1.1. The Cosmic Microwave Background Radiation

The cosmic microwave background radiation (CMBR) is the dominant radiation field in the Universe, and one of the most powerful cosmological tools that has yet been found. 25 years after its discovery by Penzias & Wilson (1965) ⁽²⁾ much is now known about the properties of the radiation (see the recent review by Partridge 1995), and a vigorous community studies the CMBR to extract all the cosmological and astrophysical data that it carries.

Within a few years of the discovery of the CMBR, it was established the radiation field is close to isotropic, with a spectrum characterized by a single temperature, T_rad 2.7 K. The specific intensity of the radiation is therefore close to

(1)

which corresponds to a peak brightness I_max ~ 3.7 x 10^-18 W m^-2 Hz^-1 sr^-1 at _max ~ 160 GHz, a photon density n ~ 4 x 10⁸ photons m^-3, and an energy density u ~ 4 x 10^-14 J m^-3, which can also be expressed as a mass density ~ 5 x 10^-31 kg m^-3, much less than the critical density

(2)

required to close the Universe. In these equations, h is Planck's constant, c is the speed of light, is the frequency, k_B is the Boltzmann constant, G is the gravitational constant, and h₁₀₀ = H₀/100 km s^-1 Mpc^-1 is a dimensionless measure of the value of the Hubble constant, H₀. Recent estimates give 0.5 h₁₀₀ 0.8 (e.g., Sandage et al. 1996; Falco et al. 1997; Sandage & Tammann 1997; Freedman et al. 1997).

Although specific small parts of the sky (stars, radio sources, and so on) are brighter than the CMBR, overall the CMBR constitutes the major electromagnetic radiation field in the Universe and contributes about 60 per cent of the relativistic energy density (the other 40 per cent being provided by the neutrinos, assumed to be massless here). The integrated brightness of the sky in the CMBR is not small, and a comparison with a bright radio source may be useful. Cygnus A is one of the brightest extragalactic radio sources at low frequencies. A comparison of the relative brightness of Cygnus A and the CMBR, as observed by a telescope with a 1 square degree beam, is shown in Figure 1. It can be seen that the CMBR easily dominates over a wide range of frequencies above 10 GHz. It is not signal strength that makes measuring the intensity of the CMBR difficult, but rather the problem of making absolute measurements, since the CMBR is present in all directions with almost equal intensity.

Figure 1.The spectrum of the microwave background radiation, and the microwave background radiation after passage through an (exaggerated) scattering atmosphere with y = 0.1 and = 0.05 (as defined in Sections 3 and 6), compared with the integrated emission from the bright radio source Cygnus A as observed by a telescope with solid angle beam = 1 square deg. Note that the microwave background radiation dominates at high frequencies. Scattering (the Sunyaev-Zel'dovich effect) causes a fractional decrease in the low-frequency intensity of the CMBR that is proportional to y. The location of the cross-over point, where the scattered CMBR and the unscattered CMBR have equal brightness, is a measure of . This scattered spectrum was calculated using the Kompaneets formula (59), rather than the relativistic results (eq. 51) of Rephaeli (1995a), and hence is only accurate for low cluster gas temperatures (see Sec. 3.3), although the difference is imperceptible in this figure.