2.5. Cluster radial peculiar velocity

The use of the kinematic SZ effect to measure the radial velocity of a cluster of galaxies relies heavily on the separation of the kinematic and thermal SZ effects. This requires excellent relative spectral calibration (Sec. 2.1.1) over a wide range of frequencies -- LaRoque (2004) fitted the spectrum of Abell 2163 over a decade of frequency in order to obtain their limit on its radial peculiar velocity, and errors in the relative calibration cause errors in the apparent spectral shape of the kinematic effect which can have large effect on the radial velocity.

Since the kinematic effect and primordial structure in the MBR have the same spectrum, the kinematic effect is intrinsically confused by the lumpiness of the MBR (Sec. 2.3.2). This confusion limits the velocity accuracy that can be achieved on any single cluster: the level of this limit depends on the angular scale being examined, but exceeds about 200 km s^-1 for any plausible present-day observation. Hence the statistical measurement of the radial velocity distribution of clusters of galaxies, as derived from a sample of clusters, is likely to be more useful than the measurement of an apparent radial velocity of any single cluster.

2.5.1. Bandpass calibration

Since the spectrum of the thermal effect is steeply rising through the null at about 218 GHz, and observations of the intensity of the combined thermal and kinematic effect in this part of the spectrum are usually made using bolometers with wide spectral bandpasses, it is clear that the bandpasses must be well known to avoid distorting the apparent shape of the spectrum. Leakage of power into the detector (principally from higher frequencies) could be a significant source of problems.

2.5.2. Cluster velocity substructure

While the kinematic SZ effect is usually discussed in terms of a coherent motion of the entire cluster relative to the Hubble flow, simulations generally show that the largest gas motions arise from substructures within clusters. The largest of these substructures are due to infalling groups, or the residual gas motions from mergers. While this implies that there is significant small-scale kinematic SZ effect structure, which is amenable to interferometric study, the amplitude of individual effects is small, and the superposition of the effects over a large fraction of the cluster tends to produce a level of kinematic effect noise which again reduces the accuracy of any measurement of the overall radial velocity of the cluster. Line-of-sight superpositions of these substructures will also occur, and will tend to confuse their details.

2.5.3. Other substructure

We should also note that the assumption of a smooth global mass distribution leading to smooth density and temperature distributions is certainly incorrect. There are a number of substructures found in the X-ray images of clusters which affect the density and temperature locally, and these will change the SZ effects to the extent that the substructures produce pressure changes, just as they alter the X-ray appearances of clusters. The (thermal) SZ effect is proportional to the integrated line-of-sight electron pressure, and so a detailed SZ image of a cluster might show

• pressure changes at cold fronts (e.g., as in Abell 2142; Markevitch 2000);
• line-of-sight effects from cavities in the gas (e.g., near radio galaxies where radio-faint plasma bubbles are moving, or stationary, in the intracluster medium -- note that the non-thermal SZ effect from the relativistic electrons will be too small to compensate for the missing gas even if the bubbles are in pressure equilibrium; Birkinshaw 1999);
• pressure jumps from shocks around infalling groups or sub-clusters, as for example in the case of 1E 0657-56, where temperature and density jumps indicate a substructure moving at Mach 3 through the intracluster medium (Markevitch 2002);
• variations in the static models eq. (25, 28) because of the slow changes and temperature gradients associated with cooling flows, which not only involve deviations from hydrostatic equilibrium but which are also likely to be non-steady;
• modest additional SZ effects from the non-thermal scatterings of populations of relativistic particles, particularly those associated with radio halo sources (Liang et al. 2002); and
• kinematic SZ effects from motions of substructures in the clusters.