We present numerical simulations of axisymmetric, magnetically driven relativistic jets. Our special-relativistic, ideal-magnetohydrodynamics numerical scheme is specifically designed to optimize accuracy and resolution and to minimize numerical dissipation. In addition, we implement a grid-extension method that reduces the computation time by up to three orders of magnitude and makes it possible to follow the flow up to six decades in spatial scale. To eliminate the dissipative effects induced by a free boundary with an ambient medium we assume that the flow is confined by a rigid wall of a prescribed shape, which we take to be z ~ ra (in cylindrical coordinates, with a ranging from 1 to 3). We also prescribe, through the rotation profile at the inlet boundary, the injected poloidal current distribution: we explore cases where the return current flows either within the volume of the jet or on the outer boundary. The outflows are initially cold, sub-Alfvénic and Poynting flux-dominated, with a total-to-rest-mass energy flux ratio μ ~ 15. We find that in all cases they converge to a steady state characterized by a spatially extended acceleration region. The acceleration process is very efficient: on the outermost scale of the simulation as much as ~ 77 per cent of the Poynting flux has been converted into kinetic energy flux, and the terminal Lorentz factor approaches its maximum possible value (Γ∞ ~= μ). We also find a high collimation efficiency: all our simulated jets (including the limiting case of an unconfined flow) develop a cylindrical core. We argue that this could be the rule for current-carrying outflows that start with a low initial Lorentz factor (Γ0 ~ 1). Our conclusions on the high acceleration and collimation efficiencies are not sensitive to the particular shape of the confining boundary or to the details of the injected current distribution, and they are qualitatively consistent with the semi-analytic self-similar solutions derived by Vlahakis and Königl. We apply our results to the interpretation of relativistic jets in active galactic nuclei: we argue that they naturally account for the spatially extended accelerations inferred in these sources (Γ∞ >~ 10 attained on radial scales R >~ 1017cm) and are consistent with the transition to the matter-dominated regime occurring already at R >~ 1016cm.

In parallel to the development of numerical simulations, analytical solutions for modelling the acceleration and the collimation of winds and jets have been proposed. We present here how meridionally self-similar solutions can be used to model the solar wind using Ulysses data at solar minimum. Such solutions may also be adapted to explain the formation core or spine jets in classical and weak TTauri stars (class II and III young stellar jets) as well as relativistic jet cores from AGN. The criterion for collimation explains how the jet evolves towards a wind as the star approaches the main sequence. A similar scenario could explain the winds from Seyfert galaxies by opposition to the powerful jets from Fanaroff Riley sources.

We present numerical simulations of axisymmetric, magnetically driven relativistic jets. Our special-relativistic, ideal-magnetohydrodynamics numerical scheme is specifically designed to optimize accuracy and resolution and to minimize numerical dissipation. In addition, we implement a grid-extension method that reduces the computation time by up to three orders of magnitude and makes it possible to follow the flow up to six decades in spatial scale. To eliminate the dissipative effects induced by a free boundary with an ambient medium we assume that the flow is confined by a rigid wall of a prescribed shape, which we take to be z ~ ra (in cylindrical coordinates, with a ranging from 1 to 3). We also prescribe, through the rotation profile at the inlet boundary, the injected poloidal current distribution: we explore cases where the return current flows either within the volume of the jet or on the outer boundary. The outflows are initially cold, sub-Alfvénic and Poynting flux-dominated, with a total-to-rest-mass energy flux ratio μ ~ 15. We find that in all cases they converge to a steady state characterized by a spatially extended acceleration region. The acceleration process is very efficient: on the outermost scale of the simulation as much as ~ 77 per cent of the Poynting flux has been converted into kinetic energy flux, and the terminal Lorentz factor approaches its maximum possible value (Γ∞ ~= μ). We also find a high collimation efficiency: all our simulated jets (including the limiting case of an unconfined flow) develop a cylindrical core. We argue that this could be the rule for current-carrying outflows that start with a low initial Lorentz factor (Γ0 ~ 1). Our conclusions on the high acceleration and collimation efficiencies are not sensitive to the particular shape of the confining boundary or to the details of the injected current distribution, and they are qualitatively consistent with the semi-analytic self-similar solutions derived by Vlahakis and Königl. We apply our results to the interpretation of relativistic jets in active galactic nuclei: we argue that they naturally account for the spatially extended accelerations inferred in these sources (Γ∞ >~ 10 attained on radial scales R >~ 1017cm) and are consistent with the transition to the matter-dominated regime occurring already at R >~ 1016cm.

Recent observations of jets in young stellar objects suggest that although both disk- and stellar-outflows seem to be present, each one of these two components may dominate at the various stages of the YSO. Over the past several years the only analytical solutions of the steady-state MHD equations which have been studied, correspond to the radially (magneto-centrifugally driven disk winds) and meridionally (thermally accelerated stellar outflows) self-similar models. In this context, we study through time dependent numerical simulations, using the PLUTO code, one prototypical case of each of these two classes examining many of their physical and numerical properties. We find that the solutions are structurally stable and robust, maintaining all their well defined features, despite several modifications they have been subject to. Therefore, their proper matching could explain a two-component jet.

Observations of collimated outflows in young stellar objects indicate that several features of the jets can be understood by adopting the picture of a two-component outflow wherein a central stellar component around the jet axis is surrounded by an extended disk-wind. The precise contribution of each component may depend on the intrinsic physical properties of the YSO and also its evolutionary stage. In this context, we study a numerical model based on such a two-component outflow by using as an initial condition a combination of two prototypical models, each describing a meridionally self-similar and a radially self-similar exact solution of the steady-state, ideal hydromagnetic equations. These two classes of radially and meridionally self-similar solutions, have already been well studied and have been found to be related to the properties of disk- and stellar-wind, respectively. By properly mixing the two solutions, a variety of models is constructed with different contribution weights for each component in the initial set-up. The models are evolved in time by using the PLUTO code and the interaction and co-existence of the two components in the jet is investigated. It is found that a steady-state is always reached, independently of the mixing parameters of the two model ingredients. Moreover, the final outcome of the time evolution stays rather close to the initial analytical solutions. The results are compared and discussed along the lines of recent observational data.

In parallel to the development of numerical simulations, analytical solutions for modelling the acceleration and the collimation of winds and jets have been proposed. We present here how meridionally self-similar solutions can be used to model the solar wind using Ulysses data at solar minimum. Such solutions may also be adapted to explain the formation core or spine jets in classical and weak TTauri stars (class II and III young stellar jets) as well as relativistic jet cores from AGN. The criterion for collimation explains how the jet evolves towards a wind as the star approaches the main sequence. A similar scenario could explain the winds from Seyfert galaxies by opposition to the powerful jets from Fanaroff Riley sources.