The initial mass function (IMF) is an empirical function that describes the mass distribution (the histogram of stellar masses) of a population of stars in terms of their theoretical initial mass (the mass they were formed with). The properties and evolution of a star are closely related to its mass, so the IMF is an important diagnostic tool for astronomers studying large quantities of stars. The IMF is relatively invariant from one group of stars to another.
The IMF is often stated in terms of a series of power laws, where the number of stars of mass within a specified volume of space is proportional to where is a dimensionless exponent. The IMF can be estimated from the initial luminosity function by using the mass-luminosity relation.
The exemplar form which of the IMF for stars more massive than our sun was discovered by Edwin Salpeter in 1955. His work favoured an exponent of . This form of the IMF is called the Salpeter function or a Salpeter IMF. It shows that the number of stars in each mass range decreases rapidly with increasing mass.
Later authors extended the work below one solar mass. Glenn E. Miller and John M. Scalo suggested that the IMF "flattened" (approached ) below one solar mass. Pavel Kroupa kept above half a solar mass, but introduced between 0.08-0.5 solar masses and below 0.08 solar masses.
There are large uncertainties concerning the substellar region.