The mapping between dark matter halo mass , galaxy stellar mass , and galaxy cold gas mass is not a simple linear relation , but is influenced by a wide array of galaxy formation processes .
We implement observationally-normalized relations between dark matter halo mass , stellar mass , and cold gas mass to explore these mappings , with specific emphasis on the correlation between different definitions of a major galaxy merger .
We always define a major merger by a mass ratio m / M > 0.3 , but allow the masses used to compute this ratio to be defined in one of three ways : dark matter halo masses , galaxy stellar masses , or galaxy baryonic masses ( stars and cold gas ) .
We find that the merger ratio assigned to any particular merger event depends strongly on which of these masses is used , with the mapping between different mass ratio definitions showing strong evolution with halo mass and redshift .
For example , major dark matter mergers ( > 0.3 ) in small galaxies ( M _ { DM } < 10 ^ { 11 } M _ { \odot } ) typically correspond to very minor stellar mergers ( < 1 / 20 ) .
These mergers contain significant dark matter mass , and should cause noticable morphological disruption to the primary galaxy , even though there is no observable bright companion .
In massive galaxies , there is an opposite effect , with bright companion galaxies corresponding to only minor dark matter mergers .
We emphasize that great care must be taken when comparing mergers based on different mass ratio definitions .