GEOMETRICAL EVIDENCE FOR DARK-MATTER - X-RAY CONSTRAINTS ON THE MASS OF THE ELLIPTIC GALAXY NGC-720

We describe (1) a new test for dark matter and alternate theories of g ravitation based on the relative geometries of the X-ray and optical s urface brightness distributions and an assumed form for the potential of the optical light, (2) a technique to measure the shapes of the tot al gravitating matter and dark matter of an ellipsoidal system which i s insensitive to the precise value of the temperature of the gas and t o modest temperature gradients, and (3) a new method to determine the ratio of dark mass to stellar mass that is dependent on the functional forms for the visible star, gas and dark matter distributions, but in dependent of the distance to the galaxy or the gas temperature. We app ly these techniques to X-ray data from the ROSAT Position Sensitive Pr oportional Counter (PSPC) of the optically flattened elliptical galaxy NGC 720; the optical isophotes have ellipticity epsilon approximately 0.40 extending out to approximately 120'' (10'' approximately 1 kpc a ssuming a distance of 20h80 Mpc). The X-ray isophotes are significantl y elongated, epsilon = 0.20-0.30 (90% confidence) for semimajor axis a approximately 100''. The major axes of the optical and X-ray isophote s are misaligned by approximately 30-degrees +/- 15-degrees (90% confi dence). Spectral analysis of the X-ray data reveals no evidence of tem perature gradients or anisotropies and demonstrates that a single-temp erature plasma (T approximately 0.6 keV) having subsolar heavy element abundances and a two-temperature model having solar abundances descri be the spectrum equally well. Considering only the relative geometries of the X-ray and optical surface brightness distributions and an assu med functional form for the potential of the optical light, we conclud e that matter distributed like the optical light cannot produce the ob served ellipticities of the X-ray isophotes, independent of the gas pr essure, the gas temperature, and the value of the stellar mass; this c omparison assumes a state of quasi-hydrostatic equilibrium so that the three-dimensional surfaces of the gas emissivity trace the three-dime nsional isopotential surfaces-we discuss the viability of this assumpt ion for NGC 720. Milgrom's Modification of Newtonian Dynamics (MOND) c annot dispel this manifestation of dark matter. Hence, geometrical con siderations require, without mention of pressure or temperature, the p resence of an extended, massive dark matter halo in NGC 720. Employing essentially the technique of Buote & Canizares (1992; Buote 1992) we use the shape of the X-ray surface brightness to constrain the shape o f the total gravitating matter. The total matter is modeled as either an oblate or prolate spheroid of constant shape and orientation having either a Ferrers (rho is similar to r(-n)) or Hernquist density. Assu ming the X-ray gas is in hydrostatic equilibrium, we construct a model X-ray gas distribution for various temperature profiles; i.e., isothe rmal, linear, and polytropic. We determine the ellipticity of the tota l gravitating matter to be epsilon approximately 0.50-0.70. Using the single-temperature model we estimate a total mass approximately (0.41- 1.4) x 10(12)h80 M . interior to the ellipsoid of semimajor axis 43.6h 80 kpc. Ferrers densities as steep as r-3 do not fit the data, but the r-2 and Hernquist models yield excellent fits. We estimate the mass d istributions of the stars and the gas and fit the dark matter directly . For a given gas equation of state and functional forms for the visib le stars, gas, and dark matter, these models yield a distance-independ ent and temperature-independent measurement of the ratio of dark mass to stellar mass M(DM)/M(stars). We estimate a minimum M(DM)/M(stars) g reater-than-or-equal-to 4 which corresponds to a total mass slightly g reater than that derived from the single-temperature models for distan ce D = 20h80 Mpc.