When a magnetically dominated superfast-magnetosonic long/soft gamma-ray burst (GRB) jet leaves the progenitor star, the external pressure support will drop and the jet may enter the regime of ballistic expansion, during which additional magnetic acceleration becomes ineffective. However, recent numerical simulations by Tchekhovskoy et al. have suggested that the transition to this regime is accompanied by a spurt of acceleration. We confirm this finding numerically and attribute the acceleration to a sideways expansion of the jet, associated with a strong magnetosonic rarefaction wave that is driven into the jet when it loses pressure support, which induces a conversion of magnetic energy into kinetic energy of bulk motion. This mechanism, which we dub rarefaction acceleration, can only operate in a relativistic outflow because in this case the total energy can still be dominated by the magnetic component even in the superfast-magnetosonic regime. We analyse this process using the equations of relativistic magnetohydrodynamics and demonstrate that it is more efficient at converting internal energy into kinetic energy when the flow is magnetized than in a purely hydrodynamic outflow, as was found numerically by Mizuno et al. We show that, just as in the case of the magnetic acceleration of a collimating jet that is confined by an external pressure distribution - the collimation-acceleration mechanism - the rarefaction-acceleration process in a magnetized jet is a consequence of the fact that the separation between neighbouring magnetic flux surfaces increases faster than their cylindrical radius. However, whereas in the case of effective collimation-acceleration the product of the jet opening angle and its Lorentz factor does not exceed ~1, the addition of the rarefaction-acceleration mechanism makes it possible for this product to become >>1, in agreement with the inference from late-time panchromatic breaks in the afterglow light curves of long/soft GRBs.

We study semi-analytical time-dependent solutions of the relativistic MHD equations for the fields and the fluid emerging from a spherical source. We assume uniform expansion of the field and the fluid and a polytropic relation between the density and the pressure of the fluid. The expansion velocity is small near the base but approaches the speed of light at the light sphere where the flux terminates. We find self-consistent solutions for the density and the magnetic flux. The details of the solution depend on the ratio of the toroidal and the poloidal magnetic field, the ratio of the energy carried by the fluid and the electromagnetic field and the maximum velocity it reaches.

When a magnetically dominated superfast-magnetosonic long/soft gamma-ray burst (GRB) jet leaves the progenitor star, the external pressure support will drop and the jet may enter the regime of ballistic expansion, during which additional magnetic acceleration becomes ineffective. However, recent numerical simulations by Tchekhovskoy et al. have suggested that the transition to this regime is accompanied by a spurt of acceleration. We confirm this finding numerically and attribute the acceleration to a sideways expansion of the jet, associated with a strong magnetosonic rarefaction wave that is driven into the jet when it loses pressure support, which induces a conversion of magnetic energy into kinetic energy of bulk motion. This mechanism, which we dub rarefaction acceleration, can only operate in a relativistic outflow because in this case the total energy can still be dominated by the magnetic component even in the superfast-magnetosonic regime. We analyse this process using the equations of relativistic magnetohydrodynamics and demonstrate that it is more efficient at converting internal energy into kinetic energy when the flow is magnetized than in a purely hydrodynamic outflow, as was found numerically by Mizuno et al. We show that, just as in the case of the magnetic acceleration of a collimating jet that is confined by an external pressure distribution - the collimation-acceleration mechanism - the rarefaction-acceleration process in a magnetized jet is a consequence of the fact that the separation between neighbouring magnetic flux surfaces increases faster than their cylindrical radius. However, whereas in the case of effective collimation-acceleration the product of the jet opening angle and its Lorentz factor does not exceed ~1, the addition of the rarefaction-acceleration mechanism makes it possible for this product to become >>1, in agreement with the inference from late-time panchromatic breaks in the afterglow light curves of long/soft GRBs.

We study semi-analytical time-dependent solutions of the relativistic magnetohydrodynamic (MHD) equations for the fields and the fluid emerging from a spherical source. We assume uniform expansion of the field and the fluid and a polytropic relation between the density and the pressure of the fluid. The expansion velocity is small near the base but approaches the speed of light at the light sphere where the flux terminates. We find self-consistent solutions for the density and the magnetic flux. The details of the solution depend on the ratio of the toroidal and the poloidal magnetic field, the ratio of the energy carried by the fluid and the electromagnetic field and the maximum velocity it reaches.

Young stellar object jets are supersonic and highly collimated plasma outflows that propagate for large distances. Although their association to star formation is a well established fact, there are still open questions such as whether the outflow is of disk or stellar origin, how the jet’s time variable structure is produced and why there is an asymmetry between the opposite bipolar flows. The increasing angular resolution of modern telescopes gradually provides the clues to clarify and understand such issues. An emerging picture is that of a two-component protostellar jet, where a high mass loss rate disk wind surrounds a hot stellar outflow. In this context, our group has carried out numerical simulations of several two-component magnetohydrodynamic jet models, setting as initial conditions a combination of two well studied analytical solutions. We investigated the dynamics and the steady state features of many interesting cases as a function of the mixing parameters and the enforced time variability. A highly significant result was the morphological reproduction of the large scale knot-like structure of many young stellar objects jets. Moreover, with the assumption of a quadrupolar disk field we found asymmetric velocities between the bipolar outflows suggesting a possible explanation for this observational fact. In this article we summarize the results on the dynamics and the velocity profiles of a few interesting two-component jet scenarios.

Context. 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. Analytical radially self-similar models successfully describe disk-winds, but need several improvements. 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. Aims: 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. This is our main goal. Methods: In order to compare our models with observed jet widths inferred from recent optical images taken with the Hubble Space Telescope (HST) and ground-based adaptive optics (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 full-width half-maximum of the emission. Results: It is shown that the untruncated analytical disk outflow solution considered here cannot fit the small jet widths inferred by observations of several jets. Furthermore, 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. Conclusions: 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.

Outflows emanating from the environment of stellar or galactic objects are a widespread phenomenon in astrophysics. Their morphology ranges from nearly spherically symmetric winds to highly collimated jets. In some cases, e.g., in jets associated with young stellar objects, the bulk outflow speeds are nonrelativistic, while in others, e.g., in jets associated with active galactic nuclei or gamma-ray bursts, it can even be highly relativistic. The main driving mechanism of collimated outflows is likely related to magnetic fields. These fields are able to tap the rotational energy of the compact object or disk, accelerate, and collimate matter ejecta. To zeroth order these outflows can be described by the highly intractable theory of magnetohydrodynamics (MHD). Even in systems where the assumptions of zero resistivity (ideal MHD), steady state, axisymmetry, one fluid description, and polytropic equation of state are applicable, the problem remains difficult. In this case the problem reduces to only two equations, corresponding to the two components of the momentum equation along the flow and in the direction perpendicular to the magnetic field (transfield direction). The latter equation is the most difficult to solve, but also the most important. It answers the question on the degree of the collimation, but also crucially affects the solution of the first, the acceleration efficiency and the bulk velocity of the flow. The first and second parts of this chapter refer to nonrelativistic and relativistic flows, respectively. These Parts can be read independently. In each one, the governing equations are presented and discussed, focusing on the case of flows that are magnetically dominated near the central source. The general characteristics of the solutions in relation to the acceleration and collimation mechanisms are analyzed. As specific examples of exact solutions of the full system of the MHD equations that satisfy all the analyzed general characteristics, self-similar models are presented.