Low-metallicity star formation: Prestellar collapse and protostellar accretion in the spherical symmetry

Abstract

The collapse of dense cores with metallicities 0-1 Zȯ is studied by hydrodynamical calculations coupled with detailed chemical and radiative processes. For this purpose, we construct a simple chemical network with nonequilibrium reactions among 15 chemical species, H+, e, H, H2, D+, D, HD, C+, C, CO, CO2, O, OH, H2O, and O2, which reproduces the abundance of important molecular coolants given by a more detailed network very well. Starting from the initial density of 104 cm-3, the evolution is followed until the formation of a hydrostatic protostar at the center ∼1021 cm-3. In a lower-metallicity gas cloud, the temperature during the collapse remains high owing to less efficient cooling. After the cloud core becomes optically thick to the thermal emission by dust, temperature evolution at the center converges to a single trajectory, except for cases with metallicity ≤10-6 Zȯ, where the temperature remains slightly higher than in higher-metallicity cases even after becoming optically thick to thermal radiation by the H2 collision-induced emission. The protostellar masses at their formation are a few 10-3 Mȯ, being slightly higher for cases with ≤10-6 Zȯ. Using the temperature evolution at the center as a function the density, we discuss the possibility of fragmentation during the dust-cooling phase. The critical metallicity for the fragmentation is 10-5 Ż assuming moderate elongation of the cloud cores at the onset of this phase. From the density and velocity distributions at the time of protostar formation, we evaluate the mass accretion rate in the subsequent accretion phase. The accretion rate is larger than the Shu accretion rate for the inside-out collapse from an initially static cloud ≈c 3s/G, where cs is the sound speed in the prestellar gas, by about a factor of 10 owing to more dynamical nature of the collapse. Using these accretion rates, we also calculate the evolution of the protostars under the assumption of stationary accretion flow. For ≥10-4Z ȯ, we succeed in following their evolution well after the arrival to the main-sequence phase. For lower-metallicity cases, however, owing to too high accretion rates ≳ a few 10-3Ṁ yr-1, the total luminosity, which consists of contribution from accretion and internal luminosity, reaches the Eddington limit, thereby rendering the stationary accretion impossible for ≳ 100 Mȯ. Finally, we discuss the possible suppression of fragmentation by heating of the ambient gas by protostellar radiation, which is considered important in the contemporary star formation. We argue that it is negligible for <10 -2 Ż. © 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.