- Formation of Relativistic Jets
- Imaging of Black Hole Accretion System
- MHD Acceleration of Relativistic Jets
- Kelvin-Helmholtz Instability of Relativistic Jets
- Current-Driven Kink Instability of Relativistic Jets
- MHD Effects in Propagating Relativistic Jets
- Relativistic Turbulence in Relativistic Shocks
- Current-Driven Kink Instability in Pulsar Wind Nebulae
- Jet Formation in Collapsars
- Development of Relativistic MHD Code

Relativistic jets occur in active galactic nuclei (AGN), in microquasars, and are thought responsible for the gamma-ray bursts (GRB). The most promising mechanism for producing relativistic jets involves magnetohydrodynamic (MHD) acceleration from an accretion disk around a black hole, and/or involves the extraction of energy from a rotating black hole. Relativistic jet properties and structure depend on black hole spin and on the properties of the accretion disk. We have simulated the formation of jets from a geometrically thin Keplerian disk using a 2.5-dimensional Boyer-Lindquist coordinate system by RAISHIN code (Hardee, Mizuno & Nishikawa 2007).

Figure shows snapshots of the non-rotating case, a = 0.0 (left panels) and the rapidly
rotating case, a = 0.95 (right panels) at each simulationfs terminal time. Matter in the disk loses angular momentum to the magnetic field and falls towards the black hole. A centrifugal barrier decelerates the falling matter and produces a shock at r < 2 r_S. Matter is accelerated outwards by the Lorentz force and the gas pressure gradient in the z-direction. In the non-rotating case the magnetic field is twisted by disk rotation near the black hole. In the rapidly rotating case the magnetic field is additionally strongly twisted by frame-dragging near the rotating black hole forming an additional inner jet component closer to the black hole and z-axis. This spine-sheath structure is like Kerr black hole results found by McKinney (2006) and by Hawley & Krolik (2006).

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In order to understand the observations from the MHD simulations, we need to calculate emission from MHD simulation results. We have calculated the emission from relativistic jets and accretion disks based on the jet formation simulation results by the RAISHIN code (Wu et al. 2007). The method of ray-tracing, where the equations of motion of individual photons are solved in the curved space-time of the Kerr metric, is used to build an image is by following rays backwards in time from the observer to the source volume elements.

Imaging of the spinning black hole general relativistic MHD simulation is shown in upper Figure. Because the jet density is low compared to the accretion disk, the emissivity is small and the jet is only weakly visible in the radiative transfer images. The images show the front face of the disk and, due to gravitational lensing, the back of the disk is also visible. In the 85 degree inclination cases lensing causes the top and bottom of the disk to appear almost symmetrically. When the accretion disk is optically thick we see only radiation from the disk surface. There are Doppler effects from orbital motion apparent in the yellowish thermal bremsstrahlung ring near the inner edge of the disk and the left hand side is somewhat brighter than the right. The ring is distorted by gravitational lensing. The jet and/or counter-jet can be seen in the 85 degree inclination cases where strongly twisted and strengthened magnetic fields lead to strong synchrotron emission. In the optically thin images disk emission dominates. This post-processing method provides a first step towards the ultimate goal of obtaining observable quantities from fully coupled radiative-dyanmical general relativistic MHD simulations.

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Proper motions observed in jets from microquasars and AGNs imply jet speeds from 0.9c up to 0.999c, and Lorentz factors in excess of 100 have been inferred for GRBs. The acceleration mechanisms capable of boosting jets to such highly relativistic speeds has not yet been fully established. Aloy & Rezzolla (2006) investigated a potentially
powerful acceleration mechanism in the context of purely hydrodynamical
flows, posing a simple Riemann problem. We performed relativistic MHD simulations to investigate the effect of magnetic fields on an acceleration boosting mechanism for fast astrophysical jet flows that result from highly overpressured, tenuous flows with an initially modest relativistic speed relative to a colder, denser external medium at rest (Mizuno et al. 2008). We found that the presence of magnetic fields in the jet can provide even more efficient acceleration of the jet than is possible in the pure hydrodynamic case.

General relativistic MHD simulations suggest that a high speed magnetically dominated gPoynting fluxh jet spine driven by magnetic fields threading the ergosphere resides within a slower moving kinetically dominated sheath driven by the magnetic fields anchored in the accretion disk and perhaps also a broader accretion disk wind. Several observed jets also show the presence of spine-sheath morphology.
In order to investigate the stability against Kelvin-Helmholtz (KH) instability of magnetized spine-sheath relativistic jets, we have performed 3D relativistic MHD simulations of weakly and strongly magnetized relativistic jets embedded in a weakly and strongly magnetized stationary or mildly relativistic (0.5c) sheath flow using the RAISHIN code (Mizuno, Hardee & Nishikawa 2007).

Results of the numerical simulations are compared to theoretical predictions from a theoretical stability analysis of the linearized RMHD equations (Hardee 2007). Simulation results confirm the theoretical prediction of increased stability of a weakly-magnetized system with mildly relativistic sheath flow to KH instabilities and the stabilization of a strongly-magnetized system with mildly relativistic sheath flow.

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The most promising mechanism for producing relativistic jets involves magnetohydrodynamic acceleration from an accretion disk around a black hole, and/or involves the extraction of energy from a rotating black hole.In such outflows, a toroidal magnetic field is wound up and in the far zone becomes dominate because the poloidal magnetic field falls off faster with expansion and distance. The most dangerous instability in configurations with toroidal magnetic field is the current driven (CD) kink mode. This instability excites large-scale helical motions that may disrupt the system.
The linear and non-linear behavior against Current-driven kink instability of strongly helically magnetized static plasma has been studied by using 3D RMHD simulations (Mizuno et al. 2009).

Simulation results show 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 on the radial density profile and strongly depends on the magnetic pitch profile.

We have also investigated the influence of a velocity shear surface on the linear and non-linear development of CD kink instability of force-free helical magnetic equilibria in 3D (Mizuno et al. 2011). We found that helically distorted density structure propagates along the jet with speed and flow structure dependent on the radius of the velocity shear surface relative to the characteristic radius of the helically twisted force-free magnetic field. The kink propagation speed increases as the velocity shear radius increases and the kink becomes more embedded in the plasma flow. For more realistic situation for relativistic jets, we have investigated the effect of jet rotation and differential motion on the linear and non-linear development of CD kink instability of force-free helical magnetic equilibria via 3DRMHD simulations (Mizuno et al. 2012). We found that, in accordance with the linear stability theory, the development of the instability depends on the lateral distribution of the poloidal magnetic field. If multiple wavelengths are excited, then nonlinear interaction eventually disrupts the initial cylindrical configuration. When the profile of the poloidal field is shallow, the instability develops slowly and eventually saturates.

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Relativistic jets has been argued that magnetic fields could play an important dynamical role, but the degree of magnetization, quantified by the magnetization parameter, sigma (the ratio of electromagnetic to kinetic energy flux), is poorly constrained by observations. A useful diagnostic for the degree of jet-magnetization can be obtained from the interaction between the decelerating jet and the ambient medium. We investigated the interaction between a magnetized relativistic flow and a static, unmagnetized external medium (Mizuno et al. 2009). A Riemann problem consisting of two uniform initial states (left: relativistic jet, right: external medium) with discontinuous hydrodynamic properties is solved analytically over a broad range of sigma.

We found that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing sigma, turning into a rarefaction wave when sigma is larger than sigma_c, at which point the magnetic pressure in the flow is balanced by the thermal pressure in the forward shock. In the rarefaction wave regime, material in the shocked region is accelerated due to the strong magnetic pressure in the flow. This magnetic acceleration mechanism may thus play an important role in the dynamics of strongly magnetized, relativistic flows. Our results have implications for understanding deceleration of strongly magnetized outflows, possibly present in GRBs and AGNs. Exact solutions indicate that the condition for the existence of a reverse shock is sigma is lower than the critical sigma value. The paucity of bright optical flashes in GRBs may be attributed to highly magnetized flows.

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In the standard GRB afterglow model, the radiation is produced in a relativistic blastwave shell propagating into a weakly magnetized plasma. Detailed studies of GRB spectra and light curves have shown that the magnetic energy density in the emitting
region is a small fraction, 10^-3 - 10^-2 of the internal energy density. However simple compressional amplification of the weak pre-existing microgauss magnetic field of the circumburst medium can not achieve this magnetization. We investigated the magnetic field amplification by turbulence in 2D relativistic MHD simulations of a mildly relativistic shock wave propagating through an inhomogeneous medium with a
Kolmogorov power spectrum (Mizuno et al. 2011).

The simulations show that the postshock region becomes turbulent owing to preshock density inhomogeneity through a process similar to the Richtmyer-Meshkov instability, and magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that a so-called small-scale dynamo is occurring in the postshock region.

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The pulsar wind nebulae (PWNe) may be considered as relativistically hot bubbles continuously pumped by an electron-positron plasma and magnetic field emanating from the pulsar. Pulsars lose their rotational energy predominantly by generating a highly magnetized, ultra relativistic wind. The wind presumably terminates at a strong reverse shock and the shocked plasma inflates a bubble within the external medium. Close to the pulsar, the energy is carried mostly by electromagnetic fields as Poynting flux; however, the common belief is that at the termination shock the wind must already be very weakly magnetized. Simple spherical models of PWNe suggest that the magnetization parameter sigma, the ratio of the Poynting to the kinetic energy flux, needs to be as small as 0.001 - 0.01 just upstream of the termination shock. Since no mechanism had been found for the extraction of energy from a large scale, axisymmetric magnetic field, Begelman (1998) suggested that the problem can be alleviated if a curren-driven (CD) kink instability destroys the concentric field structure in the nebula. We have investigated the relaxation of a hydrostatic hot plasma column containing toroidal magnetic field by the CD kink instability as a model of pulsar wind nebulae (Mizuno et al. 2011).

In our simulations the CD kink instability is excited by a small initial velocity perturbation and develops turbulent structure inside the hot plasma column. We demonstrate that, as envisioned by Begelman, the hoop stress declines and the initial gas pressure excess near the axis decreases. The magnetization parameter sigma, the ratio of the Poynting to the kinetic energy flux, declines from an initial value of 0.3 to about 0.01 when the CD kink instability saturates. Our simulations demonstrate that axisymmetric models strongly overestimate the elongation of the pulsar wind nebulae. Therefore, the previous requirement for an extremely low pulsar wind magnetization can be abandoned.

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GRBs and the afterglows are well described by the simplest model ``fireball model'', in which a relativistic outflow is generated from a compact central engine. However, the most fundamental problem has not yet been solved: what is the central engine of GRBs? From recent observations, some evidence was found for a connection between GRBs and the death of massive stars. It is probable that a major subclass of GRBs is a consequence of the collapse of a massive star. One of the most attractive scenarios involving massive stars is the ``collapsar'' model. To understand the formation and acceleration of relativistic jets from the collapsar model, we perform 2D general relativistic MHD simulations of the gravitational collapse of a magnetized rotating massive star (Mizuno et al. 2004ab).

The simulation results show the formation of a disk-like structure and the generation of a jet-like outflow inside the shock wave launched at the core bounce. We found the jet is accelerated by the magnetic pressure and the centrifugal force and is collimated by the pinching force of the toroidal magnetic field amplified by the rotation and the effect of geometry of the poloidal magnetic field. The maximum velocity of the jet is mildly relativistic (about 0.3 c).

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In order to investigate the dynamics of relativistic astrophysical objects such as relativistic jets, relativistic shocks (GRBs), and pulsar wind nebulae in numerically, we need to use numerical simulation code including relativistic magnetohydrodynamics (MHD). We have developed the new three dimensional (3D) general relativistic magnetohydrodynamic (GRMHD) code gRAISHINh by using a conservative, high-resolution shock-capturing scheme (Mizuno et al. 2006, 2011).gRAISHINh by using a conservative, high-resolution shock-capturing scheme (Mizuno et al. 2006a). The code is based on a 3+1 formalism of the general relativistic conservation laws of particle number, energy-momentum, Maxwell equations, and Ohmfs law with no electrical resistance (ideal MHD condition) in a curved spacetime. Simulation can be performed in Cartesian, cylindrical, or Boyer-Lindquist coordinates. Numerical fluxes are calculated using HLL and HLLC approximate Riemann solver scheme. Constrained transport schemes or a generalized Lagrange multiplier approach maintain a divergence-free magnetic field. Different reconstruction schemes can be employed depending upon the particular numerical task. In general, the code has proven to be robust and on average 2nd-order accurate (Mizuno et al. 2006, Mizuno et al. 2011). Code development has added a variable equation of state (EoS) and test results agree with those of Mignone & McKinney (2007). This ability is important to quantitatively correct relativistic shock treatment. The code is fully parallelized by OpenMP and MPI.

The ideal MHD approximation is a good description of the global properties and dynamics of such systems well into their nonlinear regimes. The ideal MHD limit provides a convenient form for solving the equations of RMHD and is also an excellent approximation for many relativistic astrophysical phenomena. Quite often numerical simulations using ideal RMHD exhibit violent magnetic reconnection. The magnetic reconnection observed in ideal RMHD simulations is due to purely numerical resistivity, occurs as a result of truncation errors, and hence fully depends on details of the numerical scheme and resolution. Magnetic reconnection is one of the most important phenomena in astrophysics. It is highly dynamic, and it converts magnetic energy into fluid energy. Therefore, numerical codes solving the resistive RMHD (RRMHD) equations and that allow control of magnetic reconnection according to a physical model of resistivity are highly desirable. We have newly developed resistive relativistic magnetohydrodynamic code and have investigated the role of the equation of state in resistive relativistic magnetohydrodynamics.

RAISHIN code website

The code passes all the tests in situations involving both small and large uniform conductivities. Equations of state which closely approximate the single-component perfect relativistic gas are introduced. The main conclusion is that the choice of the equation of state as well as the value of the electric conductivity can result in considerable dynamical differences in simulations involving shocks, instabilities, and magnetic reconnection.

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