EEttifRttiEnergy Extraction from Rotating Black Hole by Magnetic Reconnection Shinji Koide Kumamoto University Collaborators: Kenzo Arai (Kumamoto University) Koide & Arai, ApJ 682, 1124-1133 (2008) SCSAMM workshop 2009.8.28(Fri) Outline • Motivation • Energy extraction mechanism from black hole: Penrose process • A mechanism of energy extraction from blac k ho le throug h magne tic reconnec tion • Summary and future aspects One of Motivation: Magggpnetic reconnection in the ergosphere ΩH Ideal GRMHD simulation of uniformly magnetized plasma around rotating black hole (Komissarov 2005) Kerr x Schwarzschild radius black hole Magnetic rS field lines t 60 ergosphere 2c magnetic Frame-dragging reconnection x (if resistivity is effect significant) Kerr black hole a 0.9 Initial: uniform magnetic field (Wald solution) sprit monopole magnetic field in ergosphere ֜ magnetic reconnection in ergosphere ֜ Notation of space-time and Ergosphere Space-time around rotating black hole (Kerr metric) 0 1 2 3 2 x , x , x , x t,r,, metric ds g dx dx 3 g 2 (ittild(gravitational red-shift, g i0 Lapse function 00 gravitational potential) i1 gii g Anggyular velocity of i0 i g frame-dragging ii g Shift vector (velocity of frame dragging) ZAMO coordinates xˆ 0 , xˆ1 , xˆ 2 , xˆ 3 (local Minkowski frame) (zero angular momentum observer) Ergosphere: 1 Any matter, energy, and information never propagate against the rotation of black hole rotation in the ergosphere. Unit system: c 1, 0 1, 0 1 Conservative quantity of a particle aroundiblkhld rotating black hole • Energy-at-infinity (total energy): Rest mass energy + kinetic energy + gravitational potential E Eˆ L Eˆ P “Frame-dragging potential” Energy observed by ZAMO Eˆ m • Angular momentum Lorentz factor ˆ L g P Momentum Pˆ m v When L Eˆ / in ergosphere, the energy-at-infinity becomes negative, E 0. Penrose Process Extraction of energy of rotating black hole through particle fission in ergosphere Conservation of angular momentum LA LB LC Conservation of energy EA EB EC A→B+C (fission ֜ redistribution of angular Larger energy-at-infinity momentum) C than injected particle A E E ˆ C A When LB EB / in ergosphere, EB 0. B Fission Negative If particle B is swallowed by black energy-at- infinity Kerr Horizon hole, total mass of black hole E 0 B Black decreases. The particle C obtains HlHole energy larger than that of injected 1 Ergosphere particles: EC EA EB EA 1 M 'BH M BH EB M BH Frame Dragging Effect Energy extraction from black hole Mechanism of extraction of black hole rotational energy • Penrose process Throug h nega tive • MHD Penrose process energy-at-infinity • Blandford-Znajek mechanism To realize negative energy-at-infinity, we require redistribution of angular momentum. Mechanisms Carrier of negative energy Force for redistribution Penrose Particle Particle fission MHD Penrose Plasma Magnetic tension Blandford-Znajek Electromagnetic field ー Magnetic tension How about magnetic reconnection? Magnetic reconnection： Plasma acceltibleration by reconnec tiftion of magne tifildtic field lines Ideal MHD condition =frozen-in condition Plasma acceleration B0 0 Electric J 0 resistivity Plasma outflow Magnetic field lines Breakdown region of ideal MHD condition Magnetic sling-shot Plasma acceleration Terminal velocity vterm Magnetic tension Terminal velocityyp of plasma outflow from ma gnetic reconnection when magnetic energy is converted to kinetic energy of plasma flow (Non-relativistic case) 2 2 0 2 B0 B0 vterm vterm vA (Alfven vel oc ity ) 2 2 0 In relativistic case, we have to consider inertia of pressure. Magnetic reconnection and particle fission Particle fission Penrose process PtilParticle Magnetic reconnection Magnetic field lines NhiNew mechanism Plasma of energy extraction outflow from rotating BH? ergosphere Frame-dragging effect ω Koide & Arai 2008 Escape and fall of a pair of plasma elements ejected from magnetic reconnection region (Schematic picture) Magnetic Backward reconnection plasma E 0 ejection B E E C C A B Forward plasma Kerr ejection black Magnetic field lines Interchange hole of plasma ergosphere ω Very complex phenomena: numerical simulation with general relativistic MHD with resistivity (resistive GRMHD) Simulation of magnetic reconnectiiion in ergosp here •We require numerical simulation to understand global mechanism of the magnetic reconnection in ergosphere. • HhHowever, we have no numer ilhifical technique of resistive GRMHD. (This is reasonable because of standard formulation has causality problem. ) • To estimate the energy extraction of black hole due to magnetic reconnection, we use simplified model with combination of slab model of magnetic reconnection and general relativistic potential. Analytic model of magnetic reconnection in ergosphere Rest frame of Local slab bulk plasma approximation out C B Energy-at-ifiitinfinityoflf plasma Bulk plasma A element ejected Plasma element vˆKepler c velocity vˆ vK forwardly/backwardly with the ejected forwardly 0 K ejection velocity v’=±v’out B Plasma element E ˆ ˆ C ejected backwardly E E P EB (‘+’ = ‘C’, ‘ー’ = ‘B’) C ˆ 1 E Hˆ U int ˆ ˆ ˆ ˆ P H v Therma l Enthalpy energy v v' Velocityyp of plasma vˆ K out 1 v v' element ejected K0 out observed by ZAMO θ=π/2 1/ 2 2 ˆ 1 vˆ Lorentz factor Slab model of relativistic magnetic reconnection Anti-parallel magnetic field Magnetic x' (bulk plasma reconnection x' P' 0 rest frame) point Forward Backward ejection Current sheet ejection v’out v’ out y' y' Py'0 Py'0 0 Pair-plasma flow: Redistribution of Resistive (angular) momentum! region 0 (()gLocal approximation) We neglect • Tidal force and Coriolis’ force • Global magnetic field reaction Terminal velocity of plasma outflow from relativistic magnetic reconnection: inertia effect of pressure. Complete energy conversion of magnetic energy to kinetic energy of plasma elements (assumption): 2 Magnetic and thermal 1U B0 Particle energy 'out H H 1 U energy per particle ' 2n after reconnecti on out 0 before reconnection Then, we get maximum of 4-velocity of the plasma element due to magnetic reconnection: 2 1/ 2 1 u 2 1 u 2 u' ' v' 1 A 1 1 A D out out out 2 2 2 2 2 u 2 where A D 1 4 2 1/ 2 1 p p p u 0 0 , 0 0 0 A 2 2 2 2 2 B0 1 B0 B0 B0 1 B0 Relativistic magnetic reconnection ＜Including inertial effect of (thermal) energy＞ Analytical model (Koide & Arai 2007) 2 1/ 2 1 u 2 1 u 2 u' ' v' 1 A 1 1 A D out out out 2 2 2 2 1/ 2 uout ' p u 0 0 A B 2 1 B 2 out 'vout ' 0 0 B2 Alfven four-velocity, 0 h0 1 p p 0 0 0 2 2 2 B0 B0 1 B0 Pressure per enthalpy p p0 / h0 P 2 B0 / 2 Γ: Polytoropic index Simulation of Relativistic Magnetic Reconnection Watanabe & Yokoyama, ApJ. 2006 Momentum density 2 ： B 2 ~ c ~ c 0 Possibility of redistribution of significant momentum Comparison between analytic and numerical solutions of relativistic magnetic reconnection Analytical model (Koide & Arai 2007) 2 1/ 2 1 u 2 1 u 2 u' ' v' 1 A 1 1 A D out out out 2 2 2 2 uout ' Numerical simulation out 'vout ' (Watanabe & Yokoyama 2006) p P 2 B0 / 2 Conditions of energy extraction through magnetic reconnection C E B (1) Formation of plasma backward flow E E BH wihith negat ive energy-at-ifiiinfinity : 0 H (2) Escape of forward plasma flow to infinity: Mass of plasma element E M 1 0 H 1 Sppgyecific energy-at-infinityyp of forward and backward plasma ejection estimated by slab model ˆ 2 E 2 'out vK 'out 1 ˆ 1 vˆ ' vˆ ' 1 H K 3 K out K 3 out ' 2 ˆ 2vˆ 2 out K K Energy extraction condition through magnetic reconnec tion in ergosp here θ=π/2 Zero vˆ vˆ pressure 0 Kepler EnergyNegative extraction Bulk plasma case fromenergy-at-infinity black hole in zeroftiforma pressuretion case rotates with Keplerian velocity B0 U out 0 h A 0 0 Relativistic out reconnection Alfven Escape to infinity 2 2 4-velocity B0 h0 c Horizon 2 h0 0c p0 1 r / r Enthalpy density S Energy extraction condition through magnetic reconnec tion in ergosp here θ=π/2 Finite p0 / h0 0 pressure p / h 0.3 EnergyNegativeEnergy extraction extraction 0 0 case fromenergy-at-infinityfrom black black hole hole in in p / h 0.5 pftiforma=030.3tihoncase 0 0 0p0=0.50h0 case B0 0 U A out h0 Relativistic out 0 reconnection B2 Escape to infinity 0 2 h0 c 2 Horizon p0 / h0 0 p0 / h0 0.3 2 h c p p0 / h0 0.5 0 0 1 0 Enthalpy density r / rS Slower rotating black hole case p / h 0 Negative 0 0 energy-at-infinity Finite p0 / h0 0.3 out 0 formation pressure p0 / h0 0.5 case B 0 U A out 0 h0 Escape to infinity Note that there is no circular orbit in ergo- p / h 0 sphere when 0 0 p0 / h0 0.3 a 1/ 2 r / rS Possibility of relativistic magnetic reconnection in individual objects Relativistic magnetic reconnection is required to extract black hole rotational energy by magnetic reconnection: B0 Bcrit 0 0 c U A 1, p0 0 B idiidlindividual 0 crit possibility (g cm-3) (G) AGN M87 2×10-17 500 YES (Collapsar GRB 4 1011 2 1015 Marginal model) × × Micro- GRS1915 6 10-5 8 108 NO QSO +105 × × Typical density near the central (SI unit system) black hole, which is assumed. Energy extraction from black hole through magnetic reconnection in situation of magnetorotational instability Ergosph er e Frame-dragging effect Disk Rotating black hole Closed magnetic flux tube Frame- Magnetic dragging flux tube Closed effect magnetic flux tube Koide & Arai, submitted Numerical simulations with resistive GRMHD is demanded for further investigation.