Evolution of Massive Protostars via Disk Accretion

Mass accretion onto (proto-)stars at high accretion rates > 10^-4 M_sun/yr is expected in massive star formation. We study the evolution of massive protostars at such high rates by numerically solving the stellar structure equations. In this paper we examine the evolution via disk accretion. We consider a limiting case of "cold" disk accretion, whereby most of the stellar photosphere can radiate freely with negligible backwarming from the accretion flow, and the accreting material settles onto the star with the same specific entropy as the photosphere. We compare our results to the calculated evolution via spherically symmetric accretion, the opposite limit, whereby the material accreting onto the star contains the entropy produced in the accretion shock front. We examine how different accretion geometries affect the evolution of massive protostars. For cold disk accretion at 10^-3 M_sun/yr the radius of a protostar is initially small, about a few R_sun. After several solar masses have accreted, the protostar begins to bloat up and for M \simeq 10 M_sun the stellar radius attains its maximum of 30 - 400 R_sun. The large radius about 100 R_sun is also a feature of spherically symmetric accretion at the same accreted mass and accretion rate. Hence, expansion to a large radius is a robust feature of accreting massive protostars. At later times the protostar eventually begins to contract and reaches the Zero-Age Main-Sequence (ZAMS) for M \simeq 30 M_sun, independent of the accretion geometry. For accretion rates exceeding several 10^-3 M_sun/yr the protostar never contracts to the ZAMS. The very large radius of several 100s R_sun results in a low effective temperature and low UV luminosity of the protostar. Such bloated protostars could well explain the existence of bright high-mass protostellar objects, which lack detectable HII regions.