![]() | Annu. Rev. Astron. Astrophys. 1992. 30:
653-703 Copyright © 1993 by Annual Reviews. All rights reserved |
3.2 Observations on Angular Scales 1'-1°
Angular scales of 1'-1° are
particularly important in theories of galaxy formation which assume
the standard recombination model
(Peebles & Yu 1970)
in which the
epoch of decoupling of the radiation from the matter occurs in the
redshift range z ~ 1000-1500, and reionization occurs
late, at z 10,
when the universe is optically thin even if the
intergalactic medium is completely ionized. Observations on these
angular scales have all been filled aperture observations carried out
on single dishes, although plans are afoot to construct
interferometers which would operate at these resolutions (eg.
Lasenby et al 1991).
There have been four major efforts to detect anisotropy
on these angular scales: by Uson and Wilkinson
(1982,
1984a,
b,
c);
by the group led by Readhead at the
Owens Valley Radio
Observatory of
the California Institute
of Technology
(Readhead et al 1988,
Lawrence et al 1988,
Readhead et al 1989,
Myers 1990,
Myers et al 1991,
Myers et al 1992);
by the group led by Lubin at the University of California, Santa Barbara
(Meinhold & Lubin 1991,
Gaier et al 1992
in preparation); and by de Bernardis et al
(1988,
1989,
1990).
These four programs are discussed separately below.
3.2.1
= 86° 51'.
Uson and Wilkinson used a double differencing scheme in which the
beams were alternated on the fields of interest. They therefore
measured the difference between a center field and the mean of two
reference fields which straddled the center field at a distance of 4.5
arc minutes. This double differencing strategy is sensitive only to
second and higher derivatives of the sky temperature as a function of
position on the sky. It eliminates linear drifts and variations in
the receiver, ground spillover, etc. With this strategy there
remained a slow linear drift in the double-differenced output -
i.e. a second order term - of about 55 mK per hour which is due to
curvature in the scattered ground radiation. Each field was observed
over the same range of zenith angles, and therefore this drift could
be modelled. All of the published data have had this drift term
subtracted out, i.e. both a mean term and a drift term have been
subtracted. Uson and Wilkinson tracked their fields for either one
hour (first observing run) or two hours (second-fifth observing
runs). The culmination of this program led to firm upper limits on
anisotropy well below T/T = 10-4,
(Uson & Wilkinson 1984a,
b,
c)
and provided considerable impetus to the burgeoning amount
of theoretical work in this area. Most important, these were the
first results which appeared to rule out adiabatic fluctuations in
baryonic matter as the primary agents of galaxy formation (e.g.
Wilson & Silk 1981).
The results are shown in Figure 1a. The resulting upper limit on anisotropy calculated by Uson and Wilkinson is given in Table 3.
Experiment | Angular Scale | ![]() | Comments |
Uson & Wilkinson | 1'.4 | 2.1 | 19.5 GHz; LR test, ![]() |
1'.4 | 3.9 | Bayesian (Readhead et al. 1989) | |
Readhead et al. 1989 | 1'.8 | 1.7 | 20 GHz; Bayesian, monochromatic W(k) |
1'.8 | 1.6 | LR test, ![]() | |
12" | 9.6 | Bayesian; Gaussian W(k) | |
2'.6 | 1.9 | Bayesian; Gaussian W(k) | |
25' | 30 | Bayesian; Gaussian W(k) | |
Myers et al. 1992 | 1'.8 | 4.5 | 20 GHz; Corrected for identified sources |
Bayesian; Gaussian W(k) | |||
Berlin et al. 1984 | 4'.5-9'.5 | 1b | 3.9 GHz; 1 ![]() |
Meinhold & Lubin 1991 | 20'-30' | 3.5 | 91 GHz; Gaussian W(k) |
Alsop et al. 1992 | 30" | 15 | 180 GHz, 270 GHz & 360 GHz; Gaussian W(k) |
de Bernardis et al. 1990 | 15'-100' | 20-30 | 270 GHz; Gaussian W(k) |
a As described in the text, some of these observations detected excess variance which could not be definitively attributed to the cosmic microwave background radiation. | |||
b Amirkhanyan (1987) calculates a limit of 30-50 x 10-5 (see text). |
Uson and Wilkinson used a likelihood ratio test, to
derive their limit on anisotropy. As we described in
Section 2, likelihood
ratio tests give misleading results when used on datasets with reduced
2 values significantly
less than unity. Unfortunately the Uson
and Wilkinson data set has
2
=
0.7. This can be seen directly in the data shown in
Figure 1a, where it is clear that
the measured values of
T
are closer to zero than would be expected based on the size of the error
bars.
![]() |
Figure 1. Observations of the microwave background radiation on angular scales 1'-1°. (a) Uson & Wilkinson (1984c) at 19.5 GHz, from twelve fields; (b) Readhead et al (1989) at 20 GHz - the eight observed fields in the OVRO ``NCP'' program; (c) Myers et al (1992) at 20 GHz - the 96 fields in the OVRO ``RING'' program, showing clear evidence of fluctuations which have been only partially identified with discrete sources (see text); (d) Meinhold & Lubin (1991) at 91 GHz - the ``South Pole'' results; (e) Gaier et al (1992 in preparation) - the 32.5-35 GHz channel from the December 1990-January 1991 observations. Double switching was used in (a), (b), and (c) and single switching in (d) and (e). No offsets or drifts have been subtracted in (b) and (c). |
In the likelihood ratio test the observed variance in the means for
each field is ascribed to the incoherent addition of the variance due
to the noise in the observations (as given by the errors on each
field) and the variance due to the sky noise (which we are trying to
estimate). In the case of the present data set, given the relatively
high values of the individual errors, the low scatter of the mean
values about zero can only be accommodated in this test by ascribing a
very low value to the sky variance. It is now understood that this
pitfall can be detected in the likelihood ratio test by considering
the power in addition to the size of the test
(Readhead et al 1989,
Bernstein et al 1989,
Vittorio & Muciaccia
1991).
In the Uson
and Wilkinson data set the likelihood ratio test has a power of only
0.13, which is very low. Analysis of the data set using the Bayesian
method yields a 95% confidence upper limit on anisotropy of T/T < 3.9 x 10-5
(Readhead et al 1989).