3.4. Lensing and the SZ effect

The thermal SZ effect is a linear measure of the line-of-sight thermal energy content of a cluster of galaxies. If the cluster is isothermal and the SZ effect measures the line-of-sight electron density. Thus an SZ effect image can be converted into a map of the line-of-sight integrated baryon density. Since the baryon content of a cluster is dominated by the hot gas in the atmosphere, rather than the baryons in galaxies, an SZ effect image can be converted into a fairly accurate map of the total baryon content of a cluster. This can be compared with the total mass content of the cluster which underlies the gas density model used to fit the SZ effect (or from some deprojected mass model underlying a deprojection of the SZ data) to find baryonic mass fraction of the cluster, and to see whether this changes across the cluster (as it might if there is complicated 3-D structure: potentially this is a way of recovering the 3-D structure of a cluster (Lee and Suto 2004).

More interestingly, the baryonic content map can be compared with the total mass map derived from gravitational lensing to provide a check of the physical description of the mass and gas in the cluster, or to calculate the baryonic mass fraction using the SZ/X-ray derived distance of the cluster rather than the Hubble constant (Sec. 2.4).

For CL 0016+16, existing weak lensing data extend only to a radius _c from the cluster centre (Smail 1997), so a comparison of the total cluster mass from lensing and implied by the model is only possible in a cylinder of angular radius _c (corresponding to a linear scale of about 250 kpc). The mass results are

(44)

and so are consistent although the lensing mass estimate has a substantial error. By comparison, the total gas mass within the same cylinder is

(45)

implying a baryonic mass fraction in the cluster

(46)

which is consistent with the baryonic mass fraction that would be expected from a fair sample of matter in the Universe in the consensus cosmology

(47)

and shows no sign of evolution compared to nearby high-mass clusters (Carlstrom et al. 2002), even though the clusters for which this work has been done do not at present constitute a well-defined sample.