3. Cluster mass
To determine the cluster mass we need information on the cluster gas temperature in addition to the gas density profiles which can be calculated from the observed surface brightness profiles. One possibility to infer the cluster temperature is to use the well known and reasonably tight luminosity temperature relation for X-ray clusters as given for example by Markevitch (1998) based on recent ASCA observations. Using his relation (uncorrected for the luminosity effect of cooling flows), = , we find a temperature of 3.6 keV as used above.
We have constructed a range of mass profiles for the cluster allowing for a large temperature range from 3.6-8 keV (with a best value of 6 keV) and a range from 3-4.5 keV (with a best value of 3.6 keV) as implied by the -relation. We are allowing for different shapes of the temperature profiles using polytropic models with a range of -parameters from 0.9 to 1.3, roughly accounting for the observed temperature variations. The temperature profile for the polytropic models were normalized such as to give the nominal emission measure weighted average temperatures. The results of the mass modeling are given in Table 2 and Fig. 4. For comparison with masses estimated from a lensing analysis two-dimensional mass profiles were also calculated assuming a cut-off radius of Mpc with results also given in Table 2. The choice of the cut-off radius has little influence on the exact result. Taking for example an outer radius of Mpc, much larger than the expected virial radius of the cluster, the projected mass increases by only about 25%.
Table 2. Results for the mass profile for the cluster Cl0024+17. The masses are given in units of and the radii in units of Mpc. The first set of values gives the result for an isothermal model with keV and the values in brackets give the full model range for the first set of values. The second set of values give the corresponding parameters for an adopted temperature of keV. The column labeled 2-dim. mass gives the projected cluster mass onto the celestial sphere with an assumed outer cut-off radius of Mpc.
© European Southern Observatory (ESO) 2000
Online publication: December 8, 1999