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

Abstract

We describe (1) a new test for dark matter and alternate theories of gravitation based on the relative geometries of the X-ray and optical surface brightness distributions and an assumed form for the potential of the optical light, (2) a technique to measure the shapes of the total gravitating matter and dark matter of an ellipsoidal system which is insensitive to the precise value of the temperature of the gas and to modest temperature gradients, and (3) a 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 independent of the distance to the galaxy or the gas temperature.We apply these techniques to X-ray data from the ROSAT Position Sensitive Proportional Counter (PSPC) of the optically-attened elliptical galaxy NGC 720; the optical isophotes have ellipticity 0:40 extending out to 120 00 (10 00 1 kpc assuming a distance of 20h 80 Mpc). The X-ray isophotes are signi cantly elongated, = 0:20 0:30 (90% con dence) for semi-major axis a 100 00 . The major axes of the 1 dbuote@space.mit.edu 2 crc@space.mit.edu { 2 { discuss the viability of this assumption for NGC 720. Milgrom's Modi cation of Newtonian Dynamics (MOND) cannot dispel this manifestation of dark matter. Hence, geometrical considerations, which are essentially independent of gas pressure or temperature, require the presence 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 of 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 ( r n ) or Hernquist density.Assuming the X-ray gas is in hydrostatic equilibrium, we construct a model X-ray gas distribution for various temperature pro les; i.e. isothermal, linear, and polytropic. We determine the ellipticity of the total gravitating matter to be 0:50 0:70. Using the single-temperature model we estimate a total mass (0:41 1:4) 10 12 h 80 M interior to the ellipsoid of semi-major axis 43:6h 80 kpc. Ferrers densities as steep as r 3 do not t the data, but the r 2 and Hernquist models yield excellent ts. We estimate the mass distributions of the stars and the gas and t the dark matter directly. For a given temperature pro le of the gas and functional forms for the visible stars, gas, and dark matter, these models yield a distance-independent and temperature-independent measurement of the ratio of dark mass to stellar mass M DM =M stars . We estimate at minimum M DM =M stars 4 which corresponds to a total mass slightly greater than that derived from the single-temperature models for distance D = 20h 80 Mpc.{ 4 { of the gas. In addition, by exploiting the relative geometries of the X-ray and optical isophotes (and an assumed model for the potential of the optical light) we introduce a test for dark matter and alternate gravity theories that is highly insensit...

CLUMP-3D: three-dimensional lensing and multi-probe analysis of MACS J1206.2−0847, a remarkably regular cluster

“…A consequence of the pressure equilibrium is the X-ray shape theorem (Buote & Canizares 1994, i.e. the gas in strict hydrostatic equilibrium follows the iso-potential surfaces of the underlying matter distribution.…”

“…The black lines shows the marginalised a-priori distributions under the q-flat prior. tial after projection in the hypothesis of spheroidal symmetry for the emitting system (Buote & Canizares 1994. Here, we can directly compare the axis ratios in three dimensions without restricting assumptions on the cluster shape.…”

Observations of Metals in the Intra-Cluster Medium

“…To reconcile these observations with the chemical enrichment models, it has been postulated that galaxy groups accrete primordial gas after they have been expelling gas during most of their evolution (Renzini 1997). Buote and Canizares (1994) showed that if a galaxy spectrum has intrinsically two temperature components, the single-temperature model can give a significantly underestimated metallicity. Buote (2000b) demonstrated that in a spectrum characterised by two temperatures, one below 1 keV and one above 1 keV, with an average of ∼1 keV, the lower temperature component preferentially excites emission lines in the Fe-L complex below 1 keV (Fe XVII-XXI), while the higher temperature component excites the Fe-L lines from ∼1-1.4 keV (Fe XXI-XXIV).…”

X-ray narrow emission lines from the nuclear region of NGC 1365

“…In both these regions the abundances were determined using only a one temperature collisional emission model (the ring model also included a power law component), and using low resolution ACIS spectra (compared to the Chandra gratings and XMM-Newton RGS). It has been shown that a one temperature collisional model at sub solar abundances and a two temperature collisional model at (or near) solar abundances cannot be distinguished at CCD resolution (Buote & Canizares 1994;Buote & Fabian 1998), and as the Wang et al (2009) study took place before the publication of any high resolution soft X-ray spectra of this object, we suspect this may be the case here. Without the resolution to determine the strengths of and ratios between individual emission lines, distinguishing the contribution of collisional and photoionised emission to the soft X-ray spectrum is subject to great uncertainties, and therefore we consider these abundances also to be uncertain.…”