Two-component jet simulations I. Topological stability of analytical MHD outflow solutions

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