  In this study, the main goal is to understand the molecular cloud core
collapse through the stages of first and second hydrostatic core formation. We
investigate the properties of Larson's first and second cores following the
evolution of the molecular cloud core until formation of Larson's cores. We
expand these collapse studies for the first time to span a wide range of
initial cloud masses from 0.5 to 100 Msun. Understanding the complexity of the
numerous physical processes involved in the very early stages of star formation
requires detailed thermodynamical modeling in terms of radiation transport and
phase transitions. For this we use a realistic gas equation of state via a
density and temperature-dependent adiabatic index and mean molecular weight to
model the phase transitions. We use a gray treatment of radiative transfer
coupled with hydrodynamics to simulate Larson's collapse in spherical symmetry.
We reveal a dependence of a variety of first core properties on the initial
cloud mass. The first core radius and mass increase from the low-mass to the
intermediate-mass regime and decrease from the intermediate-mass to the
high-mass regime. The lifetime of first cores strongly decreases towards the
intermediate- and high-mass regime. Our studies show the presence of a
transition region in the intermediate-mass regime. Low-mass protostars tend to
evolve through two distinct stages of formation which are related to the first
and second hydrostatic cores. In contrast, in the high-mass star formation
regime, the collapsing cloud cores rapidly evolve through the first collapse
phase and essentially immediately form Larson's second cores.
