Numerical simulations of core-collapse supernovae
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1 Numerical simulations of core-collapse supernovae Jérôme Novak Laboratoire Univers et Théories (LUTH) CNRS / Observatoire de Paris / Université Paris-Diderot 10 th Rencontres du Vietnam, Very high energy phenomena in the Universe ICISE Quy Nhon, August, 8 th 2014
2 Plan 1 Models 2 Recent developments 3 Conclusions
3 Core-collapse supernovae Observations of supernovae reported since Antiquity (SN185) explosions common Categories, depending on the spectrum: Type I: no hydrogen. Ia: ionized silicon, Ib/Ic : strong/weak presence of helium. Type II: presence of hydrogen. IIP/IIL depending on the light curve shape, IIb: spectrum changing from II to Ib. Milisavljevic et al ALMA/Hubble/Chandra Two kinds of theoretical models: Thermonuclear supernovae: explosion of a white dwarf (runaway nuclear reactions). Core-collapse supernovae: collapse-bounce-explosion of a massive main-sequence star...
4 Open questions... Why / How do massive stars explode? What are the properties of the final compact object at the center? How / Where do heavy elements form? What are observable signals? What can we learn for fundamental physics? Ugliano et al Growing number of groups: MPA Garching (H.-T. Janka), Princeton (A. Burrows), Oak Ridge (T. Mezzacappa), Univ. Basel (M. Liebendörfer), Tokyo (S. Yamada), NAOJ/Fukuoka (K. Kotake), Caltech (C. Ott), Los Alamos (C. Fryer), France (T. Foglizzo), Univ. Valencia (M.-A. Aloy),...
5 Open questions... Why / How do massive stars explode? What are the properties of the final compact object at the center? How / Where do heavy elements form? What are observable signals? What can we learn for fundamental physics? Ugliano et al Growing number of groups: MPA Garching (H.-T. Janka), Princeton (A. Burrows), Oak Ridge (T. Mezzacappa), Univ. Basel (M. Liebendörfer), Tokyo (S. Yamada), NAOJ/Fukuoka (K. Kotake), Caltech (C. Ott), Los Alamos (C. Fryer), France (T. Foglizzo), Univ. Valencia (M.-A. Aloy),...
6 Model description
7 Collapse and bounce Massive ( 10M ) main-sequence star with onion-like structure: Iron core becomes unstable (electron degeneracy pressure) Collapse with electron captures on nuclei/free protons p + e n + ν e Central density nuclear density nuclear repulsion Shock wave expanding outwards... Janka et al. 2012
8 Shock evolution Shock stalls, due to energy loss by iron nuclei photodissociation "! Janka et al there must be some mechanism to revive the shock: transfer energy from the gravitational well to the shock.
9 Physical ingredients Progenitor model evolution for massive stars Gravitation hydrodynamics relativistic? Microphysics: equation of state for hot, dense matter, out of β-equilibrium : p(ρ, T, Y e ) very large range of densities, temperatures and asymmetry Microphysics: electron capture and neutrino reaction rates (opacities) Neutrino transport 6+1 dimensions? Magnetic field evolution resistivity? Endeve et al. 2009
10 Numerical challenges Most of supernova core-collapse simulations run on HPC centers, with millions of CPU-hours used (sometimes) for a single run: need for exaflop? PRACE/Curie Neutrino transport: 100 points in each dimension 1012 points... Hydrodynamics: high-resolution shock-capturing methods need CPU and have poor convergence properties near the shock (unavoidable?) Some physical processes may need many hydro time scales to appear (e.g. SASI) millions of time-steps (implicit for νs) Blondin & Mezzacappa 2007
11 Gravitational waves see also talk by M. Was Core-collapse supernovae are good sources of GW, although not the best ones (talk by U. Sperhake) : too close to spherical symmetry! 3 phases of GW emission associated with current simulations: bounce, post-bounce convective instabilities, long-term instabilities (SASI-like) Ott 2009 What can we learn from core-coolapse GW? multiple bounces? importance of convection? development/saturation of long-term instabilities...
12 What is missing? Recent 2D/3D runs show at best weak explosions : the released energy is too small! Kuroda et al Dimensionality: spherically symmetric simulation known not to succeed... 2D: weak explosions... 3D? Resolution: are all features resolved? (turbulence, instabilities) or simulated long enough? Neutrino transport: too much simplified? More physics: Relativistic gravity (and hydro)? Magnetic field (MRI)? Progenitor models (rotation)? Microphysics: are reaction rates and EoS controlled?...
13 Recent developments
14 Analogue SASI Standing Accretion Shock Instability: advective-acoustic cycle between the proto-neutron star surface and the stalled shock Blondin & Mezzacappa 2007 Foglizzo et al Provides energy to the shock and helps neutrino heating Exhibited in the simplified adiabatic case (pure hydro) Analogy with shallow water 2D model, studied in laboratory with a simple experiment. very strong indication for the existence of SASI in supernovae: not numerical artifact study of growth, saturation and properties of the instability, much faster than with a code public outreach...
15 Progenitor dependence Models for progenitors very sophisticated but not enough : rotation, magnetic field, stellar atmosphere, advanced nuclear burning stages... Possibility of asymmetries from nuclear burning : deviation from spherical symmetry Study of generic asymmetries Evidence of more energy transmitted to the shock Help in explosion? Couch & Ott 2013
16 Magnetic field Magnetic field is present in massive main-sequence stars By conservation of magnetic flux, can reach (usual) pulsar observed values... what about magnetars? τ a /τ h (a) BG in =100 m 50 m 25 m time after bounce [ms] Sawai & Yamada 2014 Magneto-rotational instability (MRI) is very likely to appear during core-collapse : differential rotation, magnetic field are present Very poor knowledge on initial magnetic field and rotation profile Need for very high numerical resolution in global simulations What is the resistivity of matter at such densities and temperatures?
17 General relativity τ adv /τ heat [s] τ heat [s] τ adv [s] G15 M15 S15 N15 G time [s] Mueller et al Relativity ( is needed both ) for 2GM gravity Rc and ( v ) hydrodynamics c 0.3 But difficult to build a code: coupling of dimensions in hydro, many non-linear equations for gravity, nightmare for neutrinos... Deepening of gravitational well: more energy available Vs. more difficulties for the shock to escape... Unexpected : GR helps the shock!
18 Lν e (10 52 erg s 1 ) D 2D 3D M(M s 1 ) Nordhaus et al D simulations Dimensionality can have great influence on the explosion mechanism: 1D (spherical symmetry) : no convective / turbulent motion 2D (axial symmetry) : inverse energy cascade for turbulence For neutrinos: exchange of energy in the radial directions Debate on the necessity of full 3D simulations : does it help the shock to escape? Recent simulations in 3D / GR, with sophisticated neutrino transport do not show any such trend... Hanke et al. 2013
19 Microphysics Input from the nuclear and particle physics communities: Peres et al New equations of state, considering full nuclear statistical equilibrium distribution (e.g. Hempel & Schaffner-Bielich 2010) or additional particles, as hyperons (e.g. Oertel et al. 2012) New electron capture rates change the shock energy (Fantina et al. 2012) Full nuclear distribution Vs. mean nucleus : not much effect what about neutrino rates? Phase transition to quarks or hyperons second shock reviving the first? (Sagert et al. 2009) Not expected in core-collapse to a neutron star; relevant for the collapse to a black hole?
20 Neutrino transport Neutrino transport uses a distribution function f(t, x i, p i ) : almost impossible to solve without symmetry / approximation Leakage scheme (in GR: Sekiguchi 2010) Flux-limited diffusion (not relativistic, Bruenn et al. 1978) Momenta schemes + M1 closure relation (Gonzalez et al. 2007, possibly relativistic) Isotropic Diffusion Scheme Approximation (not relativistic, Liebendörfer et al. 2009) Spectral transport / ray-by-ray-plus (in GR: Müller et al. 2010) Full Boltzmann (in GR : Peres et al. 2014) Trapped Particles Σ j (j+χ)f s (j+χ)f t Matter Liebendörfer et al Gonzalez et al. 2007
21 Conclusions Rapidly evolving field: first 3D-GR runs, 3D-MHD approach,... Multi-disciplinary field: collaborations with nuclear/particle physics better microphysics Heavy numerical simulations, but also laboratory physics and/or analytic approaches on simplified problems Recent 3D simulations do not provide any definitive answer on the explosion mechanism (un)fortunately... Possible answers: neutrino heating + SASI? magnetic field (generic mechanism?) microphysics : ν-reaction rates, electron captures,...??? (not neutrino oscillations) But we see them explode! Do we need more computer power, or a better physical model?
22 Conclusions Rapidly evolving field: first 3D-GR runs, 3D-MHD approach,... Multi-disciplinary field: collaborations with nuclear/particle physics better microphysics Heavy numerical simulations, but also laboratory physics and/or analytic approaches on simplified problems Recent 3D simulations do not provide any definitive answer on the explosion mechanism (un)fortunately... Possible answers: neutrino heating + SASI? magnetic field (generic mechanism?) microphysics : ν-reaction rates, electron captures,...??? (not neutrino oscillations) But we see them explode! Do we need more computer power, or a better physical model?
23 Blondin, J.M. & Mezzacappa, A., Nature 445 p.58 (2007) References Bruenn, S.W. et al., Astrophys. Space Sci. 59, P.261 (1978) Couch, S.M. & Ott, C.D., Astrophys. J. Lett. 778, P.L7 (2013) Endeve, E. et al., Astrophys. J. 713 P.1219 (2010) Fantina, A.F. et al., Astron. Astrophys. 541, A30 (2012) Foglizzo, T. et al., Phys. Rev; Lett (2012) Gonzalez, M. et al., Astron. Astrophys. 464, P.429 (2007) Hanke, F. et al., Astrophys. J. 770, 66 (2013) Hempel, M. & Schaffner-Bielich, J., Nucl. Phys. A 837, P.210 (2010) Janka, H.-T. et al., Prog. Theo. Exp. Phys., A309 (2012) Kuroda, T. et al., Phys. Rev. D (2014) Liebendörfer, M. et al., Astrophys. J. 698, p.1174 (2009) Müller, B. et al, Astrophys. J. Suppl. 189, 104 (2010) Müller, B. et al, Astrophys. J. 756, 72 (2012) Milisavljevic, D. et al., Astrophys. J. 767, 71 (2013) Nordhaus, J. et al., Astrophys. J. 720, P.694 (2010) Oertel, M. et al., Phys. Rev. C 85, (2012) Peres, B. et al., Phys. Rev. D 87, (2013) Peres, B. et al., Class. Quantum Grav (2014) Sagert, I. et al., Phys. Rev. Lett. 102, (2009) Sawai, H. & Yamada, S., Astrophys. J. Lett. 784 p.l10 (2014) Sekiguchi, Y., Class. Quantum Grav. 27, (2010) Ugliano et al., Astrophys. J. 757, p.69 (2012)
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