The mass function for stars in a cluster - A theoretical derivation

Astronomy and Astrophysics – Astrophysics

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Interstellar Gas, Molecular Clouds, Star Clusters, Stellar Evolution, Stellar Mass Accretion, Globular Clusters, Mass Distribution, Protostars, Shock Wave Propagation, Stellar Models

Scientific paper

A theoretical mass function has been derived for stars in a cluster under the assumption that the initial fragmentation of a gas cloud is into similar massed stellar nuclei, the fragmentation being triggered off in a sequence due to the passage of a density wave. The stellar nuclei thus form at different times, the maximum spread in the formation time being the shock crossing time. Subsequently, these nuclei increase in mass by accreting matter from the surrounding space. The final mass of the star is determined by the time for which accretion proceeds. Assuming the rate of fragment formation to be dependent on the geometry of the cloud, the mass distribution for stars in a model cluster has been determined for a number of different cases. The results for all of these are in general agreement with observation. However, the best agreement was seen to be for a cylindrical distribution with the shock moving in the plane of symmetry.

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