X-ray scaling relations of early-type galaxies

X-ray luminosity, temperature, gas mass, total mass, and their scaling relations are derived for 94 early-type galaxies using archival $Chandra$ X-ray Observatory observations. Consistent with earlier studies, the scaling relations, $L_X \propto T^{4.5\pm0.2}$, $M \propto T^{2.4\pm0.2}$, and $L_X \propto M^{2.8\pm0.3}$, are significantly steeper than expected from self similarity. This steepening indicates that their atmospheres are heated above the level expected from gravitational infall alone. Energetic feedback from nuclear black holes and supernova explosions are likely heating agents. The tight $L_X - T$ correlation for low-luminosities systems (i.e., below 10$^{40}$ erg/s) are at variance with hydrodynamical simulations which generally predict higher temperatures for low luminosity galaxies. We also investigate the relationship between total mass and pressure, $Y_X = M_g \times T$, finding $M \propto Y_{X}^{0.45\pm0.04}$. We explore the gas mass to total mass fraction in early-type galaxies and find a range of $0.1-1.0\%$. We find no correlation between the gas-to-total mass fraction with temperature or total mass. Higher stellar velocity dispersions and higher metallicities are found in hotter, brighter, and more massive atmospheres. X-ray core radii derived from $\beta$-model fitting are used to characterize the degree of core and cuspiness of hot atmospheres.