SIMBAD references

Motivated by recent observations that detect an outer boundary for starless cores, and evidence for time-dependent mass accretion in the Class 0 and Class I protostellar phases, we re-examine the case of spherical isothermal collapse in the case of a finite mass reservoir. The presence of a core boundary, implemented through a constant-volume approximation in our simulation, results in the generation of an inward-propagating rarefaction wave. This steepens the gas density profile from r^–2 (self-similar value) to r^–3 or steeper. After a protostar forms, the mass accretion rate evolves through three distinct phases: (1) an early phase of decline in, which is a non-self-similar effect due to rapid and spatially non-uniform infall in the pre-stellar phase; (2) for large cores, an intermediate phase of near-constant from the infall of the outer part of the self-similar density profile, which has low (subsonic) infall speed in the pre-stellar phase; and (3) a late phase of rapid decline in when accretion occurs from the region affected by the inward-propagating rarefaction wave. Our model clouds of small to intermediate size make a direct transition from phase (1) to phase (3) above. Both the first and second phase (if the latter is indeed present) are characterized by a temporally increasing bolometric luminosity L_bol, while L_bolis decreasing in the third (final) phase. We identify the period of temporally increasing L_bolwith the Class 0 phase, and the later period of terminal accretion and decreasing L_bolwith the Class I phase. The peak in L_bol corresponds to the evolutionary time when 50±15 per cent of the cloud mass has been accreted by the protostar. This is in agreement with the classification scheme proposed in the early 1990s by André et al.; our model adds a physical context to their interpretation. We show how our results can be used to explain tracks of envelope mass M_envversus L_bolfor protostars in Taurus and Ophiuchus. We also develop an analytic formalism that successfully reproduces the protostellar accretion rate from profiles of density and infall speed in the pre-stellar phase. It shows that the spatial gradient of infall speed that develops in the pre-stellar phase is a primary cause of the temporal decline in during the early phase of protostellar accretion.