We have revisited the X-ray scaling relations of early-type galaxies (ETG) by investigating, for the first time, the L X,Gas-M Total relation in a sample of 14 ETGs. In contrast to the large scatter (a factor of 102-103) in the L X,Total-L B relation, we found a tight correlation between these physically motivated quantities with an rms deviation of a factor of three in L X,Gas = 1038-1043 erg s–1 or M Total = a few × 1010 to a few × 1012 M ☉. More striking, this relation becomes even tighter with an rms deviation of a factor of 1.3 among the gas-rich galaxies (with L X,Gas > 1040 erg s–1). In a simple power-law form, the new relation is (L X,Gas/1040 erg s–1) = (M Total/3.2 × 1011 M ☉)3. This relation is also consistent with the steep relation between the gas luminosity and temperature, L X,Gas ~ T Gas4.5, identified by Boroson et al., if the gas is virialized. Our results indicate that the total mass of an ETG is the primary factor in regulating the amount of hot gas. Among the gas-poor galaxies (with L X,Gas39 erg s–1), the scatter in the L X,Gas-M Total (and L X,Gas-T Gas) relation increases, suggesting that secondary factors (e.g., rotation, flattening, star formation history, cold gas, environment, etc.) may become important.
