Annu. Rev. Astron. Astrophys. 1992. 30:
653-703 Copyright © 1993 by Annual Reviews. All rights reserved |
3.3.3
Boughn and Cottingham and their collaborators have made observations
on a series of balloon flights using a single conical horn antenna
equipped with a ruby maser operating at 19.2 GHz with a bandwidth of
400 MHz
(Cottingham 1987,
Boughn et al 1990,
1991,
1992).
The aim was to have a 3° beam,
which would have required a 3 meter horn at this frequency - far too
long for the required stability against wind on a balloon. The horn
was therefore shortened to 0.9 meter and equipped with a polyethylene
lens to flatten the wavefront. The antenna was rotated about the
vertical axis at 1.5 rpm, and scanned a circle at constant zenith
angle of 45°. A major objective of this program was to obtain
an actual map of a large area of the sky. This dictated the
single horn configuration, and the system was Dicke switched between
the sky and a 4.3 K cold load. In dual-beam systems many linear drift
terms can be eliminated to high precision with difference
measurements, but these are not suitable for making actual images. In
the present case, accurate sky maps were obtained, but the data first
had to be corrected for offsets of ~ 0.1K and drifts of the order
of 50 mk/hr. The response of the maser across the 400 MHz band varied
by over 10dB and the effective bandpass was 210 MHz.
The first flight of the instrument was in May, 1986, from Palestine,
Texas
(Cottingham 1987).
In these observations the Dicke switch
frequency was 8 Hz. The resulting sky map was sufficiently sensitive
(1.5 mK per 3 x 3° beam) to place the limit on
anisotropy on scales from 3-25° given in
Table 4.
This instrument has since been flown on another flight from Palestine,
Texas, and two flights from Alice Springs, Australia
(Boughn et al 1990).
The data from the Alice Springs flights are not yet fully
analyzed, but the data from the two Palestine flights have been
analyzed (see
Boughn et al. 1991,
1992).
Boughn et al calculated a model of the expected Galactic contribution
from synchrotron radiation based on the 408 MHz map of
Haslam et al (1982).
In portions of the sky where they could compare this Galactic
model with their observations they agreed only to within a factor two,
which was probably due to a combination of systematic errors and
spectral index variations over the frequency range 0.4-19 GHz.
They subtracted the mean level and best-fit dipole and their
calculated Galactic model from the data, and analyzed the residuals.
In view of the quantity of data it was not easy to apply the
likelihood ratio test in the usual way.
Boughn et al (1991)
have therefore adopted an alternative approach in which they simulate the
experiment plus the model they are testing in the following manner.
They first assume a specific model which is described by the
correlation function C() of
the temperature, T, of the
microwave background radiation. They define a statistic, S', given by:
where i and j are the
actual measurement errors for the different fields in their
observations, C'() is the
correlation function convolved with
the antenna beam pattern and (ij) is the angular
separation of the positions corresponding to Ti and
Tj. The
statistic S' is not identical to the likelihood ratio
statistic, S, but it is used in a similar way. A Monte Carlo
analysis is used to generate the distribution of S' based on
the distribution of the Ti given by C(). They then vary
the value of the rms temperature fluctuations and so determine the
distribution of S' for different levels of fluctuation. They
next calculate the observed value of the statistic,
S'obs, given by Equation 9, where Ti,
Tj are now observed
temperatures after subtracting means and drift values. The value of
S'obs is then compared with the family of distributions
of S'. A confidence level, 1-,
is chosen and from
the family of S' distributions one then selects that
distribution, S', for
which the probability of a
greater value of S' is equal to . The rms
fluctuations corresponding to this distribution, Trms, provide the
upper bound which is sought.
Fluctuations with rms amplitude greater than Trms have a probability
< . We use ``''
because it is being used in the same way as the size in the
likelihood-ratio test.
Boughn et al use this method
not only to estimate upper limits on anisotropy as described in the
preceding paragraph based on the actual measurements of Ti and
Tj, but also
to calculate the expected level of observed T
fluctuations assuming that the rms variations due to the intrinsic
microwave background radiation fluctuations are zero. In this ``null
test'' the Ti
and Tj
generated in their Monte
Carlo tests are due to instrumental noise alone. The median value of
this distribution is then an estimate of the expected value of S' in the
absence of fluctuations, and this value is used in place
of S'obs to define the ``expected upper bound'' in the
absence of intrinsic fluctuations. Corresponding values of Trms are shown in
Figure 4a, together with the limits
based on the actual measurements. In these simulations they ran 100 or 200
Monte Carlo tests for the results shown in
Figure 4a, and in
Table 4, respectively. The scatter
in different runs indicates that the
uncertainties in these results due to the analysis statistics alone
are ~ 10% and 5%, respectively. They adopt two forms for
C(), or, equivalently, W(k)
- monochromatic and
Gaussian. Only the results for the Gaussian spectrum are given here.
As can be seen in Figure 4a, the
fluctuations in sky temperature
are significantly larger than expected from the noise level in these
observations. Thus it is clear that some anisotropy has been
detected. Boughn et al ascribe this to Galactic synchrotron emission
which has not been correctly accounted for based on the 408 MHz data
and the extrapolation to 19.2 GHz and therefore interpret their
observations in terms of upper limits, as shown in
Table 4.
Figure 4a. Limits
on the anisotropy set by
Boughn et al (1991)
at 19.2 GHz. The solid
line indicates the 95% confidence upper limit as determined in a test
similar to the likelihood ratio test, but using a slightly different
statistic, with a Monte Carlo simulation assuming a Gaussian form for
W(k) as described in the text. The dashed line indicates the level
of sensitivity of the observations determined by the same method, but
setting the fluctuations in the microwave background radiation to
zero. It is clear that fluctuations have been detected over the whole
range of angular scales from 1-30°. As in the case
of the Davies et al result
(Figure 3c), the detected
anisotropy
might all be due to Galactic synchrotron emission, but intrinsic
microwave background radiation fluctuations at a level of T/T
~ 10-5 cannot be ruled out.