David Monet a)
A Catalog of Astrometric Standards
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.
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.
To enable rapid access of specific stars in the catalog,
numbers each star using its colatitude zone (0000 to 1725 by 75) and an
eight-digit star number within each zone, separated by a decimal point.
sua2 lists A2.0 stars by
number or sky region.
imua2 lists the A2.0 stars
within an IRAF or FITS image with a world coordinate system defined in its
If you have a very fat pipe, this catalog is available via anonymous ftp
ftp://ftp.nofs.navy.mil/pub/outgoing/usnoa/. To use the
catalog with the WCSTools programs
immua2, you need only
download the .cat files for the right ascension zones in which
you are interested.
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
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.)
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 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 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,
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.
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.
- 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.
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.
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.
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.
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.
[SAO UAC Programs]
[A2.0 at USNO]