Numerical simulations with self-similar initial and boundary conditions provide a link between theoretical and numerical investigations of jet dynamics. We perform axisymmetric resistive magnetohydrodynamic (MHD) simulations for a generalized solution of the Blandford & Payne type, and compare them with the corresponding analytical and numerical ideal MHD solutions. We disentangle the effects of the numerical and physical diffusivity. The latter could occur in outflows above an accretion disc, being transferred from the underlying disc into the disc corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We conclude that while the classical magnetic Reynolds number Rm measures the importance of resistive effects in the induction equation, a new introduced number, Rβ = (β/2)Rm with β the plasma beta, measures the importance of the resistive effects in the energy equation. Thus, in magnetized jets with β < 2, when Rβ <~ 1 resistive effects are non-negligible and affect mostly the energy equation. The presented simulations indeed show that for a range of magnetic diffusivities corresponding to Rβ >~ 1, the flow remains close to the ideal MHD self-similar solution.

Context: Finite radius accretion disks are a strong candidate for launching astrophysical jets from their inner parts and disk-winds are considered as the basic component of such magnetically collimated outflows. Numerical simulations are usually employed to answer several open questions regarding the origin, stability and propagation of jets. The inherent uncertainties, however, of the various numerical codes, applied boundary conditions, grid resolution, etc., call for a parallel use of analytical methods as well, whenever they are available, as a tool to interpret and understand the outcome of the simulations. The only available analytical MHD solutions to describe disk-driven jets are those characterized by the symmetry of radial self-similarity. Those exact MHD solutions are used to guide the present numerical study of disk-winds. Aims: Radially self-similar MHD models, in general, have two geometrical shortcomings, a singularity at the jet axis and the non-existence of an intrinsic radial scale, i.e. the jets formally extend to radial infinity. Hence, numerical simulations are necessary to extend the analytical solutions towards the axis and impose a physical boundary at finite radial distance. Methods: We focus here on studying the effects of imposing an outer radius of the underlying accreting disk (and thus also of the outflow) on the topology, structure and variability of a radially self-similar analytical MHD solution. The initial condition consists of a hybrid of an unchanged and a scaled-down analytical solution, one for the jet and the other for its environment. Results: In all studied cases, we find at the end steady two-component solutions. The boundary between both solutions is always shifted towards the solution with reduced quantities. Especially, the reduced thermal and magnetic pressures change the perpendicular force balance at the “surface” of the flow. In the models where the scaled-down analytical solution is outside the unchanged one, the inside solution converges to a solution with different parameters. In the models where the scaled-down analytical solution is inside the unchanged one, the whole two-component solution changes dramatically to stop the flow from collapsing totally to the symmetry axis. Conclusions: It is thus concluded that truncated exact MHD disk-wind solutions that may describe observed jets associated with finite radius accretion disks, are topologically stable.

Numerical simulations with self-similar initial and boundary conditions provide a link between theoretical and numerical investigations of jet dynamics. We perform axisymmetric resistive magnetohydrodynamic (MHD) simulations for a generalized solution of the Blandford & Payne type, and compare them with the corresponding analytical and numerical ideal MHD solutions. We disentangle the effects of the numerical and physical diffusivity. The latter could occur in outflows above an accretion disc, being transferred from the underlying disc into the disc corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We conclude that while the classical magnetic Reynolds number Rm measures the importance of resistive effects in the induction equation, a new introduced number, Rβ = (β/2)Rm with β the plasma beta, measures the importance of the resistive effects in the energy equation. Thus, in magnetized jets with β < 2, when Rβ <~ 1 resistive effects are non-negligible and affect mostly the energy equation. The presented simulations indeed show that for a range of magnetic diffusivities corresponding to Rβ >~ 1, the flow remains close to the ideal MHD self-similar solution.

The main driving mechanism of relativistic jets is likely related to magnetic fields. These fields are able to tap the rotational energy of the central compact object or disk, accelerate and collimate matter ejecta. To zeroth order these outflows can be described by the theory of steady, axisymmetric, ideal magnetohydrodynamics. Results from recent numerical simulations of magnetized jets, as well as analytical studies, show that the efficiency of the bulk acceleration could be more than ∼ 50 %. They also shed light to the degree of the collimation and how it is related to the pressure distribution of the environment, the apparent kinematics of jet components, and the observed polarization properties.

The main characteristics of relativistic, steady, ideal magnetohydrodynamic (MHD) outflows are discussed, focusing on their bulk acceleration and collimation. It is shown that the Bernoulli equation relates the bulk Lorentz factor with the shape of the flow, permitting an analytic estimation of the acceleration efficiency, while the transfield force-balance equation gives a simple relation of the bulk Lorentz factor to the distance.

We consider the internal shock formation in magnetized outflows and we examine the plastic collision between such relativistic blobs taking into account a possible dissipation of magnetic flux. We find that after the collision a large amount of energy is released in thermal form and consequently we assume that this is transferred into protons which obtain a relativistic Maxwellian distribution. The relativistic thermal proton plasma is dense enough to suffer substantial energy losses through proton-proton interactions and thus to transfer its initial energy into photons, electron-positron pairs and neutrinos. We estimate the radiated spectrum by following the evolution of protons, electrons and photons as they interact with each other and with the magnetic field as well.

Context: 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-disk system as well as its evolutionary stage. Aims: This article reports a systematic separate investigation of these jet components via time-dependent simulations of two prototypical and complementary analytical solutions, each closely related to the properties of stellar outflows and disk winds. These models describe a meridionally and a radially self-similar exact solution of the steady-state, ideal hydromagnetic equations, respectively. Methods: Using the PLUTO code to carry out the simulations, the study focuses on the topological stability of each of the two analytical solutions, which are successfully extended to all space by removing their singularities. In addition, their behavior and robustness over several physical and numerical modifications is extensively examined. Therefore, this work serves as the starting point for the analysis of the two-component jet simulations. Results: It is found that radially self-similar solutions (disk winds) always reach a final steady-state while maintaining all their well-defined properties. The different ways to replace the singular part of the solution around the symmetry axis, being a first approximation towards a two-component outflow, lead to the appearance of a shock at the super-fast domain corresponding to the fast magnetosonic separatrix surface. These conclusions hold true independently of the numerical modifications and/or evolutionary constraints that the models have undergone, such as starting with a sub-modified-fast initial solution or different types of heating/cooling assumptions. Furthermore, the final outcome of the simulations remains close enough to the initial analytical configurations, thus showing their topological stability. Conversely, the asymptotic configuration and the stability of meridionally self-similar models (stellar winds) is related to the heating processes at the base of the wind. If the heating is modified by assuming a polytropic relation between density and pressure, a turbulent evolution is found. On the other hand, adiabatic conditions lead to the replacement of the outflow by an almost static atmosphere.