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The global energy budget of the hot gas flows in early-type galaxies is usedto explain the recent observational results that S0 galaxies have lower meanX-ray luminosity $L_X$ per unit optical luminosity $L_B$ than do ellipticals.This could be explained with a higher heat input or with a lower gravitationalenergy (all per unit gas mass), at fixed $L_B$. The effect of the flattening ofthe mass distribution is investigated with galaxy models described by theMiyamoto-Nagai potential--density pair, to which a dark matter halo of variousshapes is added. For these models the analytical expressions of thegravitational energy, and the stellar kinetic energy associated with variousrelative amounts of random motions and rotational streaming, are derived. It isfound that rotation cannot produce a change in the flow phase of the hot gas,independently of the galaxy shape and the presence of dark matter. The effectof flattening instead can be substantial in reducing the binding energy of thehot gas. Thus S0s and possibly non spherical Es are less able to retain asignificant halo of hot gas than rounder Es of the same $\lb$.Comment: 8 pages plus 4 figures in uuencoded compressed Postscript forma

The energetics of flat and rotating early-type galaxies and their X-ray luminosity