Understanding the formation of binary and multiple stellar systems largely comes down to studying the circumstances for the fragmentation of a condensing core during the first stages of the collapse. However, the probability of fragmentation and the
number of fragments seem to be determined to a large degree by the initial conditions. In this work we study the fate of the linear perturbations of a homogeneous gas sphere both analytically and numerically. In particular, we investigate the stability of the well-known homologous solution that describes the collapse of a uniform spherical cloud. The difficulty of the mathematical singularity in the perturbation equations is surpassed here by explicitly introducing a weak shock next to the sonic point. In parallel, we perform adaptive mesh refinement (AMR) numerical simulations of the linear stages of the collapse and compared the growth rates obtained by each method. With this combination of analytical and numerical tools, we explore the behavior of both spherically symmetric and non-axisymmetric perturbations. The numerical experiments provide the linear growth rates as a function of the cores initial virial parameter and as a function of the azimuthal wave number of the perturbation. The overlapping regime of the numerical experiments and the analytical predictions is the situation of a cold and large cloud, and in this regime the analytically calculated growth rates agree very well with the ones obtained from the simulations. The use of a weak shock as part of the perturbation allows us to find a physically acceptable solution to the equations for a continuous range of growth rates. The numerical simulations agree very well with the analytical prediction for the most unstable cores, while they impose a limit of a virial parameter of 0.1 for core fragmentation in the absence of rotation.
The fate of metals ejected by young OB associations into the Interstellar Medium (ISM) is investigated numerically. In particular, we study the enrichment of the cold gas phase, which is the material that forms molecular clouds. Following previous wo
rk, the expansion and collision of two supershells in a diffuse ISM is simulated, in this case also introducing an advected quantity which represents the metals expelled by the young stars. We adopt the simplest possible approach, not differentiating between metals coming from stellar winds and those coming from supernovae. Even though the hot, diffuse phase of the ISM receives a significant amount of metals from the stars, the cold phase is efficiently shielded, with very little metal enrichment. Significant enrichment of the cold ISM will therefore be delayed by at least the cooling time of this hot phase. No variations in cloud metallicity with distance from the OB association or with direction are found, which means that the shell collision does little to enhance the metallicity of the cold clumps. We conclude that the stellar generation that forms out of molecular structures, triggered by shell collisions cannot be significantly enriched.
