1974MNRAS.166..249P
Downloaded from https://academic.oup.com/mnras/article-abstract/166/2/249/2604754 by California Institute of Technology user on 20 May 2020
Mon. Not. R. astr. Soc.
(1974)
166,
249-257.
VARIATION
OF RADIO
SOURCE
COUNTS
WITH
DIRECTION,
FOR THE 3CR AND 4C SURVEYS
T.
J.
Pearson
(Communicated by M. S. Longair)
(Received
1973
September
19)
SUMMARY
In an investigation of variations with direction of the radio source counts
N
(S)
for the 3 CR and 4C surveys, no anisotropy has been found which is
not explicable in terms of random statistical differences between limited
samples of sources; in particular, there is no significant difference between
the slopes of the source counts in the northern
and southern galactic
hemispheres.
I.
INTRODUCTION
The counts of extragalactic radio sources have been studied extensively, as
they reflect both the geometry of the Universe and the spatial distribution of the
sources within it, although these two properties cannot be separately determined
from the source counts alone.
In
interpreting the counts it is usually assumed that
the sources are isotropically distributed in an isotropic metric, and it is important
to determine whether the source counts themselves support this assumption.
It
has been established (e.g. Ryle 1968; Longair 1971) that at high flux densities
(S
178
~
10-
2
6
W
m-
2
Hz-
1
)
the function N(S), the number of sources in unit solid
angle with flux density greater than
S,
does not agree with the predictions of any
isotropic cosmological model in which radio sources are distributed uniformly;
all such models predict that the logarithmic slope of the source counts
(3
=
-
d(log N)/d(log S)
should be less than 1·5, whereas
(3
is observed to be about 1·8. Recently, how-
ever, it has been suggested that
(3
varies with direction, and that the value of 1 ·8
is not typical of the whole sky.
Pauliny-Toth
&
Kellermann ( 1972) have found that in the NRAO survey at
5 GHz this ' anomalously ' large value of
(3
is confined to sources with steep
spectra
(a:>
o· 5, where
Soc
v-")
in the northern galactic hemisphere. Y ahil ( 1972)
has compared estimates of
(3
in the northern and southern galactic hemispheres
for two of the NRAO surveys, two Parkes surveys (at 2·7 GHz and 408 MHz)
and for the Third Cambridge survey (3CR, 178 MHz).
In
all cases he found, in
agreement with Pauliny-Toth
&
Kellermann, that
(3
is larger in the northern than
in the southern hemisphere, though the difference is not of great statistical signifi-
cance in most cases. Katgert
et
al.
(
1973) have suggested that there may be varia-
tions in
N(S)
on a scale of about
10
square degrees (1·4 GHz).
This paper describes a statistical investigation of variations in the shape of
N(S) and the value of
(3
between different parts of the 4C survey. This covers a
larger area than the NRAO surveys, and has a lower limiting flux density than the
©
Royal Astronomical Society
•
Provided by the NASA Astrophysics Data System
1974MNRAS.166..249P
Downloaded from https://academic.oup.com/mnras/article-abstract/166/2/249/2604754 by California Institute of Technology user on 20 May 2020
T.
J.
Pearson
Vol
166
3 CR and the Parkes surveys.
If,
therefore, the anisotropy detected in other surveys
is present at low frequencies and low flux densities, this analysis should detect and
locate it. For comparison, the methods have also been applied to the 3CR survey.
Section
2
describes the relevant details of the 3 CR and 4C catalogues, Section 3
the statistical methods used and Section 4 the results. In Section 5 some instru-
mental properties which might affect the results are considered, and the conclusions
are presented and discussed in Section
6.
2, THE SOURCE
CATALOGUES
The 3CR and 4C catalogues were both compiled from surveys made at
178
MHz.
3CR is complete for
S17s~
9 x
10-
26
W
m-
2
Hz-
1
,
and 4C for
S17s~
2·0
x
10-
26
W
m-2
Hz-1
(Table I).
Survey
3CR (Bennett 1962a)
4C (Pilkington
&
Scott
1965; Gower, Scott
&
Wills 1967)
TABLE
I
The source catalogues
Region of
completeness
o>
-so
-7°<0<80°
(1)
Limiting flux density
S17s
(10-
26
W
m-2
Hz-1)
9·0
2"0
9 · 7
(2)
Number of
sources with
lbl
~200
212
3161
153
(1) A number of small areas in which the sidelobes of bright sources raise the limiting
flux density have been excluded. These sources comprise about 3 per cent of the area
surveyed and contain 35 sources.
(2) For comparison with 3CR.
The 4C survey was made with an aperture-synthesis interferometer of spacing
469
A,
oriented east-west. The response of the interferometer varied with zenith
angle, and hence with declination; the small statistical corrections to the results
that this necessitates are discussed in Section 5.
·
Holden
(1966)
has investigated the isotropy of the 4C catalogue by comparing
the total numbers of sources in equal areas of the sky. There were no significant
departures from the expected Poisson distribution in areas of
25
deg
2
or more.
This result indicates that the
normalization
of the source counts does not vary
significantly with direction, but it does not exclude the possibility of small variations
in the
shape
of the curve
N(S),
in particular at high flux densities. The present
investigation, which is not concerned with normalization, is thus complementary
to Holden's, like that of Yahil
(1972).
Holden's result has been extended to lower flux densities (
0·2
<
S
1
7
s
<
1
x
10-
26
W
m'-
2
Hz-
1
) by Hughes
&
Longair
(1967)
who studied the original records of the
4C survey using the statistical method of Scheuer
(1957)
and Hewish
(1961).
They
found no evidence for variations of
N
on scales of
20
°
or more. Thus there is no
evidence for clustering of sources at
178
MHz at source densities comparable
with those considered by Katgert
et al.
(1973)
at
1·4
GHz.
©
Royal Astronomical Society • Provided by the NASA Astrophysics Data System