Simulations of protostellar collapse using multigroup radiation hydrodynamics

II. The second collapse

¹ École Normale Supérieure de Lyon, CRAL, UMR CNRS 5574, Université de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 7, France
e-mail: neil.vaytet@ens-lyon.fr
² School of Physics, University of Exeter, Exeter, EX4 4QL, UK
³ Maison de la Simulation, USR 3441, CEA – CNRS – INRIA – Université Paris-Sud - Université de Versailles, 91191 Gif-sur-Yvette, France
⁴ CEA/DSM/IRFU, Service d’Astrophysique, Laboratoire AIM, CNRS, Université Paris Diderot, 91191 Gif-sur-Yvette, France
⁵ Laboratoire de radioastronomie, UMR CNRS 8112, École Normale Supérieure et Observatoire de Paris, 24 rue Lhomond, 75231 Paris Cedex 5, France
⁶ Department of Physics, Wichita State University, Wichita, KS 67260-0032, USA
⁷ LERMA, Observatoire de Paris, ENS, UPMC, UCP, CNRS, 5 place Jules Janssen, 92190 Meudon, France

Received: 6 March 2013
Accepted: 1 July 2013

Abstract

Context. Star formation begins with the gravitational collapse of a dense core inside a molecular cloud. As the collapse progresses, the centre of the core begins to heat up as it becomes optically thick. The temperature and density in the centre eventually reach high enough values where fusion reactions can ignite, and the protostar is born. This sequence of events entails many physical processes, of which radiative transfer is of paramount importance. Simulated collapsing cores without radiative transfer rapidly become thermally supported before reaching high enough temperatures and densities, preventing the formation of stars.

Aims. Many simulations of protostellar collapse make use of a grey treatment of radiative transfer coupled to the hydrodynamics. However, interstellar gas and dust opacities present large variations as a function of frequency, which can potentially be overlooked by grey models and lead to significantly different results. In this paper, we follow up on a previous paper on the collapse and formation of Larson’s first core using multigroup radiation hydrodynamics (Paper I) by extending the calculations to the second phase of the collapse and the formation of Larson’s second core.

Methods. We have made the use of a non-ideal gas equation of state as well as an extensive set of spectral opacities in a spherically symmetric fully implicit Godunov code to model all the phases of the collapse of a 0.1, 1, and 10 M_⊙ cloud cores.

Results. We find that, for an identical central density, there are only small differences between the grey and multigroup simulations. The first core accretion shock remains supercritical while the shock at the second core border is found to be strongly subcritical with all the accreted energy being transfered to the core. The size of the first core was found to vary somewhat in the different simulations (more unstable clouds form smaller first cores) while the size, mass, and temperature of the second cores are independent of initial cloud mass, size, and temperature.

Conclusions. Our simulations support the idea of a standard (universal) initial second core size of ~3 × 10^-3 AU and mass ~1.4 × 10^-3 M_⊙. The grey approximation for radiative transfer appears to perform well in one-dimensional simulations of protostellar collapse, most probably because of the high optical thickness of the majority of the protostar-envelope system. A simple estimate of the characteristic timescale of the second core suggests that the effects of using multigroup radiative transfer may be more important in the long-term evolution of the protostar.