Birth of convective low-mass to high-mass second Larson cores

Context. Stars form as an end product of the gravitational collapse of cold, dense gas in magnetized molecular clouds. This fundamentally multi-scale scenario occurs via the formation of two quasi-hydrostatic Larson cores and involves complex physical processes, which require a robust, self-consistent numerical treatment.Aims. The primary aim of this study is to understand the formation and evolution of the second hydrostatic Larson core and the dependence of its properties on the initial cloud core mass.Methods. We used the PLUTO code to perform high-resolution, one- and two-dimensional radiation hydrodynamic (RHD) core collapse simulations. We include self-gravity and use a grey flux-limited diffusion approximation for the radiative transfer. Additionally, we use for the gas equation of state density- and temperature-dependent thermodynamic quantities (heat capacity, mean molecular weight, etc.) to account for effects such as dissociation of molecular hydrogen, ionisation of atomic hydrogen and helium, and molecular vibrations and rotations. Properties of the second core are investigated using one-dimensional studies spanning a wide range of initial cloud core masses from 0.5 M-circle dot to 100 M-circle dot. Furthermore, we expand to two-dimensional (2D) collapse simulations for a selected few cases of 1 M-circle dot, 5 M-circle dot, 10 M-circle dot, and 20 M-circle dot. We follow the evolution of the second core for >= 100 years after its formation, for each of these non-rotating cases.Results. Our results indicate a dependence of several second core properties on the initial cloud core mass. Molecular cloud cores with a higher initial mass collapse faster to form bigger and more massive second cores. The high-mass second cores can accrete at a much faster rate of approximate to 10(-2) M-circle dot yr(-1) compared to the low-mass second cores, which have accretion rates as low as 10(-5) M-circle dot yr(-1). For the first time, owing to a resolution that has not been achieved before, our 2D non-rotating collapse studies indicate that convection is generated in the outer layers of the second core, which is formed due to the gravitational collapse of a 1 M-circle dot cloud core. Additionally, we find large-scale oscillations of the second accretion shock front triggered by the standing accretion shock instability, which has not been seen before in early evolutionary stages of stars. We predict that the physics within the second core would not be significantly influenced by the effects of magnetic fields or an initial cloud rotation.Conclusions. In our 2D RHD simulations, we find convection being driven from the accretion shock towards the interior of the second Larson core. This supports an interesting possibility that dynamo-driven magnetic fields may be generated during the very early phases of low-mass star formation.