Neutrino Cooled Accretion Disk as the Central Engine of Gamma Ray Bursts

N. Kawanaka, S. Mineshige & S. Nagataki (Yukawa Institute for Theoretical Physics)APCTP Winter School on Black Holes Astrophysics 2006, Jan. 17-20

Abstract : It is often theoretically hypothesized that the enormous power released from gamma ray bursts is generated by the accretion of a massive torus with approximately solar mass onto a stellar-mass black hole. Such a torus (or a disk) would become so dense and hot that the main cooling process would be neutrino radiation. We study the steady-state structure of this disk considering the degeneracy of electrons and neutrinos, the opacity of neutrinos, and the equation of state of nuclear matter. The stability of the disk is also discussed.

§1. Introduction

Gamma Ray Burst (GRB) ：・ duration : ～ 0.01-1000 sec

・ the energy of gamma ray :

　～ 10keV-1MeV

・ highly time-varying lightcurve

・ relativistic jet?

(compactness problem, afterglow etc.)

・ total energy : ～ 1051 ergPiran 1999

What is the central engine?

Neutrino Dominated Accretion Flow （ NDAF）

・ The remnant of the collapse of a massive star, NS-NS merger etc.

・ ρ ～ 1012 g/cm3

・ T ～ 1011 K

・ mainly cooled via neutrino radiation

BH Accretion disk

Liberate the energy via neutrino pair annihilation in the baryon-poor region

Fireball Formation？

Previous Studies ：

• neutrino-thin approximation (Popham, Woosley & Fryer 1999, Narayan, Piran & Kumar 2001, Kohri & Mineshige 2002)

• taking into account the opacity of neutrino (Di Matteo, Perna & Narayan 2002, Kohri, Narayan & Piran 2005)

We want to know the structure of NDAF taking into account the effects of EOS, lepton conservation and neutrino flavors.

§2. The Model

・ The central black hole…M = 3Msun 　 gravity : Newtonian

・ Hydrostatic equilibrium, mass accretion rate=const. ( ～ 1Msun /sec)

・ α-viscosity…Trφ = αP

・ Energy balance : Q+vis=Q-

ν+Q-rad+Q-

adv

・ βequilibrium :μp+μe=μn+μν

・ Equation of State : Lattimer & Swesty (1991)

・ Neutrino transfer : Two stream approximation (Di Matteo et al. 2002)

Assumptions

Neutrino reactions

NN

epnnn

NNNNee

pennep

ii

eee

iiii

ee

,~ ,

, ,

, ,

§3. Results

solid line, dashed line, dot-dashed line : mass accretion rate = 0.1Msun/s, 1.0Msun/s, 10Msun/s

density temperature

Cooling process

thick line : neutrino radiation

thin line : advection

Neutrino luminositythick line:electron neutrino

thin line:anti-electron neutrino

§4. Discussions

Low accretion rate:advection dominant in outer region, neutrino dominant in inner region

High accretion rate:advection dominant because of neutrino trapping

The higher the mass accretion rate is, the flatter the slope of neutrino luminosity become…neutrino trapping?

・ With the mass accretion rate around 10Msun/s, the outer part of the disk would be gravitaionally unstable→fragmentation→late time activity? (cf. X-ray flare in the early afterglow)

・ The neutrino luminosity from the whole disk is Lν ～ 1053 erg/s.

・ Taking into account the cross section of pair annihilation, the liberated energy would be not enough to explain the observed energy of GRBs → another liberation process? (eg. BZ effect)

・ Future Works: 1. Solve neutrino transfer more precisely, 2. Constitute the transonic solution, 3. Thermal stability, 4. Time-dependent analysis, 5. Take into account the convection, etc.

Gravitationally unstable region