3 The APM Catalog

1 Introduction

It has been almost 50 years since the National Geographic Society-Palomar Observatory Sky Survey (POSS) was carried out (1949 to 1958) using the $48^{\prime\prime}$ Oschin Schmidt at Palomar Observatory (Harrington 1952; Minkowski and Abell 1963; Lund and Dixon 1973). Since a second-epoch Palomar Survey is underway, the original POSS is now usually referred to as the first-epoch POSS or POSS-I to differentiate it from POSS-II (Reid et al. 1991). The survey covers the 31,000 deg$^2$ of sky north of $\delta\sim-33^\circ$ with 6.4$\times$6.4 degree plates in two colors: blue ($O$), centered at $\sim4100$ Å covering the range between 4900 Å and the atmospheric cutoff at $\sim$3300, and red ($E$), a 600 Å wide band centered at $\sim$6500 Å. Plots of the POSS-I bandpasses compared with the standard Johnson photometric system can be seen in Evans (1989). The nearest Johnson system bands to O and E are B and R respectively. We provide color equations for these bands in section 3.3.

Between 1991 and 1995, the SERC Automated Plate Measuring Machine (APM) at the Institute for Astronomy, Cambridge (Kibblewhite et al. 1984) was used to digitize these plates at a resolution of 7.5 microns per pixel (0.5"), the highest spatial resolution yet applied to these images (McMahon and Irwin 1992). An object catalog has been constructed from these data which includes all objects down to the plate limits -- $\sim$20.0 in $E$ and $\sim$21.5 in $O$ -- and contains approximately 2000 stars and 2000 galaxies deg$^{-2}$ at high Galactic latitudes. The catalog contains positions, magnitudes, morphological classification parameters, major and minor axes, and isophotal areas for each source; a merged catalog which matches objects between plates also contains a color (or an upper limit thereto) for each entry. An automated classification algorithm interprets the morphological parameters to classify each object. Here, we present the basic procedures which establish the astrometric and photometric calibration of the APM catalog, and discuss the limits of the image classification system.

2 APM Astrometry

The APM machine measures the $x$ and $y$ positions of all objects detected. The conversion relationship between these measured APM positions and celestial coordinates is derived by matching stars in the Tycho-ACT catalog (Hog et al. 1997; Urban, Corbin & Wycoff 1998) with stars detected on each plate using a `standard' six plate-constant model that allows for shift, rotation, scale, and shear. The algorithm uses iterative $2.5\sigma$ clipping to give a robust fit; the typical rms on the fitted positions of the Tycho stars are $0.4^{\prime\prime}$- $0.8^{\prime\prime}$.

Irwin (1994) has studied the two-dimensional systematic errors in an earlier version of the APM catalog positions by investigating the intraplate residuals between the measured positions for bright stars in the Positions and Proper Motions Catalog (Roser and Bastian 1991) and the astrometric fit. He found significant, systematic residuals ranging up to $0.5^{\prime\prime}$. In the version of the APM catalogue used herein, the astrometric analysis uses the more recent ACT catalog (Urban, Corbin & Wycoff 1998).

A residual map generated from this analysis is applied to positions in the standard APM catalog available at http://www.ast.cam.ac.uk/~apmcat. We discuss below (§ 4) the significant improvement in overall astrometric accuracy that can be derived from a comparison of radio source counterparts in the APM with FIRST survey source positions.

3 APM Photometry

The APM measures photographic density rather than flux; moreover, the central regions of all objects more than a factor of $\sim$10 brighter than the sky produce a nonlinear response and/or are saturated. The algorithms used to overcome these inherent difficulties are discussed in detail by Irwin (1985). Briefly, a local background is determined for each of $\sim$500000 locations on each plate by producing a histogram of the pixel values in 64 $\times$ 64-pixel regions ( $32^{\prime\prime} \times 32^{\prime\prime}$) and finding the mode of each distribution; two-dimensional smoothing is applied to these half million background estimates to derive a background model for the plate. The image detection algorithm then finds connected regions of pixels above a threshold level (typically $2\sigma$ above the estimated background level for the given plate position). This background-following technique has the advantage that faint objects lying in the halos of bright objects can be detected. However, large objects such as bright stars and galaxies with angular extents $>30^{\prime\prime}$ have their raw fluxes underestimated. An additional problem for large images is that the limited memory available to the software means that bright objects sometimes overflow the pixel buffers and are lost. This occurs for images with sizes greater than roughly 1-2 mm (i.e., 1-$2^{\prime}$), corresponding to stellar magnitudes brighter than $\sim 9.0$.

Another inherent problem arises in attempting to derive magnitude estimates for extended objects from saturated images. Saturation effects can be corrected for in stars by assuming that stellar images have an intrinsic density profile independent of magnitude, and that this profile can be derived from the unsaturated parts of stellar profiles. A high signal-to-noise intrinsic profile is constructed by taking the core from faint stars and the wings from brighter stars (see Bunclark & Irwin (1983) for further details). This profile can then be integrated and used to derive a calibration curve to convert saturated stellar magnitudes to a linear system. In the APM catalog, this calibration is applied to all images. This has the unfortunate consequence that galaxies, which have shallower surface brightness profiles and lower central surface brightnesses than stars of the same total magnitude, will have their magnitudes over-corrected. This is a fundamental problem for galaxy photometry determined from photographic sky survey plates (see Metcalfe, Fong, and Shanks (1995) for a discussion).

The basic APM catalog is defined to have a red-band ($E$) plate limit of $m({\rm R_e})=20.0$. This limit was established during the early stages ($\sim$1991) of the creation of the APM catalog via comparison with $\sim$10 photometric sequences (Evans 1989; Humphreys et al. 1991). Similarly, a single slope of 1.10, was assumed in converting between the linearized APM magnitudes (Bunclark & Irwin 1983) and the $\alpha$ Lyrae-based Johnson magnitude system. It was noted at the time that there were significant deviations ($\sim$1 mag) from a simple linear relation at magnitudes brighter than $\sim$15. This is not surprising bearing in mind that the POSS-I glass plates measured by the APM are copies that may have different degrees of saturation and have had their contrast stretched to enhance faint features. The assumption of a constant flux limit seemed reasonable, since the plates were all taken in similar dark sky observing conditions with exposure times that were adjusted to ensure uniform sensitivity. A similar assumption is made in all modern photographic cameras where it is assumed that all photographic film has the specified speed. The blue band ($O$) limit was defined with respect to the red limit; for the 428 fields available in March 1999, this has a range of $m(\rm B_o$)=20.6-21.3 ($\pm$1$\sigma$).

Eventually, a full photometric recalibration of the APM using the Guide Star Photometric Catalog (GSPC - Postman et al. 1998a) CCD sequences is planned. Preliminary comparisons with CCD photometry for $\sim5$% of the POSS-I plates show that the APM magnitudes for stellar objects have a global rms uncertainty of 0.5 magnitudes over the range 16 to 20, the range in which most FIRST counterparts lie. As discussed above, the uncertainties in the magnitudes of galaxies are more complex, since galaxies have a range of surface brightness distributions, and hence may have complex, partially saturated surface brightness profiles on the POSS-I plates. This is compounded by the range in calibration slopes observed. At faint magnitudes (18-20) where the image profiles are unsaturated, the APM magnitudes may be more reliable, but it is left to the reader to verify this where precise magnitudes are required. For many programs, a uniform set of magnitudes or uniform selection criteria are more critical.

It is also worth noting that almost 50 years has elapsed between the epochs of the POSS-I and FIRST surveys, so that optical variability is an additional uncertainty. Hook et al. (1994) have studied the long term variability of radio quiet quasars and found that over a rest-frame period of $\sim$10 years, a typical $m(B)=19$ quasar varies by 0.20 magnitudes (rms). The longer-term variability of FIRST optical counterparts could be studied via a comparison between the POSS-I plates and the POSS-II or UKST plates. A CCD investigation of the long-term variability of $\sim200$ quasars from the FIRST Bright Quasar Survey (White et al. 2000) is reported elsewhere (Helfand et al. 2001).

It is useful to be able to convert the magnitudes of the O and E bands to the nearest bands in the Johnson Vega-normalised magnitude system. Evans (1989) has found that over the color range 0.0 $<$ B$-$R $<$ 1.5,

$$R-E = (0.00\pm0.02) (B-R)$$ (1)

Thus one can assume;

$$R=E$$ (2)

Evans (1989) also found

$$O-E = (1.135\pm0.035) (B-R)$$ (3)

Thus we have;

$$B-R = 0.88(O-E)$$ (4)

Finally it follows from (1) and (3) that:

$$B = O-0.12(O-E)$$ (5)

Assuming central wavelengths of 4100Å and 6500Å and the Hayes and Latham (1975) calibration of Vega the monochromatic zero point of the O and E bands, i.e., the flux corresponding to a magnitude of zero, is 4550 Jy and 2980 Jy respectively. Caution is advised when using these conversions since the presence of emission lines in the O and E filters will effect the conversion.

4 Photometric Calibration Using APS

In an attempt to improve the APM photometric accuracy and uniformity, the APM magnitudes in regions covered by the FIRST survey were recalibrated plate-by-plate using magnitudes from the Minnesota Automated Plate Scanner POSS-I catalog (APS, Pennington et al. 1993) which are more uniform than the APM magnitudes because they were calibrated on a plate-by-plate basis. The APS catalog was created by scanning the same POSS-I plate material as the APM and so should be fully consistent with the APM since it has the same bandpasses, epoch, and so on.

An alternative approach would have been simply to use the APS catalog in place of the APM catalog to get optical counterparts for the FIRST sources. We preferred the APM catalog because the APS catalog is not complete over the POSS-I area and does not cover the southern sky at all, and because the APS catalog retains only sources that appear on both the red and blue plates, discarding a significant fraction ($\sim$40%) of the faint radio source counterparts near the plate limits. Analysis of the reliability of these single band detections is discussed in section 5.2 and shows that 92.7% of the blue-only matches within 1" are real, and 97.5% of the red-only matches within 1" are real matches.

We matched the entire FIRST catalog against the APS catalog, extracting all objects within $20^{\prime\prime}$ of each radio position, and then matched the resulting list of optical sources with the equivalent APM/FIRST match list. For each APM plate, we determined independent linear fits (zero-point and slope) for $E$ and $O$ that transform the APM magnitudes to the APS scale. The fit was based on APM/APS matches closer than $5^{\prime\prime}$ that are classified as stellar by the APS (which uses a different photometry method for non-stellar objects.)

For 8 of the 148 POSS-I plates covering the FIRST area, there were insufficient APS sources available to determine the photometric calibration because the corresponding plate was unavailable in the APS catalog. For those plates, we bootstrapped a photometric solution using APM sources in the overlapping regions of neighboring plates. The set of zero-points and slopes for all 148 plates is available on the FIRST website.

This calibration procedure substantially improves the APM photometry. This is clearly seen in the magnitude discrepancies for APM objects in the plate overlap regions, which provide two or more independent magnitude measurements per object. Figure 1 shows the distribution of APM magnitude differences before and after calibration; the rms scatter decreases from 0.45 to 0.30 magnitudes, and the scatter for bright sources is reduced by an even larger factor. Since the plate overlap regions lie at the extreme edges of the POSS-I plates, they are probably the worst-calibrated areas on the plates; consequently, we estimate that the recalibrated APM magnitudes are accurate to better than $\sim$ 0.2 magnitudes rms.

Figure 2 shows that the principal problem with the APM magnitudes is a magnitude-dependent error. We display the differences between the mean calibrated $O$ and $E$ magnitudes and the original APM magnitudes as a function of magnitude. Both colors display a quasi-linear trend, with the total error varying by $\sim0.5$ magnitudes over an eight-magnitude span. While these curves have been derived from a small subset of all APM scans, it is likely that application of the corrections they imply will improve significantly the photometric accuracy of the catalog.

Figure 1: The accuracy of APM magnitudes as determined from a comparison of stellar objects taken from two different plates in the narrow overlap regions near the POSS-I plate edges. (a) Magnitude differences using the original APM magnitudes. The dashed line is a Gaussian with $\sigma =0.45$. (b) Magnitude differences after photometric calibration using the APS catalog. The dashed line is a Gaussian with $\sigma =0.30$. The recalibrated magnitudes are substantially improved.

Figure 2: The differences between the calibrated and raw APM magnitudes as a function of magnitude for the (a) $E$ and (b) $O$ plates derived from the 148 POSS-I plates covering the FIRST survey area.

5 APM Classification

The APM scans result in a parameterization of each detected image which includes an $x,y$ position, a peak intensity, a total isophotal intensity, second moments of the intensity distribution, and areal profiles (defined as the number of pixels above preset levels which increase by powers of two above the threshold level). In addition, a classification parameter is calculated which reports by how many sigma the object differs from the stellar point-spread function on each plate. The stellar psf is derived as a function of magnitude to take into account saturation effects.

These parameters are then used to classify all images into one of four categories: stellar (consistent with the magnitude- and position-dependent point spread function, cl$=-1$), non-stellar (a measurably extended source, cl=1), merged objects (sources with two local maxima within a single set of connected above-threshold pixels, cl=2), and noise (objects with nonphysical morphologies, cl=0).

For further details of the principles involved, see Maddox et al. (1991a,b). Very bright images can often be misclassified, since the limited set of parameters does not provide an adequate description and the background-following algorithm attempts to track over them in order to detect the faint images in the source halos. The merged/non-stellar boundary is not as reliable as the stellar/non-stellar boundary, so merged stars are often found in the non-stellar list (with a smaller number of galaxies in the merged list). Some objects classified as noise are real; objects found on both plates are the obvious examples. Objects classified as noise which match FIRST sources are also likely to be real, and we do not generally exclude these from our analysis.

Bright objects (e.g., $O, E < 13$) cover a large number of pixels in the APM scans and, as a consequence, magnitude and source-size estimates are very sensitive to small uncertainties in the plate sky level and details of the background-following algorithm; as a result, large uncertainties in the parameter estimations can result, and very bright sources can even be completely missing from the catalog. In addition, bright galaxies with complex surface brightness distributions can be broken up into a swarm of discrete sources. At fainter magnitudes, the limitations of the plate material make reliable separation of stellar and non-stellar sources problematic. Since our goal here is to determine the completeness and reliability for the catalog of radio source counterparts, we do not attempt a comprehensive analysis of the APM catalog's classification accuracy. Instead we perform several straightforward comparisons with existing catalogs of bright stars and bright galaxies and with CCD images which serve to characterize the APM completeness and reliability with respect to FIRST identifications.

6 APM Reliability at Bright Magnitudes

1 Galaxies

We have examined the DSS images, APM $O$- and $E$-plate catalogs, and FIRST images in the vicinity of 1000 entries in the UGC galaxy compilation (Nilson 1973). The UGC purports to be an angular-size limited sample for objects with blue diameters $>1^{\prime}$; it is complete for $V<14.5$, but includes entries down to $V=18$. This provides a direct measure of the completeness of our identification of FIRST sources with bright galaxies and the accuracy with which the galaxy parameters are reported in the APM catalog.

Of the 1000 UGC catalog entries, seven were found to have no galaxy brighter than $V=17$ within $3^{\prime}$ on the DSS. Another dozen entries had only very small-diameter objects ( $<20^{\prime\prime}$) in the vicinity, while three were extended, but very low surface brightness objects. Finally, in seventeen cases, there were two (and in one case three) galaxies of comparable brightness within 1-2$^{\prime}$ of the UGC position, and it was not possible without further investigation to distinguish which was the cataloged object.

In only 1 of the 1000 cases was no object present in the APM catalog, and that case corresponded to one of the extremely low-surface brightness galaxies; in virtually all cases, in fact, the UGC galaxy was detected on both plates. Over 275 of the 1000 UGC galaxies are detected in the FIRST catalog, and all of these correspond to objects in the APM source list. Thus, bright galaxies missing from the APM catalog are not a source of incompleteness in identifying FIRST counterparts.

Classifications, colors, and magnitudes for bright APM galaxies are, however, more problematic. First, for the reasons discussed above, colors and magnitudes for bright galaxies are at best estimates, and can be grossly in error for the brightest objects ($E<12$; see § 3.3). Second, of the 1000 UGC galaxies, 28 were classified as stellar on both plates; 26 were listed as stellar on the blue plate while correctly classified on the red, while 82 were classified as stellar on the red plate, but correctly identified as extended on the blue plate. Among the FIRST-detected galaxies, stellar misclassifications had a higher frequency by a factor of 2 to 3 ($\sim$ 20% in total), presumably because many of these radio detections represent galaxies with a bright active (stellar) nucleus.

For $\sim80$ galaxies, entries appear in both the $O$ and $E$ catalogs, but their centroids are sufficiently far apart that they are not identified as the same object, and so remain listed as separate objects (without measured colors) in the merged catalog. These are slightly over-represented among the radio detections, most likely as a result of the high radio-detected fraction of interacting/merging galaxies whose complicated surface brightness profiles confuse the source-finding algorithm. Finally, somewhat less than 4% of the UGC galaxies have size and shape parameters significantly discrepant from the images, either as a consequence of including a nearby star in the profile, breaking up a large galaxy into many components, or some other such error; these are also more common (6%) among the radio detections owing to the high fraction of interacting systems FIRST detects.

In summary, then, the APM catalog is $>99$% complete for bright galaxies in the sense that it contains at least one entry at the galaxy location, and in $\sim97\%$ of the cases, the object is classified as a galaxy on at least one of the two plates. The descriptions of the magnitudes, shapes, and colors of the optical objects, however, are subject to large errors, and should be checked by examination of the DSS and/or other catalog resources such as NED before they are used for purposes other than simple identifications.

2 Stars

As noted in the Introduction, the number of stars detected at centimeter wavelengths is small, and the number of quasars brighter than $E=14$ is even smaller. Thus, the completeness of the APM for bright stellar objects is not a major issue in the identification of FIRST counterparts. Nonetheless, for the record, we briefly comment on APM reliability and completeness for bright stellar objects.

Helfand et al. (1999) report on the detection of 21 radio stars in the FIRST region under discussion here with magnitudes in the range $1.6<V<14.1$. All but the three brightest objects ($V<4.5$) are recorded in the APM catalog, and more than half are classified as stellar on at least one plate. Since most true stellar identifications with radio sources are impossible without proper motion information, however, and the number of extragalactic bright stellar counterparts is vanishing small, any incompleteness at bright magnitudes for stellar objects in the APM catalog is largely irrelevant to FIRST source identification.

7 APM Reliability at Fainter Magnitudes

In order to assess the completeness and reliability of the APM counterparts list in the magnitude range $15<E<20$, we use statistics from work in progress to identify FIRST sources in the 16 deg$^2$ deep I-band imaging survey ($I<24$) of Postman et al. (1998b; see Helfand et al. 1998 for a preliminary report on this FIRST identification program).

A total of 345 counterparts to FIRST sources discovered in the I-band CCD data were selected for comparison with the APM catalog; this included all 323 objects with $I<20$ and the additional 22 stellar objects with $20<I<21$. All 123 objects with $I<18.0$ were detected on both plates and over 90% (75%) are correctly classified on the $E$ ($O$) plates. Over 93% of the 87 objects with $18<I<19$ were also detected on both plates, although the classifier performs somewhat less well, with 63% correctly classified on the $E$ plate. For $I>19$, more than 40% of the $I$-band objects are still detected on the $E$ and/or $O$ plates, of which half are correctly classified on the $E$ plate. This near to the plate limit, it is clearly difficult to distinguish between stellar and extended objects; nonetheless, only one of the 27 spectroscopically identified quasars with $17<I<21$ in this $I$-band field is misclassified as non-stellar on both plates. Similarly, we have found that fewer than 5% of the non-Seyfert quasi-stellar objects in the Veron-Cetty and Veron (1998) catalog with $R<18$ are mistakenly classified as galaxies on both plates (Gregg et al. 1996).

Using an APM magnitude-limited sample at $E<19.0$, we find that 62% of galaxies are classified correctly on both plates. An additional 28% are classified correctly on the $E$ plate and are at or below the plate limit on the $O$ plate, while another 4% are classified correctly in $O$ and incorrectly in $E$; only 6.5% are misclassified on both plates. For stellar images, the score is similar, with 14/26 correct on both plates and another seven classified correctly on one plate. In summary, for $E<19$, 92% of all objects are classified correctly on at least one plate.

As a further check on the incompleteness of the APM catalog, we have compared a subset of the database with the APS catalog of the POSS-I (Pennington et al. 1993). The APS catalog contains only objects detected on both plates, so it does not include the faintest APM objects which are often detected on only a single plate. This is nonetheless a very useful test of completeness and accuracy for the APM catalog, since the APS started with the same plate material but used completely independent scanning hardware and processing software.

The APS catalog test set contains 61,000 unique objects that match 71,000 different APM objects within a matching radius of 10"; the objects were drawn from areas on the plates within $20^{\prime\prime}$ of FIRST sources, and thus include both real radio source identifications and random background sources. There are 532 APS objects (0.9%) that have no matching APM source. Most of these are very near the catalog limit: 364 have $E>20$ or $O>21$, leaving only 168 (0.3%) that are reasonably bright. Checking the Digitized Sky Survey reveals that the great majority of these objects are blended with other nearby objects in the APM catalog (and usually classified as such), leading to poor agreement in the positions from the two catalogs. Furthermore, we should note that we have not examined the plates by eye at the locations of these ``missing'' sources, and some could be spurious APS entries which are legitimately absent in the APM catalog. Thus, the fraction of objects that is simply missing from the APM catalog above $E=20$ ($O=21$) is very small, certainly less than 0.1%.

Occasionally the positions measured by the APM on the $O$ and $E$ plates are sufficiently different that the red and blue detections are not recognized as being a single source and so two entries (one $E$-only and one $O$-only) appear in the APM catalog (§ 3.6.1). This can lead to incomplete radio source identification. In our APS test sample, there are $\sim730$ cases (1.2%) where a single APS source matches a close pair ($<10$") of $E$-only and $O$-only objects from the same APM plate. We consider these objects to be cases where a single source has been split into two catalog entries. The majority of these split objects are bright (Fig. 3) and are further examples of the complex and/or blended objects that occasionally caused trouble for the bright UGC galaxies discussed above. The median $E$ magnitude of these objects is 16.1; the fraction of such objects is $<1\%$ for the magnitude range 15-20 in which most radio counterparts are found.

Figure 3: The distribution as a function of APM $E$ magnitude of the fraction of objects that appear in the APM catalog as a pair of sources, one detected only on the $O$ plate and one detected only on the $E$ plate. These split objects are quite bright and are typically either large complex galaxies or close, blended objects. The fraction of such objects in the range of most FIRST identifications ($15<E<20$) is very low.