3. Scientific Priorities for the Survey

The primary desiderata for the design of the FIRST survey were:

positional accuracy sufficient to achieve a large number of optical identifications with low chance coincidence rates;

sensitivity sufficient to probe populations below the break in the radio curve;

angular resolution sufficient to provide for morphological classification of sources and avoidance of source confusion in regions such as high redshift galaxy clusters which have an angular scale of .

We discuss each of these issues briefly here.

3.1. Source Positions

While considerable information on the source type and radiation mechanism of a radio emitter can be derived from observations of its radio morphology, spectrum, and polarization characteristics, optical observations are still required to establish the source's distance and to classify it unambiguously. Given the faint magnitudes of optical counterparts to radio sources at the mJy level - a identification rate is only achieved at (Kron, Koo, and Windhorst 1985) - and the high surface density of optical objects on the sky at these magnitudes ( ), accurate radio positions are required to obtain high reliability identifications with a low rate of chance coincidences. Figure 1 displays the false identification rate as a function of optical source density which led to the choice of the -configuration for the FIRST survey. At the POSS I limit of , 50%of the sky has a surface density in stars and galaxies of , producing a 25%false rate for the D-configuration survey. At the SDSS limit of , the entire FIRST survey region has a density objects , and the maximum surface density encountered is . This leads to a C-configuration false rate of and a D-configuration false rate of , but leaves the B-configuration rate at less than 8%. In addition, the fact that 55%of sources which will appear point-like in the D-configuration are, in fact, extended and/or multiple sources (see § 7.3) leads to an additional uncertainty in their positions and increased difficulty in finding optical counterparts. In § 7.1, we show that we have achieved the theoretical positional accuracy of using the B-configuration. In a subsequent paper, we demonstrate the practical implementation of an optical identification program for FIRST using the Cambridge/Institute of Astronomy APM scans of the POSS I plates (McMahon et al. 1995).

3.2. Flux Density Limit

Figure 2a presents the curve for radio sources observed at 20 cm (Condon 1984). At flux densities mJy, the radio population is dominated by active galactic nuclei (AGN) including radio galaxies, BL Lac objects, and radio-loud quasars. Below 3 mJy, however, the curve flattens substantially, indicating the presence of a new population. Several authors (Windhorst et al. 1985; Oort 1987; and Thuan and Condon 1987) have identified this new component with moderate redshift star-forming galaxies. In Figure 2b, we show the expected contributions of these two principal source classes as a function of limiting flux density (Condon 1984). At the FIRST threshold, we will detect AGN and over 250,000 star-forming galaxies. § 9 lists some of the scientific advances we can expect with such massive samples in hand.

3.3. Source Morphology

Radio sources exhibit a wide range of morphological types which provide clues to the source class, emission mechanism, and properties of the surrounding medium. Among high Galactic latitude sources, stars, radio pulsars, and many AGN such as BL Lac objects, OVV quasars, and, in general, flat and inverted spectrum sources, are point-like at a resolution of a few arcseconds. Other AGN, from nearby low-power radio galaxies to distant quasars, display jets, halos, and large-scale radio lobes. When these objects are found in dense cluster environments, the lobes are often distorted by the motion of the parent galaxy through the intracluster medium, producing head-tail sources (Owen et al. 1979). Distant sources may be distorted into arcs of emission by gravitational focusing from foreground clusters (Soucail 1991). The thermal emission detected from star-forming galaxies may be highly concentrated in a nuclear starburst, or spread more generally throughout the galactic disk. Finally, the physical clustering of sources in galaxy groups, clusters, and larger scale structures can present a source confusion problem more severe than that determined from consideration of the alone. For the final adopted parameters of the FIRST survey, we reach a source surface density of sources with resolution elements , a factor of 100 removed from the confusion limit.

The high angular resolution which allows detailed morphological studies, our optical-quality astrometry, and FIRST's faint flux density threshold has a concomitant price: some of the flux from extended sources will be resolved out, leading to 1) a survey threshold that is a function of source size, and 2) the systematic underestimate of extended source flux densities. The magnitude of these effects depends on the intrinsic size distribution for the sources of interest. Windhorst et al. (1990) have examined the size distribution of faint radio sources by collecting data from all of the major 1.4 GHz surveys, and deriving expressions for the mean angular size as a function of flux density, as well as the integral angular size distribution function. They find

where is the fraction of sources larger than angular size , and the median angular size at flux density is given by

where is measured in mJy at 1.4 GHz.

As shown in § 7, the fraction of the flux density from a Gaussian source resolved out by the B configuration is only 3%at FWHM, 16%at , and 23%at . However, CLEAN bias (also discussed in § 7) is a larger problem for extended sources, and must be included in a calculation of the fraction of sources that will be missing from any FIRST catalog as a result of resolution effects. In Table 1, we tabulate the values of , , and for flux density levels ranging from 30 mJy (the limit of the best existing centimetric catalog) to 1 mJy; is the angular size at which, owing to CLEAN bias and resolution effects, a source falls below our search algorithm's peak flux density threshold of 0.75 mJy.

These estimates suggest we will miss of sources with integrated flux densities between 5 and 50 mJy, and one third of all sources between 1 and 5 mJy. However, this estimate is too pessimistic for several reasons. First, using a peak-flux search algorithm to find extended sources on maps optimized for point source sensitivity (e.g., made using natural weighting) is far from the optimal strategy for finding extended objects; indeed, as we show in § 7.2, a much larger fraction of faint sources actually appear in our maps. Secondly, the numbers in the table have been calculated from experiments which insert Gaussian sources of various sizes into our raw UV data and then determine what fraction of the true flux density is recovered in the maps. Real extended objects, however, often have bright, compact features which will raise the peak flux density in the map above our threshold.

The VLA A-configuration observations of the Westerbork LBDS sources (Oort et al. 1987; Oort 1988) demonstrate this latter effect. A total of 145 sources with integrated flux densities mJy at 20 cm as detected with the Westerbork beam were observed at the VLA; 14 of the larger objects were resolved into multiple components. After accounting for CLEAN bias and resolution effects, and imposing a 0.75 mJy peak flux density threshold, we would detect all but 20 of the 166 components. We would miss of those between 1 and 2 mJy, of sources from 2 to 5 mJy, and only 1 of the 82 sources brighter than 5 mJy. This is consistent with the comparison of our images with a VLA deep survey of the same region which we present in § 7.2.