General-Relativistic Simulations of Stellar Collapse and The Formation of Stellar-Mass Black Holes
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1 General-Relativistic Simulations of Stellar Collapse and The Formation of Stellar-Mass Black Holes Christian D. Ott, TAPIR, Caltech Work in Collaboration with: Evan O Connor, Fang Peng, Christian Reisswig, Ulrich Sperhake (all Caltech), Adam Burrows (Princeton), Erik Schnetter, Frank Löffler, Peter Diener (LSU), Ian Hawke (Southampton)
2 The Core-Collapse Scenario M > 8-10 M SUN C. D. GR19, Mexico City, 2010/07/06 2
3 The Core-Collapse Scenario Core Bounce at nuclear density. M > M SUN C. D. GR19, Mexico City, 2010/07/06 3
4 The Core-Collapse Scenario C. D. GR19, Mexico City, 2010/07/06 4
5 The Supernova Problem Radius (km) Animation by Evan O Connor Shock always stalls due to dissociation & neutrino losses (no prompt hydrodynamic explosions). C. D. GR19, Mexico City, 2010/07/06 5
6 The Core-Collapse Scenario C. D. GR19, Mexico City, 2010/07/06 6
7 The Core-Collapse Scenario C. D. GR19, Mexico City, 2010/07/06 7
8 The Core-Collapse Scenario C. D. GR19, Mexico City, 2010/07/06 8
9 The Core-Collapse Scenario This talk! C. D. GR19, Mexico City, 2010/07/06 9
10 Core Collapse Timeline (SASI: Standing Accretion Shock Instability) Energy reservoir: few x erg (100 B) Time frame for explosion: s after bounce. Explosion energy: BH formation at baryonic 1 B (+ E bind envelope) PNS mass M Sun (?). What stars do/don t explode? -> CCSN Mechanism? -> Conditions for BH formation? -> Connection to GRBs? C. D. GR19, Mexico City, 2010/07/06 10
11 Maximum Neutron Star Mass Observation of old NSs most solid (approved by Jim Lattimer!): J (NS in NS/WD or NS/MS system) -> / M Sun (see C. D. GR19, Mexico City, 2010/07/06 11
12 Maximum Neutron Star Mass Observation of old NSs most solid (approved by Jim Lattimer!): J (NS in NS/WD or NS/MS system) -> / M Sun *O Connor & Ott 2010b+ T = 0.1 MeV ν-less β-equilibrium C. D. GR19, Mexico City, 2010/07/06 12
13 Studying Black Hole Formation Protoneutron star collapse is a purely-gr phenomenon. Published work: 1D: Lagrangian GR neutrino- radiation-hydro, very few detailed models. *Seidel 91, Liebendörfer et al. 04, Sumiyoshi et al. 06, 07, 08, Fischer et al D/3D: Collapse of isolated NS or collapsing polytropes. No microphysics/neutrinos. [Baiotti et al. 05, 06, Shibata & Sekiguchi 05+ Our new approach: [O Connor & Ott 2010, O Connor & Ott 10b (in prep.), Ott et al. 2010b (in prep.)+ (1) Study systematics of BH formation in the limiting case of 1.5D (spherical symmetry + rotation) using the code GR1D. -> Parameter study in EOS, progenitor structure, rotational setup. (2) Include efficient microphysics/neutrino-transport technology that can be extended to multi-d. (3) Perform 3+1 GR simulations of most interesting cases to study multi-d dynamics and gravitational-wave emission. C. D. GR19, Mexico City, 2010/07/06 13
14 GR1D *O Connor & Ott 2010 CQG+ GR1D: Open-Source 1.5D GR hydrodynamics code. Available from Eulerian Radial-gauge, polar-slicing (-> Schwarzschild-like coordinates). [Gourgoulhon 91, Romero et al. 96+ Choice of coordinates greatly simplifies GR hydro equations (zero shift). Disadvantage: Cannot evolve past horizon formation (like May & White, Misner & Sharp, van Riper formulations). GR Hydro equations in GR1D Implemented as semi-discrete finite-volume scheme with PPM reconstruction, HLLE Riemann solver and Runge-Kutta time integration. C. D. GR19, Mexico City, 2010/07/06 14
15 GR1D: Approximate Rotation Rotation in 1D: Shellular constant Ω on spherical shells. Effective centrifugal force: Extra term in equation for r momentum: + additional terms in metric quantities due to φ momentum. Central density, 40-M Sun model put into rotation with increasing initial central angular velocities. *O Connor & Ott Conservation of baryonic mass and angular momentum. C. D. GR19, Mexico City, 2010/07/06 15
16 GR1D: EOS & Microphysics Multiple finite-temperature microphysical nuclear EOS: H. Shen et al. 1998, Lattimer & Swesty 1991 with K={180,220,375} MeV. EOS tables available in HDF5 format on Neutrinos during collapse: effective Y e (ρ) approx. [Liebendörfer 05+. Postbounce: 3-flavor, energy-averaged (gray) neutrino leakage scheme. Approximate neutrino heating: Nuclear Reaction Network & consistent multi-species advection. (work in progress). C. D. GR19, Mexico City, 2010/07/06 16
17 Stellar-Mass Black Hole Formation C. D. GR19, Mexico City, 2010/07/06 17
18 Stellar-Mass Black Hole Formation There is no direct/prompt black hole formation. Generic: M IC = M PNS at bounce M SUN. Set by nuclear physics, electron capture and general collapse hydrodynamics. Inner core easily stabilized by stiff core of the nuclear force + nucleon degeneracy. Exception: Very massive stars, M > 150 M Sun C. D. GR19, Mexico City, 2010/07/06 18
19 Parameter Study: Progenitor Compactness *O Connor & Ott 2010b in prep.+ C. D. NRDA 2010, Perimeter Institute, 2010/06/26 19
20 Influence of Rotation *O Connor & Ott 2010b in prep.+ C. D. GR19, Mexico City, 2010/07/06 20
21 Prospects for Nonaxisymmetric Instabilities? (T/ W ) dynamical > 0.27, (T/ W ) secular > Low-T/ W instability: Dynamical shear instability. C. D. GR19, Mexico City, 2010/07/06 *O Connor & Ott 2010b in prep.+ Nonaxisymmetric Instability: Redistribution of angular momentum -> limit on protoneutron star spin. 21
22 Black Hole Birth Spin Spin of the nascent BH is limited to a* < 1 by nonaxisymmetric instabilities in the protoneutron star. *O Connor & Ott 2010b in prep.+ C. D. GR19, Mexico City, 2010/07/06 22
23 The Core-Collapse Supernova Long Gamma-Ray Burst Connection [see Woosley & Bloom 2006] 2 competing GRB central scenarios: (1) Millisecond Magnetars [Bucciantini, Quataert, Metzger et al , (Dessart et al. 08)+ (2) Collapsars [Woosley/MacFadyen et al.] -> 3+1 GR approach required to study CCSN-GRB connection C. D. GR19, Mexico City, 2010/07/06 23
24 Computational Framework Zelmani Core-Collapse Simulation Package composed of: Cactus: Open-source software framework for HPC, developed at the Center for Computation & Technology at LSU. Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of numerical GR (McLachlan code, open source). General-Relativistic Hydrodynamics (GRHydro, open source). Adaptive Mesh Refinement (Carpet driver, open source). Implementation of GR1D leakage scheme and multiple finite-temperature nuclear EOS (open source/open physics). Code is able to dynamically form black holes and track subsequent accretion evolution. Full 3D simulations scale to O(2048) compute cores. Simplified runs scale to O(10000) cores. C. D. GR19, Mexico City, 2010/07/06 24
25 Exploratory Simulations of 3D BH Formation 3+1 D, but restricted to an octant with symmetry boundary conditions. 75-M Sun low-metallicity progenitor model of Woosley, Heger, & Weaver 02. Simplified EOS: Piecewise polytrope with thermal component and supernuclear Γ = 2.4. Approximate neutrino cooling, no neutrino heating: [Ott et al in prep.] Temperature T via ideal gas of n and p. Optical depth τ : fit from GR1D simulation. Moderate rotation, Ω 0 = {0,1} rad/s. Initial uniform rotation in inner 1 M Sun. 11 levels of AMR. Excision of hydrodynamics inside horizon. C. D. GR19, Mexico City, 2010/07/06 25
26 3D BH Formation: First Results [Ott et al in prep.] C. D. GR19, Mexico City, 2010/07/06 Soon to come: More rapid rotation, full 3D without symmetries. 26
27 Gravitational Waves from BH Formation [Ott et al in prep.] Convection/ Turbulence BH Formation and BH Ringdown Core Bounce 40 M Sun, WW95 model Ω 0 = 1.5 rad/s a* = 0.7 (results preliminary) C. D. GR19, Mexico City, 2010/07/06 27
28 C. D. GR19, Mexico City, 2010/07/06 28
29 Summary No direct (or prompt) BH formation in ordinary massive star collapse. A protoneutron star (PNS) phase always precedes BH formation. Extensive 1.5D parameter study of BH formation: Nonaxisymmetric instability will limit protoneutron star spin and enforce a* < 1 for the nascent BH. First 3D simulations of collapse, PNS phase, PNS collapse, and post-bh formation phase -> first gravitational waveforms indicate characteristic GW signature of BH formation. Much work ahead: 3D without symmetry constraints, GRMHD, neutrino leakage/transport. C. D. GR19, Mexico City, 2010/07/06 29
30 Supplemental Slides C. D. GR19, Mexico City, 2010/07/06 30
31 Example: Black Hole Formation in Failing Core-Collapse Supernovae *O Connor & Ott 2009, see also Sumiyoshi et al. 2006, 2007, 2008, Fischer et al Radius (km) Radius (km) Simulations and animations by Evan O Connor C. D. GR19, Mexico City, 2010/07/06 31
32 C. D. GR19, Mexico City, 2010/07/06 32
33 Comparison with Full Transport Fischer et al GR1D GR1D reproduces full transport to 25% in terms of L ν and to 10% in terms of the time of BH formation, but is roughly 10 times faster. -> allows for parameter study. C. D. GR19, Mexico City, 2010/07/06 33
![Computational Cost & Scaling [Based on GR+GRHD] 9 levels of refinement, each 400 3 zones, 400 3D grid functions -> Memory footprint > 2 TB (including inter-process buffers) 1 single-zone update: 50](/docs-images/86/94634270/images/34-1.jpg "kflop; total timesteps: 1 M (fine grid). -> 1500 Petaflops. Factor 5-10 larger with radiation transport.")
34 Computational Cost & Scaling [Based on GR+GRHD] 9 levels of refinement, each zones, 400 3D grid functions -> Memory footprint > 2 TB (including inter-process buffers) 1 single-zone update: 50 kflop; total timesteps: 1 M (fine grid). -> 1500 Petaflops. Factor 5-10 larger with radiation transport. (Franklin results are extrapolated from Black Hole scaling test) Weak scaling of a 9-level AMR test calculation of the coupled GR + GRHD system, evolving a neutron star. C. D. GR19, Mexico City, 2010/07/06 C. D. GR19, Mexico City, 2010/07/06 34
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