Fragmentation of a Cloud and the Mass Function of Stars in Galactic Clusters

The process of star formation in a contracting interstellar cloud is investigated. The growth of density fluctuations is discussed and the cloud is considered to disintegrate into many fragments during its contraction. The interstellar cloud has a'finite angular momentum. Therefore the free-fall contraction of the cloud is stopped by the centrifugal force at a certain stage. Afterward the fragments move randomly in the cloud. The collision time of the fragments with one another is nearly equal to or shorter than their contraction time, and the evolution of fragments cannot be studied without considering their mutual collisions. The kinetic energy of fragments, which is dissipated into the thermal energy by collisions, is much smaller than the dissociation energy of H 2 molecules for a cloud of about 1041\!J(!). Then the temperature of the fragments, which has risen to about lOOOoK as a result of the collision, falls rapidly by the- cooling processes due to H 2 molecules and grains, and the fragments do not disperse after the collision. This suggests that some of the collisions lead to the coalescence of the fragments which take part in them. The coalescence process of the fragments is investigated by means of a simplified model in order to derive the mass function of the stars in a star cluster. The results are compared with the mass functions of stars in galactic clusters