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(shortened for babbage) We describe (1) a new test for dark matter andalternate theories of gravitation based on the relative geometries of the X-rayand optical surface brightness distributions and an assumed form for thepotential of the optical light, (2) a technique to measure the shapes of thetotal gravitating matter and dark matter of an ellipsoidal system which isinsensitive to the precise value of the temperature of the gas and to modesttemperature gradients, and (3) a method to determine the ratio of dark mass tostellar mass that is dependent on the functional forms for the visible star,gas and dark matter distributions, but independent of the distance to thegalaxy or the gas temperature. We apply these techniques to X-ray data from theROSAT Position Sensitive Proportional Counter (PSPC) of the optically-flattenedelliptical galaxy NGC 720. The X-ray isophotes are significantly elongated,$\epsilon = 0.20 - 0.30$ (90% confidence) for semi-major axis $a\sim100\arcsec$. The major axes of the optical and X-ray isophotes are misalignedby $\sim 30\deg \pm 15\deg$ (90% confidence). We conclude that matterdistributed like the optical light cannot produce the observed ellipticities ofthe X-ray isophotes independent of the gas pressure, the gas temperature, andthe value of the stellar mass.Comment: 63 pages, PostScrip

Geometrical evidence for dark matter: X-ray constraints on the mass of the elliptical galaxy NGC 720