From clouds to stars^*

Protostellar collapse and the evolution to the pre-main sequence I. Equations and evolution in the Hertzsprung-Russell diagram

¹ Max-Planck-Institut für extraterrestrische Physik, Giessenbachstraße, 85748 Garching, Germany
² Institut für Theoretische Astrophysik der Universität Heidelberg, Tiergartenstraße 15, 69121 Heidelberg, Germany
³ Interdisziplinäres Zentrum für Wissenschaftliches Rechnen der Universität Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany

Corresponding author: G. Wuchterl, wuchterl@mpe.mpg.de

Received: 16 June 1999
Accepted: 8 November 2002

Abstract

We present the first study of early stellar evolution with “cloud” initial conditions utilizing a system of equations that comprises a solar model solution. All previous studies of protostellar collapse either make numerous assumptions specifically tailored for different parts of the flow and different parts of the evolution or they do not reach the pre-main sequence phase. We calculate the pre-main sequence properties of marginally gravitationally unstable, isothermal, equilibrium “Bonnor-Ebert” spheres with an initial temperature of and masses of 0.05 to 10 . The mass accretion rate is determined by the solution of the flow equations rather than being prescribed or neglected. In our study we determine the protostar's radii and the thermal structure together with the mass and mass accretion rate, luminosity and effective temperature during its evolution to a stellar pre-main sequence object. We calculate the time needed to accrete the final stellar masses, the corresponding mean mass accretion rates and median luminosities, and the corresponding evolutionary tracks in the theoretical Hertzsprung-Russell diagram. We derive these quantities from the gas flow resulting from cloud collapse. We do not assume a value for an “initial” stellar radius and an “initial” stellar thermal structure at the “top of the track”, the Hayashi-line or any other instant of the evolution. Instead we solve the flow equations for a cloud fragment with spherical symmetry. The system of equations we use contains the equations of stellar structure and evolution as a limiting case and has been tested by a standard solar model and by classical stellar pulsations (Wuchterl & Feuchtinger 1998; Feuchtinger 1999; Dorfi & Feuchtinger 1999). When dynamical accretion effects have become sufficiently small so that a comparison to existing hydrostatic stellar evolution calculations for corresponding masses can be made, young stars of appear close to the location of the Henyey part of the respective classical evolutionary track and at substantially larger ages for given luminosities than those inferred from previous calculations. stars appear at lower luminosities, to the left of the corresponding Hayashi-tracks and are about older than an a-priori hydrostatic stellar evolution model at the same luminosity. They burn most of their deuterium during the main accretion phase before mass accretion halts and they become visible. They do not become fully convective during the entire evolution calculated, i.e., up to 1.5 Myr. Altogether the structure of our solar mass star at 1 Myr, with its raditive core and convective envelope, resembles the present Sun rather then a fully convective object. Very low mass stars and proto brown dwarfs close to the substellar limit appear with luminosities close to those at the “top of the tracks”, giving ages roughly in accordance with classical values, tentatively at to higher effective temperatures.