A combined analysis of cluster mass estimates from strong lensing, X-ray measurement and the universal density profile

We present a combined analysis of mass estimates in the central cores of galaxy clusters from the strong lensing, the X-ray measurements and the universal density profile (NFW). Special attention is paid to the questions (1)whether the previously claimed mass discrepancy between the strong lensing and X-ray measurements is associated with the presence of cooling/non-cooling flows, (2)whether the cusped NFW density model can provide a consistent cluster mass with the strong lensing result and (3)whether a non-zero cosmological constant can be of any help to reducing the strong lensing – X-ray mass ratios. We analyse a sample of 26 arc-like images among 21 clusters,the X-ray data of which are available in archive. The X-ray and NFW cluster masses are obtained by assuming that the intracluster gas is isothermal and in hydrostatic equilibrium with the underlying gravitational potential of the clusters. A statistical comparison of these three mass estimates reveals that the mass discrepancies for all the events are well within a factor of 2, if X-ray measurement uncertainties are included. In particular, we confirm the result of Allen that the larger mass discrepancy is only detected in the intermediate cooling, especially non-cooling flow clusters, thus attributing the mass discrepancy to the local dynamical activities in the central regions. We show that the NFW profile yields a consistent cluster mass with the conventional X-ray measurement, which is interpreted as the consequence of the common working hypothesis behind the two methods. Any difference between these two models must occur at even smaller radii (e.g. within the arc-like images) or at large radii. It appears that the introduction of the cusped density profile as the dark matter distribution of clusters cannot raise the cluster masses enclosed within arc-like images. Finally, a non-zero cosmological constant is able to moderately reduce the mass ratios of mlens to mxray. These results, together with the excellent agreement between the X-ray, optical and weak lensing determined cluster masses on scales greater than the X-ray core sizes found in the early work, indicate that the mass discrepancy between strong lensing and other methods in the intermediate cooling and non-cooling flow clusters is likely to have arisen from both the oversimplification of lensing model and the inappropriate application of isothermality and equilibrium hypothesis in the central regions of clusters where the local dynamical activities make a non-negligible contribution to both mass estimates.