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Publ. Astron. Soc. Jpn (2014) 66 (2), L1 (1–6) doi: 10.1093/pasj/pst030 Advance Access Publication Date: 2014 March 28 Letter L1-1 Letter From supernovae to neutron stars Yudai SUWA Yukawa Institute for Theoretical Physics, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502 *E-mail: [email protected] Received 2013 October 2; Accepted 2013 November 28 Abstract Gravitational collapse, bounce, and explosion of an iron core of an 11.2 M star are simulated by two-dimensional neutrino-radiation hydrodynamic code. The explosion is driven by the neutrino heating aided by multi-dimensional hydrodynamic effects such as convection. Following the explosion phase, we continue the simulation focusing on the thermal evolution of the protoneutron star up to 70 s when the crust of the neutron star is formed, using one-dimensional simulation. We find that the crust forms at a high-density region (ρ 10 14 g cm 3 ) and it proceeds from inside to outside. This is the first self-consistent simulation that successfully follows from the collapse phase to the protoneutron star cooling phase based on multi-dimensional hydrodynamic simulation. Key words: hydrodynamics — instabilities — neutrinos — supernovae: general 1 Introduction Core-collapse supernovae are transitions of massive stellar cores into neutron stars (hereafter NSs). These phenomena are significantly dynamical events, since the central density increases by 10 6 (from 10 9 g cm 3 to 10 15 g cm 3 ) and the radius decreases by 100 (from 1000 km to 10 km) within only 1 s. A NS can be divided into two components, the (super- fluid) core and the crust. In the crust, Coulomb forces dom- inate the thermal fluctuation and nuclei crystallize into a periodic (body centered cubic) lattice structure that mini- mizes the Coulomb energy. The presence of the crust implies typical aspects of NSs. For example, the cooling curve of old pulsars is characterized by the heat conductivity in the crust (for a review and references therein, see Yakovlev & Pethick 2004), and the giant flares of soft-gamma ray repeaters are conjectured to originate from the sudden release of the mag- netic field energy, which is stored below the crust and breaks the crust when the magnetic stress overwhelms the crustal stress (Thompson & Duncan 2001). The relationship with pulsar glitches (Ruderman et al. 1998) and the gravitational waves from mountains on the crust (Horowitz & Kadau 2009) are also discussed. The crust, however, does not exist just after the supernova explosion sets in. At first, the neutron star is very hot ( temperature T 10 11 K) so that it entirely behaves as fluid (a so-called protoneutron star—PNS). As the PNS cools down by neutrino emission, at some point the thermal energy becomes comparable to the Coulomb energy, and nuclei form a lattice structure, which corresponds to the crust formation. Recently, thanks to the growing computer resources and development of the numerical scheme, we have several numerical studies that have performed multi-dimensional (multi-D) hydrodynamic simulations with neutrino radia- tive transfer and succeeded in making the shock expan- sion up to outside the iron core (e.g., Buras et al. 2006; Burrows et al. 2006; Marek & Janka 2009; Suwa et al. 2010; Takiwaki et al. 2012; uller et al. 2012; C The Author 2014. Published by Oxford University Press on behalf of the Astronomical Society of Japan. All rights reserved. For Permissions, please email: [email protected] at University of Adelaide on December 10, 2014 http://pasj.oxfordjournals.org/ Downloaded from

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Page 1: From supernovae to neutron stars

Publ. Astron. Soc. Jpn (2014) 66 (2), L1 (1–6)doi: 10.1093/pasj/pst030

Advance Access Publication Date: 2014 March 28Letter

L1-1

Letter

From supernovae to neutron stars

Yudai SUWA∗

Yukawa Institute for Theoretical Physics, Kyoto University, Oiwake-cho, Kitashirakawa,Sakyo-ku, Kyoto 606-8502

*E-mail: [email protected]

Received 2013 October 2; Accepted 2013 November 28

Abstract

Gravitational collapse, bounce, and explosion of an iron core of an 11.2 M� star aresimulated by two-dimensional neutrino-radiation hydrodynamic code. The explosion isdriven by the neutrino heating aided by multi-dimensional hydrodynamic effects such asconvection. Following the explosion phase, we continue the simulation focusing on thethermal evolution of the protoneutron star up to ∼ 70 s when the crust of the neutronstar is formed, using one-dimensional simulation. We find that the crust forms at ahigh-density region (ρ ∼ 1014 g cm−3) and it proceeds from inside to outside. This is thefirst self-consistent simulation that successfully follows from the collapse phase to theprotoneutron star cooling phase based on multi-dimensional hydrodynamic simulation.

Key words: hydrodynamics — instabilities — neutrinos — supernovae: general

1 Introduction

Core-collapse supernovae are transitions of massive stellarcores into neutron stars (hereafter NSs). These phenomenaare significantly dynamical events, since the central densityincreases by ∼ 106 (from ∼ 109 g cm−3 to ∼ 1015 g cm−3)and the radius decreases by ∼ 100 (from ∼ 1000 km to∼ 10 km) within only ∼ 1 s.

A NS can be divided into two components, the (super-fluid) core and the crust. In the crust, Coulomb forces dom-inate the thermal fluctuation and nuclei crystallize into aperiodic (body centered cubic) lattice structure that mini-mizes the Coulomb energy. The presence of the crust impliestypical aspects of NSs. For example, the cooling curve of oldpulsars is characterized by the heat conductivity in the crust(for a review and references therein, see Yakovlev & Pethick2004), and the giant flares of soft-gamma ray repeaters areconjectured to originate from the sudden release of the mag-netic field energy, which is stored below the crust and breaksthe crust when the magnetic stress overwhelms the crustal

stress (Thompson & Duncan 2001). The relationship withpulsar glitches (Ruderman et al. 1998) and the gravitationalwaves from mountains on the crust (Horowitz & Kadau2009) are also discussed. The crust, however, does notexist just after the supernova explosion sets in. At first,the neutron star is very hot ( temperature T ∼ 1011 K) sothat it entirely behaves as fluid (a so-called protoneutronstar—PNS). As the PNS cools down by neutrino emission,at some point the thermal energy becomes comparable tothe Coulomb energy, and nuclei form a lattice structure,which corresponds to the crust formation.

Recently, thanks to the growing computer resources anddevelopment of the numerical scheme, we have severalnumerical studies that have performed multi-dimensional(multi-D) hydrodynamic simulations with neutrino radia-tive transfer and succeeded in making the shock expan-sion up to outside the iron core (e.g., Buras et al. 2006;Burrows et al. 2006; Marek & Janka 2009; Suwa et al.2010; Takiwaki et al. 2012; Muller et al. 2012;

C© The Author 2014. Published by Oxford University Press on behalf of the Astronomical Society of Japan.All rights reserved. For Permissions, please email: [email protected]

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Bruenn et al. 2013). The shock expansion was obtainedby multi-D effects that amplify the neutrino heatingrate such as convection and standing accretion shockinstability (SASI), even though state-of-the-art one-dimensional (1D) simulations failed to produce the explo-sion (Rampp & Janka 2000; Liebendorfer et al. 2001;Thompson et al. 2003; Sumiyoshi et al. 2005). Using thesefacts, we are now able to carry on the numerical simula-tion of NS crust formation, which can be called the true NSformation, by using self-consistent exploding models.

In this letter, we report the simulation result from theonset of an iron core collapse to the formation of the neu-tron star crust. Though the explosion mechanism of super-novae is still under a thick veil, in this letter we rely onthe standard scenario, i.e., the delayed explosion scenario,in which the neutrino heating is crucial and the neutrinotransfer equation should be solved in order to estimatethe neutrino-heating rate. In previous studies, Burrows andLattimer (1986) investigated the long-term evolution of theKelvin–Helmholtz cooling phase of PNSs starting from ahand-made initial condition, which imitates the hydrody-namical profiles after the bounce; see also Pons et al. (1999)for a recent study. More recently, Fischer et al. (2010,2012) performed simulations with fully general-relativisticradiation-hydrodynamic code up to ∼ 10 s. Since their codeis 1D and no self-consistent explosion of an iron core can bereproduced, they artificially amplified the charged currentreaction rate in order to produce explosion (one exemptionis an 8.8 M� progenitor, which, however, has an O-Ne-Mgcore, not an iron core). Therefore, this letter represents thefirst study using a self-consistent neutrino-radiation hydro-dynamic simulation in multi-D, which successfully followsthe very long-term evolution of a massive stellar core; thecore collapse of an iron core, the bounce and the shockformation at the nuclear density, the shock expansion, theneutrino-driven wind phase, and finally the PNS coolingphase. In addition, this letter investigates when the crustforms inside the PNS, which is studied for the first timeusing a core-collapse supernova simulation.

In this letter, section 2 is devoted to the explanation ofnumerical methods. In section 3, we give the results of oursimulation, focusing on the thermal evolution of the PNS.We summarize our results and discuss their implicationsin section 4.

2 Numerical method

The numerical methods used are basically the same asin our previous papers (Suwa et al. 2010, 2011, 2013).With the ZEUS-2D code (Stone & Norman 1992) asa base for the solver of hydrodynamics, we employ anequation of state (EOS) of Shen et al. (1998), whichis able to reproduce recently discovered massive NSs of

Demorest et al. (2010) and Antoniadis et al. (2013), andsolve the spectral neutrino radiative transfer equation forνe and νe using isotropic diffusion source approximation(IDSA), which is well calibrated to reproduce the resultsof a full Boltzmann solver (Liebendorfer et al. 2009). Theweak interaction rates for neutrinos are calculated by usingthe formulation of Bruenn (1985). The simulations areperformed on a grid of 300 logarithmically spaced radialzones up to 5000 km, with the least grid width being 1 kmat the center and 128 equidistant angular zones covering0 < θ < π for two-dimensional (2D) simulation. As for thecontinuous 1D simulation, the same radial zoning is usedand “one” angular grid is employed. In order to resolvethe steep density gradient at the PNS surface and removethe outermost region with density ρ < 105 g cm−3, whichis the lowest value of the EOS table, we perform rezoningseveral times for the later 1D run. Eventually, the radiusof the minimum grid (and the least grid width) is 300 mand the maximum grid edge is located at 100 km from thecenter. The total mass of the PNS is conserved over theserezonings within ∼ 0.1% error. For neutrino transport, weuse 20 logarithmically spaced energy bins reaching from 3to 300 MeV. As for the initial condition, we employ an11.2 M� model from Woosley, Heger, and Weaver (2002),with which several papers reported successful explosion(Buras et al. 2006; Marek & Janka 2009; Takiwaki et al.2012; Suwa et al. 2013).

3 Results

The basic picture of a core-collapse supernova is as follows(Bethe 1990; Janka 2012; Kotake et al. 2012): (i) the col-lapse of an iron core driven by the energy loss due to thephotodissociation of iron and the electron capture; (ii) theneutron star formation and the bounce shock production;(iii) the shock stall due to neutrino cooling; (iv) the shockrevival by neutrino heating; (v) the neutrino-driven windphase; and (vi) the neutron star cooling phase. Previoushydrodynamic studies have focused only on the earlyphases, mostly the shock revival process, which is less than∼ 1 s after the bounce (by phase iv; but see Fischer et al.2010 for phase v). The PNS cooling has a much longertimescale ∼ O(10) s, so that a fully consistent simulationhas not been done so far.

Here, we perform a two-dimensional simulation of thecollapse, the bounce, and the onset of the explosion byneutrino heating up to 690 ms after the bounce. The corebounce occurs 150 ms after the simulation starts, withthe central density at ≈ 3.1 × 1014 g cm−3. Soon after thebounce, the shock propagates outside the neutrinosphere,convection sets in and the convective plumes hit the shock.In this simulation, the shock does not stall and a successful

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Fig. 1. Trajectories of selected mass coordinates from 1.01 M� to1.33 M� by a step of 0.02 M�. The thick solid line indicates the positionof 1.3 M�, which indicates the mass of the PNS, and the thick dottedline represents the shock radius at the northern pole. The left panel isthe result of 2D simulation and the right panel is that of continuous1D simulation, with the connection done at ∼ 690 ms after the bounce.The shrinkage of the PNS can be seen. There are several discontinu-ities, for example ∼ 1.2 s post-bounce, which are due to the rezoning tomake the resolution finer and remove the outermost region where thedensity becomes too small to use the tabular equation of state. Thesediscontinuities do not cause any serious problems in this simulation.

explosion occurs (see Suwa et al. 2013 for more details).After that, all hydrodynamic quantities are averaged overthe angle1 and the spherically symmetric simulation is fol-lowed up to ∼ 70 s when the crust formation condition issatisfied. Note that the whole simulation is performed usingthe “same” code so that there is no discontinuity betweenthese 2D and 1D simulations. If we use different codes toconnect the different times and physical scales, some breaksof physical quantities could occur (e.g., total mass, totalmomentum, or total energy). Therefore, a consistent simu-lation with the same code has the advantage of removingthese breaks.

In figure 1, the time evolution of selected mass coordi-nates is presented. The mass within ∼ 1.3 M� contracts toa PNS and the outer part expands as ejecta of the super-nova. The shock (thick dotted line) propagates rapidly tooutside the iron core driven by neutrino heating aidedby the convective fluid motion. The estimated diagnosticenergy (Suwa et al. 2010, so-called the explosion energy)determined by summing up the gravitationally unboundfluid elements in this model is ∼ 1050 erg, so that a real-istic explosion simulation is still not achieved. This is,however, one of the successful explosion simulations. Theterm “successful” means that the simulation successfullyreproduces the structure containing a remaining PNS andescaping ejecta. Previous exploding models obtained by

1 This treatment does not produce any strange phenomena for the PNS because thePNS is almost spherically symmetric for the case without rotation.

Marek and Janka (2009) and Suwa et al. (2010) certainlyacquired the expanding shock wave up to outside the ironcore, but most of the post-shock materials were in-fallingso that the mass accretion onto the PNS did not settle andthe mass of the PNS continued to increase. Thus these sim-ulations were not fully successful explosions. On the otherhand, Suwa et al. (2013) and this work successfully repro-duce the envelope ejection so that we can determine the“mass cut,” which gives the final mass of the compact object(i.e., NS or black hole). This is because the progenitor usedin this study has a steep density gradient between iron coreand silicon layer so that the ram pressure of in-falling mate-rial rapidly decreases when the shock passes the iron coresurface. This is a similar situation to the explosion simula-tion of the O-Ne-Mg core of an 8.8 M� progenitor reportedby Kitaura, Janka, and Hillebrandt (2006), in which theneutrino-driven explosion was obtained in a “1D” simula-tion owing to the very steep density gradient of this specificprogenitor. Note that the progenitor in this study does notexplode with spherical symmetry even though it has a steepdensity gradient. However, with the help of convection, thisprogenitor explodes in 2D simulation and the shock earnsenough energy to blow away the outer layers.

In figure 2, we show the hydrodynamic quantities (ρ,T, entropy s, and electron fraction Ye) at several selectedtimes, i.e., 10 ms, 1 s, 10 s, 30 s, and 67 s after the bounce.One can find by the density plot that the PNS shrinks dueto neutrino cooling. Note that for the post-bounce timetpb � 10 s the central temperature increases because of theequidistribution of the thermal energy that can be foundin the entropy plot, in which one finds that entropy at thecenter increases due to entropy flow from the outer part. Fortpb � 10 s, the PNS evolves almost isentropically and boththe entropy and the temperature decrease due to neutrinocooling. This can be called the PNS cooling phase. One canfind from the Ye plot that neutrinos take out the leptonnumber as well.

Figure 3 represents the time evolution in the ρ–T plane.The line colors and types are the same as figure 2. In thisplane, we show three black solid lines that indicate the cri-teria for crust formation. The critical temperature for lat-tice structure formation is given by Shapiro and Teukolsky(1983) as

Tc ≈ Z2e2

�kB

(4π

3ρYexa

Zmu

)1/3

(1)

≈ 6.4 × 109 K(

175

)−1 (ρ

1014 g cm−3

)1/3 (Ye

0.1

)1/3

×( xa

0.3

)1/3(

Z26

)5/3

, (2)

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Fig. 2. Time evolution of the density (left top), the temperature (left bottom), the entropy (right top), and the electron fraction (right bottom). Thedensity and the temperature are given as functions of the radius and the entropy and the electron fraction are functions of the mass coordinate. Thecorresponding times measured from the bounce are 10 ms (red solid line), 1 s (green dashed line), 10 s (blue dotted line), 30 s (brown dot-dashedline), and 67 s (grey dot-dot-dashed line), respectively. (Color online)

Fig. 3. The time evolution in the ρ–T plane. The color and type of linesare as in figure 2. Three thin solid black lines indicate the critical linesfor crust formation. See text for details. (Color online)

where Z is the typical proton number of the compo-nent of the lattice, e is the elementary charge, � isa dimensionless factor describing the ratio between thethermal and Coulomb energies of the lattice at the meltingpoint, kB is the Boltzmann constant, xa is the mass fractionof heavy nuclei, and mu is the atomic mass unit, respectively.The critical lines are drawn using parameters of � = 175(see, e.g., Chamel & Haensel 2008), Ye = 0.1, and xa = 0.3.As for the proton number, we employ Z = 26, 50, and 70from bottom to top. Although the output for the typicalproton number by the equation of state is between ∼ 30 and35, there is an objection that the average proton numbervaries if we use the NSE composition. Furusawa et al.(2011) represented the mass fraction distribution in theneutron number and proton number plane and implied thateven larger (higher proton number) nuclei can be formed

in the thermodynamic quantities considered here. There-fore, we here parametrize the proton number and show thedifferent critical lines depending on the typical species ofnuclei. In addition, there are several improved studies con-cerning � that suggest the larger value (e.g., Horowitz et al.2007), which leads to a lower critical temperature corre-sponding to later crust formation, although the value is stillunder debate.

The critical lines imply that the lattice structure is formedat the point with the density of ∼ 1013−14 g cm−3 and at thepost-bounce time of ∼ 70 s. Of course these values (espe-cially the formation time) strongly depend on the parame-ters employed, but the general trend would not change verymuch even if we included more sophisticated parameters.

4 Summary and discussion

In this letter, we performed a very long-term simulation ofthe supernova explosion for an 11.2 M� star. This is thefirst simulation of an iron core starting from core collapseand finishing in the PNS cooling phase. We focused on thePNS cooling phase by continuing the neutrino-radiation-hydrodynamic simulation up to ∼ 70 s from the onset ofcore collapse. By comparing the thermal energy and theCoulomb energy of the lattice, we finally found that thetemperature decreases to ∼ 3 × 1010 K with the densityρ ∼ 1014 g cm−3, which almost satisfies the critical condi-tion for the formation of the lattice structure. Even thoughthere are still several uncertainties for this criterion, thisstudy could give us useful information about the crust for-mation of a NS. We found that the crust formation wouldstart from the point with ρ ≈ 1013−14 g cm−3 and that it pre-cedes from inside to outside, because the Coulomb energy

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strongly depends on the mean interstice between compo-nents so that a higher density exhibits earlier formation.

Next, we comment on our assumptions in this study. Weperformed 2D simulation for the explosion phase following1D simulation for the neutrino-driven wind phase and PNScooling phase. It is well known that convection and SASIactivity are different between 2D and 3D in the explosionphase, so that a 3D simulation should be performed (seeTakiwaki et al. 2013; Couch 2013). In addition, in thePNS cooling phase we observed the negative entropy gra-dient and negative lepton fraction gradient as functions ofthe radius, which indicate that these regions are convec-tively unstable so that in multi-D simulation the convectivemotion could change the evolution quantitatively. How-ever, it is still too computationally expensive to perform 3Dsimulation with neutrino radiative transfer up to 70 s post-bounce, and we think that our findings in this work will notchange in a qualitative sense even when 3D simulations forsuch a long term are available in the future. The possibledirection in multi-D simulation for the crust formation isthe following: the convective motion could transfer the heatfrom inside to outside more efficiently than the radiation sothat the temperature at the surface of the PNS should behigher compared to a 1D run at the early time. However,for the late time, the neutrino luminosity could becomesmaller with convection than without convection (see, e.g.,Roberts et al. 2012). This means that the surface tempera-ture decreases faster if we consider convection, which couldlead to faster formation of the crust. In order to obtain thefinal answer for the convective effects on crust formation,the long-term evolution with multi-D hydrodynamic sim-ulation is strongly required, which is beyond the scope ofthis letter and will be presented in forthcoming papers.

In addition to the dimensionality, we employed sev-eral simplifications in this study, i.e., the specific nuclearequation of state (EOS) by Shen et al. (1998), the sim-plified neutrino interactions based on Bruenn (1985), thesimplified neutrino transfer scheme by isotropic diffusionsource approximation (IDSA: Liebendorfer et al. 2009), andneglecting the general relativistic (GR) effects. These treat-ments could lead to a quantitative difference in the crustformation time, so that more sophisticated simulations arenecessary to obtain more realistic values. In the following,we briefly discuss the possible direction for improving thesephysics one by one. First, the EOS affects the structureof the PNS, especially its radius. The Shen EOS, whichis used in this study, predicts ∼ 15 km for a cold NSwith 1.4 M�, which is relatively larger than the suggestedvalue obtained by analysis of X-ray binaries (e.g., Steineret al. 2010). A different EOS, which exhibits a smallerNS radius, would result in a higher temperature for crustformation and later formation of the crust. Secondly, the

weak interactions used in this study are based on Bruenn(1985), in which some interactions playing an importantrole at the PNS cooling phase are missing, e.g., nucleon–nucleon bremsstrahlung. Therefore, our simulation couldunderestimate the cooling rate and overestimate the tem-perature. Due to this underestimation of the cooling, theshrinkage of the PNS is rather slow in this study (sev-eral seconds; see figures 1 and 2) compared to previousstudies (� 1 s, see, e.g., Fischer et al. 2010). In addi-tion, missing some interactions might cause the dip inthe ρ–T plane shown in figure 3. We can expect thatmore improved simulations including these interactionsmight lead to the earlier formation of the crust. Thirdly,IDSA is known to produce considerable error aroundthe decoupling layer between the optically thick and thinregions (Berninger et al. 2012). This error comes from thesimple description of IDSA, in which we naively decom-pose the distribution function of neutrinos into a trappedpart and a free-streaming part (Liebendorfer et al. 2009).This treatment significantly simplifies the transport equa-tions for each limit and can make the neutrino-radiationhydrodynamic simulations computationally reasonable, sothat we can perform such a long-term simulation usingEulerian grid-based code. However, since this simplifica-tion exhibits error at the transition layer, which determinesthe boundary condition of the diffusion equation for neu-trinos and might change the thermal evolution even inthe deep core, a more sophisticated transport scheme isnecessary to obtain a more realistic time for crust forma-tion. Finally, GR effects, which are neglected in this study,may change the crust formation time because the strongergravity exhibits a more compact NS. More compact PNSshave higher entropy, which moves points in the upper-leftdirection slightly in the ρ–T plane so that the GR effectsare expected to delay the crust formation. Lastly, it shouldbe noted that even though the current study is based on thesimplifications described above, we believe that the quali-tative features obtained here will not change dramaticallyeven if we include more sophisticated physics, i.e., the crustforms at ∼ 10–100 s after PNS formation near the centerand the crust-formation front propagates from inside tooutside.

Acknowledgments

We thank the referee for providing constructive comments andhelp in improving the contents of this letter, and M. Liebendorfer,T. Muranushi, K. Sumiyoshi, M. Takano, and N. Yasutake for stim-ulating discussion. The numerical computations in this study were inpart carried out on XT4 and XC30 at CfCA in NAOJ and SR16000at YITP in Kyoto University. This study was supported in part byGrants-in-Aid for the Scientific Research from the Ministry of Educa-tion, Science, and Culture of Japan (Nos. 23840023 and 25103511)and the HPCI Strategic Program of Japanese MEXT.

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References

Antoniadis, J., et al. 2013, Science, 340, 448Berninger, H., Frenod, E., Gander, M., Liebendorfer, M., Michaud,

J., & Vasset, N. 2012, arXiv:1211.6901Bethe, H. A. 1990, Rev. Mod. Phys., 62, 801Bruenn, S. W. 1985, ApJS, 58, 771Bruenn, S. W., et al. 2013, ApJ, 767, L6Buras, R., Janka, H., Rampp, M., & Kifonidis, K. 2006, A&A, 457,

281Burrows, A., & Lattimer, J. M. 1986, ApJ, 307, 178Burrows, A., Livne, E., Dessart, L., Ott, C. D., & Murphy, J. 2006,

ApJ, 640, 878Chamel, N., & Haensel, P. 2008, Living Rev. Relativity, 11, 10Couch, S. M. 2013, ApJ, 775, 35Demorest, P. B., Pennucci, T., Ransom, S. M., Roberts, M. S. E., &

Hessels, J. W. T. 2010, Nature, 467, 1081Fischer, T., Martınez-Pinedo, G., Hempel, M., & Liebendorfer, M.

2012, Phys. Rev. D, 85, 083003Fischer, T., Whitehouse, S. C., Mezzacappa, A., Thielemann, F., &

Liebendorfer, M. 2010, A&A, 517, A80Furusawa, S., Yamada, S., Sumiyoshi, K., & Suzuki, H. 2011, ApJ,

738, 178Horowitz, C. J., Berry, D. K., & Brown, E. F. 2007, Phys. Rev. E,

75, 066101Horowitz, C. J., & Kadau, K. 2009, Phys. Rev. Lett., 102, 191102Janka, H.-T. 2012, Annu. Rev. Nucl. Part. Sci., 62, 407Kitaura, F. S., Janka, H., & Hillebrandt, W. 2006, A&A, 450, 345Kotake, K., Takiwaki, T., Suwa, Y., Iwakami Nakano, W.,

Kawagoe, S., Masada, Y., & Fujimoto, S. 2012, Adv. Astron.,2012, 428757

Liebendorfer, M., Mezzacappa, A., Thielemann, F.-K., Messer,O. E., Hix, W. R., & Bruenn, S. W. 2001, Phys. Rev. D, 63,103004

Liebendorfer, M., Whitehouse, S. C., & Fischer, T. 2009, ApJ, 698,1174

Marek, A., & Janka, H. 2009, ApJ, 694, 664Muller, B., Janka, H.-T., & Marek, A. 2012, ApJ, 756, 84Pons, J. A., Reddy, S., Prakash, M., Lattimer, J. M., & Miralles,

J. A. 1999, ApJ, 513, 780Rampp, M., & Janka, H. 2000, ApJ, 539, L33Roberts, L. F., Shen, G., Cirigliano, V., Roberts, L. F., Shen, G.,

Cirigliano, V., Pons, J. A., Reddy, S., & Woosley, S. E. 2012,Phys. Rev. Lett., 108, 061103

Ruderman, M., Zhu, T., & Chen, K. 1998, ApJ, 492, 267Shapiro, S. L., & Teukolsky, S. A. 1983, Black Holes, White Dwarfs,

and Neutron Stars: The Physics of Compact Objects (New York:Wiley-Interscience)

Shen, H., Toki, H., Oyamatsu, K., & Sumiyoshi, K. 1998, Nucl.Phys., A637, 435

Steiner, A. W., Lattimer, J. M., & Brown, E. F. 2010, ApJ, 722, 33Stone, J. M., & Norman, M. L. 1992, ApJS, 80, 753Sumiyoshi, K., Yamada, S., Suzuki, H., Shen, H., Chiba, S., &

Toki, H. 2005, ApJ, 629, 922Suwa, Y., Kotake, K., Takiwaki, T., Liebendorfer, M., & Sato, K.

2011, ApJ, 738, 165Suwa, Y., Kotake, K., Takiwaki, T., Whitehouse, S. C.,

Liebendorfer, M., & Sato, K. 2010, PASJ, 62, L49Suwa, Y., Takiwaki, T., Kotake, K., Fischer, T., Liebendorfer, M.,

& Sato, K. 2013, ApJ, 764, 99Takiwaki, T., Kotake, K., & Suwa, Y. 2012, ApJ, 749, 98Takiwaki, T., Kotake, K., & Suwa, Y. 2013, arXiv:1308.5755Thompson, C., & Duncan, R. C. 2001, ApJ, 561, 980Thompson, T. A., Burrows, A., & Pinto, P. A. 2003, ApJ, 592, 434Woosley, S. E., Heger, A., & Weaver, T. A. 2002, Rev. Mod. Phys.,

74, 1015Yakovlev, D. G., & Pethick, C. J. 2004, ARA&A, 42, 169

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