2.4. Cluster mass distribution
While it is possible to infer the total mass distribution of a cluster using X-ray data and the assumption of hydrostatic equilibrium (Sec. 2.2.2), a better approach may be to use weak lensing. The advantage of this method is that a weak lensing measurement of the ellipticity field induced by a cluster can be converted into a map of the surface mass density of the cluster, tot, which is a linear projection of the total mass density along the line of sight. The ratio of a thermal SZ effect map of the cluster to this tot is then proportional to the projected baryonic mass fraction along each line of sight (if the cluster is isothermal). Simulations (Umetsu 2004) show that blank-field SZ effect and lensing maps can provide an estimate of the baryonic content and redshift of clusters detected through either their shear field or their SZ effects.
This use of the SZ effect relies on the absolute calibration (Sec. 2.1.1), in order to get the baryonic content, and the assumption of isothermality (Sec. 2.2.1), just as the SZ/X-ray approach to the baryon fraction. Otherwise this application is subject principally to the problems of all lensing studies, for example the question of the redshift distribution of the background screen of galaxies and the possibility of multiple structures near the line of sight. While these issues may affect the absolute value of the baryonic content calculated, they should have little effect on the image of the projected baryonic content that can be made, and so the combination of SZ and lensing data may be a useful probe of the large-scale gas-dynamical processes at work in clusters.