***Really Important Stuff***
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***The Rest Of The Stuff***
A Catalog of Astrometric Standards
David Monet a)
Alan Bird a), Blaise Canzian a), Conard Dahn a), Harry Guetter a), Hugh Harris a), Arne Henden b), Stephen Levine a), Chris Luginbuhl a), Alice K. B. Monet a), Albert Rhodes a), Betty Riepe a), Steve Sell a), Ron Stone a), Fred Vrba a), Richard Walker a)
a) U.S. Naval Observatory Flagstaff Station (USNOFS)
b) Universities Space Research Association (USRA) stationed at USNOFS.
============== Abstract =======================
USNO-A2.0 is a catalog of 526,280,881 stars, and is based on a re-reduction of the Precision Measuring Machine (PMM) scans that were the basis for the USNO-A1.0 catalog. The major difference between A2.0 and A1.0 is that A1.0 used the Guide Star Catalog (Lasker et al. 1986) as its reference frame whereas A2.0 uses the ICRF as realized by the USNO ACT catalog (Urban et al. 1997).
A2.0 presents right ascension and declination (J2000, epoch of the mean of the blue and red plate) and the blue and red magnitude for each star. Usage of the ACT catalog as well as usage of new astrometric and photometric reduction algorithms should provide improved astrometry (mostly in the reduction of systematic errors) and improved photometry (because the brightest stars on each plate had B and V magnitudes measured by the Tycho experiment on the Hipparcos satellite). The basic format of the catalog and its compilation is the same as for A1.0, and most users should be able to migrate to this newer version with minimal effort.
This file contains a discussion of the differences between A1.0 and A2.0, and those points not discussed remain unchanged. For convenience, the documents circulated with the A1.0 catalog are included in this distribution.
================= Discussion =========================
1. REFERENCE FRAME
USNO-A2.0 has adopted the ICRS as its reference frame, and uses the ACT catalog (Urban et al. 1997) for its astrometric reference catalog. The Hipparcos satellite established the ICRS at optical wavelengths, but stars in the Hipparcos catalog are saturated on deep Schmidt survey plates as are the brighter Tycho catalog stars. Fortunately, the fainter Tycho stars have measurable images, so each survey plate can be directly tied to the ICRS without an intermediate astrometric reference frame. The proper motions contained in the ACT catalog are more accurate than those in the Tycho catalog, so the ACT was adopted as the reference catalog. USNO-A1.0 use the Guide Star Catalog v1.1 as its astrometric reference catalog, and the availability of the ACT was the driving force behind the compilation of USNO-A2.0.
2. STAR NAMES
USNO-A2.0 continues the policy established for USNO-A1.0 of not assigning an arbitrary name to each object. Without explicit star names, the IAU recommendation is to use the coordinates for the name. Since USNO-A2.0 contains a complete astrometric rereduction, the coordinates of objects are not the same, so the names for USNO-A1.0 stars are NOT PRESERVED in USNO-A2.0. If you need a name for a star, you can use either the coordinates or the zone and offset so long as you are careful to cite USNO-A2.0 as the source.
(If anybody has a clever solution to the problem of star names that does not waste lots of space or CPU cycles, please let me know.)
3. PHOTOMETRIC CALIBRATION
The Tycho catalog provides B and V magnitudes for its stars. USNO-A2.0 uses these and Henden's photometric conversion tables between (B,V) and (O+E+J+F) to set the bright end of the photometric calibration for each plate. This is an improvement over USNO-A1.0.
Unfortunately, GSPC-II and other large catalogs of faint photometric standards are not available, so the faint end of the photometric calibration came from the USNO CCD parallax fields in the North, and from the Yale Southern Proper Motion CCD calibration fields (van Altena et al. 1998) for fields near the South Galactic pole. Hence, the faint photometric calibration of USNO-A2.0 may not be any better than for USNO-A1.0. Sorry. When better sources of faint photometric calibration data become available, new versions of USNO-A will be compiled.
A new algorithm for doing computing the photometric calibration.
a) Since there are 300 or more ACT(==Tycho) stars on each plate, the computed J+F+O+E magnitude for each star can be computed from B+V. Given the relatively poor nature of this conversion, subtleties of the various photometric systems were ignored. Please remember that all Tycho stars are toasted on deep Schmidt plates, and we were lucky that PMM could compute decent positions and brightnesses for any of them. Four solutions were done (O+E+J+F) which fit an offset for each plate and a common slope for all plates. For example, there were 825 free parameters in the solution for the 824 POSS-I O plates, 824 offsets and 1 slope. This solution isn't quite as good as fitting individual slopes for "good" plates, but is much more stable than fitting individual slopes for "bad" plates.
b) There are 215 POSS fields and 42 SERC/ESO fields with faint faint photometric standards. Again, the ensemble of plates was divided into 4 solutions (O+E+J+F), and the fit allowed an offset for each plate but a common value for the linear and the quadratic term. For example, there were 217 free parameters in the POSS-I O plate solution, 215 offsets, 1 slope, and 1 quadratic term. Again, this offers stability at the expense of accuracy on the "good" plates.
c) A number of iterative solutions for using the calibrated plates to calibrate the rest were tried, and most failed. Finally, a stable solution was found. For each of the 4 sets of plates, the faint zero points were fit as a function of the bright zero points. Using this relationship, the faint zero points for all plates were computed. (We chose to use the fit instead of the individual solutions for those plates which had the faint photometric standards.) Note that this relationship provided the fifth (and final) parameter for the photometric calibration (i. e., bright offset, bright slope, faint offset, faint slope, faint quadratic).
Once the coefficients were known for all plates, the overlap zones on adjacent plates were used to smooth the solution over the whole sky. In an iterative scheme, the faint mean error for each plate was computed from all stars in common with other plates, and then the faint offset was adjusted after all the mean errors were computed. This algorithm converged in 3 or 4 iterations, and makes the plate-to-plate photometry as uniform as possible given the paucity of faint standards.
d) No vignetting function was used.
4. ASTROMETRIC CALIBRATION
A startling result of the comparison between PMM and ACT is that decent astrometry can be done on stars as bright as about 11th magnitude. Visually, these images have spikes and ghosts, and are not the sort of images commonly associated with the word "astrometry". Since there are 300 or more ACT stars on a single Schmidt plate, each plate can be tied directly to the reference catalog without an intermediate coordinate system. This solution includes corrections for systematic errors in the focal plane and for magnitude equation, and these are discussed below. It should be emphasized that the raw measures are the same for USNO-A2.0 and USNO-A1.0, and the difference is in how these are combined to produce the coordinates found in the catalog.
a) Schmidt telescopes have field-dependent astrometric errors, and these must be sensed and removed. Because there are hundreds of reference stars on each plate, the algorithm used was as follows. Data from the exposure log are used to do the transformation from mean to apparent to observed to tangent plane coordinates using the relevant routines from Pat Wallace's SLALIB package. The first set of solutions finds the best cubic solution between the PMM measures (corrected for the known Schmidt telescope pin cushion distortion) and the predicted positions. Once an ensemble of these solutions have been done, the residuals are accumulated in 5mm by by 5mm boxes of position on the plate. By combining the residuals from hundreds of plates, the systematic pattern can be determined with good precision. The second step is to repeat the cubic fit between predicted and observed positions after correcting the observed positions using the pattern determined in the first step. Examination of the systematic pattern produced by the second step indicated that there was a small residual pattern that arose from the interdependence of the fixed pattern and the cubic polynomial fit. A third iteration was done, and the resulting systematic pattern was consistent with random noise.
The iterative process of determining the systematic pattern of astrometric distortions was done separately for each telescope in each color, and intermediate solutions based on zones of declination were examined for the effects of gravitational deflection. None were found, so the final patterns were determined through the co-addition of all plates taken by a particular telescope in a particular color. Hence, USNO-A2.0 uses 4 specific patterns instead of the single mean pattern used for USNO-A1.0.
b) Inspection of the astrometric residuals from high declination fields (where the overlop between plates is large) showed that there was a significant radial pattern. This, and the analysis of the residuals from the UJ reductions for the USNO-B catalog, suggested that magnitude equation was present. This is hardly a surprise because the images of Tycho stars show spikes, ghosts, and other problems whereas the faint stars show relatively clean images. The effect is small to non-existent within a radius of ~2.2 degrees of the center, and then rises to 1.0 arcsecond at ~3.0 degrees and continues to rise into the corners. The effect is more or less the same for the POSS-I O, POSS-I E, and SERC-J plates, but a different behavior was seen for the ESO-R plates. The source of this different behavior is not understood, and may indicate a software problem associated with the different size of the ESO plates (300x300 mm vs 14x14 in).
The analysis of the UJ plates (like POSS-II J except with a 3 minute exposure) shows a similar behavior when the Tycho stars are subdivided into bins of <9, 9, 10, 11, and 12 magnitude. Since the nominal difference between UJ and POSS-I is something like 4 magnitudes, the effect was assumed to be zero for stars fainter than 15 and rises linearly until it becomes the same for all stars brighter than 11. This is an empirical correction, and more work needs to be done to verify its behavior.
5. NUMERICAL REFOCUS
The most common mode for the PMM to mis-measure a plate is that it does not determine the distance between the camera and the plate accurately. The PMM starts by using the granularity of the emulsion as a signal for setting the focus (i.e., minimum background smoothness), and then does 15 exposures separated by 0.5 millimeters to compute the actual pixels per millimeter. In many cases, this algorithm is not sufficient, and the raw scans have relatively large astrometric errors, and show a sawtooth pattern in the residuals.
Since PMM saves many more data than are contained in this catalog, it is possible to refocus the plate after the scan. To do this, the known positions of the ACT stars are fit as a function of the new Z distance between the camera and the plate. Minimization of these residuals indicates what the proper focus should have been, and then the entire set of raw measures are corrected for this effect. In general, this processed tightens the histogram of the number of plates as a function of the astrometric error. The good scans are unaffected but the bad scans get better. This algorithm has been applied to all plates used in USNO-A2.0.
6. EPOCH OF COORDINATES
In USNO-A1.0, the coordinates were computed from the positions measured on the blue plate (O or J), so they were J2000 at the epoch of the blue plate. For USNO-A2.0, we believe that the uncertainties in the positions are no longer dominated by systematic errors, so it makes sense to average the blue and red positions. Hence, USNO-A2.0 coordinates are J2000 at the epoch of the mean of the blue and red exposure. For POSS-I plates, this difference is trivial because the plates were taken on the same night. For SERC-J and ESO-R, there can be a significant epoch difference between the blue and red plate, and stars with small proper motions will be affected. Note that stars with large proper motions will be selectively deleted from the SERC-J+ESO-R portion of the sky because they will fail the test of blue and red positions within a 2 arcsec radius, and that this omission depends on the epoch difference of the plates for the individual fields.
7. MULTIPLE ENTRIES
We have done our best to remove multiple entries of the same star, but they still remain. The improved astrometric reduction decreased the number of stars in the catalog by about 0.8% (about 4 million stars), but this reduction is masked by the increase in the number of stars associated with moving the north/south transition from about -33 degrees to about -17.5 degrees. In the north/south overlap zone, double entries are generated for stars with large proper motions since if they were detected in each survey separately but moved far enough to escape the double detection removal algorithm. There shouldn't be too many of these, but they may be obvious because they are statistically brighter than the typical catalog entry.
8. BRIGHT STARS
Images for stars brighter than about 11th magnitude are so difficult to measure that their computed positions may differ with the correct position by more than the 2 arcsecond coincidence radius used in the reductions. For really bright stars, all that appears are an ensemble of spurious detections associated with diffraction spikes, halos, and ghosts. To make USNO-A2.0 a useful catalog, bright stars were inserted into it so that the catalog is a better representation of the optical sky. For may applications, it is better to know that a bright star is nearby than it is to insist that the poorly measured objects be deleted from the catalog. In compiling USNO-A2.0, a list of all ACT stars that were correlated with PMM detections was kept. For these stars, USNO-A2.0 contains the PMM position, not the ACT position, and the flag bit is set to indicate the correlation. In the compilation process, all uncorrelated ACT stars were inserted into the catalog using the ACT coordinates. However, ACT is not complete at the bright end because it omits stars with low astrometric quality. Hence, a final pass inserted all Tycho stars that do not appear in the ACT catalog at the Tycho position. According to the documents published with the Tycho catalog, every effort was made to make it complete at the bright end, even for stars with low astrometric quality.
Note that one should not use the coordinates of ACT and Tycho stars presented in USNO-A2.0 for critical applications. ACT stars appear at the epoch of the plate, but because the proper motions for the non-ACT Tycho stars are unreliable, these stars appear at the epoch of the Tycho catalog.
9. PRETTY PICTURES
The all-sky pretty pictures generated from USNO-A2.0 used an algorithm to reduce the over-density of southern stars that arises from the fainter limiting magnitudes of the SERC-J and ESO-R plates. This was done by using a random number generator and omitting the star if the random number was less than 0.45. That is to say, the southern over-density is not quite a factor of 2 more objects per unit area than found from the northern surveys. Again, all objects are in USNO-A2.0 and the over-density was removed to make the pretty pictures.
11. SOURCE CODE
As with USNO-A1.0, we have published the source code for all computations and for all calibration. The compilation code is in ALPHA13.TAR in the directories ./newbin/procN. The code for the numerical refocus is in NEWBIN.TAR ./newbin/newz0 and for the fixed pattern removal in ./newbin/tycho2xtaff.
The code is published as a service to those who wish to understand USNO-A2.0 and not so that we can be ripped off. Please respect the intellectual property rights contained in the source code, and do not make us wake up the lawyers.
Enjoy! If you use USNO-A2.0 for neat stuff, drop me an e-mail.