The CD Kink Instability in Magnetically Dominated The CD Kink Instability in Magnetically Dominated Relativistic JetsRelativistic Jets**

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

Ken-Ichi Nishikawa1 , Y. Mizuno1, Y. Lyubarsky2, P.E.Hardee3

, 1NSSTC/ CSPAR/ University of Alabama in Huntsville, USA, 2Ben-Gurion University, Israel, 3 University of Alabama, Tuscaloosa, USA

4. Initial Conditions

*COSPAR 2010, Bremen, Germany, July 18-25, 2010

2. Instability of Relativistic Jets

6. Results: Sub-Alfvenic Jet

• 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

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

• 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

M87: jet launching and collimation region

Force-free helical magnetic field: CD kink unstable a = characteristic radius of plasma column Magnetic pitch (P=RBz/B): increasing, constant, decreasing Density profile: constant or decreasing (=0 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

Time evolution (volume-averaged kinetic energy transverse to the z-axis)

tA: Alfven crossing time

Dotted: increasing pitchSolid: constant pitchDashed: decreasing pitch

Constant density Decreasing density

Density Isosurface & white magnetic field lines

Constant pitchIncreasing pitch Decreasing pitch

• 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

• Increasing pitch: Amplitude growth ceases at late times.• Constant pitch: Amplitude growth slows at late times.• Decreasing pitch: Amplitude growth continues throughout simulation.

For more detail, please see

Mizuno et al. 2009, ApJ, 700, 684Mizuno et al. 2010, ApJ, submitted

Initial Conditions

• Sub-Alfvenic jet (vj=0.2c) with force-free B field (KH stable)• Radial profile: decreasing density (=0 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

(Mizuno et al., 2009)

5. Results: Static Plasma Column

ts=50 ts=50

(Mizuno et al. 2010, ApJ, submitted )

• For relativistic force-free configurations• 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

• 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

3. MotivationInitial radial profile

Black: constant densityRed: decreasing density

Solid: constant pitchdotted: increasing pitchDashed: decreasing pitch

Kink Propagation: maximum density position in x-y plane at z = 6a

Temporal Properties:

Red: Rj=a/2, Orange: Rj=a, Green: Rj=2a,Blue: Rj=4a, Black: no jet

Density Isosurfaces & velocity vectors

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)

• Precessional perturbation at inlet induces growth of the CD kink.• Helical structure propagates with continuous spatial kink growth.

(Mizuno et al. 2010 in prep)

vj

ts=40

5 mas 0.4 pc ~700 Rs

@ 15o jet viewing angle

5 mas ~ 1.55 pc ~ 2700 R s

Beam: ~ 0.4 x 0.2 mas, 0.3 mas ~ 0.024 pc ~ 42Rs

(Acciari et al., 2009, Science, 325, 444)

Consistent with non-relativistic linear analysis In Appl et al. (2000)

Density isosurfaces (color) with white magnetic field lines.

Rj=a/2 Rj=4a

z/Rj