Transcript PPT

Magnetic Field Amplification by
Turbulence in A Relativistic
Shock Propagating through An
Inhomogeneous Medium
Yosuke Mizuno
Institute of Astronomy
National Tsing-Hua University
Collaborators
M. Pohl (Univ Potsdam), J. Niemiec (INP, PAN), B. Zhang (UNLV),
K.-I. Nishikawa (NSSTC/UAH), P. E. Hardee (UA)
Mizuno et al., 2011, ApJ, 726, 62
Introduction
• In Gamma-Ray Bursts (GRBs), radiation is produced in a relativistic blastwave
shell propagating weakly magnetized medium.
• Detail studies of GRB spectrum and light curves show eB=Emag/Eint=10-3-10-1.
• But, simple compressional amplification of weak pre-existing magnetic field can
not account for such high magnetization (e.g., Gruzinov 2001).
⇒ Need magnetic field amplification process
• Leading hypothesis for field amplification in GRBs
• Microscopic plasma process
– Relativistic Weibel instability (e.g., Medvedov & Loeb 1999, Spitkovsky 2008,
Nishikawa et al. 2009)
– But it remains unclear whether magnetic fields will persist at sufficient strength in the
entire emission region (e.g., Waxman’s talk)
• In MHD (Macroscopic plasma process), relativistic magnetic turbulence (e.g.,
Sironi & Goodman 2007)
– If preshock medium is strongly inhomogeneous, significant vorticity is produced in
shock transition
– Vorticity stretches and deforms magnetic field lines leading to its amplification
•
Direct observational motivation for relativistic turbulence in GRB outflows
– Significant angular fluctuation is invoked to explain large variation of gamma-ray
luminosity in prompt emission (Relativistic turbulent model) (e.g., Narayan & Kumar
2009, Kumar & Narayan 2009; Lazar et al. 2009, Zhang & Fan 2010)
Introduction (cont.)
• Fast variable flares (X-ray/TeV gamma) observed in blazars may come
from small regions ~ a few Schwarzschild radii
• Marscher et al. (1992) proposed relativistic shock passes through
turbulent jet plasma in the jet flow
• Synchrotron emission from
Supernova remnant (SNRs) (expanding
nonrelativistic spherical blast wave) is
generally consistent with compression
of interstellar magnetic field (~ a few
micro-Gauss)
• However, year-scale variability in
synchrotron X-ray emission of SNRs
suggests to magnetic field
amplification up to milli-Gauss level
(e.g., Uchiyama et al. 2007)
• Magnetic field amplification beyond
Chandra X-ray image of western shell of SNR
RX J1713.7-3946 (Uchiyama et al. 2007)
simple shock compression is necessary
to achieve this level in SNRs
Propose
• Non-relativistic MHD shock simulations including preshock
density fluctuation are shown a strong magnetic field
amplification caused by turbulence in postshock region (e.g.,
Giacalone & Jokipii 2007)
• A relativistic blast wave as in GRBs, AGN jets should
experience strong magnetic field amplification by turbulence.
• In order to investigate magnetic field amplification by
relativistic turbulence we perform 2D Relativistic MHD
simulations of a relativistic shock wave propagating through a
inhomogeneous medium
RAISHIN Code (3DGRMHD)
Mizuno et al. 2006a, 2011c, & progress
• RAISHIN utilizes conservative, high-resolution shock capturing
schemes (Godunov-type scheme) to solve the 3D GRMHD
equations (metric is static)
Ability of RAISHIN code
• Multi-dimension (1D, 2D, 3D)
• Special & General relativity (static metric)
• Different coordinates (RMHD: Cartesian, Cylindrical, Spherical and GRMHD:
Boyer-Lindquist of non-rotating or rotating BH)
• Different schemes of numerical accuracy for numerical model (spatial
reconstruction, approximate Riemann solver, constrained transport schemes, time
advance, & inversion)
• Using constant G-law and variable Equation of State (Synge-type)
• Parallel computing (based on OpenMP, MPI)
Initial Condition
• Relativistic shock propagates in an inhomogeneous medium
• Density: mean rest-mass density (r0=1.0) + small fluctuations ( following 2D
Kolmogorov-like power-law spectrum, P(k) ∝1/[1+(kL)8/3], <dr2>1/2=0.012r0)
established across the whole simulation region (e.g., Giacalone & Jokipii 2007).
• Relativistic flow: vx=0.4c in whole simulation region
• Magnetic field: weak ordered field (b=pgas /pmag=103), parallel (Bx) or
perpendicular (By) to shock direction
• Boundary:
– periodic boundary in y direction
– a rigid reflecting boundary at x=xmax to create a shock wave. (shock propagates in –x
direction)
– new fluid continuously flows in from the inner boundary (x=0) and density
fluctuations are advected with the flow speed
• Computational Domain: (x, y)=(2L, L) in 2D Cartesian with N/L=256 grid
resolution
• Simulation method: WENO5 in reconstruction, HLL Approximate Riemann
solver in numerical flux, and CT scheme for divergence-free magnetic field
Time Evolution:
parallel shock case
vx=0.4c, Bx case
Postshock Structure
Parallel shock
Perpendicular shock
vx=0.4c, t=10.0
• Density fluctuation in preshock medium induces turbulent motion in postshock region
through a process similar to Richtmyer-Meshkov instability
• Since preexisting magnetic field is much weaker than the post shock turbulence, turbulence
motion can easily stretch and deform the frozen-in magnetic field resulting in its distortion and
amplification
• Amplified magnetic field evolves into a filamentary structure.
• This is consistent with previous non-relativistic work (Giacalone & Jokipii 2007; Inoue et al.
2009)
vx=0.4c, t=10.0
Plot on z=1.0
Perpendicular shock
1D Cross Section Profile
Shock front
up
Parallel shock
downstream
• Shock propagation speed vsh ~ 0.17c, relativistic Mach number Ms~4.9 (shock strength)
• Density jumps by nearly a factor of 4
• Transverse velocity is strongly fluctuating (vy_max ~0.04c, <vturb>~0.02c) and subsonic (<cs>
~0.32c), mostly super-Alfvenic (<va> ~ 0.002c).
• Total magnetic field strength is also strongly fluctuated and amplified locally more than 10
times.
Parallel shock
Perpendicular shock
Spherically integrated spectra in post shock
region
Solid: t=4, Dashed: t=6
Dotted: t=8, Dash-dotted: t=10
Energy Spectrum
• Kinetic energy spectra almost follow a
Kolmogorov spectrum (initial density
spectrum still exists in postshock region)
• Magnetic energy spectra are almost flat
and strongly deviate from a Kolmogorov
spectrum.
• Flat magnetic energy spectrum is
generally seen in turbulent dynamo
simulation (e.g., Brandenburg 2001;
Schekochihin et al. 2004).
• Same properties are also observed in
super-Alfvenic driven turbulence (e.g.,
Cho & Lazarian 2003) and in RMHD
turbulence induced by a KH instability
(Zhang et al. 2009)
Magnetic Field Amplification
Mean magnetic field in
postshock region
Peak total magnetic field strength in
postshock region
• Mean postshock magnetic field is gradually increasing with time and not saturated yet.
•Mean postshock magnetic field is stronger for perpendicular shock (By) than parallel
shock (Bx)
• The perpendicular magnetic field is compressed by a factor of 3 as the shock, and
additional magnetic field amplification by turbulent motion is almost same as for a
parallel magnetic field
• Peak field strength is much larger than mean magnetic field.
Magnetic Field Amplification
(fast flow case, vx=0.9c)
Mean magnetic field in
postshock region
Peak total magnetic field strength in
postshock region
• Mean postshock magnetic field is gradually increasing with time and not saturated yet.
• Mean postshock magnetic field is stronger for perpendicular case (By) than parallel case (Bx)
• The perpendicular magnetic field is compressed by a factor of 3 as the shock, and additional
magnetic field amplification by turbulent motion
• Peak field strength is much larger than mean magnetic field
• In comparison with slow flow case (vx=0.4c), growth time is faster and magnetic field
strength (mean and peak) is larger
Summery
• We have performed 2D RMHD simulations of propagation of
a relativistic shock through an inhomogeneous medium
• The postshock region becomes turbulent owing to the
preshock density inhomogeneity
• Magnetic field is strongly amplified by the turbulent motion in
postshock region
• The magnetic energy spectrum is flatter than Kolmogorov
spectrum, which is typical for a small-scale dynamo
• The total magnetic field amplification from preshock value
depends on the direction of homogeneous magnetic field
• The time scale of magnetic field growth depends on the shock
strength
• The mean magnetic field strength in postshock region is still
increasing. So longer simulations with a larger simulation box
are needed to follow the magnetic field amplification to
saturation