The Connection between the Interstellar Cloud Mass Spectrum and the Stellar Mass Spectrum in Star‐forming Regions

Abstract

We discuss a connection between the mass spectrum of interstellar gas clouds and the mass spectrum of formed stars. Our consideration of this problem is given in terms of what we call the partial effectiveness of star formation, i.e., the number of stars of mass m formed in a cloud of mass M per unit interval of stellar masses. This function transfers the statistical properties of the interstellar cloud population to the statistical properties of the stellar population. We show that this function can be obtained phenomenologically in the sense that its derivation does not require any theoretical speculations about particular processes involved in star formation but is based only on a consideration of the observed statistical properties of ensembles of interstellar gas clouds and newly formed stars. We show that these stars are not homogeneously distributed in the interval of allowed stellar masses. Their distribution is peaked around some specific mass (depending on cloud mass) and decreases rapidly outside the vicinity of this mass. We also show that the number of stars with masses in a given interval formed in a cloud of mass M, the mass of these stars, and the specific star formation efficiency are strong functions of stellar and/or cloud masses. Therefore, the mean statistical characteristics of star formation, such as, for example, the star formation efficiency, which are usually used to describe star formation phenomena, may not be applicable in many particular problems.