National Space Science & Technology Center/UAH

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1 Ken Nishikawa National Space Science & Technology Center/UAH 1. Basic Plasma Physics What is Plasma? 2. Simulation methods Macroscopic and Microscopic Processes 3. Fluid (GRMHD) Simulations Global Dynamics of Plasmas 4. Kinetic (RPIC) Simulations Kinetic Dynamics of Plasmas 5. Radiation Standard radiation model Self-consistent t model "GRB Physics at Kavli Institute for Astronomy and Astrophysics (KIAA), May 18-22, /39

2 Yosuke Mizuno National Space Science and Technology Center (NSSTC) Center for Space Plasma and Aeronomic Research/ The University of Alabama in Huntsville Co-authors and active collaborators: M. Takahashi hi (Aichi Univ. of Edu.), K. Shibata (Kwasan Obs/Kyoto Univ.), S. Yamada (Waseda Univ.), S. Koide (Kumamoto Univ.), S. Nagataki (Kyoto Univ./YITP), K.-I. Nishikawa (NSSTC/UAH), P. Hardee (Univ. of Alabama), G.J. Fishiman (NSSTC/NASA-MSFC), D. H. Hartmann (Clemson Univ.), B. Zhang g( (UNLV), D. Proga (UNLV), S.V. Fuerst (Stanford Univ.), K. Wu (UCL), Y. Lyubarsky (Ben-Gurion Univ.), K. Ghosh (NSSTC), C. Fendt (MPIA), P. Coppi (Yele Univ.), P. Biermann (MPIfR)

3 Context 1. Introduction 2. 2D GRMHD simulations of jet formation 3. Stability of relativistic jets 4. MHD boost mechanism of relativistic jets 5. Magnetohydrodynamic effects in propagating relativistic jets 6. Current-driven kink instability in static force free equilibrium i helical l magnetic configuration i 7. Summary and future plan

4 Astrophysical Jets Astrophysical jets: outflow of highly collimated plasma Microquasars, Active Galactic Nuclei, Gamma-Ray Bursts, Jet velocity ~c, Relativistic Jets. Generic systems: Compact object (White Dwarf, Neutron Star, Black Hole)+ Accretion Disk M87 Key Problems of Astrophysical Jets Acceleration mechanism and radiation processes Collimation i Long term stability

5 Relativistic Jets in Universe Mirabel & Rodoriguez 1998

6 Modeling of Astrophysical Jets Energy conversion from accreting matter is the most efficient mechanism Gas pressure model Jet velocity ~ sound speed (maximum is ~0.58c) Difficult to keep collimated structure Radiation pressure model Can collimate by the geometrical structure of accretion disk (torus) Difficult to make relativistic speed with keeping collimated structure Magnetohydrodynamic (MHD) model Jet velocity ~ Keplerian velocity of accretion disk make relativistic speed because the Keplerian velocity near the black hole is nearly light speed Can keep collimated structure by magnetic hoop-stress Direct extract of energy e from a rotating black hole (Blandford d & Znajek 1977, force-free model)

7 MHD model Acceleration Magneto-centrifugal force (Blandford-Payne 1982) Like a force worked a bead when swing a wire with a bead Magnetic pressure force Like a force when stretch a spring Direct extract a energy from a rotating black hole Collimation Magnetic pinch (hoop stress) Like a force when the shrink a rubber band Magnetic field line Centrifugal force outflow (jet) Outflow (jet) Magnetic field line Magnetic field line accretion

8 Requirment of Relativistic MHD Astrophysical jets seen AGNs show the relativistic speed (~0.99c) The central object of AGNs is suppermassive black hole (~ solar mass) The jet is formed near black hole Require relativistic treatment (special or general) In order to understand the time evolution of jet formation, propagation and other time dependent phenomena, we need to perform relativistic magnetohydrodynamic (MHD) simulations

9 Applicability of MHD Approximation MHD describe macroscopic behavior of plasmas if Spatial scale >> ion Larmor radius Time scale >> ion Larmor period But MHD can not treat Particle acceleration Origin of resistivity Electromagnetic waves

10 Recent Work for Relativistic Jets Investigate the role of magnetic fields in relativistic jets against three key problems Jet formation Jet acceleration and radiation process Acceleration of particles to very high energy Jet stability Kelvin-Helmholtz instability Current-Driven instability Recent research topics Development of 3D general relativistic MHD (GRMHD) code RAISHIN GRMHD simulations of jet formation and radiation from Black Hole magnetosphere A relativistic MHD boost mechanism for relativistic jets Particle-In-Cell (PIC) simulations of relativistic jets Stability analysis of magnetized spine-sheath relativistic jets

11 2. 2D GRMHD Simulation of Jet Formation Mizuno et al. 2006b, Astro-ph/ Hardee, Mizuno, & Nishikawa 2007, ApSS, 311, 281 Wu et al. 2008, CJAA, Supplement, 2008, 8, 226

12 2DGRMHDSi Simulation of fjet tformation Initial condition Geometrically thin Keplerian disk (ρ d /ρ c =100) rotates around a black hole (a=0.0, 0.95) The back ground corona is freefalling to a black hole (Bondi solution) o The global vertical magnetic field (Wald solution) Numerical Region and Mesh points 11(0 1.1(0.75) r S < r <20 r S, 003< 0.03< θ < π/2, with 128*128 mesh points Schematic picture of the jet formation near a black hole

13 Time evolution (Density) non-rotating BH case (B 0 =0.05,a=0.0) Parameter B 0 =0.05 a=0.0 Color: density White lines: magnetic field lines (contour of poloidal vector potential) Arrows: poloidal velocity

14 Time evolution (Density) rotating BH case (B 0 =0.05,a=0.95) Parameter B 0 =0.05 a=0.95 Color: density White lines: magnetic field lines (contour of poloidal vector potential) Arrows: poloidal velocity

15 Non-rotating BH ρ β Bφ Fast-rotating BH Results The matter in the disk loses its angular momentum by magnetic field and falls to a black hole. A centrifugal barrier decelerates the falling matter and make a shock around r=2rs. The matter near the shock region is accelerated by the J B force and the gas pressure gradient and forms jets. These results are similar to previous work (Koide et al. 2000, Nishikawa et al. 2005). In the rotating black hole case, additional inner jets form by the magnetic field twisted resulting from frame-dragging effect. v tot White curves: magnetic field lines (density), toroidal magnetic field (plasma beta) vector: poloidal velocity

16 W EM : Lorentz force W gp : gas pressure gradient Results (Jet Properties) gp g p g Non-rotating BH Fast-rotating BH Outer jet: toroidal velocity is dominant. The magnetic field is twisted by rotation of Keplerian disk. It is accelerated mainly by the gas pressure gradient (inner part of it may be accelerated by the Lorentz force). Inner jet: toroidal velocity is dominant (larger than outer jet). The magnetic field is twisted by the frame- dragging effect. It is accelerated mainly by the Lorentz force

17 Relativistic Radiation Transfer Wu et al., 2008, CJAA We have calculated the thermal free-free emission and thermal synchrotron emission from a relativistic flows in black hole systems based on the results of our 2D GRMHD simulations (rotating BH cases). We consider a general relativistic radiation transfer formulation (Fuerst & Wu 2004, A&A, 424, 733) and solve the transfer equation using a ray-tracing algorithm. In this algorithm, we treat general relativistic effect (light bending, gravitational lensing, gravitational redshift, frame- dragging effect etc.). Image of Emission, absorption & scattering

18 Radiation images of black hole-disk system We have calculated lated the thermal freefree emission and thermal synchrotron emission from a relativistic flows in black hole systems (2D GRMHD simulation, rotating BH cases). We consider a GR radiation transfer formulation and solve the transfer equation using a ray-tracing algorithm. The radiation image shows the front side of the accretion disk and the other side of the disk at the top and bottom regions because the GR effects. We can see the formation of twocomponent jet based on synchrotron emission and the strong thermal radiation from hot dense gas near the BHs. Radiation image seen from θ=85 (optically thin) Radiation image seen from =45 (optically thick) Radiation image seen from =85 (optically thick)

19 3. Stability Analysis of Magnetized Spine-Sheath Relativistic Jets Mizuno, Hardee & Nishikawa, 2007, ApJ, 662, 835 Hardee, 2007, ApJ, 664, 26 Hardee, Mizuno & Nishikawa, 2007, ApSS, 311, 281

20 Instability of Relativistic Jets When jets propagate outward, there are possibility to grow of two major instabilities Kli Kelvin-Helmholtz l lt (KH) instability Important at the shearing boundary flowing jet and external medium Current-Driven (CD) instability Important in twisted magnetic field Interaction of jets with external medium caused by such instabilities leads to the formation of shocks, turbulence, acceleration of charged particles etc. Used to interpret many jet phenomena quasi-periodic wiggles and knots, filaments, limb brightening, jet disruption etc Limb brightening of M87 jets (observation)

21 Spine-Sheath Relativistic Jets (observations) M87 Jet: Spine-Sheath (two-component) Configuration? HST Optical Image (Biretta, Sparks, & Macchetto 1999) VLA Radio Image (Biretta, Zhou, & Owen 1995) Typical Proper Motions > c Optical ~ inside radio emission Jet Spine? Typical Proper Motions < c Radio ~ outside optical emission Sheath wind? Observations of QSOs show the evidence of high speed wind (~ c)(Pounds et al. 2003): Related to Sheath wind Spine-sheath configuration proposed to explain limb brightening in M87, Mrk501jets (Perlman et al. 2001; Giroletti et al. 2004) TeV emission in M87 (Taveccio & Ghisellini 2008) broadband emission in PKS jet (Siemiginowska et al. 2007)

22 Spine-Sheath Relativistic Jets (GRMHD Simulations) In many GRMHD simulation of jet formation (e.g., Hawley & Krolik 2006, McKinney 2006, Hardee et al. 2007), suggest that ajetspinedriven by the magnetic fields threading the ergosphere may be surrounded dby a broad sheath wind driven by the magnetic fields anchored in the accretion disk. Non-rotating BH Fast-rotating BH Disk Jet/Wind BH Jet Disk Jet/Wind Total velocity distribution of 2D GRMHD Total velocity distribution of 2D GRMHD Simulation of jet formation (Hardee, Mizuno & Nishikawa 2007)

23 Key yquestions of Jet Stability When jets propagate outward, there are possibility to grow of two instabilities Kelvin-Helmholtz (KH) instability Current-Driven (CD) instability How do jets remain sufficiently stable? What are the Effects & Structure of KH / CD Instability in particular jet configuration (such as spine-sheath configuration)? We investigate these topics by using 3D relativistic MHD simulations

24 3D Simulations of Spine-Sheath Jet Stability Initial condition Mizuno, Hardee & Nishikawa, 2007 Cylindrical super-alfvenic jet established across the computational domain with a parallel magnetic field (stable against CD instabilities) Solving 3D RMHD equations in Cartesian coordinates (using Minkowski spacetime) Jet (spine): u jet = c (γ j =2.5), ρ jet = 2 ρ ext (dense, cold jet) External medium (sheath): u ext = 0 (static), 0.5c (sheath wind) Jet spine precessed to break the symmetry (frequency, ω=0.93) RHD: weakly magnetized (sound velocity > Alfven velocity) RMHD: strongly magnetized (sound velocity < Alfven velocity) Numerical box and computational zones -3 r j < x,y< 3r j, 0 r j < z < 60 r j (Cartesian coordinates) with 60*60*600 zones, (1r j =10 zones) Previous works: jet propagation simulation of Spine-Sheath jet model (e.g., Sol et al. 1989; Hardee & Rosen 2002)

25 Simulation results: global structure (nowind, weakly magnetized case) 3D isovolume of density with B-field lines show the jet is disrupted by the growing KH instability Longitudinal cross section y y z Transverse cross section show the strong interaction between jet and external medium x

26 Effect of magnetic field and sheath wind 1D radial velocity profile along jet v w =0.0 v w =0.5c v w =0.0 v w =0.5c Previous works: Study the effect of sheath wind on KH modes for non-rel HD RMHD and RHD simulations (Hanasaz & Sol 1996, 1998; Hardee & Rosen 2002) The sheath flow reduces the growth rate of KH modes and slightly increases the wave speed and wavelength as predicted from linear stability analysis. The magnetized sheath reduces growth rate relative to the weakly magnetized case The magnetized sheath flow damped growth of KH modes. Criterion for damped KH modes: (linear stability analysis)

27 4. MHD Boost mechanism of Relativistic Jets Mizuno, Hardee, Hartmann, Nishikawa & Zhang, 2008, ApJ, 672, 72

28 A MHD boost for relativistic jets The acceleration mechanism boosting relativistic jets to highly-relativistic speed is not fully known. Recently Aloy & Rezzolla (2006) have proposed a powerful hydrodynamical acceleration mechanism of relativistic istic jets by the motion of two fluid between jets and external If the jet is hotter and at much higher pressure than a denser, colder external medium, and moves with a large velocity tangent to the interface, the relative motion of the two fluids produces a hydrodynamical structure in the direction perpendicular to the flow. The rarefaction wave propagates p into the jet and the low pressure wave leads to strong acceleration of the jet fluid into the ultrarelativistic regime in a narrow region near the contact discontinuity. Schematic picture of simulations

29 Motivation This hydrodynamical boosting mechanism is very simple and powerful. But it is likely to be modified by the effects of magnetic fields present in the initial flow, or generated within the shocked outflow. We investigate the effect of magnetic fields on the boost mechanism by using Relativistic MHD simulations.

30 Initial Condition (1D RMHD) Consider a Riemann problem consisting of two uniform initial states Right (external medium): colder fluid with larger rest-mass density and essentially at rest. Left (jet): lower density, higher temperature and pressure, relativistic velocity tangent to the discontinuity surface To investigate the effect of magnetic fields, put the poloidal (Bz: MHDA) or toroidal (By: MHDB) components of magnetic field in the jet region (left state). For comparison, HDB case is a high gas pressure, pure-hydro case (gas pressure = total pressure of MHD case) Simulation region -0.2 < x < 0.2 with 6400 grid Schematic picture of simulations

31 Hydro Case Solid line (exact solution), Dashed line (simulation) In the left going rarefaction region, the tangential velocity increases due to the hydrodynamic y boost mechanism. jet is accelerated to γ~12 from an initial Lorentz factor of γ~7 7.

32 Multi-dimensional Simulations (Initial Condition) 2D RMHD simulations of MHDA case (poloidal field). Pre-existing jet flow is established across the computational domain. Simulation region, 0.5 < x,r < 1.5, 0 < z < 5.0 with (Nx * Nz) ) = (2000 * 250) In order to investigate a possible influence of the chosen coordinate system, we perform Cartesian and cylindrical i l coordinates.

33 Multi-dimensional Simulation (Results) (B z ) A thin surface is accelerated by the MHD boost mechanism to reach a maximum Lorentz factor γ~15 from an initial Lorentz factor γ~7. The jet in cylindrical coordinates is slightly more accelerated than the jet in Cartesian coordinates, which suggests that different coordinate systems can affect sideways expansion, shock profile, and acceleration (slightly). The field geometry is an important factor.

34 MHD Case HDA case (pure hydro) : dotted line MHDA case (poloidal) l) MHDB case (toroidal) HDB case (hydro, high-p) When gas pressure becomes large, the normal velocity increases and the jet is more efficiently accelerated. When a poloidal magnetic field is present, stronger sideways expansion is produced, and the jet can achieve higher speed due to the contribution from the normal velocity. When a toroidal magnetic field is present, although the shock profile is only changed slightly, the jet is more strongly accelerated in the tangential direction due to the Lorentz force. The geometry of the magnetic field is a very important geometric parameter.

35 Dependence on Magnetic Field Strength Solid line: exact solution, Crosses: simulation Magnetic field strength is measured in fluid flame poloidal (B z z) toroidal (B y ) When the poloidal magnetic field increases, the normal velocity increases and the tangential velocity decreases. When the toroidal magnetic field increases, the normal velocity decreases and the tangential velocity increases. In both of cases, when the magnetic field strength increases, maximum Lorentz factor also increases. Toroidal magnetic field provides the most efficient acceleration.

36 Summary We have developed a new 3D GRMHD code ``RAISHIN by using a conservative, high-resolution shock-capturing scheme. We have performed simulations of jet formation from a geometrically thin accretion disk near both non-rotating and rotating black holes. Similar to previous results (Koide et al. 2000, Nishikawa et al. 2005a) we find magnetically driven jets. It appears that the rotating black khole creates a second, faster, and more collimated inner outflow. Thus, kinematic jet structure could be a sensitive function of the black hole spin parameter.

37 Summary (cont.) We have investigated stability properties of magnetized spine-sheath relativistic jets by the theoretical work and 3D RMHD simulations. The most important result is that destructive KH modes can be stabilized even when the jet Lorentz factor exceeds the Alfven Lorentz factor. Even in the absence of stabilization, spatial growth of destructive KH modes can be reduced by the presence of magnetically sheath flow (~0.5c) around a relativistic jet spine (>0.9c)

38 Summary y( (cont.) We performed relativistic magnetohydrodynamic simulations of the hydrodynamic boosting mechanism for relativistic jets explored by Aloy & Rezzolla (2006) using the RAISHIN code. We find that magnetic fields can lead to more efficient acceleration of the jet, in comparison to the purehydrodynamic case. The presence and relative orientation of a magnetic field in relativistic i jets can significant ifi modify the hydrodynamic boost mechanism studied by Aloy & Rezzolla (2006).

39 Yosuke Mizuno National Space Science and Technology Center CSPAR/ University of Alabama in Huntsville Collaborators B. Zhang (UNLV), B. Giacomazzo (MPIG, AEI), K.-I. Nishikawa (NSSTC/UAH), P. E. Hardee (UA), S. Nagataki (YITP, Kyoto Univ.), D. H. Hartmann (Clemson Univ.) Mizuno et al. 2009, ApJ, 690, L47 第 21 回理論懇シンポジウム, 国立天文台, Dec

40 Abstract We solve the Riemann problem for the deceleration of an arbitrarily magnetized ed relativistic jets injected ed into a static unmagnetized medium in one dimension. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization σ (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when σ exceeds a critical value, σ c, defined by the balance between the magnetic pressure in the jet and the thermal pressure in the forward shock. In the rarefaction wave regime, we find that the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value. This acceleration mechanism is due to the strong magnetic pressure in the jet.

41 Role of Magnetic Field in Relativistic Jet The magnetic fields play an important role in relativistic jets/ejecta The degree of magnetization (quantified by σ) is poorly constrained by observations. The addition of magnetic field in the jet alters the condition for formation of a reverse shock (RS) as well as the strength of the RS (Kennel & Coroniti 1984) Analytical studies of the deceleration of a GRB fireball with arbitrary magnetization (Zhnag & Kobayashi 2005) suggest some novel behavior that does not exist in pure hydrodynamic model However, a consensus as to the conditions required for the existence of the RS has not yet been achieved (Zhang & Kobayashi 2005; Giannios et al. 2008) GRB blast wave model

42 Purpose of fthis Study We investigate the interaction between magnetized relativistic jet/ejecta and an unmagnetized external medium A Riemann Problem is solved both analytically and numerically over a broad range of. Mizuno, Y., B. Zhang, B. Giacomazzo, K.-I. Nishikawa, P. Hardee, S. Nagataki, and H. Hartmann, Magnetohydrodynamic Effects in Propagating Relativistic Jets: Reverse Shock and Magnetic Acceleration, ApJ, 2009, 690, L47

43 The Riemann Problem Consider a Riemann problem consisting of two uniform initial states Right (external medium): cold fluid with constant rest-mass density and essentially at rest. Left (jet): higher density, higher pressure, relativistic velocity normal to the discontinuity surface To investigate the effect of magnetic fields, put toroidal (By) components of magnetic field in the jet region (left state) Density: rho_l=100.0, rho_r=1.0 Pressure: p_l=1.0, p_r=0.01 Velocity: Vx_L=0.995c (γ=10), Vx_R=0.0c Adiabatic index: 4/3 Calculation box: (transition at 1.0) RMHD exact solution calculation code: Giacomazzo & Rezzolla (2006)

44 Jet-Medium Interaction σ: magnetization In Riemann profile, parameter =E mag /E kin S: shock, C: contact discontinuity R: rarefaction wave σ=0.1 (black) SCS profile, reverse shock (RS) propagate in the flow σ=1.0 (red) SCS profile, RS becomes weaker and propagate faster These features are expected from analytical work σ=10.0 (green) RCS profile, rarefaction wave propagate in the flow Density, pressure in the flow decrease and flow velocity increases σ= (blue) RCS profile, flow velocity is more accelerated σ=2.7 7 (yellow) Critical sigma value, neither reverse shock nor a rarefaction wave is established density Solid: Gas pressure Dashed: Mag pressure Lorentz factor

45 Physical Conditions for Reverse Shock or Magnetic Acceleration Four regions: (1) unshocked medium, (2) shocked medium, (3) shocked ejecta, (4) unshocked ejecta Based on relativistic shock jump conditions with adiabatic index Γ=4/3 and Thermal pressure generated in the forward shock region Constant speed across the contact discontinuity, γ 2 =γ 3 Relation between gas pressure and internal energy, p 2 =u 2 /3 The condition for existence of the reverse shock/ rarefaction wave pressure balance between forward shock (p gas, 2 ) and ejecta (p mag, 4 ) Reverse shock: p gas,2 > p mag, 4 ; Rarefaction wave: p gas, 2 < p mag, 4 Critical sigma value

46 Dependence on magnetization parameter Pressure of shocked flow Lorentz factor of propagating RS or RR to Alfven Lorentz factor ratio Gas pressure in FS to magnetic pressure in flow ratio Shocked Lorentz factor Magnetization parameter, σ increases, Gas pressure decrease with σ smooth transition from RS regime to reverse rarefaction wave regime Transition of shock to rarefaction σ~0.7 07in γ L =5, σ~2.7 27in γ L =10, σ~ in γ L =20 cases respectively The critical σ increases with γ L, so that a RS can exist in the high-σ σ regime if γ L is sufficiently large Another condition for a RS: shock speed in the fluid frame is higher than the speed of the Alfven wave, γ RS,RR > γ A p FS /p B and γ RS,RR /γ A reach unity at the same critical σ Two RS conditions have intrinsically the same physical origin (see Giannios et al. 2008)

47 Terminal Lorentz factor The terminal Lorentz factor after magnetic acceleration can be estimated analytically by requiring that the thermal pressure in the forward shock region balances the magnetic pressure in the region through h which h the rarefaction wave has propagated From the definition of magnetized parameter, σ=b 2 /γρ, this condition becomes In the initial Lorentz factor, γ 4 =γ L =10 case with σ=100, the terminal Lorentz factor of flow is γ t ~24.7 (γ 1 =γ R =1, γ 4 =γ L =100), this is good agreement with the exact solution of the Riemann problem

48 Magnetic Acceleration Efficiency Terminal Lorentz factor Acceleration Efficiency While a jet with a higher initial Lorentz factor reaches a higher terminal Lorentz factor, that with a lower initial Lorentz factor reaches a higher terminal Lorentz factor, that with a lower initial Lorentz factor experiences a higher acceleration efficiency. Acceleration efficiency from equation for terminal Lorentz factor,

49 Discussion The observed paucity of bright optical flashes in GRBs (e.g., Roming et al. 2006) may be attributed to highly magnetized ejecta The magnetic acceleration mechanism suggests that σ and γ are not independent parameters at the deceleration radius. For high-σ flow, ejecta would experience magnetic acceleration at small radii, before reaching the coasting regime; the coasting Lorentz factor (initial Lorentz factor for th e afterglow) = terminal Lorentz factor Variable emission observed in some TeV blazars suggests very high h Lorentz factor in AGN jets (Aharonian et al. 2007) Our results suggest the possibility of magnetic acceleration occurring where highly magnetized jet material overtakes more weakly magnetized jet material. In this case magnetically accelerated Lorentz factor behind FS can significantly exceed the Lorentz factor of the overtaken jet material

50 Summery We have investigated i the interaction i between magnetized relativistic jet/ejecta and unmagnetized static medium We confirm that the reverse shock propagating in the flow becomes weak when the jet is magnetized We found the new acceleration mechanism by the rarefaction wave propagating in the jet when the flow is strongly magnetized Critical magnetization for new acceleration mechanism depends on the initial iti jet velocity; the jet with higher initial Lorentz factor needs strong magnetization Terminal Lorentz factor depends on the magnetization of jet

51 Current Driven instability From MHD model of jet formation, jets launch with twisted magnetic field from the black hole magnetosphere In such configuration, the most dangerous instability is current driven (CD) kink mode (see Mizuno et al (in press)) This instability excites large-scale helical motions and it disrupts the system Relativistic CD kink instability was studied only in linear approximation (e.g., Lyubarskii 1999) The investigation of nonlinear behavior of CD kink instability is important for the stability and structure of relativistic jets Need 3D relativistic MHD simulation

52 Force free equilibrium of a static cylinder poloidal magnetic field component: increasing: 0.5 < α < 1, decreasing: 1 < α, constant: α = 1 Mizuno et al. 2009, ApJ, in press, (arxiv: )

53 Initial conditions of CD kink simulations Initial radial profiles

54 Time evolution of CD kink k inst

55 3D evolution of CD kink inst

56 Summary of CD kink mode m = ±1 1 mode becomes unstable kink grows as linear theory predicted nonlinear behavior depends on the density and magnetic pitch radial profile pitch profile increase in the magnetic pitch with radius: reduced growth rate in the linear late transition to non linear behavior pitch profile fl decrease in the magnetic pitch: more rapid growth in the the linear growth stage earlier transition to non linear behavior

57 Plan of Operation Study numerically non-linear evolution of different kinkunstable configurations When the instability saturates, t disrupts, and final state t Coupling KH and CD instabilities What is fastest growth modes in magnetized relativistic jets? Take into account rotation, velocity shear, and expansion Take into account several jet configuration Top-hat jets (Mizuno et al. 2007) Spine-sheath jet configuration (Mizuno et al. 2007) Boosted boundary layer jets (Mizuno et al. 2008) etc