### 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 a dark matter halo's galaxies with stellar masses
within a range interval, as a function of halo mass.
In other words, the count of galaxies with stellar masses
within some range *(m +/- dm)/2* that reside within a halo
within some mass range *(M +/- DM)/2*, i.e., a function of m and M.
Sometimes such a CSMF is split into one specific to halos' central galaxies
versus another specific to halos' satellite galaxies.
Such CSMFs might result from compiling data,
and devising heuristic mathematical formulae to match it.
Alternately such a function might be devised based on physical arguments.
This approach to characterizing galaxies within halos by mass
is modeled after the conditional luminosity function.

Such CSMFs are used in **halo models**, models 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 in the term CSMF, the phrase *mass function* is meant
to indicate it deals with physical masses.
The 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,galaxies,function,mass*)
**Further reading:**

https://ui.adsabs.harvard.edu/abs/2009ApJ...695..900Y/abstract

https://ned.ipac.caltech.edu/level5/March18/Wechsler/Wechsler2.html

**Referenced by pages:**

halo mass function

probability mass function (PMF)

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