Three-dimensional Boltzmann-Hydro Code for Core-collapse in Massive Stars. II. The Implementation of Moving-mesh for Neutron Star Kicks

We present a newly developed moving-mesh technique for the multi-dimensional Boltzmann-Hydro code for the simulation of core-collapse supernovae (CCSNe). What makes this technique different from others is the fact that it treats not only hydrodynamics but also neutrino transfer in the language of the 3+1 formalism of general relativity (GR), making use of the shift vector to specify the time evolution of the coordinate system. This means that the transport part of our code is essentially general relativistic although in this paper it is applied only to the moving curvilinear coordinates in the flat Minknowski spacetime, since the gravity part is still Newtonian. The numerical aspect of the implementation is also described in detail. Employing the axisymmetric two-dimensional version of the code, we conduct two test computations: oscillations and runaways of proto-neutron star (PNS). We show that our new method works fine, tracking the motions of PNS correctly. We believe that this is a major advancement toward the realistic simulation of CCSNe.

[1]  A. Burrows,et al.  TWO-DIMENSIONAL CORE-COLLAPSE SUPERNOVA MODELS WITH MULTI-DIMENSIONAL TRANSPORT , 2014, 1403.6115.

[2]  Anthony Mezzacappa,et al.  Stellar core collapse : a Boltzmann treatment of neutrino-electron scattering , 1993 .

[3]  H. Janka,et al.  A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE. IV. THE NEUTRINO SIGNAL , 2014, 1402.3415.

[4]  E. Livne,et al.  Features of the Acoustic Mechanism of Core-Collapse Supernova Explosions , 2007 .

[5]  Eirik Endeve,et al.  The Development of Explosions in Axisymmetric Ab Initio Core-Collapse Supernova Simulations of 12-25 $M_\odot$ Stars , 2014 .

[6]  Timothy D. Brandt,et al.  The hydrodynamic origin of neutron star kicks , 2011, 1112.3342.

[7]  K. Langanke,et al.  Shell-model calculations of stellar weak interaction rates: II. Weak rates for nuclei in the mass range in supernovae environments , 2000, nucl-th/0001018.

[8]  R. W. Lindquist.  Relativistic transport theory , 1966 .

[9]  A. Kageyama,et al.  ``Yin-Yang grid'': An overset grid in spherical geometry , 2004, physics/0403123.

[10]  A. Burrows,et al.  CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. III. MULTIGROUP RADIATION HYDRODYNAMICS , 2012, 1207.3845.

[11]  Chris L. Fryer,et al.  44Ti gamma-ray emission lines from SN1987A reveal an asymmetric explosion , 2015, Science.

[12]  Kuo-Chuan Pan,et al.  TWO-DIMENSIONAL CORE-COLLAPSE SUPERNOVA SIMULATIONS WITH THE ISOTROPIC DIFFUSION SOURCE APPROXIMATION FOR NEUTRINO TRANSPORT , 2015, 1505.02513.

[13]  H. Nagakura,et al.  THE INFLUENCE OF INELASTIC NEUTRINO REACTIONS WITH LIGHT NUCLEI ON THE STANDING ACCRETION SHOCK INSTABILITY IN CORE-COLLAPSE SUPERNOVAE , 2013, 1305.1510.

[14]  M. Rampp,et al.  Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport II. Models for different progenitor stars , 2006 .

[15]  H. Janka,et al.  Electron capture rates on nuclei and implications for stellar core collapse. , 2003, Physical review letters.

[16]  H. Nagakura,et al.  General Relativistic Hydrodynamic Simulations and Linear Analysis of the Standing Accretion Shock Instability around a Black Hole , 2008, 0808.4141.

[17]  M. Rampp,et al.  Two-dimensional hydrodynamic core-collapse supernova simulations with spectral neutrino transport - I. Numerical method and results for a 15 solar mass star , 2005, astro-ph/0507135.

[18]  H.-Th. Janka,et al.  SASI ACTIVITY IN THREE-DIMENSIONAL NEUTRINO-HYDRODYNAMICS SIMULATIONS OF SUPERNOVA CORES , 2013, 1303.6269.

[19]  B. Muller,et al.  Non-Radial Instabilities and Progenitor Asphericities in Core-Collapse Supernovae , 2014, 1409.4783.

[20]  A. Burrows,et al.  SHOULD ONE USE THE RAY-BY-RAY APPROXIMATION IN CORE-COLLAPSE SUPERNOVA SIMULATIONS? , 2015, 1512.00113.

[21]  B. Müller.  The dynamics of neutrino-driven supernova explosions after shock revival in 2D and 3D , 2015 .

[22]  P. Giommi,et al.  Asymmetries in core-collapse supernovae from maps of radioactive 44Ti in Cassiopeia A , 2014, Nature.

[23]  S. Yamada,et al.  NEW EQUATIONS OF STATE BASED ON THE LIQUID DROP MODEL OF HEAVY NUCLEI AND QUANTUM APPROACH TO LIGHT NUCLEI FOR CORE-COLLAPSE SUPERNOVA SIMULATIONS , 2013, 1305.1508.

[24]  F. Timmes,et al.  THE THREE-DIMENSIONAL EVOLUTION TO CORE COLLAPSE OF A MASSIVE STAR , 2015, 1503.02199.

[25]  E. Müller,et al.  Multidimensional supernova simulations with approximative neutrino transport. I. Neutron star kicks and the anisotropy of neutrino-driven explosions in two spatial dimensions , 2006, astro-ph/0601302.

[26]  T. Fischer,et al.  THE ISOTROPIC DIFFUSION SOURCE APPROXIMATION FOR SUPERNOVA NEUTRINO TRANSPORT , 2007, 0711.2929.

[27]  K. Kotake,et al.  A COMPARISON OF TWO- AND THREE-DIMENSIONAL NEUTRINO-HYDRODYNAMICS SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE , 2013, 1308.5755.

[28]  A. Burrows,et al.  Two-dimensional, Time-dependent, Multigroup, Multiangle Radiation Hydrodynamics Test Simulation in the Core-Collapse Supernova Context , 2003, astro-ph/0312633.

[29]  Postbounce Evolution of Core-Collapse Supernovae: Long-Term Effects of the Equation of State , 2005, astro-ph/0506620.

[30]  E. Muller,et al.  An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows , 2010, 1003.1633.

[31]  A Mezzacappa,et al.  Consequences of nuclear electron capture in core collapse supernovae. , 2003, Physical review letters.

[32]  S. Yamada,et al.  A NEW BARYONIC EQUATION OF STATE AT SUB-NUCLEAR DENSITIES FOR CORE-COLLAPSE SIMULATIONS , 2011, 1103.6129.

[33]  H. Janka,et al.  A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMIC CODE FOR CORE-COLLAPSE SUPERNOVAE. I. METHOD AND CODE TESTS IN SPHERICAL SYMMETRY , 2010, 1001.4841.

[34]  S. Woosley,et al.  EVOLUTION AND EXPLOSION OF MASSIVE STARS * , 1978, Reviews of Modern Physics.

[35]  W. R. Hix,et al.  Improved estimate of electron capture rates on nuclei during stellar core collapse , 2009, 0909.0179.

[36]  Kohsuke Sumiyoshi,et al.  THREE-DIMENSIONAL BOLTZMANN HYDRO CODE FOR CORE COLLAPSE IN MASSIVE STARS. I. SPECIAL RELATIVISTIC TREATMENTS , 2014, 1407.5632.

[37]  H. Nagakura,et al.  THE STANDING ACCRETION SHOCK INSTABILITY IN THE DISK AROUND THE KERR BLACK HOLE , 2009, 0901.4053.

[38]  K. Kotake,et al.  Explosion Geometry of a Rotating 13 $\ M_{\odot}$ Star Driven by the SASI-Aided Neutrino-Heating Supernova Mechanism , 2009, 0912.1157.

[39]  Lifan Wang,et al.  Spectropolarimetry of Supernovae , 2008, 0811.1054.

[40]  Timothy D. Brandt,et al.  Theoretical Support for the Hydrodynamic Mechanism of Pulsar Kicks , 2010, 1010.0674.

[41]  S. Couch,et al.  Two-dimensional Core-collapse Supernova Explosions Aided by General Relativity with Multidimensional Neutrino Transport , 2015, 1511.07443.

[42]  K. Kotake,et al.  A NEW MULTI-ENERGY NEUTRINO RADIATION-HYDRODYNAMICS CODE IN FULL GENERAL RELATIVITY AND ITS APPLICATION TO THE GRAVITATIONAL COLLAPSE OF MASSIVE STARS , 2015, 1501.06330.

[43]  Multidimensional radiation/hydrodynamic simulations of proto-neutron star convection , 2005, astro-ph/0510229.

[44]  S. Yamada,et al.  NEUTRINO TRANSFER IN THREE DIMENSIONS FOR CORE-COLLAPSE SUPERNOVAE. I. STATIC CONFIGURATIONS , 2012, 1201.2244.

[45]  H. Janka,et al.  A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE. II. RELATIVISTIC EXPLOSION MODELS OF CORE-COLLAPSE SUPERNOVAE , 2012, 1202.0815.

[46]  E. O’Connor,et al.  THE SENSITIVITY OF CORE-COLLAPSE SUPERNOVAE TO NUCLEAR ELECTRON CAPTURE , 2015, 1508.07348.

[47]  Shoichi Yamada,et al.  JET PROPAGATIONS, BREAKOUTS, AND PHOTOSPHERIC EMISSIONS IN COLLAPSING MASSIVE PROGENITORS OF LONG-DURATION GAMMA-RAY BURSTS , 2010, 1009.2326.

[48]  O. E. Bronson Messer,et al.  THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVA SIMULATED USING A 15 M⊙ PROGENITOR , 2015, 1505.05110.

[49]  Department of Astrophysical Sciences,et al.  Two-Dimensional Multiangle, Multigroup Neutrino Radiation-Hydrodynamic Simulations of Postbounce Supernova Cores , 2008, 0804.0239.

[50]  A. S. Umar,et al.  An Investigation of Neutrino-driven Convection and the Core Collapse Supernova Mechanism Using Multigroup Neutrino Transport , 1996, Astrophysical Journal.

[51]  Yuichiro Sekiguchi,et al.  Conservative form of Boltzmann's equation in general relativity , 2014 .

[52]  O. E. Bronson Messer,et al.  ON THE REQUIREMENTS FOR REALISTIC MODELING OF NEUTRINO TRANSPORT IN SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE , 2011, 1112.3595.

[53]  A. Schwope,et al.  Proper motions of thermally emitting isolated neutron stars measured with Chandra , 2009, 0901.1006.

[54]  M. Obergaulinger,et al.  A new multidimensional, energy-dependent two-moment transport code for neutrino-hydrodynamics , 2015, 1501.02999.

[55]  E. Livne,et al.  Anisotropies in the Neutrino Fluxes and Heating Profiles in Two-dimensional, Time-dependent, Multigroup Radiation Hydrodynamics Simulations of Rotating Core-Collapse Supernovae , 2004 .