MAGIICAT III. Interpreting Self-similarity of the Circumgalactic Medium with Virial Mass Using Mg II Absorption

In Churchill et al., we used halo abundance matching applied to 182 galaxies in the Mg II Absorber-Galaxy Catalog (MAGIICAT) and showed that the mean Mg II λ2796 equivalent width follows a tight inverse-square power law, W_r (2796)vprop(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 <= log M _h/M _⊙ <= 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 = 10⁴-10^4.5 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 ~= 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 <= 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.