Relativistic Outflow Formation by Magnetic Field around Rapidly Rotating Black Hole Shinji Koide （ Toyama University ） Black Hole 2003, October 29 (Wed), Kyoto International Community House General relativistic magnetohydrodynamic (MHD) simulation shows relativistic outflow is driven around rapidly rotating black hole by radial magnetic field. This is the first self-consistent solution of spontaneous relativistic outflow formation in black hole magnetosphere.

Relativistic Jets in the Universe 1) Active galactic nuclei, Quasars: γ>10 2) Microquasars: γ~ 3 3) Gamma-ray bursts: γ> 100 ~ ~ Relativistic Jet Formation Mechanism Acceleration of plasma/gas Collimation of plasma/gas outflow by Magnetic Field

Acceleration Mechanism of Magnetically-Driven Jet (Blandford & Payne 1982) Magnetic filed lines are twisted by rotating plasma around central object Magnetic pressureMagnetic tension Blow off plasmaRotate plasma Centrifugal force Plasma outflow (Uchida & Shibata 1985) Steady-state theory & Numerical simulations (Kudoh & Shibata 1998) ： V jet ～ V rot ～ V Kepler Rotating plasma disk B Jet V rot r rot Central object Jet Pinch effect of twisted magnetic flux tube

Any material, energy, and information rotates the same direction of the black hole rotation. The plasma in it behaves like heavy rapidly rotating disk! Relativistic Jet Acceleration by Magnetic Field Rotating Plasma Disk B Relativistic jet Rotating Black Hole Frame Dragging Effect Ergosphere Relativistic jet ： V jet ～ c V Kepler ～ c Direct Outflow from Ergosphere ・ Central object: Rapidly Rotating Black hole ( a = J/J max ～ 1) ・ r rot ～ r H ⇒ (Black hole horizon)

Direct Outflow from Ergosphere Initial Magnetic Field Configuration Uniform magnetic field case (Koide et al. 2002) ◆ Powerful energy emission ⇒ Negative energy region in ergospere ◆ No outflow No centrifugal force along vertical magnetic field lines. Radial magnetic field case (split monopole field) Significant centrifugal force along oblique magnetic field lines. Uniform, strong magnetic field rHrH R z Uniform, thin plasma  r Kerr black hole Ergosphere Centrifugal force Radial magnetic field rHrH R z  r Kerr black hole Ergosphere Centrifugal force Thin plasma

Initial Condition: Simple system of rotating black hole, thin plasma, and radial magnetic field Black Hole: (nearly maximally rotating black hole) Magnetic Field ： Radial magnetic field B 0 =B(R=r S,z=0) Plasma ： Magnetic field dominates: ρ 0 =0.018B 0 2 /c 2 Gas falling near the horizon. Hydrostatic equilibrium far from black hole.,,,,

General Relativistic MHD Equations in Kerr Space-Time General relativistic equation of conservation laws and Maxwell equations: ∇  ( n U  ) = 0 (conservation of particle number) ∇ T  = 0 (conservation of energy and momentum) ∂  F  ∂ F   ∂ F  = 0 ∇  F  = - J Frozen-in condition: F  U  = 0 Kerr Metric ： ds 2 = g  dx  dx  ; g  = - h 0 2 ; g ii  = - h i 2 ; g 0i  = - h i 2  i (i=1,2,3) ; g ij  = 0 (i≠j) n : proper particle number density. p : proper pressure. c : speed of light. e : proper total energy density, e = mnc 2 + p / (  -1). m : rest mass of particles.  : specific heat ratio. U  : velocity four vector. A  : potential four vector. J  : current density four vector. ∇  : covariant derivative. g  : metric. T  : energy momentum tensor, T  = p g  + ( e + p ) U  U + F  F  - g  F  F  /4. F  : field-strength tensor, F  =∂  A -∂  A  (Maxwell equations)

Vector Form of General Relativistic MHD Equation (3+1 Formalism) where (conservation of particle number) (equation of motion) (equation of energy) (Maxwell equations) (ideal MHD condition) : (Lapse function) : (shift vector) general relativistic effect special relativistic effect : (shift velocity ) Special relativistic mass density,  Special relativistic total momentum density Special relativistic total energy density

c Lines: Magnetic field surfaces Arrows: Velocity of plasma z/rSz/rS R/rSR/rS Kerr black hole Ergosphere Numerical Result: Initial Condition r S =2GM BH /c 2

R/rSR/rS z/rSz/rS c Kerr black hole Lines: Magnetic field surfaces Arrows: Velocity of plasma Ergosphere V max =0.86c (Lorentz factor 2.0) τ S =r S /c (Unit of time)

Relativistic Outflow driven by Magnetic Field from Ergosphere Magnetic field lines Kerr black hole Ergosphere t = 10.7  S Plasma Magnetic field flux tube acts as propeller screw!

Time Evolution Lines: Magnetic field surfaces Arrows: Velocity of plasma 0 Kerr black hole r S =2GM BH /c 2 Color: Azimuthal Component of Magnetic Field, B φ 2 V max =0.86c (Lorentz factor 2.0) τ S =r S /c (Unit of time)

Plasma Acceleration Force Magnetic tension ⇒ Centrifugal force Magnetic pressure/ten- sion ⇒ blow off plasma

Summary General Relativistic MHD simulation shows that magnetic field configuration dominates relativistic outflow formation near rapidly rotating black hole ( ). □ Uniform magnetic field case (Koide et al. 2002): Powerful magnetic energy emission. No outflow. ■ Radial magnetic field case (present result): Relativistic plasma outflow from ergosphere. Lorentz factor, 2.0 ( V max =0.86c ). The plasma is accelerated by magnetic force (Lorentz force). Contribution of magnetic pressure/tension ( ⇒ blow off plasma) and magnetic tension ( ⇒ centrifugal force) are almost comparable. The outflow is not pinched by magnetic field significantly and no collimated jet is found. After the long term simulation, it is expected that the magnetic tension of the twisted magnetic flux tube pinches the outflow to form a relativistic jet.

A Model of Relativistic Jet Formation of Gamma- ray Bursts: Collapsor/Hypernova model Fe C+O H He collapse Relativistic Jet from Ergosphere Jet from Disk Accretion Disk Kerr BH Ergosphere Magnetic Field Lines Rotating C+O star (M~30M SUN ) Central region of relativistic jet formation of gamma-ray burst Magnetic Field Lines Magnetic reconnection? Falling Plasma