initial mass function

The initial mass function (IMF) is an empirical distribution function (essentially an unnormalized probability density function) that describes the distribution of initial masses of stars. It is typically given as N(m)dm.

• m - mass of a star.
• N(m) - number of stars at that mass.

Edwin Salpeter developed an early IMF in 1955, the Salpeter function (or Salpeter IMF):

N(m)dm = C1 × (m/MSun)-C2(dm/MSun)

• C₁ - constant reflecting local stellar density.
• C₂ - 2.35.

Later versions of the IMF such as the Chabrier IMF generally provide ways to determine the two constants, and the Kroupa IMF presumes three mass regimes, each with an associated exponent. An IMF can be derived from a luminosity function and a mass-luminosity relation.

Note that in the term IMF, the phrase mass function is meant to indicate it deals with physical masses. Such a phrase also occurs in probability terminology (probability mass function) for a totally different, incompatible concept: a function yielding the probability of some discrete random variable taking on a given value.