## 3. Mass distributionsIn this section we will described the method we used to deduce the cluster total mass, gas mass and other associated physical parameters from the X-ray data and compare some of these parameters (e.g. velocity dispersion) with the optical data available. We will assume that the gas is in hydrostatic equilibrium and isothermal. The X-ray surface brightness given in equation 1corresponds exactly to a gas distribution of if the gas extends all the way to infinity. Through the equation of hydrostatic equilibrium, the gas distribution is related to the cluster gravitational potential as follows: where is the gas temperature,
is the proton mass and where is the central 3-D velocity dispersion and is related to through . Thus from Poisson's equation the total mass density is given by: and the cluster total mass is given by: From the X-ray spectral data, we found the best estimate emission
measure and temperature assuming Raymond-Smith spectra. Thus we have
the X-ray flux, , within a radius of
(i.e. 0.65 Mpc) over the We compare the X-ray deduced velocity dispersion of the cluster with the measured galaxy velocity dispersion. From Jean's equation for a spherical, steady state system with isotropic velocity distribution, we can deduce the 3-D velocity dispersion from the potential given in equation 4and the total mass density (equation 5) if the galaxy number distribution follows that of the total mass. Thus the 3-D velocity dispersion in this case is given by where is the 3-D radius in core radius units and is the 3-D velocity dispersion at the centre. In producing the above analytic expression, we have assumed that the cluster extends to infinity and that the galaxies can be treated as test particles in the cluster potential with a distribution that follows the mass. Fig. 3 shows the galaxy number count isocontours overlaid on the X-ray image. The southern structure in the isopleth map was identified with a background group (Colless 1987). Note also the coincidence between the X-ray emission and the optical structures. Since the cluster is fairly regular, it can be circularly averaged to produce a galaxy number density distribution. We found that the galaxy density distribution thus deduced agreed well with the shape of the projected mass distribution, thus justifying the mass-follows-light assumption. The line of sight velocity dispersion , can be projected from the 3-D dispersion through (Merritt 1987): where is the projected mass density, is the projected radius in core radius units. Therefore, the line of sight velocity dispersion is given by (see Appendix of Mellier
We can thus estimate from
and and deduce
Mpc km s Given the electron density and gas temperature we can calculate the central cooling time, , given by (Sarazin 1988) and for A 2717, it amounts to Gyr which is smaller than the Hubble time ( Gyr). Thus in the absence of heating, cooling occurs within the centre of the cluster with a cooling radius of kpc. Pending further evidence of the existence of a cooling flow, this maybe one of the few cases where a WAT is found in a cooling flow cluster (c.f. Burns 1990). © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |