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).