### 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.

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

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

https://arxiv.org/abs/astro-ph/0304382

**Referenced by:**

dense core mass function (DCMF)

power law

stellar population synthesis code

star formation (SF)

stellar birth rate function

X-ray luminosity function (XLF)

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