2002A&A...395..321S

We present the results of high-resolved, hydrodynamic calculations of the spherical gravitational collapse and subsequent accretion of nonsingular subcritical and critical A=0.2 logatropes, starting with initial configurations close to hydrostatic equilibrium. Two sequences of models with varying masses and the same central temperature T_c=10K are defined, which differ only in the fiducial value of the truncation pressure (p_s/k=1.3x10⁵cm^–3K and 1.0x10⁷cm^–3K). 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 1M_☉ sphere, while only ∼0.02% behaves this way in a critical (≃92.05M_☉) 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 1M_☉ 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 {dot}(M)_acc as high as ∼5-6x10^–5M_☉/yr for logatropes close to the critical mass. In contrast, a subcritical 1M_☉ logatrope reaches a maximum value of ∼8x10^–7M_☉/yr for the lower p_s sequence compared to ∼5x10^–6M_☉/yr 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.