Formation of solar-type stars in spherical symmetry. I - The key role of the accretion shock

Abstract

Time-dependent hydrodynamical calculations of the self-gravitational collapse of a homogeneous Jeans unstable 1 M/sub sun/ protostellar cloud are examined to determine the extent to which the physical results reported in the literature depend on the particular numerical methods employed. It is found that the use of large artificial viscosity in the numerical treatment of shock fronts over-estimates the heating of the gas, underestimating the rate of production of radiation. Damping of core oscillations by increasing the inertial mass in contraction phases artificially slows the contraction, therefore overestimating the core radius. Large discretization errors lead to difficulties with numerical energy conservation, resulting in overlarge values for radius and total luminosity. A calculation employing a numerical method seeking to avoid these difficulties is presented. When numerical uncertainties are taken into account, the most likely physical solution produces a radius for the final core of about 2 R/sub sun/ and a total luminosity of order 1 L/sub sun/ when all the mass is assembled in the core. The maximum luminosity during the accretion phase is approximately 30 L/sub sun/. In the shock front surrounding the stellar core almost all the kinetic energy gained from the gravitational acceleration is directly transformed into outgoing radiation more » and is not deposited in the internal energy of the gas, in good agreement with the assumptions of the early work of Larson. The structure of the second shock front during the main accretion phase is examined in detail, and the evolution in the Hertzsprung-Russell diagram is discussed. « less