### initial mass function

(IMF)
(function describing initial mass of stars)

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.

The IMF can be derived from the luminosity function and the mass-luminosity relation.

Note that the phrase mass function is to indicate it deals with physical masses. The two-word phrase is used in probability (probability mass function) for an incompatible concept: a function yielding the probability of some discrete random variable taking on a given value.

(model,relation,stars,mass,function)
http://en.wikipedia.org/wiki/Initial_mass_function