The CD Kink Instability in Magnetically Dominated Relativistic

The CD Kink Instability in Magnetically Dominated * Relativistic Jets Ken-Ichi 1 Nishikawa , Y. 1 Mizuno , Y. 2 Lyubarsky , 3 P. E. Hardee , 1 NSSTC/ CSPAR/ University of Alabama in Huntsville, USA, 2 Ben-Gurion University, Israel, 3 University of Alabama, Tuscaloosa, USA The relativistic jets associated with blazar emission from radio through Te. V 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 Te. V 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 3 D 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 M 87 gle n a ng 00 R s i w 7 ie 2 v ~ t o je pc 5 5 5 @ 1 s ~ 1. a 5 m • 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 ~ 42 Rs 5 mas 0. 4 pc ~700 Rs M 87: 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) • For relativistic force-free configurations (Mizuno et al. , 2009) 4. Initial Conditions Initial radial profile 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=r 0 B 2) Numerical box: -16 a < x, y < 16 a, 0 < z < 16 a (Cartesian coordinates: 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; Mc. Kinney & 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 t. A: 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, Ap. J, submitted ) Initial Conditions • Sub-Alfvenic jet (vj=0. 2 c) with force-free B field (KH stable) • Radial profile: decreasing density (r=r 0 B 2) with constant pitch • Jet velocity shear radius: Rj=a/2, a, 2 a, 4 a • Numerical box: -8 a < x, y < 8 a, 0 < z < 12 a (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 = 6 a Red: Rj=a/2, Orange: Rj=a, Green: Rj=2 a, Blue: Rj=4 a, Black: no jet Spatial Properties: Initial Conditions • Sub-Alfvenic jet (vj=0. 2 c, 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: 6 Rj x 20 Rj (Cartesian: 180 x 400 zones) Density Isosurfaces & velocity vectors vj Rj=4 a 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 & 2 a *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, Ap. J, 700, 684 Mizuno et al. 2010, Ap. J, submitted