| © 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*_{e}*dl*,
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} ~ 10^{44}*h*^{-2}
ergs^{-1}, *R*_{c} ~ 0.2*h*^{-1} Mpc,
and *kT*_{x}
4 keV, the bremsstrahlung
relation
(*L*_{x}
*n*_{e}^{2} *R*_{c}^{3}
*T*_{x}^{0.5},
Section 3.1) implies a
central gas density of
*n*_{e}
3 × 10^{-3}*h*^{1/2} electrons
cm^{-3}, thus yielding
_{0}
3 × 10^{-3}*h*^{-1/2}
[_{0} =
0.0064*n*_{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).