Sources which appear in more than one grid image (multiply observed sources) have been used extensively for image quality control ([BWH95]). In our earlier paper, we demonstrated that source positions, flux densities, and morphologies are reproducible from image to image. In general, source positions down to the survey threshold were found to be internally consistent to better than 1" (90% confidence). For brighter sources (flux density > 5 mJy) fitted source sizes were self-consistent to better than 0."5. Flux densities for point sources were also found to be highly reproducible and, when corrected for CLEAN bias as described above, gave results consistent with a deep VLA pointing which fell within the survey area. Below, we present new information on the accuracy of catalog parameters, concluding with a summary of the uncertainties which should be adopted when utilizing the FIRST catalog.
The utility of the high quality astrometry we infer from the multiply
observed source analysis is dependent on tying FIRST positions to an
absolute reference frame. The best set of radio astrometric standards
currently available are the MERLIN calibrators (Patnaik, private
communication). In our original paper, we reported a mean offset for
46 objects which fell within our initial 300 
of
. However, the MERLIN calibrators were originally
chosen to be bright and predominantly point-like at 3.7 cm. Closer
examination reveals that a significant fraction of these objects are
extended and/or have complex morphologies in the 20 cm FIRST images. Of
the 115 MERLIN calibrators which fall within the current survey area,
79 have measured extents of 
and are the only component
within their HAPPY island. Employing only these objects in the
comparison eliminates all but one object
with a discrepancy
of 
(Fig. 4); the mean offsets in RA and Dec
are 
and 
,
respectively. The RMS position error for this set of 79 bright,
point-like sources is 0."22, and there are no systematic trends
with RA or Dec with an amplitude as large as 0."1.
Figure:
Differences between FIRST positions and MERLIN astrometric calibration
standard positions. The FIRST positions show excellent astrometric
accuracy with no signs of any systematic offsets compared to the MERLIN
standards.
[Johnston et al. 1995] have recently published a definitive sample of 436
extragalactic radio source position calibrators with positional
accuracies of better than 0."003 in both coordinates. Twenty-eight
of these sources lie within the FIRST coverage region and 24 have FIRST
sizes of 
, only 9 of which are in the MERLIN sample. For
this independent set of calibrators, we find mean offsets in RA and Dec
of 
and 
, respectively, and an RMS position
offset of 
. Thus, we are confident that the FIRST positions
are tied to the radio reference frame with a systematic uncertainty of
, and that systematic position errors are 
throughout the survey region.
The linkage between the radio and optical reference frames has been the subject of considerable recent research ([Argue et al. 1984]; [Lindegren & Kovalevsky 1995]; [Johnston et al. 1995] and references therein). We will discuss an empirical comparison of FIRST sources to the APM POSS-I plate scan positions in a subsequent paper ([McMahon et al. 1996]). As we have found a number of systematic discrepancies at the subarcsecond level when comparing FIRST sources to a variety of plate-scan catalogs, we advise workers requiring this level of accuracy to investigate empirically any systematic differences which may be present. We also caution stellar radio astronomers that the possibility of significant proper motions must be considered when searching for stellar counterparts to FIRST sources ([Becker et al. 1996]).
As noted in [BWH95], the multiply observed sources demonstrate
that our procedures to determine source sizes are consistent from image
to image. Figure 5 displays the distribution of major
axis values for all 138,665 sources in the catalog. Over 29,000 of the
sources are larger than the 5."4 beam size and are clearly
resolved. For comparison, this figure also shows the expected
distribution based on the flux-dependent model of 1.4 GHz source sizes
from [Windhorst et al. 1990] (see § 6 for the details of
this model.) The observed FIRST size distribution is in reasonably
good agreement with the model; the discrepancy at larger sizes is due
to double sources that appear in our catalog as two smaller components
rather than as a single extended object. Pairs of objects separated by
have been merged in the [Windhorst et al. 1990] distribution.
Figure:
Solid: Cumulative distribution of major axis FWHM values for all
138,665 sources in the FIRST source catalog. Dashed: distribution
expected from the Windhorst et al. (1990) flux-dependent size
distribution. The discrepancy at larger sizes is
due to double sources that appear in the FIRST catalog as two
smaller components rather than as a single extended object.
All extended sources are represented in the catalog as one or more elliptical Gaussians; in some cases this may not provide a high-fidelity representation of the complete source morphology, but in most instances such a representation is adequate. Figure 6 displays an example of a pair of complex sources. The left panel is the FIRST survey image, while the right panel shows the Gaussian representation of these sources as they appear in the FIRST catalog. The Gaussian deconvolution does an excellent job of capturing the morphology of these complex sources, including the bent-double morphology of the southeastern source and the peculiar ring-like morphology of the brighter object. From this and other examples we have examined, a computer vision approach could probably be used to select such objects directly from the catalog. However, certain detailed features, such as the slight asymmetry of the southernmost lobe, could only be revealed through visual inspection of the original images.
Figure:
Comparison of a FIRST image (left) with the elliptical Gaussian model
from the FIRST catalog (right) for two complex sources. The field is
centered at RA = 
, Dec =
(2000). The catalog contains 6
components, two for the bent double and four for the ring-like object.
While not a perfect model for this complex source, the catalog
components clearly give a very useful, high-fidelity representation of
the objects.
Large extended and complex sources such as those discussed above make up a relatively small fraction of the total catalog. A larger fraction is comprised of sources having measured sizes between 1" and 5" after deconvolution of the 5."4 restoring beam. Both for purposes of deriving radio source statistics and for optical identification programs, it is important to determine the degree to which the sizes and position angles of the fitted ellipses for these sources reflect the true underlying source morphology. To investigate this, we have utilized the A-configuration snapshot survey of unresolved Green Bank 6 cm radio sources brighter than 50 mJy carried out by Lehar (1991; hereafter [L91]) as part of a search for gravitational lenses. Contour plots were generated for each of the 178 sources from that project which fell within the FIRST survey region and a detailed comparison of source positions, extents, and orientations was carried out. Despite the wide disparity in observing frequency (20 cm vs. 3.6 cm) and spatial frequency sensitivity (the maximum baseline was 9 times greater as measured in wavelengths for the Lehar survey), this clearly demonstrates that the FIRST catalog can accurately describe structure on scales smaller than the 5."4 beam.
Eighty-one of the 178 sources are listed as point-like in
[L91]. We find that 52 of these are, indeed, isolated objects
substantially smaller than our beam, and we use them to determine
empirically the limit to which we can resolve source structure (the
other 29 [L91] point sources are the cores of complex radio
sources with total angular extents in our maps of 0.'2 to
2' and are not useful for this purpose). Of the 52 isolated
point sources, 44 have measured major axes 
(51 of 52 have
minor axes in this range), and all but three are smaller than 1."8.
The sources with the three largest measured sizes all show evidence of
a core-jet morphology, and it is likely that the steeper spectrum
extended emission is undetected in the [L91] high-frequency
maps; i.e., the indications of extent in the FIRST images are probably
real. Thus, in all future work, we will adopt a major axis upper limit
of 2."0 as defining the point-source population of the FIRST
catalog.
Of the remaining 92 objects for which high resolution maps are available, 15 are classified as faint or undetected in [L91]. We find that all of these correspond to extended components of complex sources, and have simply been resolved out in the 3.6 cm observations. For the other 77 objects, [L91] presents maps with a resolution of 0."24 which reveal a host of complex source morphologies; detailed comparison of these with the corresponding FIRST images allows us to assess further the utility of our catalog's morphological parameters at size scales smaller than 10".
Most of these objects exhibit the classical double-lobe radio source
structure with or without a core component; the remainder can be best
described as having core-jet morphologies. In 57 of the 77 cases, the
FIRST sizes as determined from our component fitting are within 25% of
the extents measured in the high frequency images which have twenty
times the resolution. In most of the remaining cases, the FIRST sizes
are somewhat larger, most likely reflecting the presence of additional
steep-spectrum extended emission which is undetected in the 3.6 cm
maps. In addition, the FIRST position angles provide an excellent
indication of source orientations: in 31 of 34 cases with linearly
aligned components displaying a maximum extent of 
, the
FIRST position angle differs from that of the resolved linear structure
by 
. This excellent agreement of source extent and
orientation extends down to sizes of 2". Our ability to extract
accurate morphological parameters down to this size scale both provides
another confirmation of FIRST map fidelity and assures that efficient
optical identification programs can be carried out for both point-like
and extended objects.
In [BWH95] there was an extensive discussion of FIRST's
photometric accuracy based on internal comparisons using multiply
observed sources and external comparisons using a few previously
published deep VLA pointings. In § 4.3, we have
updated our understanding of the `CLEAN bias', an effect that appears
to reduce the peak flux density of all sources in the FIRST catalog by
mJy/beam. Here, we extend our evaluation of FIRST
photometric accuracy by comparing FIRST flux densities to the NRAO VLA
Sky Survey (NVSS; [Condon et al. 1994]). which is also now being carried
out using the VLA at a wavelength of 20 cm. At the current time, there
is an overlap of 
between the two surveys in the
RA range 
- 
.
The primary difficulty in comparing flux densities between the NVSS and FIRST surveys is the factor of 8 difference in angular resolution (5."4 vs. 45" FWHM). The high resolution FIRST survey will partially resolve extended sources that appear point-like in the NVSS, so the flux density of extended sources will be smaller in FIRST than in the NVSS. On the other hand, the NVSS will fail to resolve distinct sources closer together than 50", further confusing the comparison between the two surveys. To eliminate this latter effect, we restrict the comparison to isolated FIRST sources whose nearest neighbor in the FIRST catalog is at least 100" distant. This reduces the number of sources common to the two surveys to 7,318.
In Figure 7 we plot the ratio of the flux densities from
the two surveys as a function of the source major axis FWHM as measured
by NVSS. For the smallest sources in the survey ( FWHM),
the mean ratio is 
. This includes corrections for CLEAN
bias of 0.25 and 0.40 mJy/beam for FIRST and NVSS respectively. The
mean in each bin was calculated by weighting each of the source pairs
according to the noise in the ratio, with the noise parameters taken
from this paper for FIRST and from the 1995 August 16 draft of the NVSS
source catalog description (ftp://gibbon.cv.nrao.edu/pub/nvss/catalog.ps).
As expected at the outset of the survey, FIRST partially resolves
sources much larger than our 5."4 beam and underestimates their
flux densities.
Many (perhaps most) extended NVSS sources are resolved into several components by FIRST, with the total flux lost from the sum of the components being less than would be lost from a single, very extended Gaussian component. Such multi-component matches are precluded in this comparison by our requirement that the FIRST source be isolated. As a result, for a randomly selected NVSS source having a given size, Figure 7 represents an upper limit for the amount of flux lost in the FIRST catalog. On the other hand, this distribution should accurately describe the flux lost from each FIRST component as a function of the component extent.
Figure:
Mean ratio of the FIRST flux density to the NVSS flux density as a
function of NVSS source size for 7,318 isolated sources in the FIRST
catalog. The excellent agreement for small sizes indicates agreement
in the FIRST and NVSS flux calibration scales. The arrows show the
median sizes for 1 mJy and 30 mJy sources (Windhorst et al. 1990). The
dashed line is a model fit: 
, where
the size 
is measured in arcseconds. The great majority of
sources in the FIRST catalog have lost little flux due to overresolution.
In Figure 8 we display a scatter plot comparing the FIRST and NVSS flux densities source by source for objects that appear to be point sources in both surveys. Over three orders of magnitude, the flux scales of the two surveys are in superb agreement.
Figure:
Comparison of FIRST flux densities with NVSS flux densities for point
sources. Both flux densities have been corrected for CLEAN bias. The
flux scales agree very well over 3 orders of magnitude in brightness.
Combining the results of [BWH95] and the work presented above, we recommend the following uncertainties be adopted in utilizing the FIRST catalog:
Source flux densities --
The uncertainty in the peak flux density 
is given by the rms
noise 
at the source position (col. 5). The CLEAN bias for
extended sources has been under-estimated in noisy fields
(§ 4.3) and may vary due to other effects, so the
true noise in may be larger than . The uncertainty in
the integrated flux density 
can be considerably greater depending
on the source size and morphology; for sources not well-described by
our elliptical Gaussian model, can either be under- or
over-estimated. For bright sources, the accuracy of the flux density
determinations are limited by 
systematic effects. (These are
due to a combination of many effects, including small calibration
errors, uncertainties in the primary beam correction factor, mismatches
between the Gaussian model and the actual source shape, etc. 5% is
a conservative estimate; the actual errors are smaller for most sources.)
Analysis
of multiply observed sources has revealed that in a few percent of all
fields, systematic flux calibration errors produce a larger offset in
the flux scale. As these fields are reobserved, the coadded images
which contain them will be replaced; a current list of names of
questionable fields can be found on the FIRST homepage.
Source positions --
Point sources at the detection limit of the catalog have positions
accurate to better than 
at 90% confidence. An empirical
expression for the positional accuracy at 90% confidence is 
arcsec, where 
is the
beam size, is either the
major or minor axis FWHM as given in the catalog, and SNR is the peak
flux density signal-to-noise ratio given by 
. The uncertainty is elliptical for elliptical sources. The
limit on positional accuracy for bright sources is 
,
which is 
% of the synthesized beam FWHM B.
Systematic astrometric errors are less than 
.
Source sizes --
Uncertainties depend on both the brightness and the intrinsic source
extent. Nearly unresolved objects at the catalog flux density limit
have uncertainties of about 
(i.e., faint objects with quoted
major axes of or less are consistent with point sources).
Larger objects have somewhat more accurate sizes. An
empirical estimate of the uncertainty as a function of flux density and
size is
where 
is the RMS
uncertainty in the fitted size 
. Flux on
scales larger than 
is largely resolved out by these
B-configuration observations (Fig. 7).
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