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

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

2. 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

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

4. Inferred high speed: Variability compactness too high opacity to unless the Lorentz factor > 100 Total energy emitted in gamma rays: Assuming isotropic emission up to Eg = 1054erg (wide distribution). With beaming correction Eg ~ 1051erg (“standard energy reservoir”) Total energy in the jet: From afterglow observations Ejet = few 1051erg ~ Eg High-velocity supernovae or hypernovae Es ~ 1052erg.

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

6. 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). Disk binding energy (a =1): Accretion shock Accretion disk 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 Collapsing stellar envelope

7. Mechanisms of tapping the disk energy Neutrino heating Magnetic braking fireball MHD wind photons B B Blandford & Payne (1982) Proga et al. (2003) Fujimoto et al.(2006) Mizuno et al.(2004) Eichler et al.(1989), Aloy et al.(2000) MacFadyen & Woosley (1999) Nagataki et al.(2006) ?

8. Tapping the rotational energy of black hole Blandford & Znajek (1977), Meszaros & Rees (1997) Black hole rotational energy (a =1): Power of the Blandford-Znajek mechanism: a - spin parameter of the black hole (0 < a < 1), Y - the magnetic flux of black hole. Y =1027G cm2 is the highest value observed in magnetic stars: Ap, white dwarfs, neutron stars (magnetars). Ghosh & Abramowicz (1997), Livio et al.(1999): the electromagnetic power of the accretion disk may dominate the BZ power (?)

9. 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!

10. Blandford-Znajek effect When free charges are introduced this field can sustain electric currents along the field lines penetrating the black hole ergosphere. 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 (2008arXiv0804.1912K )

11. Can we capture the BZ-effect with modern numerical RMHD schemes?Yes! (Komissarov 2004, Koide 2004, McKinney & Gammie, 2004 ) Lorentz factor B • 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 B The solution develops steady-state paired-wind behind the expanding spherical wave front. Komissarov (2004)

12. Numerical solution versus analytical • - 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.

13. III. Activation of BZ mechanism 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 (Newtonian results) Apply at the ergosphere, r = 2rg= 2GM/c2 : Thus, the energy density of magnetic field must exceed that of matter for the BZ-mechanism to be activated!

14. In terms of , the integral mass accretion rate, and , the magnetic flux threading the black hole hemisphere, this condition reads [ in fact, we anticipate ] 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

15. “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; k = 1.2 k = 1.6 The critical value of k is indeed close to unity. It depends on a but weakly. log10r log10r

16. IV. Collapsar GRMHD simulations Based on Barkov & Komissarov (2008) and more recent results 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: • neutrino cooling (Thompson et al.,2001); • realistic equation of state, (HELM, Timmes & Swesty, 2000); • dissociation of nuclei (Ardeljan et al., 2005); • no neutrino heating (!);

17. Solid body rotation. Uniform magnetization R=4500 km Y= 4x1027-4x1028G cm2 black hole M=3M3 a=0.9 • 2D axisymmetric • GRMHD; • Kerr-Schild metric; • Starts at 1s from • collapse onset. • Lasts for < 1s outer boundary, R= 104 km free fall accretion (Bethe 1990)

18. Results • No explosion in models with k< 0.3; movie. log10r • Bipolar explosions in models with k> 0.3; movie: log10 p/pmand v; small scale movie: log10 p/pm;large scale The critical value of k is smaller because of the angular momentum in the accreting matter. (see figure)

19. 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) 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 ) • The observer jet power agrees very well with the theoretical BZ power: ( see plot )

20. Unloading of black hole magnetosphere accretion shock stagnation point black hole “exhaust” “relieved” magnetic lines magnetic “cushion” accretion disk Critical value log10 (B2/4prc2)

21. Unloading of black hole magnetosphere accretion disk magnetic “cushion” black hole “exhaust” “relieved” magnetic lines accretion shock stagnation point log10 (B2/4prc2)

22. IV. Discussion We have shown how BZ-mechanism could drive GRB explosions. However, this requires both fast rotationand strong magnetic field ofstellar cores of GRB progenitors.This is problematic for solitary stars: • 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).

23. Disk dynamo. A possible way out? - turbulent magnetic field (scale ~ H, disk height) - turbulent velocity of a-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!

24. However, • 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!?

25. Binary progenitor. Another possible way out? The fast rotation of highly magnetized star may arise • In a very close synchronized binary; • 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.

26. V. Conclusions BHs of collapsars can drive powerful GRB explosions via BZ-mechanism provided (i) BHs accumulate very large magnetic flux , ~ 1027 - 3x1028 Gcm2; (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.

27. unit length=4km t=0.4s log10 Bf/Bp log10 B return

28. Integral jet energy flux event horizon return

29. Weak dependence of k on a return