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CENTRAL ENGINES OF GRB JETS

Maxim Barkov
Space Research Institute, Russia, University of Leeds, UK

Serguei Komissarov
University of Leeds, UK


Plan of this talk

· · · · ·

Gamma-Ray-Bursts ­ very brief review, Models of Central Engines, Numerical simulations I: Magnetar model, Numerical simulations II: Collapsar model, Conclusions


I. Gamma-Ray-Bursts
Discovery: Vela satellite (Klebesadel et al.1973);
Konus satellite (Mazets et al. 1974);

Cosmological origin:
2. Beppo-SAX satellite ­ X-ray afterglows (arc-minute resolution) , optical afterglows ­ redshift measurements ­ identification of host galaxies (Kulkarni et al. 1996, Metzger et al. 1997, etc) 1. Compton observatory ­ isotropic distribution (Meegan et al. 1992);

Supernova connection of long duration GRBs:
1. Association with star-forming galaxies/regions of galaxies; 2. Few solid identifications with supernovae, SN 1998bw, SN 2003dh and others... 3. SN bumps in light curves of optical afterglows. 4. High-velocity supernovae ( 30,000km/s) or hypernovae (1052erg).


Spectral properties:
Non-thermal spectrum from 0.1MeV to GeV:

Bimodal distribution (two types of GRBs?):

short duration GRBs

long duration GRBs


Variability:
· smooth fast rise + decay; · several peaks; · numerous peaks with substructure down to milliseconds

Total power:

Inferred high speed:
Too high opacity to

assumption of isotropic emission unless Lorentz factor > 100


Inferred collimation:
afterglow light curve with achromatic break beamed radiation

velocity vector v

(Piran, 2004)

decelerating and expanding source


Relativistic jet/pancake model of GRBs and afterglows:

jet at birth

pancake later


II. Models of central engines
(1) Potential of disk accretion onto stellar mass black holes:
disk binding energy: thin disk life time: - accreted mass - disk outer radius - gravitational radius - Shakura­Sunyaev parameter

Ultra-dense Hyper-Eddington neutrino cooled disks !!!


(1.1) Merger of compact stars ­ origin of short duration GRBs?
Paczynsky (1986); Goodman (1986); Eichler et al.(1989); Neutron star + Neutron star Neutron star + Black hole White dwarf + Black hole Black hole + compact disk

Burst duration: 0.1s ­ 1.0s Released binding energy:


(1.2) Collapsars­ origin of long duration GRBs?
Iron core collapses into a black hole: "failed supernova". Rotating envelope forms hyper-accreting disk Accretion disk Accretion shock Woosley (1993) MacFadyen & Woosley (1999)

Collapsing envelope

The disk is fed by collapsing envelope. Burst duration > few seconds


(1.3) Mechanisms for tapping the disk energy
Neutrino heating fireball Magnetic braking

MHD wind
B B

Eichler et al.(1989), Aloy et al.(2000) MacFadyen & Woosley (1999) Nagataki et al.(2006) (? ? ? )

Blandford & Payne (1982) Proga et al. (2003) Fujimoto et al.(2006) Mizuno et al.(2004)


(2) Potential of a neutron star (millisecond magnetar):
Usov(1992), Thompson(1994), Thompson(2005), Bucciantini et al.(2006,2007)

Rotational energy: Wind Power: (i) ultra-relativistic (ii) non-relativistic

Gamma-Ray-Repeaters and Anomalous X-ray pulsars - isolated neutron stars with dipolar(?) magnetic field of 1014- 1015 G (magnetars); (Woods & Thompson, 2004)


(3) Potential of black hole rotation:
Blandford & Znajek (1977), Meszaros & Rees (1997)

Black hole rotational energy: Power of the Blandford-Znajek mechanism: - poloidal magnetic field near the BH horizon


III. Computer simulations: Magnetar model
Setup
v v v emerging magnetic field (R =20km) v

GR MHD 2D

free fall zone v outer boundary, R= 104 km v

v

"radiation bubble" energy deposition zone (R=200km)

Neutrinosphere (inner boundary, R=15km)


Free fall model of collapsing star (Bethe, 1990)
radial velocity: mass density: accretion rate: (Delayed explosion, t=1s.) + specific angular momentum: l=1016 sin cm2/s

Energy of radiation bubble (heat):


Inner boundary (R=15km):
Rotation period: P=2ms; poloidal velocity: vp=0 Mass density: =3â 109g/cm3; gas temperature: T=4 Mev (Thompson et al.,2001); Neutrino luminosity: L(R,T)= 6.5â 1051 erg/s in each flavour; Neutrino energy: E=3.15T=12.6 Mev in each flavour; Magnetic field: "squashed" dipole, B0=1015 G; Gravity: gravitational field of magnetar only (Schwarzschild metric); no self-gravity; Microphysics: neutrino transport ­ optically thin regime; neutrino cooling and heating (Thompson et al.,2001); realistic equation of state, (HELM, Timmes & Swesty, 2000); dissociation of nuclei (Ardeljan et al., 2005); Ideal Relativistic MHD - no physical resistivity (only numerical);


results
Mass accretion rate Delayed explosion power

movie 1: Model A: inner region , R<1000 km radius; colour image - log(), g/cm3

movie 2: Model A: inner region, R<1000 km radius; lines and colour ­ poloidal magnetic field lines


Model A, t=0.2s

unit length=2km

log10

density (g/cm3);

vp/c


Summary or results:
· · · · · · · Jets are formed Jets power Total energy of Expected burst Jet advance spe Expected break Jet flow speed immediately after the supernova explosion. magnetar duration (spin-down time) ed out time

Good news for the magnetar model of long duration GRBs !


IV. Computer simulations: Collapsar model
Setup
black hole M=3M3 a=0.9 B v v v v

GR MHD 2D
Bethe's free fall model

Solid body rotation

v B

Dipolar magnetic field

differential rotation; angular momentum

l=1017 sin cm2/s

Uniform magnetization R=4500km B0= 3x109-3x1010G

Same microphysics as in magnetar simulations (no neutrino heating)


results
Model parameters: (1) Bethe's C1=3, 9 (2) Magnetic field B0=1010G, 3x1010G (3) Black hole hole rotation parameter, a=0, 0.9 movie 1: B0=1010G, C1=9, a=0.9 inner region - 800 km radius; colour image - log(), g/cm3 B0=31010G, C1=9, a=0.9 inner region - 800 km radius; colour image - log(), g/cm3 B0=31010G, C1=9, a=0.9 inner region - 16000 km radius; colour image - log(P/Pm),

movie 2:

movie 3:


unit length=4km t=0.4s

log10 (g/cm3), magnetic field lines, and velocity vectors


log10 (g/cm3), magnetic field lines, and velocity vectors


log10

log10 Pm/P


log10 B

log10 B/B

p


Jets are powered mainly by the black hole via the Blandford-Znajek mechanism !!

· No explosion if a=0; · Jets originate from the black hole; · ~70% of total magnetic flux is accumulated by the black hole; · Energy flux in the ouflow ~ energy flux through the horizon (disk contribution < 20%); · Theoretical BZ power:


Summary or results:
· · · · · · · · Jets are formed when BH accumulates sufficient magnetic flux. Jets power Total energy of BH Expected burst duration (? ) Jet advance speed Expected jet break out time Jet flow speed (method limitation) Jets are powered by the Blandford-Znajek mechanism

Good news for the collapsar model of long duration GRBs !


V. Conclusions
· There is a number of promising models for the central engines of GRBs. · Theoretical models are sketchy and numerical simulations are only now beginning to explore them. · Our results suggest that: 1) Millisecond magnetars can indeed drive long duration GRB jets of medium power ( up to fewâ 1052 erg/s). These jets can be produced at very early stages of successful supernova explosions; 2) Black holes of failed supernovae can drive very powerful GRB jets via Blandford-Znajek mechanism if the progenitor star has strong poloidal magnetic field B0 >109G;