© CAMBRIDGE UNIVERSITY PRESS 1999

3.10. The Sunyaev-Zeldovich Effect in Clusters

The Sunyaev-Zeldovich (1972) effect is a perturbation to the spectrum of the cosmic microwave background radiation as it passes through the hot dense intracluster gas. It is caused by inverse Compton scattering of the radiation by the electrons in the cluster gas.

At the long-wavelength side of the background radiation spectrum, the hot gas lowers the brightness temperature seen through the cluster center by the fractional decrement

(43)

where T = 2.73 K is the microwave radiation temperature, ₀ is the Thomson scattering optical depth through the cluster (₀ = _T n_edl, where _T is the Thomson scattering cross section and dl is the distance along the line of sight), T_x is the intracluster gas temperature, and m_e is the electron mass.

For typical observed rich cluster parameters of L_x ~ 10⁴⁴h^-2 ergs^-1, R_c ~ 0.2h^-1 Mpc, and kT_x 4 keV, the bremsstrahlung relation (L_x n_e² R_c³ T_x^0.5, Section 3.1) implies a central gas density of n_e 3 × 10^-3h^1/2 electrons cm^-3, thus yielding ₀ 3 × 10^-3h^-1/2 [₀ = 0.0064n_e(cm^-3) R_c(kpc)]. Therefore

(44)

This temperature decrement remains constant over the cluster core diameter

(45)

and decreases at larger separations.

The effect has been detected in observations of some rich, X-ray luminous clusters (e.g., Coma, A665, A2163, A2218, Cl 0016+16) (Birkinshaw et al. 1984; Jones et al. 1993; Wilbanks et al. 1994; Herbig et al. 1995).