Relativistic MHD Simulations of Relativistic Jets. Yosuke Mizuno NASA Postdoctoral Program Fellow NASA Marshall Space Flight Center (MSFC) National Space Science and Technology Center (NSSTC). Context. Introduction Development of 3D GRMHD code 2D GRMHD simulations of Jet Formation
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Relativistic MHD Simulations of Relativistic Jets
NASA Postdoctoral Program Fellow
NASA Marshall Space Flight Center (MSFC)
National Space Science and Technology Center (NSSTC)
Mirabel & Rodoriguez 1998
Energy conversion from accreting matter is the most efficient mechanism
make relativistic speed because the Keplerian velocity near the black hole is nearly light speed
Require relativistic treatment (special or general)
Mizuno et al. 2006a, Astro-ph/0609004
∇n (r Un) = 0(conservation law of particle-number)
∇nTmn= 0(conservation law of energy-momentum)
∂mFnl + ∂nFlm + ∂lF mn= 0
∇mFmn= - Jn
r : rest-mass density. p : proper gas pressure. u: internal energy. c: speed of light.
h : specific enthalpy, h =1 + u +p / r.
G: specific heat ratio.
Umu : velocity four vector. Jmu : current density four vector.
∇mn : covariant derivative. gmn : 4-metric,
Tmn : energy momentum tensor, Tmn = r h Um Un+pgmn+FmsFns -gmnFlkFlk/4.
Fmn : field-strength tensor,
a: lapse function,
bi: shift vector,
(Particle number conservation)
U (conserved variables)
Fi (numerical flux)
S (source term)
√-g : determinant of 4-metric
√g : determinant of 3-metric
Detail of derivation of GRMHD equations
Anton et al. (2005) etc.
Mizuno et al. (2006)
Exact solution: Giacomazzo & Rezzolla (2006)
Balsara Test1 (Balsara 2001)
Black: exact solution, Blue: MC-limiter, Light blue: minmod-limiter, Orange: CENO, red: PPM
400 computational zones
Mizuno et al. 2006b, Astro-ph/0609344
Hardee, Mizuno, & Nishikawa 2007, ApSS, 311, 281
Wu et al. 2008, CJAA, submitted
Numerical Region and Mesh points
Schematic picture of the jet formation near a black hole
White lines: magnetic field lines (contour of poloidal vector potential)
Arrows: poloidal velocity
White curves: magnetic field lines (density), toroidal magnetic field (plasma beta)
vector: poloidal velocity
Wu et al., 2008, CJAA, submitted
Image of Emission, absorption & scattering
Radiation image seen from q=85 (optically thick)
Radiation image seen from q=85 (optically thin)
Radiation image seen from q=45 (optically thick)
Mizuno, Hardee & Nishikawa, 2007, ApJ, 662, 835
Hardee, 2007, ApJ, 664, 26
Hardee, Mizuno & Nishikawa, 2007, ApSS, 311, 281
M87 Jet: Spine-Sheath Configuration?
HST Optical Image (Biretta, Sparks, & Macchetto 1999)
VLA Radio Image (Biretta, Zhou, & Owen 1995)
Typical Proper Motions > c
Optical ~ inside radio emission
Jet Spine ?
Typical Proper Motions < c
Sheath wind ?
Non-rotating BH Fast-rotating BH
BH Jet Disk Jet
Total velocity distribution of 2D GRMHD Simulation of jet formation
(Hardee, Mizuno & Nishikawa 2007)
Mizuno, Hardee & Nishikawa, 2007
3D isovolume of density with B-field lines show the jet is disrupted by the growing KH instability
Longitudinal cross section
Transverse cross section show the strong interaction between jet and external medium
Mizuno, Hardee, Hartmann, Nishikawa & Zhang, 2008, ApJ, 672, 72
-0.2 < x < 0.2 with 6400 grid
Schematic picture of simulations
Solid line (exact solution), Dashed line (simulation)
In the left going rarefaction region, the tangential velocity increases due to the hydrodynamic boost mechanism.
jet is accelerated to g~12 from an initial Lorentz factor of g~7.
HDA case (pure hydro) : dotted line
MHDA case (poloidal)
MHDB case (toroidal)
HDB case (hydro, high-p)
Solid line: exact solution, Crosses: simulation
Magnetic field strength is measured in fluid flame