### 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 = C_{1} × (m/M_{Sun})^{-C2}(dm/M_{Sun})

- C
_{1} - constant reflecting local stellar density.
- C
_{2} - 2.35.

Later versions of the IMF such as the **Chabrier IMF** generally
provide ways to determine the two constants.
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.

(*model,relation,stars,mass,function*)
**Further reading:**

http://en.wikipedia.org/wiki/Initial_mass_function

http://jila.colorado.edu/~pja/astr3830/lecture06.pdf

https://ui.adsabs.harvard.edu/abs/2003PASP..115..763C/abstract

https://ui.adsabs.harvard.edu/abs/1955ApJ...121..161S/abstract

**Referenced by pages:**

Akaike information criterion (AIC)

dense core mass function (DCMF)

probability mass function (PMF)

power law

stellar population synthesis code

star formation (SF)

stellar birth rate function

stellar demographics

X-ray luminosity function (XLF)

Index