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X-ray Scaling Relation in Early-Type Galaxies: Dark Matter as a Primary Factor in Retaining Hot Gas

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.