Annu. Rev. Astron. Astrophys. 1993. 31: 689-716
Copyright © 1993 by . All rights reserved

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3.1. CBR Fluctuations

After successively lower and lower limits were set to the upper bound on the quadrupole component by many experiments [the best prior limit was given by the Relikt satellite (Klypin et al 1987)], the COBE DMR team announced (Smoot et al 1992) a value of Qrms = 13 ± µk or DeltaT / T = 5 × 10-6. At 10° (full width Gaussian window), the COBE team found DeltaTrms = 30 ± 5µk, fixing the amplitude at that scale (comoving wavelength ~ 300 Omega0-0.4 h-1 Mpc). Since this value is based on observations at several frequencies (which permit one to check that the fluctuations have the correct spectral signature) and on many independent areas far from the ecliptic and the Galactic plane, this result should be reliable. The COBE team also found that, over the angular scales investigated, the power-law spectral index n was determined to be n = 1.1 ± 0.6, providing (weak) support for the HZP value, n = 1, but allowing considerable room for revision. According to Efstathiou et al (1992), the COBE measurements imply an amplitude on the galactic scale of sigma8 = 1.08 ± 0.25; other groups (e.g. Wright et al 1992) find a similar value.

Smaller scale measurements of CBR fluctuations are both less conclusive and more difficult to interpret. For the standard recombination picture, the horizon at last scattering is approximately 2°. This could increase to nearly 10° for maximal reionization, but in general for scales smaller than those of the COBE instrument, post recombination effects must be considered. The 6° ULISSE (de Bernardis et al 1992) balloon experiment gives an upper limit about 1.4 times the CDM prediction (normalized to COBE), and it is therefore consistent with the model.

At the 1.5° scale, the Gaier et al (1992) south pole experiment sets a 95% confidence level upper bound of (DeltaT / T) leq 1.4 × 10-5. This is quite close to the CDM prediction of (DeltaT/T) = 1.3 × 10-5 for the COBE normalization. The Owens Valley "Ring" experiment set a limit on the 2.6' scale of (DeltaT / T) < 1.9 × 10-5 (Myers et al 1993) and now appears to have detected fluctuations (at the 95% confidence level). After removal of contamination due to foreground nonthermal extragalactic radio sources, the authors estimate (DeltaT / T) = 3.3 × 10-6 on the 1-5 arcminute scale. This is considerably above the CDM prediction of 1.0 × 10-6 but within the range of what might be expected due to secondary processes (Ostriker & Vishniac 1986, Vishniac 1987).

These secondary effects, caused by interactions between CBR photons and moving or heated electrons, were described initially by Zeldovich & Sunyaev (1969). Since they are intrinsically due to nonlinear processes, and highly dependent on the distribution of shock-heated gas, a full hydrodynamic treatment is required. Scaramella et al (1993) summarize earlier work and present the latest results for a CDM model. They find that the small-scale fluctuations have, as expected, a strong non-Gaussian tail with high values of (deltaT / T) following a roughly log-normal distribution. The mean level of (deltaT / T) is due to heated gas at relatively large redshift and is unobservably small (y approx 10-5.5). The fluctuating component is due primarily to low redshift heated gas (observationally identified primarily with clusters of galaxies). The thermal component of the secondary fluctuations is found to be (deltaT / T)rms approx 0.8 × 10-6 (theta / 10°)-1/4 for the COBE normalization, and for Omegab = 0.06. This makes a negligible correction on the COBE scales but approaches significance at the 3' Ring experiment scale. The velocity component of the total secondary fluctuations is typically an order of magnitude smaller than the thermal component.

In sum, the CDM model, after normalization to the COBE DMR 10° measurement, is in accord with all other CBR measurements except insofar as it may predict a slight excess at small angular scales, corresponding to the few Mpc comoving length scales. As we shall see, this defect recurs as other observational tests are made on that scale.

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