcheck{*
 \def\t@mp{#1}*
 \ifx\@mpty\t@mp
   \def\t@mp{#3}*
   \ifx\@mpty\t@mp
     \global\c@ntrollinefalse
   \else
     \immediate\closeout\j@insplitout
     \warnopenout\j@insplitout{#2}*
     \global\c@ntrollinetrue
   \fi
 \else
   \global\c@ntrollinefalse
 \fi}*
\gdef\joinfiles#1\into#2{*
 \message{< Joining following files into}*
 \warnopenout\j@insplitout{#2}*
 \message{:}*
 {*
 \edef\w@##1{\immediate\write\j@insplitout{##1}}*
\w@{% This collection of files was produced with CERN psbox package}*
\w@{% To decompose and tex it:}*
\w@{%-save this with a filename CONTAINING ONLY LETTERS and a .TEX}*
\w@{% extension (say, JOINTFIL.TEX), in some uncrowded directory;}*
\w@{%-make sure you can \string\input\space psbox.tex (version>=1.3);}*
\w@{%  (else ftp cs.nyu.edu(=128.122.140.24):pub/TeX/psbox/, then get}*
\w@{%  and tex the file psboxall.tex; more info in psbREAD.ME)}*
\w@{%-tex JOINTFIL.TEX using Plain, or LaTeX, or whatever is needed by}*
\w@{%  the first file in the joining (after splitting JOINTFIL.TEX into}*
\w@{%  it's constituents, TeX will try to process it as it stands).}*
\w@{\string\input\space psbox.tex}*
\w@{\string\splitfile{\string\jobname}}*
\w@{\string\let\string\autojoin=\string\relax}*
}*
 \expandafter\tre@tfilelist#1, \endtre@t
 \immediate\closeout\j@insplitout
 \message{>}*
}*
\gdef\tre@tfilelist#1, #2\endtre@t{*
 \readfilename#1\relax
 \ifx\@mpty\lastreadfilename
 \else
   \immediate\openin\j@insplitin=\lastreadfilename\relax
   \ifeof\j@insplitin
     \errmessage{I couldn't find file \lastreadfilename}*
   \else
     \message{\lastreadfilename}*
     \immediate\write\j@insplitout{%Beginning-Of-File-Named:\lastreadfilename}*
     \executeinspecs{\global\read\j@insplitin to\oldj@ininline}*
     \loop
       \ifeof\j@insplitin\immediate\closein\j@insplitin\n@teoffalse
       \else\n@teoftrue
         \executeinspecs{\global\read\j@insplitin to\j@ininline}*
         \toks0=\expandafter{\oldj@ininline}*
         \let\oldj@ininline=\j@ininline
         \immediate\write\j@insplitout{\the\toks0}*
       \fi
     \ifn@teof
     \repeat
   \immediate\closein\j@insplitin
   \fi
   \tre@tfilelist#2, \endtre@t
 \fi}*
}%
% To be put at the end of a file, for making a tar-like file containing
%   everything it used.
\def\autojoin{%
 \immediate\write\psbj@inaux{\string\into{psbjoint.tex}}%
 \immediate\closeout\psbj@inaux
 \expandafter\joinfiles\GlobalInputList\into{psbjoint.tex}%
}%
%----------------------------------------------------------------
%  Annotations & Captions etc...
%
%
% \centinsert{anybox} is just a centered \midinsert, but is included as
%    people barely use the original inserts from TeX.
%
\def\centinsert#1{\midinsert\line{\hss#1\hss}\endinsert}%
\def\psannotate#1#2{\vbox{%
  \def\ps@nnotation{#2\global\let\ps@nnotation=\relax}#1}}%
\def\pscaption#1#2{\vbox{%
   \setbox\drawingBox=#1
   \copy\drawingBox
   \vskip\baselineskip
   \vbox{\hsize=\wd\drawingBox\setbox0=\hbox{#2}%
     \ifdim\wd0>\hsize
       \noindent\unhbox0\tolerance=5000
    \else\centerline{\box0}%
    \fi
}}}%
% for compatibility with older versions, but \psfig is a bad name!
%\def\psfig#1#2#3{\pscaption{\psannotate{#1}{#2}}{#3}}
%\def\psfigurebox#1#2#3{\pscaption{\psannotate{\psbox{#1}}{#2}}{#3}}
%
% \at(#1;#2)#3 puts #3 at #1-higher and #2-right of the current
%    position without moving it (to be used in annotations).
\def\at(#1;#2)#3{\setbox0=\hbox{#3}\ht0=0pt\dp0=0pt
  \rlap{\kern#1\vbox to0pt{\kern-#2\box0\vss}}}%
%
% \gridfill(ht;wd) makes a 1cm*1cm grid of ht by wd whose lower-left
%   corner is the current point
\newdimen\gridht \newdimen\gridwd
\def\gridfill(#1;#2){%
  \setbox0=\hbox to 1\pscm
  {\vrule height1\pscm width.4pt\leaders\hrule\hfill}%
  \gridht=#1
  \divide\gridht by \ht0
  \multiply\gridht by \ht0
  \gridwd=#2
  \divide\gridwd by \wd0
  \multiply\gridwd by \wd0
  \advance \gridwd by \wd0
  \vbox to \gridht{\leaders\hbox to\gridwd{\leaders\box0\hfill}\vfill}}%
%
% Useful to measure where to put annotations
\def\fillinggrid{\at(0cm;0cm){\vbox{%
  \gridfill(\drawinght;\drawingwd)}}}%
%
% \textleftof\anybox: Sample text\endtext
%   inserts "Sample text" on the left of \anybox ie \vbox, \psbox.
%   \textrightof is the symmetric (not documented, too uggly)
% Welcome any suggestion about clean wraparound macros from
%   TeXhackers reading this
%
\def\textleftof#1:{%
  \setbox1=#1
  \setbox0=\vbox\bgroup
    \advance\hsize by -\wd1 \advance\hsize by -2em}%
\def\textrightof#1:{%
  \setbox0=#1
  \setbox1=\vbox\bgroup
    \advance\hsize by -\wd0 \advance\hsize by -2em}%
\def\endtext{%
  \egroup
  \hbox to \hsize{\valign{\vfil##\vfil\cr%
\box0\cr%
\noalign{\hss}\box1\cr}}}%
%
% \frameit{\thick}{\skip}{\anybox}
%    draws with thickness \thick a box around \anybox, leaving \skip of
%    blank around it. eg \frameit{0.5pt}{1pt}{\hbox{hello}}
% \boxit{\anybox} is a shortcut.
\def\frameit#1#2#3{\hbox{\vrule width#1\vbox{%
  \hrule height#1\vskip#2\hbox{\hskip#2\vbox{#3}\hskip#2}%
        \vskip#2\hrule height#1}\vrule width#1}}%
\def\boxit#1{\frameit{0.4pt}{0pt}{#1}}%
%
%
\catcode`\@=12 % cs containing @ are unreachable
%
% CUSTOMIZE YOUR DEFAULT DRIVER:
%    Uncomment the line corresponding to your TeX system:
%\psfortextures%     For TeXtures on the Macintosh
%\psforoztex   %     For OzTeX shareware on the Macintosh
%\psfordvitops %     For the DVItoPS converter for TeX on IBM mainframes
 \psfordvips   %     For DVIPS converter on VAX and UNIX
%\psfordvitps  %     For dvitps from TeXPS package under UNIX
%\psfordvialw  %     For dvialw, UNIX public domain
%\psonlyboxes  %     Blank Boxes (when all else fails).

astro-ph0204511.extracted_bib
\begin{thebibliography}{}
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\end{thebibliography}