core-collapse supernova explosion simulations

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Core-collapse supernova explosion simulations C. Y. Cardall a a Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6354, United States of America Neutrinos play important roles in the pre-collapse evolution, explosion, and aftermath of core-collapse su- pernovae. Detected neutrino signals from core-collapse supernovae would provide insight into the explosion mechanism and unknown neutrino mixing parameters. Achieving these goals requires large-scale, multiphysics simulations. For many years, several groups have performed such simulations with increasing realism. Current simulations and plans for future work of the Oak Ridge group are described. 1. Why is there neutrino emission from core-collapse supernovae? Towards the end of its life the inert core of a massive star is supported by electron degen- eracy pressure. As the mass of the core increases the electrons become increasingly relativistic, and once they reach the speed of light they have noth- ing more to give. This is the basic physics behind the Chandrasekhar limit, and when the mass of the core exceeds it, dynamical collapse ensues. The collapsing interior divides into an inner core, in sonic contact with itself, and an outer core whose infall is supersonic. Collapse of the inner core halts when the nucleons begin to overlap. A shock wave forms when supersonically infalling material slams into the inner core. The shock moves out, heating the material through which it passes, and eventually will give rise to the optical emission we know as a supernova. This does not happen right away, however. At around 150 or 200 km the shock stalls due to energy losses to electron capture neutrino emis- sion from shock-heated material and photodis- integration of heavy nuclei falling through the shock. The mechanism of shock revival—that is to say, the explosion mechanism—remains a sub- ject of active investigation. But since the 1980s Support from the Office of Nuclear Physics, DOE, and the Office of Advanced Scientic Computing Research, DOE, is gratefully acknowledged. Oak Ridge National Laboratory is managed by UT-Battelle for the DOE. the delayed neutrino-driven explosion mechanism has been a primary paradigm: beyond the so- called ‘gain radius,’ heating by neutrino absorp- tion outweighs cooling by electron capture, and on longer timescales (hundreds of milliseconds) may re-energize the shock [1]. At least five phases of neutrino emission can be identified. First, in the infall phase electron capture yields electron neutrino emission. Next, a tremendous burst of electron neutrinos results from prodigious electron capture in the shock- heated neutrino-transparent material when the outward-moving shock passes beyond neutrino trapping density. During the accretion phase the deceleration of infalling material provides a con- tinuing source of warm matter that emits neutri- nos and antineutrinos of all flavors. This phase ceases when the explosion takes off and accretion is reversed, giving rise to the Kelvin-Helmholtz phase in which trapped neutrinos slowly diffuse out with hardening spectra but decreasing lumi- nosities. Once contraction ceases, a final cooling phase is marked by declining average neutrino en- ergies as well, over tens of seconds. 2. What goes into simulations of stellar collapse and its aftermath? Determining the heating and cooling rates that affect the fate of the shock requires neutrino transport. Deep inside the newly-born neutron star, where neutrinos are trapped and slowly Nuclear Physics B (Proc. Suppl.) 217 (2011) 275–277 0920-5632/$ – see front matter © 2011 Elsevier B.V. All rights reserved. www.elsevier.com/locate/npbps doi:10.1016/j.nuclphysbps.2011.04.118

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Page 1: Core-collapse supernova explosion simulations

Core-collapse supernova explosion simulations

C. Y. Cardalla ∗

aPhysics Division, Oak Ridge National Laboratory,Oak Ridge, TN 37831-6354, United States of America

Neutrinos play important roles in the pre-collapse evolution, explosion, and aftermath of core-collapse su-pernovae. Detected neutrino signals from core-collapse supernovae would provide insight into the explosionmechanism and unknown neutrino mixing parameters. Achieving these goals requires large-scale, multiphysicssimulations. For many years, several groups have performed such simulations with increasing realism. Currentsimulations and plans for future work of the Oak Ridge group are described.

1. Why is there neutrino emission fromcore-collapse supernovae?

Towards the end of its life the inert core ofa massive star is supported by electron degen-eracy pressure. As the mass of the core increasesthe electrons become increasingly relativistic, andonce they reach the speed of light they have noth-ing more to give. This is the basic physics behindthe Chandrasekhar limit, and when the mass ofthe core exceeds it, dynamical collapse ensues.The collapsing interior divides into an inner core,in sonic contact with itself, and an outer corewhose infall is supersonic. Collapse of the innercore halts when the nucleons begin to overlap.A shock wave forms when supersonically infallingmaterial slams into the inner core. The shockmoves out, heating the material through which itpasses, and eventually will give rise to the opticalemission we know as a supernova.

This does not happen right away, however. Ataround 150 or 200 km the shock stalls due toenergy losses to electron capture neutrino emis-sion from shock-heated material and photodis-integration of heavy nuclei falling through theshock. The mechanism of shock revival—that isto say, the explosion mechanism—remains a sub-ject of active investigation. But since the 1980s

∗Support from the Office of Nuclear Physics, DOE, andthe Office of Advanced Scientic Computing Research,DOE, is gratefully acknowledged. Oak Ridge NationalLaboratory is managed by UT-Battelle for the DOE.

the delayed neutrino-driven explosion mechanismhas been a primary paradigm: beyond the so-called ‘gain radius,’ heating by neutrino absorp-tion outweighs cooling by electron capture, andon longer timescales (hundreds of milliseconds)may re-energize the shock [1].

At least five phases of neutrino emission canbe identified. First, in the infall phase electroncapture yields electron neutrino emission. Next,a tremendous burst of electron neutrinos resultsfrom prodigious electron capture in the shock-heated neutrino-transparent material when theoutward-moving shock passes beyond neutrinotrapping density. During the accretion phase thedeceleration of infalling material provides a con-tinuing source of warm matter that emits neutri-nos and antineutrinos of all flavors. This phaseceases when the explosion takes off and accretionis reversed, giving rise to the Kelvin-Helmholtzphase in which trapped neutrinos slowly diffuseout with hardening spectra but decreasing lumi-nosities. Once contraction ceases, a final coolingphase is marked by declining average neutrino en-ergies as well, over tens of seconds.

2. What goes into simulations of stellarcollapse and its aftermath?

Determining the heating and cooling rates thataffect the fate of the shock requires neutrinotransport. Deep inside the newly-born neutronstar, where neutrinos are trapped and slowly

Nuclear Physics B (Proc. Suppl.) 217 (2011) 275–277

0920-5632/$ – see front matter © 2011 Elsevier B.V. All rights reserved.

www.elsevier.com/locate/npbps

doi:10.1016/j.nuclphysbps.2011.04.118

Page 2: Core-collapse supernova explosion simulations

diffuse outwards, their distribution is nearlyisotropic. As they begin to decouple in the semi-transparent regime between the proto neutronstar and the shock, their angular distribution be-comes more and more strongly forward-peaked.Moreover, this transition happens differently fordifferent neutrino energies. Ultimately, therefore,knowledge of the neutrino heating and coolingrates relies on knowledge of the neutrino distri-bution functions: at every instant in time andat every point in space, we would like to knowhow many neutrinos there are with a given en-ergy moving in a given direction. This requiresimplicit solution of the Boltzmann equation orsomething equivalent. This ultimately should bedone in three spatial dimensions as demandedby the presence of convection, rotation, magneticfields, and the stationary accretion shock insta-bility (SASI) [2–4].

Currently it is not computationally tractable toinclude in simulations all of the relevant physicsin all six dimensions of phase space for tens ofseconds of physical evolution. Accordingly, dif-ferent types of simulations have been developedthat cover different phases and aspects of neutrinoemission. Simulations aimed at understandingthe explosion mechanism, which typically coverabout 1 second of physical time, are the most de-tailed overall in terms of their multidimensionaland multiphysics character. Recently a coupleof these codes have been run for several seconds,perhaps up to 20 seconds, but only in spheri-cal symmetry [5,6]. Simulations of proto neu-tron star evolution have been done but only inspherical symmetry and with much more heav-ily approximated multiphysics, including ‘diffu-sion only’ neutrino transport [7]. Another type ofcalculation is the only kind to include flavor mix-ing: these are of the ‘free streaming’ of neutrinos(including nonlinear refractive effects) outside theprotoneutron star, without time evolution, on afixed matter profile (see review talk in these pro-ceedings). They are spherically symmetric, butthey do have higher energy resolution, and higherangle resolution when included, than simulationsof the explosion mechanism.

3. What is the status of simulations focus-ing on the explosion mechanism?

The delayed neutrino-driven explosion mecha-nism, which has been a primary paradigm sincethe 1980s [1], has had its difficulties but has re-cently made a comeback. In the early to mid1990s axisymmetric simulations with ‘grey’ neu-trino transport, in which the entire momentumspace was integrated out, exhibited robust ex-plosions thanks to convection behind the shockthat increased the efficiency of neutrino heating[8,9]. These were called into question in the late1990s and early 2000s by early axisymmetric sim-ulations with energy-dependent neutrino trans-port, which failed to explode [10,11]. Energy-and angle-dependent neutrino transport was ad-dressed by several groups in the early 2000s, astep which at first could only be undertaken bygoing back to spherical symmetry [12–14]. Therewas agreement that explosions did not occur inthis type of simulation, except for the lowest massprogenitors [15]. Some of the more recent simu-lations of the mid to late 2000s, in axisymme-try and with partial energy dependence, contin-ued in the failure to explode by neutrino heat-ing. However a previously unimagined ‘acoustic’explosion mechanism was observed: one of theproto neutron star’s vibrational modes was ex-cited to large amplitudes, radiating sound wavesthat steepened into shocks and heated the mate-rial as they traversed the density gradient [16]. Intwo other groups’ simulations [17,18] of the sametime period, however, neutrino-driven explosionswere once again observed.

The Oak Ridge / Florida Atlantic / NorthCarolina State collaboration, with which I amassociated, has two major projects. One ofthem, CHIMERA, has recently seen explosionsin axisymmetry with energy-dependent neutrinotransport [17], with progenitors of 12, 15, 20,and 25 M�. The explosions take off between200 and 300 ms after bounce in all cases. Thatthe explosions are driven by neutrino heating issuggested by a comparison of the advection andneutrino heating time scales: the time at whichthe advection time scale exceeds the heating timescale corresponds well to the time the explosions

C.Y. Cardall / Nuclear Physics B (Proc. Suppl.) 217 (2011) 275–277276

Page 3: Core-collapse supernova explosion simulations

take off. A corresponding three-dimensional fullmultiphysics run with this code has also beenstarted. The other major project of our collabora-tion, GenASiS, is ultimately aimed at addressingthe full dimensionality of the neutrino transportproblem, with reasonable intermediate steps.

In summary, more tractable multiphysics com-putations that reduce the dimensionality of spaceand momentum space in different ways, andthat use different physics implementations andnumerical methods, have not seen completeconvergence of simulation outcomes. At thepresent time there are both agreements anddisagreements among recent multiphysics super-nova simulations. Three groups (ORNL, Garch-ing, Princeton) agree that the stationary ac-cretion shock instability (SASI) is important tothe explosions they see. The Princeton group—which uses multi-group flux-limited diffusion neu-trino transport—sees acoustically-driven explo-sions, while those produced by the ORNL andGarching codes—which both use so-called ‘ray-by-ray’ transport in spherical coordinates—areneutrino-driven. In the acoustic mechanism, theplunging streams associated with the SASI excitethe vibrational modes of the proto neutron starthat then radiate sound waves. In the neutrino-driven explosions, the SASI increases the advec-tion time, and its plunging streams help main-tain neutrino luminosities. The neutrino-drivenexplosions occur earlier than the acoustic ones.The absence of neutrino-driven explosions in thePrinceton simulations may be due to the absenceof energy redistribution processes in the neutrinotransport, and the absence of even approximategeneral relativity. The absence of the acousticmechanism in the ORNL and Garching simula-tions could be due to the fact that the neutrino-driven explosions take off before it can develop.However there are theoretical reasons to doubtthe acoustic mechanism [19]. Note also that theORNL 15 M� explosion takes off earlier than theGarching one, but a direct comparison is compli-cated by the fact that the latter uses a different,and rotating, progenitor.

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