A Radiation Hydrodynamic Model for Protostellar Collapse. II. The Second Collapse and the Birth of a Protostar

We carry out radiation hydrodynamic calculations to study physical processes in the formation of a 1 M☉ protostar. Following our previous work, calculations pursue the whole evolution from the beginning of the first collapse to the end of the main accretion phase. The adiabatic core formed after the initial collapse (i.e., the first core) experiences further gravitational collapse triggered by dissociation of molecular hydrogen, which leads to the formation of the second core, i.e., the birth of a protostar. The protostar grows in mass as accreting the infalling material from the circumstellar envelope, while the protostar keeps its radius at ~4 R☉ during the main accretion phase. These typical features in the evolution are in good agreement with previous studies. We consider two different initial conditions for the density distribution: homogeneous and hydrostatic cloud cores with the same central density of 1.415 × 10-19 g cm-3 . The homogeneous core has the total mass of 1 M☉ while the hydrostatic core has 3.852 M☉. For the initially homogeneous model, the accretion luminosity rapidly rises to the maximum value of 25 L☉ just after the birth of a protostar, and declines gradually as the mass accretion rate decreases. In contrast, the luminosity increases monotonically with time for the initially hydrostatic model. This difference arises because the mass accretion rate varies depending on the inward acceleration at the initial stage, which affects the luminosity curve. A less massive hydrostatic core would possess the similar properties in the luminosity curve to the 3.852 M☉ case, because a hydrostatic cloud core with mass lower than 3.852 M☉ can be shown to provide a smaller mass accretion rate after the birth of a protostar and a more gradual rise in the luminosity curve. Our numerical code is designed to provide the evolution of the spectral energy distribution (SED) along with the dynamical evolution in our spherically symmetric calculations. We confirm that the SED evolves from a 10 K graybody spectrum to hotter spectra typical for class I and flat spectrum sources. The SED for the class 0 sources corresponds to the age of 2 × 104 yr, which is smaller by an order of magnitude than the typical age of class I objects. Considering possible nonspherically symmetric effects, we suggest that observed class 0 sources should consist of the "genuine" class 0 objects, which are as young as 104 yr, and more evolved protostars on edge-on view ("class 0-like class I" objects). The contamination of edge-on class I objects into class 0 sources are not negligible because they are more abundant than genuine class 0 objects. Since observations indicate that the class 0 sources are typically more luminous than class I sources, the initially hydrostatic model, where the luminosity increases monotonically with time, does not match the observations. The initially homogeneous model, in contrast, shows a tendency consistent with the observations. Compiling our results and other theoretical and observational evidence, we illustrate an evolutionary picture of protostar formation. In terms of the evolutionary time and the inclination to an observer, we find that protostellar objects are clearly categorized.