Formation and evolution of BH and accretion disk in Collapsar

Transcription

1 Formation and evolution of BH and accretion disk in Collapsar Yuichiro Sekiguchi National Astronomical Observatory of Japan arxiv :

2 Motivation

3 Collapsar model of GRB Central engine : Black hole + Disk Formed after collapse of rotating massive star (Woosley 1993) Energy sources for GRB Jet: e - e + plasma production via neutrino pair annihilation Geometrical and thermodynamical structure of disk should be calculated Poyning flux generation via BZ process Mass and spin of black hole formed should be calculated in a self-consistent manner Fully general relativistic simulation is one of the most promising approaches

4 GRB-progenitor core model Dilemma : Type-Ib/c SN association vs Disk formation Stars should have been lost H/He layer (usually by stellar wind) angular momentum loss at the same time of mass loss Some peculiar evolution model is required Resolutions suggest higher-entropy massive core Highly different from ordinary onion-like SN core He star merger model (Fryer & Heger 2005) Binary interaction model (van den Huevel & Yoon 2007) Chemically homogeneous evolution (Yoon & Langer 2006, Woosley & Heger 2006) PopIII stellar core (Schneider et al. 2002) GRBs are anomalous, then, progenitor core also may be Collapse of high-entropy core has not been studied in detail Fully general relativistic simulation!

5 Setting of simulation

6 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 General relativistic lepton-neutrino hydrodynamics : Neutrino transfer equations (GR leakage) Lepton-number conservation equations High resolution shock capturing scheme Microphysics As sophisticated as SN simulation Nuclear EOS table Weak interactions Detailed neutrino opacities Basic equations BH (Hydro.) excision technique d Ye dt d Y e dt d Y e dt d Y x dt e cap e cap e cap pair a a pair pair T T plasmon a b e cap Q a (,stream) b plasmon plasmon Brems (leak) b Brems Brems leak x Q (leak) b leak e leak e

7 Initial conditions Simplified model ( constant s (entropy per baryon) & Ye ) s = (5-)8k B, Ye = 0.5, core mass ~ (8-)15 Msolar Rotation profiles are added (based on Woosley & Heger 2006) Initial models are SLOWLY rotating in the sense j < j ISCO, Sch.BH

8 Simulation Results

9 Evolution path in ρ-t plane Evolution path Gas pressure dominated Electron degenerate pressure dominated Pe = Pgas Ordinary SN core

10 Gas pressure dominated bounce The collapsing core experiences gas pressure dominated bounce EOS is stiffened Γ=4/3(degenerate electron) Γ=5/3 (ideal gas) A shock wave is formed The shock becomes accretion shock Bounce is weak and ram pressure is large BH is formed eventually

11 10 53 erg/s e e x Accretion shock

12 10 53 erg/s e e x

13 Geometrically-thin disk phase Heating source : Shocks at the surface of disk Cooling source : neutrinos, advection Advection vs neutrinos t t diff adv ~ ~ H c R v ~ ~ H 0.1c R 0.1c Infalling matter R >> H t diff << t adv

14 Disk expansion As a result of subsequent accretion of highangular-momentum matter Density optical depth thermal energy H increases When t diff = t adv, neutrinos are trapped Ram pressure Disk expand to be geometrically-thick torus

15 Accretion disk in collapsar is convectively unstable! Point: the disk is, effectively, heated form below In inner region Shock heating is stronger Neutrino cooling is less efficient Negative entropy gradient SN component? Convective luminosity is sufficient (Milosavljevic et al.2010) Convective activities

16 KH instability Infalling matter v ~ 0.3c Convective eddy ~ 0.1c

17 Angular momentum is transported inward Negative time-averaged Reynolds stress Inward Angular momentum transport (cf. CDAF)

18 Evolution of BH and disk BH mass : 6.5Msolar 14Msolar BH spin : Critical for disk properties, pair annihilation efficiency, BZ efficiency Disk mass : 0.1Msolar 0.8Msolar

19 Mass accretion rate Large mass accretion due to high entropy Thin disk phase : ~ 20-40Msolar/s Convective phase : ~ 5-10Msolar/s, highly time variable Possible origin of time variable shell formation for int.-shock

20 Neutrino luminosity Efficiency Thin disk : ~ 0.01 Thick torus: ~ 0.1 Just before BH formation, L ~ erg/s Thick torus emits L ~ erg/s, time-variable Thin disk emits L ~ erg/s neutrinos and anti-neutrinos are almost equally emitted

21 Importance of BH spin Efficiency of exchange of gravitational binding energy : ~ 0.01 (a=0) ~ 0.4 (a=1) Disk properties : no neutrino trapping for a=0 Efficient cooling, no/very-weak negative entropy gradient No convective activities, no time variability a = 0 a = 0.95 Chen & Beloborodov (2007)

22 Dependence of the initial rotation

23 Unstable Solberg-Hoiland frequency [Hz] Rapidly rotating model Centrifugally supported, geometrically thick torus is immediately formed because of rapid rotation Copious neutrino emissions (~ erg/s ) from the torus Convection is suppressed due to stabilizing epicyclic mode Without epicyclic mode With epicyclic mode Neutrino emission from the torus

24 Slowly rotating model The thin disk does not expand in our simulation time When fluids with higher j fall onto disk in a later phase, the disk will expand to be a thick torus and convection may set in Neutrino luminosity is low as ~ erg/s Density [log g/cm 3 ] AH formation

25 Application to GRB

26 Neutrino pair annihilation Zalamea & Beloborodov (2010) Good news: L L Lpair ~ erg/s for our model Strong dependence on dot(m)^(9/4) early phase BZ powered Jet McKinney (2005) fω = 3 (a=0.8), 10 (a=0.9), 80 (a=1.0) ~ 10 % can be used for Jet (McKinney 2005) LBZ ~ erg/s for our model Weaker dependence on dot(m)^(1) later phase

27 Summary First full GR simulation of collapse of slowly rotating high-entropy core to BH + Disk Moderately rotating model thin Disk thick Torus transition accretion flow is convectively unstable (cf. CDAF) convection induces time-varying neutrino luminosity Slowly rotating model thin disk formation the transition might occur in a later phase Rapidly rotating model thick torus is immediately formed convection is suppressed due to stabilizing epicyclic mode Both neutrino pair annihilation and BZ processes can produce sufficient energy

28 e e x Thank you very much!