Formation of BH-Disk system via PopIII core collapse in full GR

1. Formation of BH-Disk system via PopIII core collapse in full GR National Astronomical Observatory of Japan Yuichiro Sekiguchi

2. Introduction • Collapsar scenario of GRB (e.g. MacFadyen & Woosley 1999) • GRB central engine： BH + Disk • Rapid rotation • Energy deposition • Neutrino pair annihilation (Mezaros & Rees 1992) • GR effects will be important (e.g. Asano & Fukuyama 2001) • MHD processes and BZ mechanism (e.g. Komissarov & Barkov 2007) • Strong magnetic fields (B~1015 G) play active roles • PopIII stellar core collapse • Massive (prompt BH formation) • low metallicity (GRB may prefer low metallicity (e.g. Modjaz et al. 2008)) • high entropy (higher neutrino luminosity expected) • Smaller (seed) B-fields

3. Introduction • GRBs could be powerful tool to explore the ancient universe • PopIII star can be a progenitor of GRB ? • Towards clarifying the above question, we performed simulations of popIII stellar core collapse in full general relativity • The first simulation of BH + Disk formation via popIII core collapse in full GR • Relevant microphysical processes are considered • Neutrino luminosities are calculated • Explore the neutrino-pair-annihilation scenario

4. Basic equations • Einstein’s equations : BSSN formulation • 4th order finite difference in space, 3rd order Runge-Kutta time evolution • Gauge conditions : 1+log slicing, dynamical shift • Puncture evolution in BH spacetime • General relativistic hydrodynamics : • High resolution shock capturing scheme • BH excision technique in BH spacetime • Lepton conservation equations: • Electron fraction • Neutrino fractions

5. Summary of microphysics • EOS: Tabulated EOS can be used • Currently Shen EOS + electrons + radiation + neutrinos • Weak rates • e± capture :FFN 1985, rate on NSE back ground • e± annihilation: Cooperstein et al. 1985, Itoh et al. 1996 • plasmon decay: Ruffert et al. 1996, Itoh et al. 1996 • Bremsstrahlung: Burrows et al. 2006, Itoh et al. 1996 • Neutrino emissions • GR neutrino leakage scheme based on Rosswog & Liebendoerfer 2004 • Opacities based on Burrows et al. 2006 • (n, p, A) scattering and absorption • with higher order corrections

6. Initial conditions • Simplified models ( s (entropy per baryon) = Ye = const ) • s = 7kB, 8kB, Ye = 0.5 • core mass ~ 10—20 Msolar • Nest step: stellar-evolution model (e.g. Ohkubo et al. 2009) • Rotation profiles • ‘Slowly’, ‘moderately’,and ‘rapidly’ rotating models Bond et al. (1984)

7. Weak bounce • Do not directly collapse to BH • Weak bounce • At bounce • ρ ~ 1013 g/cm3 • subnuclear ! • T ~ 18 MeV • Ye ~ 0.2

8. Bounce due to gas pressure • He → 2p + 2n • Gas pressure (Γ=5/3) increase • Indeed Γth >4/3 • Gas pressure dominates at ρ~1013g/cm3, T~18 MeV • EOS becomes stiffer ⇒ weak bounce

9. Slowly rotating model • After the weak bounce, a BH is eventually formed • Soon after the BH formation, geometrically thin accretion disk forms around the BH • Neutrino spheres (and bounce shock) are swallowed into BH • Low luminosity ( ~< 1053 erg/s) AH formation Density [log g/cm3]

10. Rapidly rotating model Entropy per baryon [ kB]

11. Rapidly rotating model • Large amount of matters with j > jISCO due to the rapid rotation • Centrifugally supported, geometrically thick torus is formed • ‘ neutrino torus ’ is formed • Copious neutrino emissions from the torus • High luminosity ( ~ 1054 erg/s ) Neutrino emission from the torus Density [log g/cm3]

12. Moderately rotating model • Geometrically thin disk forms at first • As the Pdisk (Pram) increases (decreases), disk height H increases • As the disk expands, the density (and temperature) decrease • The disk becomes optically thin for neutrinos ⇒ neutrino emission • Thermal pressure decreases and the disk shrinks • Neutrinos will be re-trapped and the pressure increases again

13. Moderately rotating model • As the disk expands, luminosities increase > 1054 erg/s • Time varying neutrino-luminosities ? • Simulation is ongoing • ‘ Long term ’ ( > 200 ms ) simulation of BH spacetime

14. Expected neutrino pair annihilation Neutrino luminosity ~ 1054 erg/s for moderately and rapidly rotating models Average energy ~ 20-30MeV According to the results by Setiawan et al. pair annihilation luminosities of >1052 erg/s are expected Setiawan et al. (2005) To estimate the pair annihilation rates more accurately, Ray-tracing calculations are planned Harikae et al. 2010

15. Summary • GRBs could be powerful tool to explore the ancient universe • PopIII star can be a progenitor of GRB ? • ⇒ for sufficiently rapidly rotating popIII core, massive torus is formed around BH • ⇒ the neutrino luminosities are as high as 1053-54 erg/s • ⇒ neutrino-pair-annihilation may be a promising energy-deposition mechanism • A more sophisticated model is required

16. Neutrino luminosities Slow Moderate Rapid

18. Calibration of the code • Collapse of spherical presupernova core • Comparison with the results in 1D GR Boltzmann solver (Liebendorfer et al. 2004) • Good agreement in luminosity, etc.

19. Evolution of BH mass • Assuming Kerr BH geometry • BH mass = 6~7 Msolar • Rotational energy = MBH – Mirr～ 1054 erg • If strong magnetic field exists, the rotational energy can be extracted • Mass accretion rates is still large as > several Msolar/s

20. ~300km Neutrino interactions are important The results in which first order correction to the neutron / proton magnetic moment is considered