The Evolution of Spherical Protostars with Masses Formula

The calculations reported in Paper I for the collapse of a spherical protostar have been improved and extended to a wider range of masses with calculations for masses of 0·25, 0·5, 1·0, 1·5, 2·0, 3·0, 5·0 and 10 solar masses. The method and the assumptions used are similar to those of Paper I except that a better approximation for the temperature distribution in the collapsing protostellar envelope has been incorporated. For masses less than |~\,1·5\,M_| the results are similar to those obtained previously for a protostar of |1·0\,M_|⁠, and they show that a star in this mass range first appears near the lower end of its Hayashi track. For masses greater than |~\,1·5\,M_| the entropy and the radius of the star never become large enough for a ‘Hayashi ’ phase to exist, and the star first appears on the radiative pre-main sequence track. For masses greater than |~\,3\,M_|⁠, the central stellar core evolves all the way to the main sequence before beginning to shine through its surrounding cloud; thus no ‘normal’ pre-main sequence stars should be observed with masses much greater than |~\,3\,M_|⁠. The model calculations have been compared with most of the observations thought to relate to star formation or newly-formed stars, with the following results: (1) The early stages of the present protostar models resemble closely some of the dark globules discussed by Bok and others. (2) The infra-red sources in the Orion nebula appear to be best interpreted as protostars of various masses. (3) The observed properties of T Tauri stars and similar objects with dense circumstellar nebulosity are in general agreement with the predicted properties of newly formed stars. (4) The distribution of the pre-main sequence stars of young clusters in the HR diagram is consistent with theoretical expectations based on the present models. Several sources of scatter, including an age spread of |≈ 10⁷| yr, are probably present. (5) FU Ori and V1057 Cyg may be explainable as a result of the rapid dissipation of a protostellar shell by radiation pressure or a stellar wind.