### Conditional Stellar Mass Function

**(CSMF, Conditional Mass Function, CMF)**
(function characterizing galaxies within a halo of a given mass)

The **Conditional Stellar Mass Function** (**CSMF**, also called
the **Conditional Mass Function** or **CMF**)
is a parameterized, unnormalized Probability Density Function giving the average number
of galaxies with stellar masses within a range interval
within a halo of a given mass, i.e., the number of galaxies
with stellar masses within range (m +/- dm)/2 that reside in
a halo of mass M. It is a concept, and the actual function is
determined through compiling data, and mathematical formulae
are heuristically devised to match it and/or devised based on
physical arguments. It is modeled after the Conditional Luminosity Function.

A CSMF is an element of a **Halo Model**, a model that
explains the galaxies in Dark Matter Halos,
relating them to Dark Matter distributions produced
by Cosmology simulations, presumably to match observation
of large Surveys such as Sloan Digital Sky Survey.

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,galaxies,probability density function,function,mass*)
http://arxiv.org/abs/0808.0539

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