Halo Mass Definitions
This document describes the Colossus mechanisms for dealing with halo mass and radius definitions.
Allowed mass and radius definitions
Halo masses and radii are most commonly defined using spherical overdensity mass definitions. A spherical overdensity radius is the radius within which the halo has an overdensity \(\Delta\) with respect to some reference density, usually the mean or critical density of the universe:
where the mdef
parameter determines the density threshold \(\rho_{\rm mdef}\). Another
common mass definition is via the friends-of-friends algorithm
(Davis et al. 1985). Some Colossus
functions can also handle splashback radii and masses (see Splashback radius).
The mdef
parameter can take on the following values in Colossus:
Type |
mdef |
Examples |
Explanation |
---|---|---|---|
Matter |
|
|
Integer times the mean matter density of the universe |
Critical |
|
|
Integer times the critical density of the universe |
Virial |
|
|
An overdensity that varies with redshift (Bryan & Norman 1998) |
Any SO |
|
|
Any spherical overdensity mass definition |
Friends-of-friends |
|
|
Friends-of-friends mass (any linking length) |
Splashback (mean) |
|
|
Splashback computed from the mean of the particle apocenter distribution |
Splashback (percentile) |
|
|
Splashback computed from percentiles (50-90) of the particle apocenter distribution |
Some functions furthermore use an rmdef
parameter which denotes spherical overdensity radii
by R<mdef>
(e.g., R200m
) and masses by M<mdef>
, e.g. M500c
. Not all mass
definitions are allowed in all functions. For example, functions dealing with SO masses will
typically not accept *
or fof
.
Modules
The functions in the halo.mass module are split into various sub-modules:
The
mass_so
module contains functions that are purely related to spherical overdensity, i.e., that do not depend on the particular form of the density profile. This includes density thresholds, converting mass to radius and vice versa, and the dynamical time.The
mass_defs
module contains functions related to converting SO mass definitions into one another, as well as computing pseudo-evolution.The
mass_adv
module contains advanced functions that rely on other modules such as concentration, as well as some non-SO mass definitions.The
splashback
module contains functions related to the splashback radius and mass.
Please see the following documentation pages for more information: