Supernova neutrino challenges
P. de Groot\address[MCSD]{Mathematics and Computer Science Section, % Elsevier Science B.V.,
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astro-ph0502232.tex
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\title{Supernova neutrino challenges}

%\author{P. de Groot\address[MCSD]{Mathematics and Computer Science Section, 
%        Elsevier Science B.V., \\ 
%        P.O. Box 103, 1000 AC Amsterdam, The Netherlands}%
%        \thanks{Footnotes should appear on the first page only to
%                indicate your present address (if different from your
%                normal address), research grant, sponsoring agency, etc.
%                These are obtained with the {\tt\ttbs thanks} command.},
%        R. de Maas\addressmark\thanks{For following authors with the same
%                address use the {\tt\ttbs addressmark} command.},
%        X.-Y. Wang\address{Economics Department, University of Winchester, \\
%        2 Finch Road, Winchester, Hampshire P3L T19, United Kingdom}
%        and
%        A. Sheffield\addressmark[MCSD]\thanks{To reuse an addressmark
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\author{C. Y. Cardall\address{Physics Division, Oak Ridge National Laboratory, \\
      Oak Ridge, TN 37831-6354, United States of America}%
      \address{Department of Physics and Astronomy, University of Tennessee, \\
	Knoxville, TN 37996-1200, United States of America}%
        \thanks{This work was supported 
by  Scientific Discovery Through
Advanced Computing (SciDAC), a program of the Office of Science of the U.S. Department of Energy (DoE); and by Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the DoE under contract DE-AC05-00OR22725.}}
       
\begin{document}

%\begin{abstract}
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\begin{abstract}
%Neutrinos associated with core-collapse supernovae present ongoing observational,
%theoretical, and computational challenges. 
%A principal challenge is the computational difficulty of six-dimensional neutrino radiation hydrodynamics; while this has provoked a long history of uncertainty in the explosion mechanism, recent work highlighting low-mode convection and a newly-recognized  instability in spherical accretion shocks points toward a possible resolution. As part of its goal of elucidating the explosion mechanism, the Treacle Supernova Initiative is committed to meeting the full complexity of the computational challenge. The understanding of supernova neutrino emission gained in detailed simulations provides a potential basis for learning about two major remaining unknowns surrounding neutrino flavor mixing: the value of the mixing angle $\theta_{13}$, and distinguishing between ``normal'' and ``inverted'' mass hierarchies.
A principal `supernova neutrino challenge' is the computational difficulty of six-dimensional neutrino radiation hydrodynamics. The variety of resulting approximations has provoked a long history of uncertainty in the core-collapse supernova explosion mechanism, but recent work highlighting low-mode convection and a newly-recognized  instability in spherical accretion shocks may signal (yet another) resolution. As part of its goal of elucidating the explosion mechanism, the Terascale Supernova Initiative is committed to meeting the full complexity of the computational challenge. The understanding of supernova neutrino emission gained in detailed simulations provides a potential basis for learning about two major remaining unknowns in neutrino flavor mixing: the value of the mixing angle $\theta_{13}$, and distinguishing between ``normal'' and ``inverted'' mass hierarchies.
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% typeset front matter (including abstract)
\maketitle

%\section{THE CHALLENGES OF CORE-COLLAPSE SUPERNOVAE}
\section{CORE-COLLAPSE SUPERNOVAE}

%Supernovae have been challenging us for centuries. Their very existence helped overturn worldviews.  Their explosion mechanisms and remnants involve all four fundamental forces, and many (if not most) branches of physics. 
%A cornucopia of electromagnetic observables continues to provide intriguing puzzles, and yields some clues regarding the violent proceedings of a massive star's death. 
%But direct observational penetration of the secrets of neutron star birth and initiation of the explosive ejection of the stellar envelope demands extraordinary efforts aimed at the detection of gravitational waves and neutrinos, the only messengers carrying direct information from the extreme conditions of a newly-collapsed stellar core. 
%And the associated theoretical penetration---required for both the prediction and interpretation of expected gravitational wave and neutrino signals---comprises
%algorithmic and computational challenges that will challenge computational physicists and tax state-of-the-art supercomputers for many years.

%In western civilization, supernovae played a role in changing prevailing notions of the universe in at least two eras. Remarkably, of the handful of supernovae in our Milky Way Galaxy recorded by humanity, two were observed by Tycho (1572) and Kepler (1604). Tycho's detailed observations established that the `new and never previously seen star' of 1572---and also another transient celestial phenomenon, a comet of 1577---were beyond the moon's orbit, `new phenomena in the ethereal world,' contributing to the overthrow of the Aristotelian worldview that included immutable heavens. In modern times, supernovae figured in the debate over whether 
%the spiral nebulae 
%are separate galaxies, each an `island universe' comparable to our Milky Way. It was recognized 
%that the `novae' or `new stars' seen in these nebulae would have to be much more luminous than typical novae occuring in our galaxy. 
%The phrases 
%``giant novae,'' novae of ``impossibly great absolute magnitudes,'' 
%``exceptional novae,'' and the German term 
%``Hauptnovae'' or ``chief novae'' were used during the 
%1920s \cite{osterbrock01}.
%In a review article, Zwicky explained that it was deduced that `supernovae' 
%were about a thousand times as luminous as `common novae,' and 
%claimed that ``Baade and I first introduced the term `supernovae' in seminars and in a lecture course on astrophysics at the California Institute of Technology in 1931'' \cite{zwicky40}.

%Supernovae are classified by astronomers into two broad classes based on their optical spectra \cite{filippenko97}.
%These classes are `Type I,' which have no hydrogen features, and 
%`Type II,' which have obvious hydrogen features. These types have further 
%subcategories, depending on the presence or absence of silicon and 
%helium features in Type I, and the presence or absence of narrow 
%hydrogen features in the case of Type II. In particular, 
%supernovae of Type Ia exhibit strong silicon lines, 
%those of Type Ib have helium lines, and those of Type Ic do not have 
%either of these. Astronomers have also identified a number of distinct
%characteristics in supernova light curves
%(total luminosity as a function of time). 

%There are two basic physical mechanisms for supernovae, but these do not line up cleanly with the observational categories of Type I and Type II. Type Ia supernovae are caused by accretion of matter from a companion star onto a white dwarf, which induces a thermonuclear runaway that consumes the entire white dwarf.
%Supernovae of Type Ib, Ic, and II are produced by a totally different mechanism: the catastropic collapse of the core of a massive star. The observational distinctions of presence or absence of hydrogen or helium turn out to be unrelated to the mechanism; they depend on whether the outer hydrogen and helium layers of the star---which have nothing to do with the collapsing core---have been lost to winds or accretion onto a binary companion during stellar evolution. Of the two
%physical mechanisms, core-collapse supernovae are the focus of the
%present discussion.

%I now consider the core-collapse supernova process in more detail.
Shortly after the discovery of the neutron in the early 1930s, Baade and Zwicky declared, 
``With all reserve we advance the view that supernovae represent the
transitions from ordinary stars to {\em neutron stars,} which in their final
stages consist of extremely closely packed neutrons'' \cite{baade34}. 
This turned out to be true, at least for some `core-collapse' supernovae (those of Type Ib/Ic/II); a black hole is another possible outcome. 
%(Type Ia supernovae, which are caused by the thermonuclear detonation or
%deflagration of a white dwarf star, are interesting in their own right and useful standardizable candles for observational cosmology, but are not expected to be significant sources of neutrinos.)
The dominant fleshing-out of the core collapse process in the last two decades
%\footnote{See for example Ref. \cite{burrows90} for some information on earlier views of the mechanism.} 
has been
the delayed neutrino-driven explosion mechanism
\cite{wilson85,bethe85}.

A core-collapse supernova results from the evolution of a massive star.
For most of their existence, stars burn hydrogen into helium. 
In stars at least eight times as massive as the Sun ($8\ M_\odot$), 
temperatures and densities become sufficiently high to burn 
through carbon to oxygen, neon, and magnesium; in stars of at least $\sim 10\ M_\odot$, burning continues through silicon to iron group elements. 
The iron group nuclei are the most tightly bound, and here burning in 
the core ceases. 

The iron core---supported by electron 
degeneracy pressure instead of gas thermal pressure, because of cooling
by neutrino emission from carbon burning onwards---eventually 
becomes unstable. Its inner portion undergoes homologous collapse
(velocity proportional to radius), and the outer portion collapses 
supersonically. 
Electron capture on nuclei is one instability leading to collapse, and 
this process continues throughout collapse, producing neutrinos.
These neutrinos escape freely
until densities %and temperatures 
in the collapsing core
become so high that even neutrinos are 
trapped. 

Collapse is halted soon after the matter exceeds nuclear density; 
at this point (``bounce''), a shock wave forms at the boundary between the homologous
and supersonically collapsing regions. The shock begins to move out,
but after the shock passes
some distance beyond the surface of the newly-born neutron star, 
it stalls as energy 
is lost to neutrino emission and endothermic dissociation of heavy 
nuclei falling through the shock.

It is natural to consider neutrino heating as a mechanism for
shock revival, because neutrinos dominate the energetics of
the post-bounce evolution.
Initially, the nascent neutron star is a hot thermal bath of dense nuclear matter, 
electron/positron pairs, photons, and neutrinos, containing most of 
the gravitational potential energy released during core collapse. 
Neutrinos, having the weakest interactions, are the most efficient 
means of cooling; they diffuse outward on a time scale of seconds, 
%towards a semi-transparent region near the surface of the neutron star, 
and eventually escape with about 99\% of the released gravitational energy.

%Whatever the proximate mechanism of explosion turns out to be, 
%the explosion accounts for only about 1\% of energy budget of the system; hence
%all contributions to the energy budget should be accurately tracked.
Because neutrinos dominate the energetics of the system, 
a detailed understanding of their evolution will be integral to 
%any
%detailed and 
definitive accounts of the supernova process.
If we want to understand the explosion---which accounts for only about 1\% of 
the energy budget of the system---we should carefully account for the
neutrinos' much larger contribution to the energy budget.

What sort of computation is needed to follow the neutrinos' evolution?
 Deep inside the newly-born neutron star, 
 the neutrinos and the fluid are tightly coupled (nearly in equilibrium);  but as 
 %the 
 neutrinos are transported from inside the neutron star, they go from a nearly isotropic diffusive regime to strongly forward-peaked free-streaming. Heating 
 %of material 
 behind the shock occurs precisely in 
this transition region, and modeling this process accurately requires tracking both the energy and angle dependence of the neutrino distribution functions at every point
in space. 

A full treatment of this six-dimensional neutrino radiation hydrodynamics
problem is a major challenge, 
%remaining 
too costly for 
%currently available 
contemporary
computational resources. While much has been 
learned over the years through simulation of model systems of reduced dimensionality, there is as yet no robust confirmation of the delayed neutrino-driven scenario described above (see Sec. \ref{sec:history}).

Of interest are recent detections of a handful of unusually energetic Type Ib/c supernovae (often called `hypernovae') in connection with gamma-ray bursts. %pose additional challenges to theory and observation. 
%Prominent examples of this supernova/gamma-ray burst connection include SN1998bw/GRB980425 \cite{galama98,iwamoto98}, SN2002lt/GRB021211 \cite{dellaValle03}, SN2003dh/GRB030329 \cite{hjorth03,stanek03}, and SN2003lw/GRB031203 \cite{thomsen04,cobb04,malesani04,galYam04}; there are probably many others (see, for example, Ref. \cite{zeh04}). Like many gamma-ray bursts without direct evidence for a supernova connection, GRB030329 has evidence of a jet; GRB980425 and GRB031203 do not, and are also underluminous gamma-ray bursts (but still unusually energetic Type Ib/c supernovae) \cite{ghirlanda04,soderberg04}. 
Some show evidence for jets, and some do not. 
Determining the relative rates of jet-like hypernovae, non--jet-like hypernovae, and `normal' supernovae,
% is an important observational task, and determining 
and the possible associated variety of mechanisms, are %is an interesting theoretical challenge.
important challenges.

In summary, the details of how the stalled shock is revived
sufficiently to continue plowing through the outer layers of the
progenitor star are unclear. In normal supernovae, it may well be that some combination of neutrino heating 
%of material 
behind the shock, convection, and instability of the spherical
accretion shock leads to the explosion (see Sec. \ref{sec:history}). It is tempting to think that rotation 
%(for example, Ref. \cite{thompson04}) 
and magnetic fields 
%(for example, Ref. \cite{wheeler04}) 
may play a more significant role in the rare jet-like hypernovae, perhaps giving birth to `magnetars,' the class of neutron stars with unusually large magnetic fields. %(Observations of two nearby supernova remnants may suggest that rotation and magnetic fields also operate in normal supernovae, perhaps subdominantly \cite{burrows04b}).


\section{HISTORY OF NEUTRINO RADIATION HYDRODYNAMICS}
\label{sec:history}

From the description of the core-collapse supernova process in the
previous section, several key aspects of physics that a simulation must 
address can be identified: gravity, fluid dynamics (including equation of state and composition), neutrino transport and interactions, and perhaps magnetic fields. Ideally each of these aspects would be implemented in general relativity. 

Here the last two decades' progress on just one of these simulation aspects is sketched: the high dimensionality (three space and three momentum space dimensions---not to mention time dependence) of neutrino radiation hydrodynamics (see Table 1). The development of this aspect of the simulations is intertwined with important advances in the field, but of course does not represent every insight relevant to the explosion mechanism obtained via simulation or otherwise. 
%Advances in the treatment of neutrino interactions are not discussed here; see for example
%Ref. \cite{burrows04a}.

\begin{table*}
\caption{Selected neutrino radiation hydrodynamics milestones in stellar collapse  simulations studying the long-term fate of the shock.
%(not intended as a comprehensive compilation of insights into the supernova phenomenon, via simulation or otherwise). 
The ``Yes'' entries in the  ``Explosion'' column are all marked with an asterisk as a reminder that questions about the simulations---described in the main text---have prevented a consensus about the explosion mechanism. 
``Total dimensions'' is the average of ``Fluid space dimensions'' and  ``$\nu$ space dimensions,'' added to ``$\nu$ momentum dimensions.''
The abbreviation ``N'' stands for `Newtonian,' while ``PN''---for `Post-Newtonian'---stands for some attempt at inclusion of general relativistic effects, and ``GR'' denotes full relativity. A space dimensionality in quotes---like ``1.5''---denotes an attempt at modeling higher dimensional effects within the context of a lower dimensional simulation. For the fluid, this is a mixing-length prescription in the neutron star (``NS'') or the heating region (``HR'') behind the stalled shock. For neutrino transport, it indicates one of two approaches: multidimensional diffusion in regions with strong radiation/fluid coupling, matched with a spherically symmetric `light bulb' approximation in weakly coupled regions (``thick/thin''); or the (mostly) independent application of a spherically symmetric formalism/algorithm to separate spatial angle bins (``ray-by-ray'').
%In the ``Fluid space dimensions'' column, ``Post-Newtonian'' refers to a gravitational potential enhanced by general relativistic effects, ``GR'' indicates general relativity, and ``1.5'' denotes a mixing-length representation of neutron star convection in the neutron star (``NS'') and the heating region (``HR'') behind the stalled shock. 
}
\begin{tabular}{@{}lcccccc}
\hline
Group & Year & Explosion & Total  & Fluid space  & $\nu$ space & $\nu$ momentum
	     \\
	     &       & & dimensions    & dimensions & dimensions & space dimensions \\
\hline
Lawrence & 1982 & Yes$^*$ & 2 & 1  & 1 & 1    \\
 Livermore \cite{bowers82,wilson85,bethe85} & & & & (PN)  & &(${\cal O}(v/c)$)  \\
\hline
Lawrence & 1985 & Yes$^*$ & ``2.25'' & ``1.5'' NS  & 1 & 1  \\
 Livermore \cite{mayle85,wilson88} & & & & (PN)  & &(${\cal O}(v/c)$)  \\
\hline
Florida & 1987 & No & 2 & 1  & 1 & 1  \\
Atlantic \cite{bruenn85,bruenn87,bruenn91,bruenn93}  & & & & (GR)  & &(${\cal O}(v/c)$) \\
\hline
Lawrence & 1989 & Yes$^*$ & ``2.25'' & ``1.5'' NS+HR  & 1 & 1   \\
 Livermore \cite{mayle90,mayle91,wilson93} & & & & (GR)  & & (GR) \\
\hline
Lawrence & 1992 & Yes$^*$ & 2 & 2 HR  & 2 & 0  \\
 Livermore \cite{miller93} & & & & (N)  & &(N) \\
\hline
Los  Alamos & 1993  & Yes$^*$ & ``1.75'' & 2  & ``1.5'' & 0 \\
\cite{herant94}   & & & & (N)  & thick/thin &(PN) \\
Arizona & 1994 & Yes$^*$ & ``1.75'' & 2  & ``1.5'' & 0  \\
\cite{burrows95}  &  & & & (N)  & ray-by-ray & (N) \\
\hline
Florida & 1994  & No & ``2.25'' & ``1.5'' NS & 1 & 1 \\
Atlantic \cite{bruenn94,bruenn95} & & & & (GR)  & &(${\cal O}(v/c)$) \\
\hline
Oak Ridge & 1996 & No & ``2.5'' & 2 & 1 & 1  \\
\cite{mezzacappa98a,mezzacappa98b} & & & & (N)  & &(${\cal O}(v/c)$) \\
\hline
Max Planck & 2000 & No, Yes$^*$ & 3 & 1 & 1 & 2  \\
\cite{rampp00,rampp02,kitaura03,janka04b} & &  (ONeMg)& & (N)  & &(${\cal O}(v/c)$) \\
Oak Ridge & 2000 & No & 3 & 1 & 1 & 2  \\
\cite{mezzacappa93b,mezzacappa93c,mezzacappa99,liebendoerfer00,mezzacappa01} & & & & (N)  & &(${\cal O}(v/c)$) \\
Arizona & 2002 & No & 3 & 1 & 1 & 2  \\
\cite{burrows00,thompson03} & & & & (N)  & &(${\cal O}(v/c)$) \\
\hline
Oak Ridge & 2000  & No & 3 & 1 & 1 & 2 \\
\cite{mezzacappa93b,mezzacappa93c,mezzacappa99,liebendoerfer01a,liebendoerfer02,liebendoerfer04} & & & & (GR)  & &(GR) \\
\hline
Los  Alamos & 2002 & Yes$^*$ & ``2.5'' & 3  & ``2'' & 0  \\
\cite{herant94,fryer02}  &  & & & (N)  & thick/thin &(PN) \\
\hline
Max Planck & 2003 & No, Yes$^*$ & ``3.75'' & 2 & ``1.5'' & 2 (${\cal O}(v/c)$,  \\
\cite{rampp02,buras03,janka02,janka04a,janka04b} & & (180$^{\mathrm{o}}$) & & (PN)  & ray-by-ray & PN) \\
\hline
\end{tabular}\\[2pt]
\label{history}
\end{table*}

I pick up the story in 1982, when simulations showing the stalled shock reenergized by neutrino heating on a time scale of hundreds of milliseconds were first performed \cite{wilson85}. This was initially achieved in a simulation with a total of 2 dimensions (spherical symmetry, and energy-dependent neutrino transport). But 
%these simulations required significant rezoning, possibly attended by nontrivial numerical error \cite{wilson85}; and further, 
with the introduction of full general relativity and a correction in an outer boundary condition \cite{mayle90}, it became clear that these models would not explode without a mock-up of a doubly-diffusive fluid instability in the newly-born neutron star that serves to boost neutrino luminosities \cite{mayle90,mayle91,wilson93,miller93}---a simulation of effective total dimensionality ``2.5'' (see Table 1). That the necessary conditions exist for this particular instability to operate has been disputed \cite{bruenn95,bruenn96,bruenn04}; and though related phenomena may operate \cite{bruenn04}, more recent simulations with energy-dependent neutrino transport and true two-dimensional fluid dynamics indicate that fluid motions are either suppressed by neutrino transport \cite{mezzacappa98a} or have little effect on neutrino luminosities and supernova dynamics \cite{buras03,janka04a}.

Recognizing that the profiles obtained in spherical symmetry implied convective instabilities, and that observations of supernova 1987A also pointed to asphericities, several groups explored fluid motions in two spatial dimensions in the supernova environment in the 1990s. %In two spatial dimensions, 
%computational limitations required approximations that
%simplified the neutrino
%transport. 

One class of simplifications allowed for neutrino transport in ``1.5'' or 2 spatial dimensions, but with
neutrino energy and angle dependence integrated out, 
reducing a five dimensional problem to  ``1.75'' or 2 effective total dimensions (see Table 1) \cite{miller93,herant94,burrows95}.
%These simulations showed convection in two regions. First, loss of electron neutrinos from the outer layers of the neutron star caused composition gradients that 
%could drive convection, which boosted neutrino luminosities by bringing hotter material to the surface. Second, heating decreased further from the neutron star surface, giving rise to a negative entropy gradient. The resulting convection 
%increased the efficiency of neutrino heating by delivering heated material to the region just behind the shock.
%These simulations exhibited explosions, suggesting that the enhancements 
%in neutrino heating behind the shock resulting from convection provided a
%robust explosion mechanism. 
These simulations exhibited explosions, and elucidated an undeniably important physical effect: a negative entropy gradient behind the stalled shock results in convection that increases the efficiency of heating by neutrinos.
However, in the scheme of Table 1, the inability to track the neutrino energy dependence in these simulations could be viewed as a minor step backwards in effective total dimensionality. The energy dependence of neutrino interactions has the important effect of enhancing core deleptonization, which makes explosions more difficult \cite{bruenn85,bruenn89a,bruenn89b}; this raised the question of whether the exploding models of the early- and mid-1990s were too optimistic. 
%More recent simulations in three spatial
%dimensions with this same
%approximate treatment of neutrino transport showed similar outcomes
%\cite{fryer02}. 

This concern about the lack of neutrino energy dependence received some support from a simulation in the late 1990s involving 
%A different simplification of neutrino transport employed in the 1990s
%was the imposition of energy-dependent
%neutrino distributions from spherically symmetric simulations
%onto fluid dynamics computations in two spatial dimensions
%\cite{mezz98b}. 
a different simplification of neutrino transport:
the imposition of energy-dependent
neutrino distributions from spherically symmetric simulations
onto fluid dynamics in two spatial dimensions
\cite{mezzacappa98b}. 
Unlike the %multidimensional 
simulations
discussed above, these did not 
%exhibit explosions
explode, casting doubt
upon claims that convection-aided
neutrino heating constituted a robust explosion mechanism.

The nagging qualitative difference between spatially multidimensional
simulations with different neutrino transport approximations 
motivated interest in the possible importance of even more complete neutrino
transport: Might the retention of both the energy
{\em and} angle dependence of the neutrino distributions improve the chances of explosion, as preliminary ``snapshot'' studies suggested \cite{messer98,burrows00}?
Of necessity, the first such simulations were performed in
spherical symmetry, which nevertheless represented an advance to a total dimensionality of 3 (see Table 1).
% (actually a three-dimensional problem, depending
%on one space and two momentum space variables). 
Results from
three different groups are in accord: Spherically symmetric models of iron core collapse 
do not explode, even with solid neutrino transport 
\cite{rampp00,mezzacappa01,thompson03} and general relativity \cite{liebendoerfer01a,liebendoerfer04}. Recently, however, it has been shown that the more modest oxygen/neon/magnesium cores of the lightest stars to undergo core collapse (8-10 M$_\odot$) may explode in spherical symmetry \cite{kitaura03,janka04b}.

The current state of the art in neutrino transport in supernova simulations determining the long-term fate of the shock has been achieved by one of the above groups (centered at the Max Planck Institute for Astrophysics in Garching), who deployed their spherically symmetric energy- and angle-dependent neutrino transport capability \cite{rampp02} along separate radial rays, with partial coupling between rays \cite{janka02}. Initial results---from axisymmetric simulations with a restricted angular domain---were negative with regards to explosions (in spite of the salutary effects of convection, and also rotation) \cite{buras03}, apparently supporting the results of Ref. \cite{mezzacappa98b}. 
An explosion was seen in one simulation \cite{janka03}
in which
certain terms in the neutrino transport equation corresponding to Doppler shifts
and angular aberration due to fluid motion were dropped; this simulation also yielded a neutron star mass and nucleosynthetic consequences in better agreement with observations than the ``successful'' explosion simulations of the 1990s \cite{herant94,burrows95}, arguably because of more accurate neutrino transport in the case of both observables. 
The continuing lesson
is that getting the details of the neutrino transport right makes a difference.

In addition to accurate neutrino transport, low-mode ($\ell = 1,2$) instabilities that can develop only in simulations allowing the full range of polar angles may make a subtle but decisive difference, as in an explosion recently reported by the Garching group \cite{janka04a,janka04b}. This achievement was presaged by earlier studies demonstrating the tendency for convective cells to merge to the lowest order allowed by the spatial domain \cite{herant92} and recognizing a new spherical accretion shock instability \cite{blondin03} (discovered independently in a different context in Ref. \cite{foglizzo02}). These global asymmetries may even be sufficient to account for observed asphericities that have often been attributed to rotation and/or magnetic fields. 

Surely every `Yes' entry in the explosion column of Table 1 has been hailed in its time as `the answer' (at least by some!), and as a community we cannot help hoping once again that these recent developments mark the turning of a corner; but important work remains to verify if this is the case. Several groups are committed to further efforts. For example, the Terascale Supernova Initiative (TSI, which includes authors of Ref. \cite{blondin03}) comprises efforts aimed at ``ray-by-ray'' simulations \cite{hix01} like those of the Garching group, as well as full spatially multdimensional neutrino transport, both with energy dependence only \cite{myra04} and with energy {\em and} angle dependence \cite{cardall04}. Delineation of the possible roles of rotation and magnetic fields are also being pursued by TSI. At least one other group is pursuing full spatially multidimensional neutrino transport \cite{livne04,walder04}.

%Livermore 1982: Explosion weak ($2-5 \times 10^{50}$ erg), substantial rezoning with attendant numerical error, post-Newtonian gravitational force inadequate, equation of state in heating region (helium vs. free nucleons), convectively unstable core.

%Explosions only seen with certain fluid mixing prescriptions, which are controversial.

%2D mixing-length calibration: \cite{miller93}.

%NES enhances deleptonization during collapse by (1) degrading neutrinos' energy so they can escape more easily, and (2) heating the matter, which increases the free proton fraction, increasing the electron capture (Bruenn 1985, 1989a,b).

%1D late-time models that don't explode: Cooperstein 1993, Herant et al. 1994

%Future work: abstracts by swesty a,b and hix

%\section{THE TERASCALE SUPERNOVA INITIATIVE}
%\label{sec:tsi}

\section{SUPERNOVA NEUTRINOS AND FLAVOR MIXING}

As one who is engaged in the long-term development of a new code to be used in supernova simulations---with results from this code not yet in hand---I have spent this opportunity discussing our field's response to the challenge of neutrino radiation hydrodynamics in core-collapse supernova simulations over the last two decades, together with many references. Hopefully this provides some understanding of the history of claims in our field, and gives an appreciation of the years of dedicated work by many individuals to advance the state of the art. But in closing, I should at least say something more directly tied to the topic of the conference! 

So how do these large-scale simulations relate to neutrino flavor mixing? At present, the simulations assume massless neutrinos, relying on the standard expectation that the effective mass from neutrino forward scattering off electrons suppresses flavor mixing in the high-density region where the explosion is launched.\footnote{In public talks (presenting analyses not yet published), G.~M. Fuller has argued that the nonlinear effects of neutrino-neutrino forward scattering might produce flavor-changing effects even at the high densities near the nascent neutron star. If this proves correct, it would take the ``supernova neutrino challenge'' already faced by collapse modelers to a whole new level.} Before reaching terrestrial detectors, however, neutrinos will pass through flavor-changing resonances at lower densities in the stellar envelope (and possibly also experience flavor-changing effects while traversing Earth before entering a detector). Hence collapse simulations provide neutrino spectra as input to studies that take these effects into account in determining possible signals in terrestrial neutrino detectors (see, for example, overviews in Refs. \cite{mirizzi05,raffelt05}). To the extent that generic energy- and time-dependent features of the signals can be motivated by the large-scale simulations, such studies provide a possible basis for learning---from neutrino detection of a future Galactic supernova---about two major remaining unknowns surrounding neutrino flavor mixing: the value of the mixing angle $\theta_{13}$, and distinguishing between ``normal'' and ``inverted'' mass hierarchies. Alternatively, to the extent that these neutrino mixing features are determined by terrestrial long-baseline neutrino experiments before the next Galactic supernova, neutrino signals will allow the details of supernova dynamics to be observed in real time. 

\def\aap{Astron. Astrophys. }
\def\aasma{Am. Astron. Soc. Meet. Abs. }
\def\apj{Astrophys. J. }
\def\apjl{Astrophys. J. Lett. }
\def\apjs{Astrophys. J. Supp. Ser. }
\def\araa{Annu. Rev. Astron. Astrophys. }
\def\baas{Bull. Am. Astron. Soc. }
\def\jcam{J. Comp. Appl. Math. }
\def\nat{Nature }
\def\npa{Nucl. Phys. A }
\def\pr{Phys. Rep. }
\def\prd{Phys. Rev. D }
\def\prl{Phys. Rev. Lett. }
\def\prv{Phys. Rev. }

%\bibliographystyle{elsart-num}
%\bibliography{bibliography}

\begin{thebibliography}{9}

\bibitem{baade34}
W.~{Baade}, F.~{Zwicky}, \prv 45 (1934) 138.

%\bibitem{burrows90}
%A.~{Burrows}, in: A.~G. {Petschek} (Ed.), Supernovae, Springer-Verlag, New
%  York, 1990, p. 143.

\bibitem{wilson85}
J.~R. {Wilson}, in: J.~M. Centrella, J.~M. LeBlanc, R.~L. Bowers (Eds.),
  Numerical Astrophysics, Jones and
  Bartlett, Boston, 1985, p. 422.

\bibitem{bethe85}
H.~A. {Bethe}, J.~R. {Wilson}, \apj 295 (1985) 14.

%\bibitem{galama98}
%T.~J. {Galama} et al., \nat 395 (1998) 670.

%\bibitem{iwamoto98}
%K.~{Iwamoto} et al., \nat 395 (1998) 672.

%\bibitem{dellaValle03}
%M.~{Della Valle} et al., \aap 406 (2003) L33.

%\bibitem{hjorth03}
%J.~{Hjorth} et al., \nat
%  423 (2003) 847.

%\bibitem{stanek03}
%K.~Z. {Stanek} et al., \apjl 591 (2003) L17.

%\bibitem{thomsen04}
%B.~{Thomsen} et al., \aap 419 (2004) L21.

%\bibitem{cobb04}
%B.~E. {Cobb} et al., \apjl 608 (2004) L93.

%\bibitem{malesani04}
%D.~{Malesani} et al., \apjl 609 (2004) L5.

%\bibitem{galYam04}
%A.~{Gal-Yam} et al., \apjl 609 (2004) L59.

%\bibitem{zeh04}
%A.~{Zeh}, S.~{Klose}, D.~H. {Hartmann}, \apj 609 (2004) 952.

%\bibitem{ghirlanda04}
%G.~{Ghirlanda}, G.~{Ghisellini}, D.~{Lazzati}, \apj 616 (2004) 331.

%\bibitem{soderberg04}
%A.~M. {Soderberg} et al., \nat 430 (2004) 648.

%\bibitem{thompson04}
%T.~A. Thompson, E.~Quataert, A.~Burrows, astro--ph/0403224.

%\bibitem{wheeler04}
%J.~C. Wheeler, S.~Akiyama, astro--ph/0412382.

%\bibitem{burrows04b}
%A.~Burrows, R.~Walder, C.~D. Ott, E.~Livne, astro--ph/0409035.

%\bibitem{burrows04a}
%A.~Burrows, S.~Reddy, T.~A. Thompson, \npa (2005) in press.

\bibitem{bowers82}
R.~L. {Bowers}, J.~R. {Wilson}, \apjs 50 (1982) 115.

\bibitem{mayle85}
R.~W. {Mayle}, Ph.D. thesis, University of California, Berkeley (1985).

\bibitem{wilson88}
J.~R. Wilson, R.~W. Mayle, \pr 163 (1988) 63.

\bibitem{bruenn85}
S.~W. {Bruenn}, \apjs 58 (1985) 771--841.

\bibitem{bruenn87}
S.~W. {Bruenn}, \prl 59 (1987) 938.

\bibitem{bruenn91}
S.~W. {Bruenn}, W.~C. {Haxton}, \apj 376 (1991) 678.

\bibitem{bruenn93}
S.~W. {Bruenn}, in: M.~W. {Guidry}, M.~R. {Strayer} (Eds.), Nuclear Physics in
  the Universe, Institute
  of Physics, Bristol, 1993, p. 31.

\bibitem{mayle90}
R.~W. {Mayle}, in: A.~G. {Petschek} (Ed.), Supernovae, Springer-Verlag, New
  York, 1990, pp. 267--289.

\bibitem{mayle91}
R.~W. {Mayle}, J.~R. {Wilson}, in: S.~E. {Woosley} (Ed.), Supernovae, Springer-Verlag, New York, 1991, p. 333.

\bibitem{wilson93}
J.~R. Wilson, R.~W. Mayle, \pr 227 (1993) 97.

\bibitem{miller93}
D.~S. {Miller}, J.~R. {Wilson}, R.~W. {Mayle}, \apj 415 (1993) 278.

\bibitem{herant94}
M.~{Herant} et al., \apj 435
  (1994) 339.

\bibitem{burrows95}
A.~{Burrows}, J.~{Hayes}, B.~A. {Fryxell}, \apj 450 (1995) 830.

\bibitem{bruenn94}
S.~W. {Bruenn}, A.~{Mezzacappa}, \apjl 433 (1994) L45.

\bibitem{bruenn95}
S.~W. {Bruenn}, A.~{Mezzacappa}, T.~{Dineva}, \pr 256 (1995) 69.

\bibitem{mezzacappa98a}
A.~{Mezzacappa} et al., \apj 493 (1998) 848.

\bibitem{mezzacappa98b}
A.~{Mezzacappa} et al., \apj 495 (1998) 911.

\bibitem{rampp00}
M.~{Rampp}, H.-T. {Janka}, \apjl 539 (2000) L33--L36.

\bibitem{rampp02}
M.~{Rampp}, H.-T. {Janka}, \aap 396 (2002) 361--392.

\bibitem{kitaura03}
F.~S. Kitaura~Joyanes, Ph.D. thesis, Technical University, Munich (2003).

\bibitem{janka04b}
H.-T. Janka et al.,
   astro--ph/0411347.

\bibitem{mezzacappa93b}
A.~{Mezzacappa}, S.~W. {Bruenn}, \apj 405 (1993) 669.

\bibitem{mezzacappa93c}
A.~{Mezzacappa}, S.~W. {Bruenn}, \apj 410 (1993) 740.

\bibitem{mezzacappa99}
A.~{Mezzacappa}, O.~E.~B. {Messer}, \jcam 109 (1999) 281.

\bibitem{liebendoerfer00}
M.~{Liebend{\" o}rfer}, Ph.D. thesis, University of Basel (2000).

\bibitem{mezzacappa01}
A.~{Mezzacappa} et al., \prl 86 (2001)
  1935.

\bibitem{burrows00}
A.~{Burrows}, T.~{Young}, P.~{Pinto}, R.~{Eastman}, T.~A. {Thompson}, \apj 539
  (2000) 865.

\bibitem{thompson03}
T.~A. {Thompson}, A.~{Burrows}, P.~A. {Pinto}, \apj 592 (2003) 434.

\bibitem{liebendoerfer01a}
M.~{Liebend{\" o}rfer} et al., \prd 63~(10) (2001) 103004.

\bibitem{liebendoerfer02}
M.~{Liebend{\" o}rfer}, S.~{Rosswog}, F.~{Thielemann}, \apjs 141 (2002)
  229.

\bibitem{liebendoerfer04}
M.~{Liebend{\" o}rfer} et al., \apjs 150 (2004) 263.

\bibitem{fryer02}
C.~L. {Fryer}, M.~S. {Warren}, \apjl 574 (2002) L65.

\bibitem{buras03}
R.~{Buras} et al., \prl
  90 (2003) 241101.

\bibitem{janka02}
H.~T. Janka et al., in: C.~L. Fryer (Ed.),
  Stellar Collapse, Kluwer, Dordrecht, 2004, p. 65.

\bibitem{janka04a}
H.-T. Janka et al., 
  astro--ph/0401461.

\bibitem{bruenn96}
S.~W. {Bruenn}, T.~{Dineva}, \apjl 458 (1996) L71.

\bibitem{bruenn04}
S.~W. Bruenn, E.~A. Raley, A.~Mezzacappa, astro--ph/0404099.

\bibitem{bruenn89a}
S.~W. {Bruenn}, \apj 340 (1989) 955.

\bibitem{bruenn89b}
S.~W. {Bruenn}, \apj 341 (1989) 385.

\bibitem{messer98}
O.~E.~B. {Messer} et al., \apj 507
  (1998) 353.

\bibitem{janka03}
H.~T. Janka, R.~Buras, M.~Rampp, \npa 718 (2003) 269.

\bibitem{herant92}
M.~{Herant}, W.~{Benz}, S.~{Colgate}, \apj 395 (1992) 642.

\bibitem{blondin03}
J.~M. {Blondin}, A.~{Mezzacappa}, C.~{DeMarino}, \apj 584 (2003) 971.

\bibitem{foglizzo02}
T.~{Foglizzo}, \aap 392 (2002) 353--368.

\bibitem{hix01}
W.~R. {Hix} et al., \baas 33 (2001) 1445.

\bibitem{myra04}
E.~S. {Myra}, F.~D. {Swesty}, \aasma 205 (2004) \#172.04.

\bibitem{cardall04}
C.~Y. Cardall, astro--ph/0404401.

\bibitem{livne04}
E.~{Livne} et al.,
  \apj 609 (2004) 277.

\bibitem{walder04}
R.~Walder et al., astro--ph/0412187.

\bibitem{mirizzi05}
A.~{Mirizzi}, these proceedings.

\bibitem{raffelt05}
G.~G. Raffelt, hep--ph/0501049.

\end{thebibliography}

\end{document}

astro-ph0502232.extracted_bib
\begin{thebibliography}{9}

\bibitem{baade34}
W.~{Baade}, F.~{Zwicky}, \prv 45 (1934) 138.

%\bibitem{burrows90}
%A.~{Burrows}, in: A.~G. {Petschek} (Ed.), Supernovae, Springer-Verlag, New
%  York, 1990, p. 143.

\bibitem{wilson85}
J.~R. {Wilson}, in: J.~M. Centrella, J.~M. LeBlanc, R.~L. Bowers (Eds.),
  Numerical Astrophysics, Jones and
  Bartlett, Boston, 1985, p. 422.

\bibitem{bethe85}
H.~A. {Bethe}, J.~R. {Wilson}, \apj 295 (1985) 14.

%\bibitem{galama98}
%T.~J. {Galama} et al., \nat 395 (1998) 670.

%\bibitem{iwamoto98}
%K.~{Iwamoto} et al., \nat 395 (1998) 672.

%\bibitem{dellaValle03}
%M.~{Della Valle} et al., \aap 406 (2003) L33.

%\bibitem{hjorth03}
%J.~{Hjorth} et al., \nat
%  423 (2003) 847.

%\bibitem{stanek03}
%K.~Z. {Stanek} et al., \apjl 591 (2003) L17.

%\bibitem{thomsen04}
%B.~{Thomsen} et al., \aap 419 (2004) L21.

%\bibitem{cobb04}
%B.~E. {Cobb} et al., \apjl 608 (2004) L93.

%\bibitem{malesani04}
%D.~{Malesani} et al., \apjl 609 (2004) L5.

%\bibitem{galYam04}
%A.~{Gal-Yam} et al., \apjl 609 (2004) L59.

%\bibitem{zeh04}
%A.~{Zeh}, S.~{Klose}, D.~H. {Hartmann}, \apj 609 (2004) 952.

%\bibitem{ghirlanda04}
%G.~{Ghirlanda}, G.~{Ghisellini}, D.~{Lazzati}, \apj 616 (2004) 331.

%\bibitem{soderberg04}
%A.~M. {Soderberg} et al., \nat 430 (2004) 648.

%\bibitem{thompson04}
%T.~A. Thompson, E.~Quataert, A.~Burrows, astro--ph/0403224.

%\bibitem{wheeler04}
%J.~C. Wheeler, S.~Akiyama, astro--ph/0412382.

%\bibitem{burrows04b}
%A.~Burrows, R.~Walder, C.~D. Ott, E.~Livne, astro--ph/0409035.

%\bibitem{burrows04a}
%A.~Burrows, S.~Reddy, T.~A. Thompson, \npa (2005) in press.

\bibitem{bowers82}
R.~L. {Bowers}, J.~R. {Wilson}, \apjs 50 (1982) 115.

\bibitem{mayle85}
R.~W. {Mayle}, Ph.D. thesis, University of California, Berkeley (1985).

\bibitem{wilson88}
J.~R. Wilson, R.~W. Mayle, \pr 163 (1988) 63.

\bibitem{bruenn85}
S.~W. {Bruenn}, \apjs 58 (1985) 771--841.

\bibitem{bruenn87}
S.~W. {Bruenn}, \prl 59 (1987) 938.

\bibitem{bruenn91}
S.~W. {Bruenn}, W.~C. {Haxton}, \apj 376 (1991) 678.

\bibitem{bruenn93}
S.~W. {Bruenn}, in: M.~W. {Guidry}, M.~R. {Strayer} (Eds.), Nuclear Physics in
  the Universe, Institute
  of Physics, Bristol, 1993, p. 31.

\bibitem{mayle90}
R.~W. {Mayle}, in: A.~G. {Petschek} (Ed.), Supernovae, Springer-Verlag, New
  York, 1990, pp. 267--289.

\bibitem{mayle91}
R.~W. {Mayle}, J.~R. {Wilson}, in: S.~E. {Woosley} (Ed.), Supernovae, Springer-Verlag, New York, 1991, p. 333.

\bibitem{wilson93}
J.~R. Wilson, R.~W. Mayle, \pr 227 (1993) 97.

\bibitem{miller93}
D.~S. {Miller}, J.~R. {Wilson}, R.~W. {Mayle}, \apj 415 (1993) 278.

\bibitem{herant94}
M.~{Herant} et al., \apj 435
  (1994) 339.

\bibitem{burrows95}
A.~{Burrows}, J.~{Hayes}, B.~A. {Fryxell}, \apj 450 (1995) 830.

\bibitem{bruenn94}
S.~W. {Bruenn}, A.~{Mezzacappa}, \apjl 433 (1994) L45.

\bibitem{bruenn95}
S.~W. {Bruenn}, A.~{Mezzacappa}, T.~{Dineva}, \pr 256 (1995) 69.

\bibitem{mezzacappa98a}
A.~{Mezzacappa} et al., \apj 493 (1998) 848.

\bibitem{mezzacappa98b}
A.~{Mezzacappa} et al., \apj 495 (1998) 911.

\bibitem{rampp00}
M.~{Rampp}, H.-T. {Janka}, \apjl 539 (2000) L33--L36.

\bibitem{rampp02}
M.~{Rampp}, H.-T. {Janka}, \aap 396 (2002) 361--392.

\bibitem{kitaura03}
F.~S. Kitaura~Joyanes, Ph.D. thesis, Technical University, Munich (2003).

\bibitem{janka04b}
H.-T. Janka et al.,
   astro--ph/0411347.

\bibitem{mezzacappa93b}
A.~{Mezzacappa}, S.~W. {Bruenn}, \apj 405 (1993) 669.

\bibitem{mezzacappa93c}
A.~{Mezzacappa}, S.~W. {Bruenn}, \apj 410 (1993) 740.

\bibitem{mezzacappa99}
A.~{Mezzacappa}, O.~E.~B. {Messer}, \jcam 109 (1999) 281.

\bibitem{liebendoerfer00}
M.~{Liebend{\" o}rfer}, Ph.D. thesis, University of Basel (2000).

\bibitem{mezzacappa01}
A.~{Mezzacappa} et al., \prl 86 (2001)
  1935.

\bibitem{burrows00}
A.~{Burrows}, T.~{Young}, P.~{Pinto}, R.~{Eastman}, T.~A. {Thompson}, \apj 539
  (2000) 865.

\bibitem{thompson03}
T.~A. {Thompson}, A.~{Burrows}, P.~A. {Pinto}, \apj 592 (2003) 434.

\bibitem{liebendoerfer01a}
M.~{Liebend{\" o}rfer} et al., \prd 63~(10) (2001) 103004.

\bibitem{liebendoerfer02}
M.~{Liebend{\" o}rfer}, S.~{Rosswog}, F.~{Thielemann}, \apjs 141 (2002)
  229.

\bibitem{liebendoerfer04}
M.~{Liebend{\" o}rfer} et al., \apjs 150 (2004) 263.

\bibitem{fryer02}
C.~L. {Fryer}, M.~S. {Warren}, \apjl 574 (2002) L65.

\bibitem{buras03}
R.~{Buras} et al., \prl
  90 (2003) 241101.

\bibitem{janka02}
H.~T. Janka et al., in: C.~L. Fryer (Ed.),
  Stellar Collapse, Kluwer, Dordrecht, 2004, p. 65.

\bibitem{janka04a}
H.-T. Janka et al., 
  astro--ph/0401461.

\bibitem{bruenn96}
S.~W. {Bruenn}, T.~{Dineva}, \apjl 458 (1996) L71.

\bibitem{bruenn04}
S.~W. Bruenn, E.~A. Raley, A.~Mezzacappa, astro--ph/0404099.

\bibitem{bruenn89a}
S.~W. {Bruenn}, \apj 340 (1989) 955.

\bibitem{bruenn89b}
S.~W. {Bruenn}, \apj 341 (1989) 385.

\bibitem{messer98}
O.~E.~B. {Messer} et al., \apj 507
  (1998) 353.

\bibitem{janka03}
H.~T. Janka, R.~Buras, M.~Rampp, \npa 718 (2003) 269.

\bibitem{herant92}
M.~{Herant}, W.~{Benz}, S.~{Colgate}, \apj 395 (1992) 642.

\bibitem{blondin03}
J.~M. {Blondin}, A.~{Mezzacappa}, C.~{DeMarino}, \apj 584 (2003) 971.

\bibitem{foglizzo02}
T.~{Foglizzo}, \aap 392 (2002) 353--368.

\bibitem{hix01}
W.~R. {Hix} et al., \baas 33 (2001) 1445.

\bibitem{myra04}
E.~S. {Myra}, F.~D. {Swesty}, \aasma 205 (2004) \#172.04.

\bibitem{cardall04}
C.~Y. Cardall, astro--ph/0404401.

\bibitem{livne04}
E.~{Livne} et al.,
  \apj 609 (2004) 277.

\bibitem{walder04}
R.~Walder et al., astro--ph/0412187.

\bibitem{mirizzi05}
A.~{Mirizzi}, these proceedings.

\bibitem{raffelt05}
G.~G. Raffelt, hep--ph/0501049.

\end{thebibliography}