Annu. Rev. Astron. Astrophys. 1992. 30: 653-703
Copyright © 1993 by . All rights reserved

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Over the last decade the anisotropy of the microwave background radiation has emerged as a field of fundamental importance to astrophysics due to its significance in theories of galaxy formation and in the quest for the physical origin of fluctuations. The history of the development of this subject may be divided into three phases: In the first phase, lasting up until about 1982, searches for anisotropy were carried out on angular scales ranging from two arc minutes to 180°, and, apart from the dipole term due to the peculiar velocity of the earth relative to the Hubble flow (eg. Fixsen et al 1983, Lubin et al 1985, Halpern et al 1985, Strukov & Skulachev 1988, Meyer et al 1991b, Smoot et al 1991b), no anisotropies were detected down to the level of DeltaT/T approx 10-4 - 10-3 expected from simple scenarios for galaxy formation. In the second phase, from ~ 1983 to ~ 1989, sensitivities were improved by a full order of magnitude, but still no intrinsic anisotropies were detected. Over the same period many theoretical models were eliminated and new models were explored which predicted fractional anisotropies approaching 10-6. We are presently in the third phase: Sensitivities on all angular scales have reached levels where confusing signals due to discrete sources or diffuse Galactic emission - due to dust, free free emission and synchrotron radiation - dominate the signals and have to be removed before the intrinsic anisotropy can be studied.

There are excellent reviews of the first phase (Weiss 1980, Partridge 1980, Wilkinson 1982, Partridge 1983) and portions of the second phase (Wilkinson 1986, Partridge 1987, Partridge 1988). In addition to thorough discussions of the observations, two of these reviews (Weiss 1980, Partridge 1988) give extensive accounts of the instrumentation and observing techniques which have been most effective in this field. In this article we attempt a comprehensive review of the observations in the second and third phases and we discuss the confusing signals which have begun to complicate the interpretation of observations. We also discuss the prospects for overcoming these difficulties. We do not discuss theories of galaxy formation and the generation of anisotropy in the microwave background radiation or other cosmological implications of the observations since these are scheduled to be reviewed in a subsequent volume in this series.

It is useful to keep in mind the mass scales that are probed by observations of the anisotropy of the microwave background radiation on different angular scales. If we assume that the microwave background radiation was last scattered at a redshift z >> 1, when the density fluctuations delta rho / rho >> 1, then the mass, M, of a sphere at the last scattering surface which subtends angular diameter Delta theta, calculated from the Robertson-Walker metric for a standard Friedmann cosmology (eg. Weinberg 1972) is given by the relation:

Equation 1 (1)

where Omega is the density parameter, and the Hubble constant H = 100 h km s-1 Mpc-1.

The range of angular scales 1-20° may have particular significance for anisotropy of the microwave background radiation since the horizon scale at z >> 1 subtends an angle:

Equation 2 (2)

Thus, if the last scattering surface of the microwave background radiation was at a redshift z approx 1500, the horizon size at last scattering subtends an angle Delta thetaHORIZON approx 1°. However if the last scattering surface was at z approx 40 then Delta thetaHORIZON approx 6°. For cosmological models with early reionization, primordial intrinsic fluctuations could be erased up to the horizon angular scale, i.e. up to, at most, angular scales of approx 6°. Reionization at z < 40 would not completely erase primordial intrinsic fluctuations up to this scale because the density of matter at later epochs is too low to give high optical depths on a Hubble length even if all the intergalactic material is fully ionized.

In order to interpret observations of the microwave background radiation, it is necessary to assume some form for the distribution on the sky of the intrinsic fluctuations. This immediately raises problems because of our ignorance concerning the form of this distribution. A complete description of the fluctuations in DeltaT comprises both the distribution in amplitude (as can be obtained from a histogram of DeltaT measurements obtained from binning the sky into small pixels), and the spatial distribution (as represented by the spatial autocorrelation function or, alternatively, the power spectrum, W, of DeltaT). In general the spatial distribution does not uniquely determine the amplitude distribution but in the case of a Gaussian spectrum, W, the amplitude distribution is completely determined. This property of a Gaussian random field - that the statistical properties are fully specified by the two-point correlation function - makes it easy to compare observations with Gaussian models. The spectrum of the sky cannot be truly Gaussian because the sky is finite, however at small angular scales models or scenarios have been proposed for which the amplitude distribution is Gaussian and the spectrum is approximately Gaussian (e.g. Bond & Efstathiou 1987). Models have also been proposed in which both the amplitude distribution and the power spectrum are strongly non-Gaussian. (e.g. Ikeuchi 1981, Ostriker & Cowie 1981, Ostriker et al 1986, Ostriker & Thompson 1987, Kofman & Pogosyan 1988, Salopek et al 1989).

In this review we will consider fluctuations in the temperature of the microwave background radiation only on angular scales up to 20°. We do not discuss the quadrupole and dipole terms here because the COBE satellite (Smoot et al 1991a, b) has obtained by far the best data to date on these scales and the situation is likely to change substantially before this review is published. While the same may be true for observations down to ~ 7°, the COBE resolution limit, we do consider observations in the range 1-20° and thus cover the region of overlap between COBE and small angular scale anisotropy measurements. We consider the two-dimensional correlation function, C, for the temperature pattern on the celestial sphere. We assume that C has circular symmetry and may therefore be expressed in terms of a single variable, phi. Thus C(phi) = < T( qhat1) T(qhat2) >, where qhat1 · qhat2 = cos phi. In the small angle approximation the power spectrum, W, of the fluctuations may then be expressed in terms of the single wavenumber variable, k, such that C(phi) and W(k) form a Hankel transform pair. The expected variance of the data can then be written

Equation 3 (3)

where F(k) is a filter function which depends upon the shape of the antenna beam and the sampling scheme on the sky. In general a Gaussian beam is a good approximation to the response of the antenna. The resulting filter functions for such a beam and for single-beam, single switched and double-switched sampling on the sky are given in Table 1. According to Equation 3 we see that, as previously stated, in order to interpret observed values of, or limits on, < (DeltaT/T)2 > in terms of the limits these place on the sky fluctuations we need to assume some form for W(k).

For the purposes of this review, we assume that the mean temperature of the microwave background radiation is T = 2.735 K, as measured by Mather et al (1990) with the COBE satellite, and, wherever possible, we have adjusted published values of DeltaT/T to conform with this value.

Table 1. Filter functions for various switching schemes

Switching scheme Filter function

Gaussian beam, no switching k/2pi e-k2phi02
Single switching, beam separation phis k/2pi e-k2phi02 (1 - J0 (kphis))
Double switching k/2pi e-k2phi02 (3/2 - 2J0 (kphis) + 1/2 J0 (2kphis))

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