On the formation of massive stars

We calculate numerically the collapse of slowly rotating, nonmagnetic, massive molecular clumps of masses 30, 60, and 120 M, which conceivably could lead to the formation of massive stars. Because radiative acceleration on dust grains plays a critical role in the clumps dynamical evolution, we have improved the module for continuum radiation transfer in an existing two-dimensional ( axial symmetry assumed) radiation hydrodynamic code. In particular, rather than using gray dust opacities and gray radiation transfer, we calculate the dusts wavelength-dependent absorption and emission simultaneously with the radiation density at each wavelength and the equilibrium temperatures of three grain components: amorphous carbon particles, silicates, and dirty ice coated silicates. Because our simulations cannot spatially resolve the innermost regions of the molecular clump, however, we cannot distinguish between the formation of a dense central cluster or a single massive object. Furthermore, we cannot exclude significant mass loss from the central object(s) that may interact with the inflow into the central grid cell. Thus, with our basic assumption that all material in the innermost grid cell accretes onto a single object, we are able to provide only an upper limit to the mass of stars that could possibly be formed. We introduce a semianalytical scheme for augmenting existing evolutionary tracks of pre-main-sequence protostars by including the effects of accretion. By considering an open outermost boundary, an arbitrary amount of material could, in principal, be accreted onto this central star. However, for the three cases considered (30, 60, and 120 M-. originally within the computation grid), radiation acceleration limited the final masses to 31.6, 33.6, and 42.9 M-., respectively, for wavelength-dependent radiation transfer and to 19.1, 20.1, and 22.9 M-. for the corresponding simulations with gray radiation transfer. Our calculations demonstrate that massive stars can in principle be formed via accretion through a disk. The accretion rate onto the central source increases rapidly after one initial free-fall time and decreases monotonically afterward. By enhancing the nonisotropic character of the radiation field, the accretion disk reduces the effects of radiative acceleration in the radial direction a process we call the "flashlight effect. The flashlight effect is further amplified in our case by including the effects of frequency-dependent radiation transfer. We conclude with the warning that a careful treatment of radiation transfer is a mandatory requirement for realistic simulations of the formation of massive stars.