THE ASTRONOMICAL JOURNAL, 117:2895-2901, 1999 June
© 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE SECOND CAPE PHOTOGRAPHIC CATALOGUE ON THE HIPPARCOS SYSTEM

N. ZACHARIAS AND M. I. ZACHARIAS1
US Naval Observatory, 3450 Massachusetts Avenue, NW, Washington, DC 20392

AND
C. DE VEGT
Hamburger Sternwarte, University of Hamburg, Gojenbergsweg 112, D-21029 Hamburg, Germany

Received 1999 February 1; accepted 1999 March 5

ABSTRACT

The Second Cape Photographic Catalogue (CPC2) is an astrometric, photographic catalog covering the entire Southern Hemisphere to a limiting magnitude of about 10.5. The Hipparcos Catalogue has been used for a new, plate-by-plate, rigorous reduction. A significant improvement over the release 1 version of the data was achieved. With an average accuracy of 53 mas and a mean epoch of 1968, the CPC2 is a key catalog for proper-motion determination. This release 2 of the CPC2 contains high-quality positions of 266,629 stars and an appendix of 8040 other stars. Catalog reduction and construction details are given, as well as a description of the final product, which is available from the US Naval Observatory.

Key words: astrometry—catalogs

     1 Also Universities Space Research Association, Washington, DC.

1. INTRODUCTION

     The Second Cape Photographic Catalogue (CPC2) is an astrometric survey based on 5687 plates taken at the Cape Observatory during the time period from 1962 to 1973, with a mean epoch of 1968. Positions for a total of 274,669 stars in the V magnitude range of about 6 to 10.5 are given in this catalog. The first release of the CPC2 (de Vegt et al. 1993; Zacharias et al. 1992) was based on the Southern Reference Star (SRS) Catalog (Smith et al. 1990). This second release is based on the Hipparcos Catalogue (ESA 1997), with greatly improved precision, accuracy, and density of reference stars to reduce the plate data. First results from this rigorous new reduction have been presented already (Zacharias, de Vegt, & Murray 1997a), and a summary of these reductions with implications for proper-motion determination was given elsewhere (Zacharias et al. 1999). This paper describes the final product, which is available from the US Naval Observatory.2

     A further refinement in the plate reductions, a block adjustment (Eichhorn 1960) of the data, is planned. The block adjustment of the CPC2 data is expected to improve the catalog only slightly (Zacharias 1992) over the current version. The major improvement is the step from using transit circle reference-star data to Hipparcos, even in a conventional plate adjustment. In order to serve the astronomical community, it was decided to release this CPC2 version now.

     With its high accuracy and weighted mean epoch almost midway between that of the Astrographic Catalogue (AC, Urban et al. 1998) and the Tycho Catalogue (ESA 1997), the CPC2 is an important catalog for proper-motion determination of stars in the 9–11 mag range in the Southern Hemisphere. In the past, the CPC2 was a major contributor for the Hipparcos Input Catalogue (INCA, Turon et al. 1992), as well as for the compiled astrometric catalogs ACRS (Corbin & Urban 1992) and PPM (Röser & Bastian 1993).

     2 See http://aries.usno.navy.mil/ad/ad.html.

2. OBSERVATIONS

     For details about the project history, the reader is referred to the papers mentioned in § 1. A short summary is given here. The project was started in the early 1960s using a new four-component lens of 200 mm aperture, a plate scale of 100&arcsec; mm-1 and a field size of 4&fdg;07. The plates were taken in declination zones, starting with the -40° to -52° zone (the original AC Cape zone), taken in 1962–1963. In 1966 the observations continued with the -30° to -40° zone, followed by the remaining zones of the Southern Hemisphere. Observations were completed in 1973. The plates were taken in a fourfold overlap pattern. Two exposures of usually 3 minutes' duration were taken on each plate; thus, there is normally a total of eight images for each star and even more for stars close to the pole, where plates overlap more than average. The astrometric limiting magnitude is about 10.5. Contrary to earlier photographic surveys, a visual-red spectral bandpass (530–640 nm) was used with the benefit of reduced refraction effects due to Earth's atmosphere. The magnitudes given in the first and this CPC2 release are photographic magnitudes in that spectral bandpass, and thus between V and R, with an estimated error of 0.1 to 0.3 mag. Magnitudes of about 4.0 or brighter are doubtful. Stars of magnitude 6.0 or brighter are affected by the proximity of the images of the two exposures per plate. All plates were measured on the GALAXY machine (Nicholson 1979) at the Royal Greenwich Observatory (RGO), concluding in 1984. The measurements were transferred to Hamburg Observatory for astrometric reductions (release 1). The data later went to the US Naval Observatory, where the present catalog was constructed.

3. REDUCTIONS

3.1. Reference Stars and (x, y)-Data

     Only the 50,629 Hipparcos stars flagged as "good" astrometric (blank field H10 = reference flag for astrometry in the Hipparcos Catalogue) within the area covered by the CPC2 plates have been used. Of these, 50,569 could be uniquely matched with the (x, y)-data and were used as reference stars. The mean standard error of a Hipparcos star position at the mean epoch of the CPC2 data is about 30 mas per coordinate. Because of the large plate size (4&fdg;07), an average of 40 Hipparcos stars could be utilized per plate, while 13 and 88 were the smallest and largest numbers, respectively.

     The mean precision of the (x, y)-measurements is 113 mas (1.13 μm) per image and coordinate (global internal error; see also Zacharias et al. 1992). As with the release 1 data, here the two exposures per plate have been combined using a linear transformation model, prior to any further reductions. In the following we refer to this as the "single" image (position), meaning coming from a single plate as opposed to a mean position derived from several plates. Thus the precision of these single images is about 113/ ≈ 80 mas per coordinate, neglecting correlations between the images.

3.2. Basic Conventional Plate Adjustment

     Initially an eight-parameter plate model was used, which includes linear and plate-tilt terms for the mapping model of the tangential coordinates to the (x, y)-data. Weights were used in the least-squares adjustment, derived from the individual formal position errors of the Hipparcos stars at the epoch of the plate plus the assumed uncertainty in the (x, y)-measures (80 mas per coordinate). A 3 σ criterion was used to reject outliers. If the σ of the adjustment exceeded 1.5 times the expected value, the largest residual was removed and the reduction repeated. Rigorous apparent place and refraction routines were used for the reference stars prior to a projection onto the tangential plane. After adjustment, all photographic positions were back-transformed into mean places.

3.3. Initial Distortion Correction

     First, systematic errors as a function of the (x, y)-coordinates have been investigated, using the residuals of the preliminary reduction with the basic model (see above). In a pilot investigation, the third-order optical distortion term was determined to be approximately 40 mas deg-3. Corrections for this term were applied to the (x, y)-data prior to the following reductions. Next, using an eight-parameter model (linear and tilt terms), all residuals were binned as a function of the x- and y-coordinates, resulting in a field distortion pattern (FDP), which has been published elsewhere (Zacharias et al. 1997a). This new FDP looks almost identical to the one derived from CPC2 release 1 data, based on SRS reference stars (Zacharias 1995). The quadratic mean correction due to the field distortions is 0.4 and 0.35 μm for the x- and y-coordinates, respectively. Thus these corrections are orders of magnitude smaller than for typical Schmidt plates. The final FDP was generated by slightly smoothing and interpolating the original FDP, a grid of 17 × 17 residual vectors. Using a lookup table by coordinates, the FDP was applied to the raw (x, y)-data prior to the following reduction steps.

3.4. Magnitude-dependent Systematic Errors

     Next, systematic errors as a function of magnitude were investigated. Magnitude equations in the CPC2 data strongly depend on the declination zone. With the use of Hipparcos reference stars, the systematic errors in the (x, y)-data are more clearly seen; however, the overall pattern is the same as was already found in the CPC2 release 1 data (for detailed plots see Zacharias et al. 1992, 1997a). Tests were also made using a plate model including linear magnitude terms, thus allowing these systematic errors to be solved on a plate-by-plate basis. However, even with the large number of reference stars available, the formal errors on the determined parameters degraded unacceptably without clear benefit, so a zonal correction method was adopted instead. For all zones, a linear correction of the coordinates as a function of magnitude was found to be sufficient. Slope coefficients, (sx, sy), were obtained from linear fits through the plots of residuals versus magnitude for each declination zone. New, corrected coordinates (xcor, ycor) were obtained from uncorrected (x, y)-data by applying the following transformation:



with all (x, y)-coordinates measured in milliarcseconds, where m is the CPC2 photographic magnitude (between V and R) of a given star and m0 is the mean photographic magnitude of a given sample (usually around 8.3 mag). Residuals from a conventional plate adjustment, with the magnitude equation corrected, still showed some systematics. Empirically, the previously obtained slope parameters were scaled by factors (about 1.5) and the process iterated until the systematic error was fully corrected. The final coefficients for all corrections of the (x, y)-data as a function of magnitude are given in Table 1.

TABLE 1     MAGNITUDE EQUATION, COMA, AND COLOR TERMS

     After solving for the pure magnitude equation, residuals were plotted versus the product of Δmag and the coordinates (as measured from the center of the plate). Systematic errors were detected, which are called coma terms. An example plot is given elsewhere (Zacharias et al. 1997a). Corrections were applied to the (x, y)-data according to



The coefficients for coma corrections, cx and cy, are also given in Table 1. Again, (xcor, ycor) and (x, y) are in milliarcseconds; however, x' and y' are in degrees. Coma terms are significant in this investigation using the Hipparcos stars, although they were not in the CPC2 release 1 reductions, because of inferior reference-star data. Applying the corrections for magnitude and coma terms did not improve the individual plate reduction σ by much (a few percent); however, systematic errors up to about 100 mas could be removed this way.

3.5. Final Distortion Correction

     After corrections for magnitude-dependent systematic errors were completed, the FDP was investigated again. Now slight differences were found as a function of the declination zone. The data were split into three areas, the Cape zone, with plate centers in the range -40° to -52°, the -29° to -39° zone, and the remaining zones. For each area an individual FDP was generated and applied in the same way as described above. After two iterations, the remaining FDP essentially vanished.

3.6. Color Terms

     Finally, systematic errors depending on the colors of the stars have been investigated, using the B-V color index from the Hipparcos Catalogue. Only for parts of the third area (outside the -29° to -52° zones) were these errors found to be significant, and corrections were applied according to



for the 0° to -28° zones, where (B-V)0 is the mean color index for a given sample. Corrections needed to be applied only for the y-coordinate; the ly parameters are also given in Table 1. In addition, a small offset of 20 mas (instead of a linear function) was applied to the y-coordinate for the -69° to -90° zone for -1.0 ≤ B-V ≤ 0.2. In order to be able to apply these corrections also to the field star positions, the Tycho B-V values were used. Virtually all CPC2 stars are included in the Tycho Catalogue (ESA 1997).

3.7. Final Plate Solution

     The (x, y)-data were corrected for an average third-order optical distortion term, field distortion pattern, and magnitude, coma, and color terms, as described above. Rigorous refraction and apparent place routines were applied. A nine-parameter plate model, with six linear (a to f), two tilt (p, q), and one distortion (D) parameter, was used in a weighted least-squares adjustment for each plate individually:



Here (ξ, η) are standard coordinates and (x, y) are the measured coordinates, while r2 stands for x2 + y2. The distortion parameter D gives corrections to the average third-order optical distortion on a plate-by-plate basis. Including this parameter was found to be necessary because of a significant variation from plate to plate. The large number of available reference stars per plate made this approach feasible. The mean adjustment error was found to be 88 mas, which is the quadratic sum of the mean reference-star precision at the epoch of the plates and the mean (x, y) measuring precision. Figures 1 to 3 show the residuals in x and y plotted versus magnitude, coma, and color, respectively, for the data of the entire catalog. A total of 209,000 residuals per coordinate were used, excluding individual residuals larger than 500 mas. Instead of (x, y)-components, the residual vectors can also be split up into radial and tangential components. Figure 4 shows the radial residuals versus radius. The data are well corrected out to the edge of the plates. The tangential residual distribution looks very similar. All those systematic errors are corrected to within about 10 mas. Taking quadratic means of individual residuals gives a measure for σx and σy, which are plotted versus plate epoch in Figure 5. The early epoch data have a slightly larger random error than do the later epoch data, likely to be caused by the greater epoch difference of that zone from the central Hipparcos epoch (1991.25).


FIG. 1.—Residuals in x and y for the entire catalog vs. magnitude. One dot is the mean over 200 individual residuals.



FIG. 2.—Residuals in x and y for the entire catalog vs. the product of magnitude and coordinate (coma term). One dot is the mean over 200 individual residuals.



FIG. 3.—Residuals in x and y for the entire catalog vs. color index. One dot is the mean over 200 individual residuals.



FIG. 4.—Radial residuals vs. radius (distance from plate center). One dot is the mean over 200 individual residuals.



FIG. 5.—Mean quadratic residuals vs. plate epoch. One dot is the mean over 200 individual residuals.


3.8. Mean Positions

     The individual photographic positions from the plate-by-plate solution as described above have been combined to mean catalog positions as follows: Weights for each individual image coordinate were calculated based on the assumed mean measuring precision and the error propagation contribution due to the plate parameter uncertainties (Eichhorn & Williams 1963). The correlation of star positions from overlapping plates due to a subset of common reference stars has been neglected here. Then a weighted mean position and mean epoch were calculated, with outliers excluded. For stars with only one individual position, the error calculated in the weighting procedure was used, so it is always only slightly larger than 80 mas, the assumed (x, y) measuring precision.

4. THE CATALOG

     The final catalog of the CPC2 release 2 is presented in two parts. Both parts are sorted by declination. The main catalog contains 266,629 stars with at least two images per star and a formal position error of 53 mas on average, with a cutoff of 200 mas per coordinate on individual stars. As an appendix, the second part contains an additional 8040 stars. Those are the stars with a formal error exceeding 200 mas in one or the other coordinate, as well as all the single-image stars. The formal errors on the single-image stars might be grossly wrong. A total of 1462 stars that were included in the release 1 catalog have been entirely dropped in this release, because of unresolved problems, showing a formal error of 500 mas or larger in at least one coordinate. Matching of individual images has been taken over from the original work made at RGO, and no problem case study was made with this investigation. Also, the photometry given in release 2 was retained from release 1; however, magnitudes are now rounded to to better indicate the precision of these photographic magnitudes. Magnitudes less than about 4.0 are doubtful. CPC2 positions and magnitudes of stars brighter than about 6th magnitude in general have to be taken with caution because of overexposure effects on the plates.

     The precision of the CPC2 catalog is a function of magnitude, which is illustrated in Figure 6, showing the results for the main part of this release. Figure 7 shows the distribution of the catalog precision. Table 2 gives an example of the catalog data, both parts being in the same format. Table 3 explains this format. All entries are integer, and all columns are separated by at least one blank. Note that, instead of the declination, the always positive south polar distance (SPD) is given, which equals the declination plus 90°.


FIG. 6.—Precision (standard error) of positions in the final main catalog as a function of magnitude. The number of stars in each magnitude bin is indicated.



FIG. 7.—Distribution of positional precision of the CPC2 release 2 main catalog.


TABLE 2     EXAMPLE OF THE CATALOG FORMAT, SHOWING THE FIRST AND LAST 10 LINESOF THE MAIN CATALOG AND APPENDIX

TABLE 3     CATALOG FORMAT EXPLANATIONS

5. CONCLUSIONS

     The CPC2 data have been brought successfully onto the Hipparcos system by a completely new reduction based on first principles. Remaining systematic errors are believed to be at the 10 mas level or below. The high accuracy and density of the Hipparcos Catalogue as compared with the previously used reference-star catalog allowed for a much more detailed study of systematic errors in the (x, y)-data. The propagation of errors from the adjustment parameters to the field star positions is also significantly reduced in this release 2 as compared with release 1, resulting in smaller random errors. However, major systematic errors, such as the FDP and magnitude terms, were found to be essentially unchanged between the two releases.

     The released data constitute an observational position catalog without proper motions. Because of its high accuracy and intermediate epoch, the CPC2 is essential for proper-motion determinations in the Southern Hemisphere when combined with other data such as the AC (Urban et al. 1998) and the UCAC-S (Gauss et al. 1996; Zacharias, Germain, & Rafferty 1997b). As a result of its fourfold overlap, the CPC2 data are most suitable for a rigorous block adjustment, which will further improve the precision and accuracy of the catalog, though only slightly over the version presented here.

     We are grateful to the Cape Observatory and Royal Greenwich Observatory staff, who observed and measured the data on which this catalog is based. We also like to thank T. E. Corbin, S. E. Urban, and the referee for useful comments on the paper.

REFERENCES