  The current study was developed to provide a database of relatively simple
numerical simulations of protostellar collapse, as a template library for
observations of cores and very young protostars, and for researchers who wish
to test their chemical modeling under dynamic astrophysical conditions. It was
also designed to identify statistical trends that may appear when running many
models of the formation of low-mass stars by varying the initial conditions. A
large set of 143 calculations of the gravitational collapse of an isolated
sphere of gas with uniform temperature and a Bonnor-Ebert like density profile
was undertaken using a 1D fully implicit Lagrangian radiation hydrodynamics
code. The parameter space covered initial masses from 0.2 to 8 Msun,
temperatures of 5-30 K and radii between 3000 and 30,000 AU. A spread in the
thermal evolutionary tracks of the runs was found, due to differing initial
conditions and optical depths. Within less than an order of magnitude, all
first and second Larson cores had masses and radii independent of the initial
conditions. The time elapsed between the formation of the first and second
cores was found to strongly depend on the first core mass accretion rate, and
no first core in our grid of models lived for longer than 2000 years, before
the onset of the second collapse. The end product of a protostellar cloud
collapse, the second Larson core, is, at birth, a canonical object with a mass
and radius of about 3 Mjup and 8 Rjup, independent of its initial conditions.
The evolution sequence which brings the gas to stellar densities can however
proceed in a variety of scenarios, on different timescales, along different
isentropes, but each story line can largely be predicted by the initial
conditions. All the data from the simulations are publicly available at this
address: http://starformation.hpc.ku.dk/grid-of-protostars.

Solar and Stellar Astrophysics;Astrophysics of Galaxies