In Churchill et al. , we used halo abundance matching applied to 182 galaxies in the Mg ii Absorption-Galaxy Catalog ( MAG ii CAT , Nielsen et al . )
and showed that the mean Mg ii \lambda 2796 equivalent width follows a tight inverse-square power law , W _ { r } ( 2796 ) \propto ( D / R _ { vir } ) ^ { -2 } , with projected location relative to the galaxy virial radius and that the Mg ii absorption covering fraction is effectively invariant with galaxy virial mass , M _ { h } , over the range 10.7 \leq \log M _ { h } / M _ { \odot } \leq 13.9 .
In this work , we explore multivariate relationships between W _ { r } ( 2796 ) , virial mass , impact parameter , virial radius , and the theoretical cooling radius that further elucidate self-similarity in the cool/warm ( T = 10 ^ { 4 - 4.5 } K ) circumgalactic medium ( CGM ) with virial mass .
We show that virial mass determines the extent and strength of the Mg ii absorbing gas such that the mean W _ { r } ( 2796 ) increases with virial mass at fixed distance while decreasing with galactocentric distance for fixed virial mass .
The majority of the absorbing gas resides within D \simeq 0.3 R _ { vir } , independent of both virial mass and minimum absorption threshold ; inside this region , and perhaps also in the region 0.3 < D / R _ { vir } \leq 1 , the mean W _ { r } ( 2796 ) is independent of virial mass .
Contrary to absorber-galaxy cross-correlation studies , we show there is no anti-correlation between W _ { r } ( 2796 ) and virial mass .
We discuss how simulations and theory constrained by observations support self-similarity of the cool/warm CGM via the physics governing star formation , gas-phase metal enrichment , recycling efficiency of galactic scale winds , filament and merger accretion , and overdensity of local environment as a function of virial mass .