Gravitational collapse of nonsingular logatropic spheres

¹ Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, Caracas 1020A, Venezuela e-mail: lsigalot@cassini.ivic.ve e-mail: esira@hubble.ivic.ve
² Dipartimento di Fisica Galileo Galilei, Università di Padova, via Marzolo n. 8, 35131 Padova, Italy e-mail: defelice@pd.infn.it

Corresponding author: L. Di G. Sigalotti, lsigalot@cassini.ivic.ve

Received: 2 May 2002
Accepted: 19 July 2002

Abstract

We present the results of high-resolved, hydrodynamic calculations of the spherical gravitational collapse and subsequent accretion of nonsingular subcritical and critical logatropes, starting with initial configurations close to hydrostatic equilibrium. Two sequences of models with varying masses and the same central temperature  K are defined, which differ only in the fiducial value of the truncation pressure ( cm^-3 K and  cm^-3 K). In all cases, we follow the calculations until the central protostar has accreted 99% of the total available mass. Thus, the models may be indicative of early evolution from the Class 0 to the Class I protostellar phase. We find that the approach to the singular density profile is never entirely subsonic. In the lower p_s sequence, about 6% of the mass collapses supersonically in a sphere, while only ∼0.02% behaves this way in a critical (92.05 ) logatrope. In the high p_s sequence the same trend is observed, with ∼0.7% of the mass now infalling supersonically at the time of singularity formation in a sphere. Immediately after singularity formation, the accretion rate rises steeply in all cases, reaching a maximum value when the central protostar has accreted ∼40% of its final mass. Thereafter, it decreases monotonically for the remainder of the evolution. Our models predict peak values of as high as ∼  yr^-1 for logatropes close to the critical mass. In contrast, a subcritical logatrope reaches a maximum value of ∼ yr^-1 for the lower p_s sequence compared to ~ yr^-1 for the higher p_s case. The results also imply that the accretion lifetimes are longer in logatropes with lower p_s, consistent with the observational evidence that star formation in clumped regions occurs on shorter timescales compared to more isolated environments.