3D Relativistic MHD Simulations of Magnetized Spine-Sheath

Relativistic JetsYosuke Mizuno

(NSSTC/NASA-MSFC/ORAU),

P. E. Hardee (UA), K.-I. Nishikawa (NSSTC/UAH)

Extragalactic Jets, Girdwood., May 21-24, 2007

Mizuno, Hardee, & Nishikawa, 2007, ApJ, in press, Astro-ph/0703190Hardee 2007, ApJ , in press, Astro-ph/0704.1621

Motivation

• When relativistic jets are generated near the central black hole region successfully and propagate in external medium

• How do jets remain sufficiently stable?

Instabilities in relativistic jets• Kelvin-Helmholtz (KH)

– Presence of velocity gradients in the flow– Important role at the shearing boundary flowing jet and ext

ernal medium • Current-driven (CD)

– Presence of strong axial electric current– Important in twisted magnetic field

• Interaction of jets with external medium leads to the formation of shocks, turbulence, acceleration of charged particles etc.

• Instabilities used to interpret many jet phenomena such as quasi-periodic wiggles and knots, filaments, li

mb brightening, jet distuption etc

Stabilities of MHD jets against KH modes (linear stability analysis)

• Linear stability analysis (e.g., Bodo et al. 1989, 1996; Hardee 1992, Hardee et al. 1997)

– Relativistic Jets might be in super-Alfvenic or super-fast magnetosonic flow (kinematic energy > magnetic energy)

→Relativistic jets are unstable against KH modes

(in sub-Alfvenic, jets are stable)

Spine-Sheath Relativistic Jets (observations)

Key Questions of Jet Stability• How do jets remain sufficiently stable in spine-sheath configuration?• What are the Effects & Structure of CD/KH Instability in spine-sheath configuration?

M87 Jet: Spine-Sheath Configuration?VLA Radio Image (Biretta, Zhou, & Owen 1995)HST Optical Image (Biretta, Sparks, & Macchetto 1999)

Typical Proper Motions < cSlow Sheath wind ?

Typical Proper Motions > cOptical ~ inside radio emissionFast Jet Spine ?

Jet Structures (Lobanov, Hardee, & Eilek 2003)

Optical & Radio twistedfilaments (green lines) & helical twist (red line)Spine-Sheath interaction ?

Spine-Sheath Relativistic Jets (GRMHD Simulations)

• GRMHD simulation results suggest that a jet spine driven by the magnetic fields threading the ergosphere may be surrounded by a broad sheath wind driven by the magnetic fields anchored in the accretion disk. • This configuration might additionally be surrounded by a less highly collimated accretion disk wind from the hot corona. • The jet speed is related to the Alfvén wave speed in the acceleration and collimation region implying Alfvén wave speeds near to light speed.

Non-rotating BH Fast-rotating BH

BH Jet Disk JetDisk Jet

Total velocity distribution of 2D GRMHD Simulation of jet formation(Mizuno et al. 2006b)

Stabilities of magnetized spine-sheath jets against KH modes

• Hardee & Rosen (2002): stabilizing influence of a surrounding magnetized sheath wind of the helically magnetized 3D trans-Alfvenic jets (in non-relativistic regime)– Jets could be stabilized to the nonaxisymmetric KH surface

modes if velocity shear Vj-Ve < surface Alfven speed VAs

• jets in relativistic regime are not fully addressed in both linear analysis and MHD simulation

→ We investigate stability analysis of magnetized spine-sheath jets in relativistic MHD regime by 3D RMHD simulations by using newly-developed 3DGRMHD code “RAISHIN”

4D General Relativistic MHD Equation• General relativistic equation of conservation laws and Maxwell equations: 　　　

　　　　　　　∇ ( U ) = 0 　　　 (conservation law of particle-

number)

　　　　　　　∇ T = 0 (conservation law of energy-momentum)

　　　　　　　∂ F∂F∂F = 0

　　　　　　　∇ F = - J

• Ideal MHD condition: FU= 0

• metric ：　 ds2=-2 dt2+gij (dxi+i dt)(dx j+j dt)

• Equation of state : p=(-1) u: rest-mass density. p : proper gas pressure. u: internal energy. c: speed of light.h : specific enthalpy, h =1 + u + p /.: specific heat ratio.U : velocity four vector. J : current density four vector.∇ : covariant derivative. g : 4-metric. lapse function,ishift vector, gij : 3-metric

T : energy momentum tensor, T = pg +h UU+FF -gF

F/4.F : field-strength tensor,

(Maxwell equations)

Changing metric →calculate special relativistic MHD equations

• Cylindrical super-Alfvenic jet established across the computational domain with a parallel magnetic field (stable against CD instabilities)• ujet = 0.916 c (γj=2.5), jet = 2 ext (dense, cold jet)• External medium outside the jet, uext = 0 (no wind), 0.5c (wind)• precession perturbation from boundary to break the symmetry (2=0.93) • RHD: weakly magnetized (sound velocity > Alfven velocity) ajet = 0.511 c , aext = 0.574 c, vA(j,e) < 0.07 c, • RMHD: strongly magnetized (sound velocity < Alfven velocity) vAj = 0.45 c, vAe = 0.56 c, aj = 0.23 c , ae = 0.30 c,• Numerical Resion and mesh points

• -3 rj< x,y< 3rj, 0 rj< z < 60 rj in Cartesian coordinates with 60*60*600 computational zones, (1rj=10 computational zone)

Initial condition for 3D RMHD simulations

Simulation results (nowind, weakly magnetized case)

3D isovolume of density with B-field lines show the jet is disrupted by the growing KH instability

Transverse cross section show the strong interaction between jet and external medium

Longitudinal cross sectiony

zx

y

3D RHD Jet Simulations & Linear Analysis

• A sheath with vw = 0.5c significantly reduces the growth rate (red dash-dot) of the surface mode at simulation frequency 2, and slightly increases the wavelength.• Growth associated with the 1st helical body mode (green dash-dot) is almost eliminated by sheath flow.

RHD Jet Dispersion Relation Solutions (Linear analysis)

Surface mode growth rate

Surface mode wavelength

1D cut of radial velocity along jet

•The moving sheath reduces the growth rate and slightly increases the wave speed and wavelength as predicted.• Substructure associated with the 1st helical body mode is eliminated by sheath flow as predicted.

Body mode substructureBody mode growth rate

Moving sheath (growth reduced)

3D RHD Jet Simulation Results at

vw=0.0

vw=0.5c

vw=0.0 vw=0.5c

Condition for damped KH modes in magnetized spine-sheath relativistic jets (from linear stability analysis)

“velocity shear” is less than the “surface” Alfvén speed:

3D RMHD Jet Simulations & Theory

The magnetized sheath reduces growth rate relative to the fluid case and the magnetized sheath flow damped growth of KH modes.

Magnetized moving sheath (damped)

Magnetized sheath (reduced growth)

1D cut of radial velocity along jet

vw=0.0

vw=0.5c

3D RMHD Jet Simulation Results at

Summary

•We have investigated stability properties of magnetized spine-sheath relativistic jets by the linear stability analysis and 3D relativistic MHD simulations.• The most important result is that destructive KH modes can be stabilized by the presence of magnetized sheath wind even when the jet is super-Alfvenic flow. • Even in the absence of stabilization, spatial growth rate of destructive KH modes can be reduced by the presence of sheath wind (~0.5c) around a relativistic jet spine (>0.9c)

風神雷神図屏風Wind God (FUSHIN) and

Thunder God (RAISHIN) Screen

By Ogata Korin (Edo era, 17 Century)Tokyo National Museum

RAISHIN (Thunder God) FUSHIN (Wind God)