Next Contents Previous

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

Equation 43 (43)

where T = 2.73 K is the microwave radiation temperature, tau0 is the Thomson scattering optical depth through the cluster (tau0 = sigmaT integ nedl, where sigmaT is the Thomson scattering cross section and dl is the distance along the line of sight), Tx is the intracluster gas temperature, and me is the electron mass.

For typical observed rich cluster parameters of Lx ~ 1044h-2 ergs-1, Rc ~ 0.2h-1 Mpc, and kTx appeq 4 keV, the bremsstrahlung relation (Lx propto ne2 Rc3 Tx0.5, Section 3.1) implies a central gas density of ne appeq 3 × 10-3h1/2 electrons cm-3, thus yielding tau0 appeq 3 × 10-3h-1/2 [tau0 = 0.0064ne(cm-3) Rc(kpc)]. Therefore

Equation 44 (44)

This temperature decrement remains constant over the cluster core diameter

Equation 45 (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).

Next Contents Previous