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The CD Kink Instability in Magnetically Dominated
*
Relativistic Jets
Ken-Ichi
1
Nishikawa
, Y.
1
Mizuno ,
Y.
2
Lyubarsky ,
3
P.E.Hardee
, 1NSSTC/ CSPAR/ University of Alabama in Huntsville, USA, 2Ben-Gurion University, Israel, 3 University of Alabama, Tuscaloosa, USA
The relativistic jets associated with blazar emission from radio through TeV gamma-rays are thought to be accelerated and collimated by strong helically twisted magnetic fields with footpoints threading the black hole
ergosphere and/or the surrounding accretion disk. The resulting magnetically dominated jet is current-driven (CD) unstable. In a resistive system instability may lead to magnetic reconnection, particle acceleration to the
high energies required by the observed TeV emission, and also to the observed kinetically dominated jets far from the central engine. We have investigated the temporal development of current-driven kink instability in
magnetically dominated relativistic jets via 3D RMHD simulations. In this investigation a static force-free equilibrium helical magnetic configuration is considered in order to study the influence of the initial configuration
on the linear and nonlinear evolution of the instability. We find that the initial configuration is strongly distorted but not disrupted by the CD kink instability. The linear growth and nonlinear evolution of the CD kink
instability depends moderately on the radial density profile and strongly on the magnetic pitch profile. Kink amplitude growth in the nonlinear regime for decreasing magnetic pitch leads to a slender helically twisted
column wrapped by magnetic field. On the other hand, kink amplitude growth in the nonlinear regime nearly ceases for increasing magnetic pitch. We also present preliminary results showing the effect of velocity shear on
the spatial and temporal development of the CD kink instability.
1. Astrophysical Jets
2. Instability of Relativistic Jets
Radio Observations of M87
• Two major instabilities:
• Kelvin-Helmholtz (KH) instability
• At the velocity shear surface between jet and
external medium
• Current-Driven (CD) instability
• In the twisted magnetic field of magnetically
dominate flows
• Relativistic jets: outflow of highly collimated plasma
• Microquasars, Active Galactic Nuclei, Gamma-Ray
Bursts, Jet velocities ~c.
• Generic systems: Compact object (White Dwarf,
Neutron Star, Black Hole）+ Accretion Disk
• Key Issues for Relativistic Jets
• Acceleration & Collimation
• Propagation & Stability
• Modeling of Jet Production
• Magnetohydrodynamics & Relativity (SR+GR)
• Modeling of Jet Emission
• Particle Acceleration & Radiation Mechanism
3. Motivation
Beam: ~ 0.4 x 0.2 mas, 0.3 mas ~ 0.024 pc ~ 42Rs
5 mas  0.4 pc ~700 Rs
M87: jet launching and collimation region
• KH instability can lead to jet twisting, twisted filaments, limb brightening, shocks,
turbulence, particle acceleration
• CD instability can lead to jet twisting, twisted filaments, magnetic reconnection,
particle acceleration
(Acciari et al., 2009, Science, 325, 444)
(Mizuno et al., 2009)
4. Initial Conditions
Initial radial profile
• For relativistic force-free configurations
Black: constant density
Red: decreasing density
Solid: constant pitch
dotted: increasing pitch
Dashed: decreasing pitch
Force-free helical magnetic field: CD kink unstable
a = characteristic radius of plasma column
Magnetic pitch (P=RBz/Bf): increasing, constant,
decreasing
Density profile: constant or decreasing (r=r0 B2)
Numerical box: -16a < x, y < 16a, 0 < z < 16a
(Cartesian coordinates:160 x 160 x 80 zones)
Boundary: periodic in axial (z) direction
Velocity perturbation: m=1(-1) and n=1(-1) modes
• Linear analysis provides conditions for instability but says little about
the impact on the system (Istomin & Pariev (1994, 1996), Begelman(1998),
Lyubarskii(1999), Tomimatsu et al.(2001), Narayan et al. (2009))
• Instability of the potentially disruptive kink mode must be followed into
the non-linear regime
• Helical structures have been found in simulations of strongly magnetized jets
(e.g., Nakamura & Meier 2004; Moll et al. 2008; McKinney & Blandford 2009)
• We study the non-linear relativistic CD kink instability
5. Results: Static Plasma Column
Time evolution
Density Isosurface & white magnetic field lines
Increasing pitch
Constant pitch
(volume-averaged kinetic energy transverse to the z-axis)
Decreasing pitch
Constant density
Decreasing density
tA: Alfven crossing time
Dotted: increasing pitch
Solid: constant pitch
Dashed: decreasing pitch
• Increasing pitch: Amplitude growth ceases at late times.
• Constant pitch: Amplitude growth slows at late times.
• Decreasing pitch: Amplitude growth continues throughout simulation.
Consistent with non-relativistic linear
analysis In Appl et al. (2000)
• Initial exponential growth (linear phase) and subsequent non-linear evolution
• Density Decline: more rapid growth & decline (less radial Alfven velocity decline)
• Pitch increase: slower growth
• Pitch decrease: more rapid growth
6. Results: Sub-Alfvenic Jet
Temporal Properties:
(Mizuno et al. 2010, ApJ, submitted )
Initial Conditions
• Sub-Alfvenic jet (vj=0.2c) with force-free B field (KH stable)
• Radial profile: decreasing density (r=r0 B2) with constant pitch
• Jet velocity shear radius: Rj=a/2, a, 2a, 4a
• Numerical box: -8a < x, y < 8a, 0 < z < 12a (160 x 160 x 120)
• Boundary: periodic in axial (z) direction
• Velocity perturbation: m=1(-1) and n=1(-1) modes
Kink Propagation: maximum density
position in x-y plane at z = 6a
Red: Rj=a/2, Orange: Rj=a, Green: Rj=2a,
Blue: Rj=4a, Black: no jet
Spatial Properties:
Initial Conditions
• Sub-Alfvenic jet (vj=0.2c, Rj=1.0) with helical force-free magnetic
field established across computational domain
• Radial profile: Decreasing density with constant magnetic pitch
• Jet spine precessed to break symmetry
• Numerical Box: 6Rj x 6Rj x 20 Rj (Cartesian: 180 x 180 x 400 zones)
Density Isosurfaces & velocity vectors
vj
Rj=4a
Rj=a/2
ts=50
(Mizuno et al. 2010 in prep)
ts=50
• Small jet radius: small kink propagation speed,
flow through kink.
• Large jet radius: fast kink propagation speed,
kink embedded in flow.
• Non-linear behavior most altered for Rj = a & 2a
*COSPAR 2010, Bremen, Germany, July 18-25, 2010
z/Rj
ts=40
Density isosurfaces (color) with
white magnetic field lines.
• Precessional perturbation at inlet
induces growth of the CD kink.
• Helical structure propagates with
continuous spatial kink growth.
For more detail, please see
Mizuno et al. 2009, ApJ, 700, 684
Mizuno et al. 2010, ApJ, submitted