An HLLC Riemann Solver for Relativistic Flows: I. Hydrodynamics

We present an extension of the HLLC approximate Riemann solver by Toro, Spruce and Speares to the relativistic equations of fluid dynamics. The solver retains the simplicity of the original two-wave formulation proposed by Harten, Lax and van Leer (HLL) but it restores the missing contact wave in the solution of the Riemann problem. The resulting numerical scheme is computationally efficient, robust and positively conservative. The performance of the new solver is evaluated through numerical testing in one and two dimensions.Comment: 12 pages, 12 figure

The bulk kinetic power of the jets of GRS 1915+105

We calculate the minimum value of the power in kinetic bulk motion of the galactic superluminal source GRS 1915+105. This value far exceeds the Eddington luminosity for accretion onto a black hole of 10 solar masses. This large value severely limits the possible carriers of the kinetic luminosity at the base of the jet, and favours a jet production and acceleration controlled by a magnetic field whose value, at the base of the jet, exceeds $10^8$ Gauss. The Blandford and Znajek process can be responsible of the extraction of the rotational energy of a Kerr black hole, if lasting long enough to provide the required kinetic energy. This time, of the order of a day, implies that the process must operate in a stationary, not impulsive, mode.Comment: 5 pages, Latex, accepted for publication in MNRAS as a lette

Recollimation shocks and radiative losses in extragalactic relativistic jets

We present the results of state-of-the-art simulations of recollimation shocks induced by the interaction of a relativistic jet with an external medium, including the effect of radiative losses of the shocked gas. Our simulations confirm that -- as suggested by earlier semi-analytical models -- the post-shock pressure loss induced by radiative losses may lead to a stationary equilibrium state characterized by a very strong focusing of the flow, with the formation of quite narrow nozzles, with cross-sectional radii as small as $10^{-3}$ times the length scale of the jet. We also study the time-dependent evolution of the jet structure induced of a density perturbation injected at the flow base. The set-up and the results of the simulations are particularly relevant for the interpretation of the observed rapid variability of the $\gamma$-ray emission associated to flat spectrum radio quasars. In particular, the combined effects of jet focusing and Doppler beaming of the observed radiation make it possible to explain the sub-hour flaring events such as that observed in the FSRQ PKS 1222+216 by MAGIC.Comment: 8 pages, 8 figures, Astronomy and Astrophysics accepte

Dynamical and radiative properties of astrophysical supersonic jets I. Cocoon morphologies

We present the results of a numerical analysis of the propagation and interaction of a supersonic jet with the external medium. We discuss the motion of the head of the jet into the ambient in different physical conditions, carrying out calculations with different Mach numbers and density ratios of the jet to the exteriors. Performing the calculation in a reference frame in motion with the jet head, we can follow in detail its long term dynamics. This numerical scheme allows us also to study the morphology of the cocoon for different physical parameters. We find that the propagation velocity of the jet head into the ambient medium strongly influences the morphology of the cocoon, and this result can be relevant in connection to the origin and structure of lobes in extragalactic radiosources.Comment: 14 pages, TeX. Accepted for A&

High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175 (2002) 645-673). The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.Comment: 32 pages, 14 figure, submitted to Journal of Computational Physics (Aug 7 2009

Linear stability analysis of magnetized relativistic jets: the nonrotating case

We perform a linear analysis of the stability of a magnetized relativistic non-rotating cylindrical flow in the aproximation of zero thermal pressure, considering only the m = 1 mode. We find that there are two modes of instability: Kelvin-Helmholtz and current driven. The Kelvin-Helmholtz mode is found at low magnetizations and its growth rate depends very weakly on the pitch parameter. The current driven modes are found at high magnetizations and the value of the growth rate and the wavenumber of the maximum increase as we decrease the pitch parameter. In the relativistic regime the current driven mode is splitted in two branches, the branch at high wavenumbers is characterized by the eigenfunction concentrated in the jet core, the branch at low wavenumbers is instead characterized by the eigenfunction that extends outside the jet velocity shear region.Comment: 22 pages, 13 figures, MNRAS in pres

A five-wave HLL Riemann solver for relativistic MHD

We present a five-wave Riemann solver for the equations of ideal relativistic magnetohydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi and Kusano for the equations of ideal MHD. The solution to the Riemann problem is approximated by a five wave pattern, comprised of two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a nonlinear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular HLL solver or the recently proposed HLLC schemes.Comment: 15 pages, 19 figures. Accepted for Publication in MNRA

A Constrained Transport Method for the Solution of the Resistive Relativistic MHD Equations

We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces and are evolved using the constrained transport formalism. Direct application of Stokes' theorem to Faraday's and Ampere's laws ensures that the resulting discretization is divergence-free for the magnetic field and charge-conserving for the electric field. Hydrodynamic variables retain, instead, the usual zone-centred representation commonly adopted in finite-volume schemes. Temporal discretization is based on Runge-Kutta implicit-explicit (IMEX) schemes in order to resolve the temporal scale disparity introduced by the stiff source term in Ampere's law. The implicit step is accomplished by means of an improved and more efficient Newton-Broyden multidimensional root-finding algorithm. The explicit step relies on a multidimensional Riemann solver to compute the line-averaged electric and magnetic fields at zone edges and it employs a one-dimensional Riemann solver at zone interfaces to update zone-centred hydrodynamic quantities. For the latter, we introduce a five-wave solver based on the frozen limit of the relaxation system whereby the solution to the Riemann problem can be decomposed into an outer Maxwell solver and an inner hydrodynamic solver. A number of numerical benchmarks demonstrate that our method is superior in stability and robustness to the more popular charge-conserving divergence cleaning approach where both primary electric and magnetic fields are zone-centered. In addition, the employment of a less diffusive Riemann solver noticeably improves the accuracy of the computations.Comment: 25 pages, 14 figure