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

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Formation of BH-Disk system via PopIII core
collapse in full GR
National Astronomical Observatory of
Japan Yuichiro Sekiguchi
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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 (B1015 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

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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

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Basic equations

• Einsteins equations BSSN formulation
• 4th order finite difference in space, 3rd order
  Runge-Kutta time evolution
• Gauge conditions 1log 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

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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

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Initial conditions

• Simplified models ( s (entropy per baryon) Ye
  const )
• s 7kB, 8kB , Ye 0.5
• core mass 1020 Msolar
• Nest step stellar-evolution model (e.g. Ohkubo
  et al. 2009)
• Rotation profiles
• Slowly, moderately, and
  rapidly
  rotating models

Bond et al. (1984)
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Weak bounce

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

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Bounce due to gas pressure

• He ? 2p 2n
• Gas pressure (G5/3) increase
• Indeed Gth gt4/3

• Gas pressure dominates at ?1013g/cm3, T18 MeV
• EOS becomes stiffer ? weak bounce

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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 ( lt 1053 erg/s)

AH formation
Density log g/cm3
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Rapidly rotating model
Entropy per baryon kB
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Rapidly rotating model

• Large amount of matters with j gt 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
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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

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Moderately rotating model

• As the disk expands, luminosities increase gt 1054
  erg/s
• Time varying neutrino-luminosities ?
• Simulation is ongoing
• Long term ( gt 200 ms ) simulation of BH
  spacetime

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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 gt1052 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
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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

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Neutrino luminosities
Slow
Moderate
Rapid
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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.

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Evolution of BH mass

• Assuming Kerr BH geometry
• BH mass 67 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 gt several
  Msolar/s

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