  We have revisited the X-ray scaling relations of early type galaxies (ETG) by
investigating, for the first time, the LX,Gas - MTotal relation in a sample of
14 ETGs. In contrast to the large scatter (by a factor of 102-103) in the
LX,Total - LB relation, we found a tight correlation between these physically
motivated quantities with a rms deviation of a factor of 3 in LX,Gas = 1038 -
1043 erg s-1 or MTotal = a few x 1010 - a few x 1012 Mo. More striking, this
relation becomes even tighter with a rms deviation of a factor of 1.3 among the
gas-rich galaxies (with LX,Gas > 1040 erg s-1). In a simple power-law form, the
new relation is (LX,Gas / 1040 erg s-1) = (MTotal / 3.2 x 1011 Mo)3. This
relation is also consistent with the steep relation between the gas luminosity
and temperature, LX,Gas ~ TGas4.5, identified by Boroson, Kim & Fabbiano
(2011), 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 LX,Gas < a few x 1039 erg s-1), the scatter in the
LX,Gas - MTotal (and LX,Gas - TGas) relation increases, suggesting that
secondary factors (e.g., rotation, flattening, star formation history, cold gas
etc.) may become important.
