Rarefaction wave in relativistic steady magnetohydrodynamic flows

We construct and analyze a model of the relativistic steady-state magnetohydrodynamic (MHD) rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.Comment: 12 pages, Accepted in Physics of Plasma

Rarefaction acceleration in magnetized gamma-ray burst jets

Relativistic jets associated with long/soft gamma-ray bursts are formed and initially propagate in the interior of the progenitor star. Because of the subsequent loss of their external pressure support after they cross the stellar surface, these flows can be modeled as moving around a corner. A strong steady-state rarefaction wave is formed, and the sideways expansion is accompanied by a rarefaction acceleration. We investigate the efficiency and the general characteristics of this mechanism by integrating the steady-state, special relativistic, magnetohydrodynamic equations, using a special set of partial exact solutions in planar geometry (r self-similar with respect to the "corner"). We also derive analytical approximate scalings in the ultrarelativistic cold/magnetized, and hydrodynamic limits. The mechanism is more effective in magnetized than in purely hydrodynamic flows. It substantially increases the Lorentz factor without much affecting the opening of the jet; the resulting values of their product can be much grater than unity, allowing for possible breaks in the afterglow light curves. These findings are similar to the ones from numerical simulations of axisymmetric jets by Komissarov et al and Tchekhovskoy et al, although in our approach we describe the rarefaction as a steady-state simple wave and self-consistently calculate the opening of the jet that corresponds to zero external pressure.Comment: 11 page

Magnetohydrodynamics of Gamma-Ray Burst Outflows

Using relativistic, axisymmetric, ideal MHD, we examine the outflow from a disk around a compact object, taking into account the baryonic matter, the electron-positron/photon fluid, and the large-scale electromagnetic field. Focussing on the parameter regime appropriate to gamma-ray burst outflows, we demonstrate, through exact self-similar solutions, that the thermal force (which dominates the initial acceleration) and the Lorentz force (which dominates further out and contributes most of the acceleration) can convert up to ~50% of the initial total energy into asymptotic baryon kinetic energy. We examine how baryon loading and magnetic collimation affect the structure of the flow, including the regime where emission due to internal shocks could take place.Comment: To be published in ApJ Letters. 4 pages, 1 figur

Linear stability analysis of relativistic magnetized jets

The stability of astrophysical jets in the linear regime is investigated by presenting the methodology to find the growth rates of the various instabilities. We perturb a cylindrical axisymmetric steady jet, linearize the relativistic ideal magnetohydrodynamic (MHD) equations, and analyze the evolution of the eigenmodes of the perturbation by deriving the differential equations that need to be integrated subject to the appropriate boundary conditions, in order to find the dispersion relation. We also apply the WKBJ approximation and additionally give analytical solutions in some subcases corresponding to unperturbed jets with constant bulk velocity along the symmetry axis.Comment: The paper was not accepted for publication by MNRAS, who kindly recommended major revision requesting numerical results in specific cases. My intention however is to present only the formalism and analytical results, detailed analysis of specific cases will be done separatel

Relativistic shocks in conductive media

Relativistic shocks are present in all high-energy astrophysical processes involving relativistic plasma outflows interacting with their ambient medium. While a well understood process in the context of relativistic hydrodynamics and ideal magnetohydrodynamics, there is little to no understanding of their propagation in media with a finite electrical conductivity. This work presents a method for the derivation and solution of the jump conditions for relativistic shocks propagating in MHD media with a finite electrical conductivity. The covariant expressions of the jump conditions are derived and the algebraic equations expressing the Rankine-Hugoniot conditions are solved numerically. This method is employed for the solution of the Riemann problem for the case of a forward and reverse shock which form during the interaction of a gamma-ray burst ejecta with the circumburst medium in order to determine the kinematics of the resulting blastwave and the dynamical conditions in its interior. Our solutions clearly depict the impact of the plasma's electrical conductivity in the properties of the post-shock medium. Two characteristic regimes are identified with respect to the value of a dimensionless parameter which has a linear dependence on the conductivity. For small values of this parameter the shock affects only the hydrodynamic properties of the propagation medium and leaves its electromagnetic field unaffected. No current layer forms in the shock front; thus this is called the current-free regime. For large values of this parameter the ideal MHD regime is retrieved. We also show that the assumption of a finite electrical conductivity can lead to higher efficiencies in the conversion of the ejecta energy into thermal energy of the blastwave through the reverse shock. The theory developed in this work can be applied to the construction of Riemann solvers for resistive relativistic MHD.Comment: 10 pages, 8 figures. Accepted for publication in A&

Comparison of synthetic maps from truncated jet-formation models with YSO jet observations

(abridged) Significant progress has been made in the last years in the understanding of the jet formation mechanism through a combination of numerical simulations and analytical MHD models for outflows characterized by the symmetry of self-similarity. In a previous article we introduced models of truncated jets from disks, i.e. evolved in time numerical simulations based on a radially self-similar MHD solution, but including the effects of a finite radius of the jet-emitting disk and thus the outflow. These models need now to be compared with available observational data. A direct comparison of the results of combined analytical theoretical models and numerical simulations with observations has not been performed as yet. In order to compare our models with observed jet widths inferred from recent optical images taken with HST and AO observations, we use a new set of tools to create emission maps in different forbidden lines, from which we determine the jet width as the FWHM of the emission. It is shown that the untruncated analytical disk outflow solution considered here cannot fit the small jet widths inferred by observations of several jets. Various truncated disk-wind models are examined, whose extracted jet widths range from higher to lower values compared to the observations. Thus we can fit the observed range of jet widths by tuning our models. We conclude that truncation is necessary to reproduce the observed jet widths and our simulations limit the possible range of truncation radii. We infer that the truncation radius, which is the radius on the disk mid-plane where the jet-emitting disk switches to a standard disk, must be between around 0.1 up to about 1 AU in the observed sample for the considered disk-wind solution. One disk-wind simulation with an inner truncation radius at about 0.11 AU also shows potential for reproducing the observations, but a parameter study is needed.Comment: accepted for publication in A & A, 14 pages, 21 figure

Relativistic Magnetohydrodynamics with Application to Gamma-Ray Burst Outflows: II. Semianalytic Super-Alfvenic Solutions

We present exact radially self-similar solutions of special-relativistic magnetohydrodynamics representing ``hot'' super-Alfvenic outflows from strongly magnetized, rotating compact objects. We argue that such outflows can plausibly arise in gamma-ray burst (GRB) sources and demonstrate that, just as in the case of the trans-Alfvenic flows considered in the companion paper, they can attain Lorentz factors that correspond to a rough equipartition between the Poynting and kinetic-energy fluxes and become cylindrically collimated on scales compatible with GRB observations. As in the trans-Alfvenic case, the initial acceleration is thermal, but, in contrast to the solutions presented in Paper I, part of the enthalpy flux is transformed into Poynting flux during this phase. The subsequent, magnetically dominated acceleration can be significantly less rapid than in trans-Alfvenic flows.Comment: 8 pages, 4 figures, submitted to the Astrophysical Journal. The companion paper is astro-ph/030348