Halo Mass Definitions¶
This document describes the Colossus mechanisms for dealing with halo mass and radius definitions.
Spherical overdensity basics¶
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 friendsoffriends algorithm
(Davis et al. 1985). 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 
Friendsoffriends 


Friendsoffriends mass (any linking length) 
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 submodules:
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 pseudoevolution.The
mass_adv
module contains advanced functions that rely on other modules such as concentration, as well as some nonSO mass definitions.The
splashback
module contains functions related to the splashback radius and mass.
Please see the following documentation pages for more information: