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

The problem of modeling the formation of solar-type stars in spherical symmetry is examined with reference to the influence of various numerical techniques on the physical results. It is found that the use of large artificial viscosity in the numerical treatment of shock fronts overestimates the heating of the gas and underestimates the rate of radiation. Large discretization errors lead to difficulties with numerical energy conservation, resulting in overlarge values for radius and total luminosity. A numerical method seeking to avoid these difficulties is presented, emphasizing an adequate treatment of the accretion shock front. 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.