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2.1. Cluster energetics

The total thermal SZ effect flux density, Sth,nu, from a cluster usually dominates the kinematic effect, so that

Equation 21 (21)

where the integrals are over solid angle and distance along the line of sight, and Uth is the total thermal energy content in the atmosphere of the cluster. The constant of proportionality in eq. (21) is composed purely of fundamental constants, the thermodynamic temperature of the MBR, and the frequency of observation, without any cosmological or structural parameters, so that a measurement of the total SZ effect from a cluster immediately provides a model-independent measure of the thermal energy of the cluster gas.

If the gas is in hydrostatic equilibrium in the cluster gravitational potential, then Uth should be closely related to the total gravitational potential energy of the cluster, so that an SZ effect survey should be able to pick out clusters of similar masses in similar dynamical states at any redshift. With redshift information from an optical follow-up programme, the evolution of cluster potential wells could be studied and compared with the predictions of cluster formation models.

However, the usefulness of such SZ measurements is critically dependent on the absolute calibration of the SZ effect data.

2.1.1. Absolute calibrations

Calibrations of radio data (Secs 1.3.2, 1.6.2) are often based on measurements of planets, and the conversion from planet measurements at one frequency to the implied flux density from a planet at another frequency depends on the properties of any planetary atmosphere, the surface, and the polarization characteristics of the telescope as well as the precision of the fundamental measurements of planetary flux densities made using absolute instruments.

Generally the complications in planetary observations are relatively minor, so that the residual absolute flux density errors depend on the original absolute calibrations of the planet properties. The radio flux density scale used for SZ effect observations is therefore good to about 5%, and this potential 5% systematic error in the flux density scale should apply to all SZ effect measurements to date.

Space-based observations of SZ effects, for example those to be made by the Planck satellite, should be better than this, since they can be calibrated by reference to the MBR dipole anisotropy, which is known from absolute measurements to higher accuracy. A cross-calibration of the planetary scale against the MBR dipole would then allow an improvement to all SZ effect measurements, and reduce their systematic errors significantly.

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