Maxim Barkov University of Leeds, UK, Space Research Institute, Russia Serguei Komissarov University of Leeds, UK TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA Blandford-Znajek mechanism and GRB jets

Plan of this talk Gamma-Ray-Bursts – very brief review; Collapsar model for long GRBs; Activation of BZ- mechanism in collapsing stars; GRMHD simulations of collapsars; Discussion

Bimodal distribution (two types of GRBs?): long duration GRBs short duration GRBs I. Gamma Ray Bursts

Total energy emitted in gamma rays: Inferred high speed: Variability compactness too high opacity to unless the Lorentz factor > 100 Assuming isotropic emission up to E  = erg (wide distribution). With beaming correction E  ~ erg (“standard energy reservoir”) Total energy in the jet: From afterglow observations E jet = few erg ~ E  High-velocity supernovae or hypernovae E s ~ erg.

( - occasionally observed) 0 - prompt emission; 1 - steep decay phase; 2 - shallow decay phase; 3 - normal decay phase; 4 - post “jet break” phase; 5 - X-ray flares. Restarting of central engine, wide Lorentz factor distribution, multi-component ejecta, and many other ideas. New question marks: Jet breaks (?) standard energy (?) Swift input

Collapsing stellar envelope Accretion shock Accretion disk Disk binding energy (a =1): Most of the dissipated energy is radiated in neutrinos which almost freely escape to infinity. 1% of the energy is sufficient to explain hypernovae and GRB-jets II. Collapsar model of central engines of long GRBs Iron core of a rotating star collapses into a black hole – “failed supernova”; Stellar envelope collapses into a hyper-accreting neutrino-cooled disk; (Woosley 1993, MacFadyen & Woosley 1999).

Mechanisms of tapping the disk energy BB Neutrino heating Magnetic braking fireball MHD wind 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) photons

Black hole rotational energy (a =1): Power of the Blandford-Znajek mechanism: Blandford & Znajek (1977), Meszaros & Rees (1997) a - spin parameter of the black hole (0 < a < 1),  - the magnetic flux of black hole.  =10 27 G cm 2 is the highest value observed in magnetic stars: Ap, white dwarfs, neutron stars (magnetars). Tapping the rotational energy of black hole Ghosh & Abramowicz (1997), Livio et al.(1999): the electromagnetic power of the accretion disk may dominate the BZ power (?)

Blandford-Znajek effect Vacuum around black holes behaves as electromagnetically active medium: Steady-state Faraday eq.: Strong electric field is generated when BH is immersed into externally supported vacuum magnetic field! In contrast to a unipolar inductor or a neutron star this field is not due to the electric charge separation on a conductor!

Blandford-Znajek effect For the perfectly conducting case with insignificant inertia of plasma the magnetosphere is described by Magnetodynamics (MD -- inertia-free relativistic MHD). Blandford and Znajek(1977) found a perturbative stationary solution for monopole magnetospheres of slowly rotating black holes. It exhibited outflows of energy and angular momentum. See for details: Komissarov (2004, mnras, 350, p427) Komissarov (2008arXiv K ) When free charges are introduced this field can sustain electric currents along the field lines penetrating the black hole ergosphere.

Can we capture the BZ-effect with modern numerical RMHD schemes? Yes! GRMHD, 2D, axisymmetry; Kerr-Schild coordinates, a=0.9; Inner boundary is inside the event horizon; Outer free-flow boundary is far away; Initially non-rotating monopole field and zero plasma speed in FIDOs frame; Magnetically-dominated regime ; wave front Lorentz factor B B (Komissarov 2004, Koide 2004, McKinney & Gammie, 2004 ) Komissarov (2004) The solution develops steady-state paired-wind behind the expanding spherical wave front.

- BZ-solution; - MHD at r = 50M; - MHD at r = 5M; This magnetically-dominated MHD solution is very close to the steady-state MD solution; Blandford-Znajek (1977) for a << 1; Komissarov(2001) for a = 0.9. Numerical solution versus analytical

What is the condition for activation of the BZ-mechanism with finite inertia of plasma? MHD waves must be able to escape from the black hole ergosphere !? Alfven speed,, free fall speed Apply at the ergosphere, r = 2r g = 2GM/c 2 : Thus, the energy density of magnetic field must exceed that of matter for the BZ-mechanism to be activated! III. Activation of BZ mechanism (Newtonian results)

In terms of, the integral mass accretion rate, and, the magnetic flux threading the black hole hemisphere, this condition reads In the context of the collapsar model for Gamma Ray Bursts with and this requires Note that the highest magnetic flux of magnetic stars measured so far is only [ in fact, we anticipate ]

“Test-this-idea” simulations (in preparation): GRMHD, 2D, axisymmetry; Kerr black hole, a = 0.9; Polytropic EOS; Free-fall accretion of initially cold plasma with zero angular momentum; Monopole magnetic field;  = 1.2  = 1.6 The critical value of  is indeed close to unity. log 10  It depends on a but weaklyweakly.

Free fall model of collapsing star: Bethe (1990) + ad hoc rotation (MacFadyen & Woosley 1999) and magnetic field; Gravity: gravitational field of Kerr black hole only; no self-gravity; Microphysics: IV. Collapsar GRMHD simulations Based on Barkov & Komissarov (2008) and more recent results neutrino cooling (Thompson et al.,2001); realistic equation of state, (HELM, Timmes & Swesty, 2000); dissociation of nuclei (Ardeljan et al., 2005); no neutrino heating (!);

black hole M=3M 3 a=0.9 Solid body rotation. Uniform magnetization R=4500 km  = 4x x10 28 G cm 2 outer boundary, R= 10 4 km free fall accretion (Bethe 1990) 2D axisymmetric GRMHD; Kerr-Schild metric; Starts at 1s from collapse onset. Lasts for < 1s

No explosion in models with  < 0.3; Bipolar explosions in models with  > 0.3; movie. log 10  movie: log 10 p/p m  and v; small scale movie: log 10 p/p m ; large scale Results The critical value of  is smaller because of the angular momentum in the accreting matter. (see figure)see figure

Explosions are powered mainly by the black hole via the Blandford-Znajek mechanism No explosion if a = 0; ~70% of total magnetic flux is accumulated by the black hole ( see plot)( see plot) This is in conflict with Olivie et al. (1999) but agrees with Newtonian simulations by Igumenshchev (2007); Energy flux in the jet ~ energy flux through the horizon; possible disk contribution < 20%; ( see plot )see plot The observer jet power agrees very well with the theoretical BZ power: ( see plot )see plot

Critical value Unloading of black hole magnetosphere accretion disk magnetic “cushion” stagnation point black hole “exhaust” “relieved” magnetic lines log 10 (B 2 /4  c 2) accretion shock

Unloading of black hole magnetosphere accretion disk magnetic “cushion” stagnation point black hole “exhaust” “relieved” magnetic lines log 10 (B 2 /4  c 2) accretion shock

IV. Discussion Evolutionary models of solitary massive stars show that even much weaker magnetic fields (Taylor-Spruit dynamo) result in too slow rotation – no collapsar disk (Heger et al. 2005) Low metalicity may save the collapsar model with neutrino mechanism (Woosley & Heger 2006) but BZ mechanism needs much stronger magnetic field. Solitary magnetic stars (Ap and WD) are slow rotators (with solid body rotation). We have shown how BZ-mechanism could drive GRB explosions. However, this requires both fast rotation and strong magnetic field of stellar cores of GRB progenitors. This is problematic for solitary stars:

- turbulent magnetic field (scale ~ H, disk height) - turbulent velocity of  -disk Application to the neutrino-cooled disk (Popham et al. 1999): The inverse-cascade in disk corona (Tout & Pringle 1996) may give larger scales. For the scale ~ R This seems a bit small for activation of BZ-mechanism! Disk dynamo. A possible way out?

The accretion rate through the polar region may strongly decline several seconds after the collapse (Woosley & MacFadyen 1999), reducing the magnetic flux required for explosion; Neutrino heating (excluded in the simulations) may also help to reduce the required magnetic flux. Two-stage GRB explosions!? However,

Binary progenitor. Another possible way out? 1.In a very close synchronized binary; 2.After spiral-in of compact star (NS or BH) during the common envelope phase (e.g. Zhang & Fryer 2001 ). In both cases the hydrogen envelope of progenitor is dispersed leaving, as required, a bare helium core. The fast rotation of highly magnetized star may arise

V. Conclusions BHs of collapsars can drive powerful GRB explosions via BZ-mechanism provided (i) BHs accumulate very large magnetic flux, ~ x10 28 Gcm 2 ; (ii) BHs rotate rapidly, a~1. The condition on magnetic field strength can be lowered if the rate of accretion directly onto the black hole is reduced; late explosions (?), neutrino assistance (?). The magnetic magnetic field is either (i) generated in the collapsar disk or (ii) relic field of the progenitor star. The latter implies close binary models in order to explain the rapid rotation of progenitor.

log 10 B  /B p log 10 B unit length=4km t=0.4s return

event horizon Integral jet energy flux return

Weak dependence of  on a