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

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~10 15 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

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

Einstein’s equations : BSSN formulation –4 th order finite difference in space, 3 rd 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 Basic equations

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 –plasmon decay: Ruffert et al. 1996, Itoh et al –Bremsstrahlung: Burrows et al. 2006, Itoh et al Neutrino emissions –GR neutrino leakage scheme based on Rosswog & Liebendoerfer 2004 –Opacities based on Burrows et al (n, p, A) scattering and absorption with higher order corrections

Simplified models ( s (entropy per baryon) = Ye = const ) –s = 7k B, 8k B, 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 Initial conditions Bond et al. (1984)

Weak bounce Do not directly collapse to BH –Weak bounce At bounce –ρ ~ g/cm 3 subnuclear ! –T ~ 18 MeV –Ye ~ 0.2

Bounce due to gas pressure He → 2p + 2n –Gas pressure (Γ=5/3) increase Indeed Γ th >4/3 Gas pressure dominates at ρ~10 13 g/cm 3, T~18 MeV EOS becomes stiffer ⇒ weak bounce

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 ( ~< erg/s) Slowly rotating model Density [log g/cm 3 ] AH formation

Rapidly rotating model Entropy per baryon [ k B ]

Large amount of matters with j > j ISCO due to the rapid rotation Centrifugally supported, geometrically thick torus is formed –‘ neutrino torus ’ is formed Copious neutrino emissions from the torus –High luminosity ( ~ erg/s ) Rapidly rotating model Neutrino emission from the torus Density [log g/cm 3 ]

Geometrically thin disk forms at first As the P disk (P ram ) 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 Moderately rotating model

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

Expected neutrino pair annihilation Setiawan et al. (2005) Neutrino luminosity ~ erg/s for moderately and rapidly rotating models Average energy ~ 20-30MeV According to the results by Setiawan et al. pair annihilation luminosities of >10 52 erg/s are expected To estimate the pair annihilation rates more accurately, Ray-tracing calculations are planned Harikae et al. 2010

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 erg/s ⇒ neutrino-pair-annihilation may be a promising energy- deposition mechanism A more sophisticated model is required

Neutrino luminosities Slow ModerateRapid

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.

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

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