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We use X-ray data obtained with the ROSAT Position Sensitive Proportional Counter (PSPC) to constrain the shape and the total mass of the flattened elliptical galaxy NGC 720 by a method which is insensitive to the precise value of the temperature of the gas or to the temperature gradient. The X-ray isophotes are flattened, having ellipticity $(\epsilon)$ $\sim 0.25$ at average distance 100'' from the center; the faintest observed optical isophotes have $\epsilon \sim 0.45$ at average distance 45'' (15'' = 2.5 kpc assuming 34 Mpc for distance to galaxy). For reasonable density distributions, the mass of the optically luminous matter can not possibly flatten the X-ray isophotes at 100'' because the equipotential confocal to the optical ellipsoid is virtually spherical at that distance. Hence, the geometry of ellipsoids requires an extended, flattened, and massive halo to produce the observed ellipticity of the X-ray isophotes.
We constrain the mass of the galaxy by assuming the total mass distribution of the luminous matter + gas + dark matter is described by an ellipsoid with mass density $\rho \sim r^{-2}, r^{-3},$ or the Hernquist form. Making the usual assumptions that the X-ray gas is an ideal gas in hydrostatic equilibrium with the potential generated by the total mass, we generate model X-ray surface brightness maps. By comparing the shape and the radial profile of the model surface brightness to that of the image we constrain the possible range of ellipticities of the total matter to be typically $0.50 - 0.70,$ and the extent of the total matter to be at least $\sim 225''$, over three times the optically luminous extent. By estimating the mass distribution of the optically luminous matter and the X-ray gas from knowledge of their surface brightness profiles, we isolate the contribution of the dark matter to the overall gravitational potential. We find that the dark matter has essentially the same shape as that derived for the total matter and that a dark mass at least ten times that of the optically luminous mass is required. Our models are inconsistent with a constant mass-to-light ratio anywhere in the galaxy.
