The mass function

9.10 Summary

We have reviewed the definition of the stellar mass function, Ψ(M), and its importance in understanding star formation mechanisms and Galactic structure parameters, such as the local mass density. At present, masses can be derived directly only for stars in binary systems with well-determined orbits, although microlensing projects may offer additional data in the future. Those stars are used to calibrate empirical mass-luminosity relationships, which can then be used to derive the field star mass function from the observed luminosity function. The most recent studies indicate that the mass function for disk stars can be well represented by a power law, Ψ(M)∝M ⁻¹ for masses between 0.1 and 1 M _⊙.

Theoretical mass-luminosity calibrations offer the only means of determining Ψ(M) for young stars still in the process of contracting onto the main sequence. There are reasonable grounds for suspecting that variations in the form of Ψⁱ(M) occur from one star-forming region to another. The strongest support for this hypothesis comes from comparing observations of dense, populous clusters, such as Orion and IC 348, against the low-density star-forming clouds in the Taurus-Auriga association. Star formation theories still abound for the origin of the IMF, with no clear outright winner to date. Models based on supersonic turbulent fragmentation appear to show promise.