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The actual cross-correlations were done as follows: north of WGACAT was correlated with the GB6 catalog with a correlation radius
of one arc minute. The resulting sample, which included 1,119 sources, was
then correlated with the NORTH20CM, this time with a correlation radius of 3
arc minutes, as the positional uncertainties of the NORTH20CM catalog are
considerably worse than those of the GB6 catalog (160 arcsec at the 90%
level compared to 10-15 arcsec at the
level). This
produced a list of 570 sources, 262 of which are unclassified (see below for
details on the classification of WGACAT sources). The 6-20 cm spectral index
was then calculated and 89 sources turned out to have
and
.The total number of candidates in the south is still growing. The
correlation of WGACAT with the PMN catalog, with a correlation
radius of one arcmin, produced a list of 541 objects, 310 of which
are unclassified. Of these, 223 are at
and
(the PMN sample reaches
). So far, 103
have turned out to have
, but this number is
bound to increase with the analysis of our October 1997 ATCA observations
and the completion of the NVSS (almost complete as of October 1997).
To evaluate our completeness it is important to derive WGACAT positional
error circles. This was done as follows.
WGACAT was cross-correlated with the Hipparcos Input Catalog (see e.g.,
Torra & Turon 1985) and the offsets between the two databases were obtained
for 6 bins of
the distance from the WGACAT field center (0 - 10 arcmin, 10 - 20 arcmin
etc.). One positional errors were then estimated by sorting the
offsets in ascending order and taking the value which included 68% of the
objects in the bin. These values, reported in Table 3, range from 13 arcsec
for the inner 10 arcmin of the PSPC field to 53 arcsec for the 50 - 60
arcmin ring.
Since the positional accuracy of radio catalogs decreases with flux, we
investigated the possibility that a one arcminute cross-correlation radius
might not be large enough at lower radio fluxes and/or large PSPC center
offsets.
We therefore cross-correlated WGACAT with the GB6 and PMN radio catalogs with a
1.5 arcmin radius. Total positional errors were derived by summing
in quadrature the X-ray and radio uncertainties, the latter obtained from
the GB6 catalog and from the PMN radio fluxes via the formulae given in the
PMN papers. The significance of the match was quantified by the
ratio between X-ray/radio offset and combined positional error. (Note that
1.5 arcmin is roughly equal to twice the combined X-ray and radio uncertainty
of a source with PSPC offset arcmin and radio flux
mJy.)
The results are as follows: for the WGACAT/PMN correlation, the number of
X-ray/radio matches using a correlation radius of 1.5 arcmin increases by
40%. Dividing the WGACAT sample in an inner (PSPC offset arcmin) and
outer (PSPC offset > 30 arcmin) region, there is a 38% increase in the
inner region and a 45% increase in the outer region. In the inner region most
of the increase is due to ``spurious'' associations, which we define for the
purpose of this experiment as those matches with ratio between offset and
positional error > 2. Of the 144 new sources, 104 are spurious,
with a net increase of ``good'' sources
. In the outer region, of
the 81 new sources, only 13 are spurious, so the number of good sources
increases by
. This simply reflects the fact that WGACAT sources
with larger offsets have larger positional uncertainties and ``real'' matches
can have X-ray/radio offsets larger than one arcmin. For the WGACAT/GB6
correlation, the results were slightly different: the increase is only 25%,
practically independent of WGACAT offset. The net increase of ``good'' matches
is only
in the inner region and
in the outer one. That
is, as the GB6 positions are better than the PMN ones, increasing the
correlation radius has a bigger effect on the WGACAT/PMN ``real'' matches than
it has on the WGACAT/GB6 matches.
As a result of this experiment, we then added to the WGACAT/PMN candidate list
the 29 unclassified sources obtained from the 1.5 arcmin correlation and
having PSPC offsets arcmin, ratio between X-ray/radio offset and
positional error
,
and
.
(Note that these WGACAT/PMN additional candidates all have relatively small
radio fluxes within a factor 2 of the PMN completeness limit.) By
comparison, only 5 of the additional GB6 sources with PSPC offset
arcmin derived from the correlation
with the larger radius had entries in the NORTH20CM catalog but all of them had
. This is easily explained: all these sources had
relatively large positional errors and therefore relatively small radio fluxes
(F(6 cm)
mJy). Therefore, only steep-spectrum radio sources
could have a 20 cm flux > 100 mJy, the limit of the NORTH20CM catalog.
In summary, based on the positional accuracy of both WGACAT and the radio
catalogs used to construct our candidate list, we expect our final sample
to be complete in terms of radio/X-ray correlations
to the radio flux limit for center offsets arcmin.
At present, these make up about 60% of our sources. At larger offsets, our
completeness limit will be at somewhat higher radio fluxes.
We have already mentioned the possibility that some of the X-ray/radio
associations are simply chance coincidences. From the number counts of
flat-spectrum radio sources (Condon 1984), we estimate that only about 20
4
objects in our sample are spurious X-ray/radio sources. Most of these will be
singled out because of their large value of the ratio between X-ray/radio
offset and positional error.