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\paperID{P2-7}	%% Corrected!
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\title{A Comparison of Large All-Sky Catalogs}

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\author{D.\ J.\ Mink, W.\ R.\ Brown, M.\ J.\ Kurtz}
\affil{Smithsonian Astrophysical Observatory, Cambridge, MA 02138}

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\contact{Doug Mink}
\email{dmink@cfa.harvard.edu}

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\paindex{Mink, D. J.}
\aindex{Brown, W. R.}
\aindex{Kurtz, M. J.}

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\authormark{Mink, Brown, \& Kurtz}

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\keywords{catalogs, world coordinate systems, image: astrometry}

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%			       Abstract
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\begin{abstract}          % Leave intact
% Accurate positions are needed to compare observations of objects made
% at various wavelengths, such as are to be found in the Virtual Observatory.
% New instruments for ground-based observing, such as multi-fiber spectrographs,
% also need very accurate positions for objects fainter than those already
% catalogued.  
Recent large catalogs have revolutionized our ability to do
astrometry with CCD images.  The recently published FITS World Coordinate
System standard has provided a standard way of parameterizing that
astrometry, and the WCSTools and SExtractor software packages allow the
automation of the ``plate-fitting" process.  
% As part of a survey to be conducted with one of these new spectrographs, we 
We have amassed 1728 15$\arcmin \times 30\arcmin$ CCD images of a portion of the northern sky.  After matching
image point sources to objects in each of the catalogs and fitting world
coordinate systems to them using the IMWCS program, we find mean residuals
between observed and catalog star positions of between 0$\farcs$09 and 0$\farcs$25 for the latest catalogs.
\end{abstract}

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%			      Main Body
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\section{Introduction}
In the last few years, several motivations for acquiring sub-arcsecond
astrometry of faint astronomical sources have arisen.  Surveys and studies
of specific objects at radio and X-ray wavelengths require exact
optical or infrared positions to identify optical counterparts.
Small aperture spectroscopes such as the 300-fiber MMT Hectospec
require input positions better than a half arcsecond.  The usual method
of acquiring positions for faint, uncatalogued objects is to match the
brighter stars in a CCD image to one of the deep catalogs which have
been developed over the past 20 years by the Space Telescope Science
Institute, the U.S. Naval Observatory, and the 2 Micron All Sky Survey.
Table 1 shows the history of those large catalogs.  At the same time,
standards and software for associating image pixels with sky positions
as world coordinate systems have been developed,
culminating in two papers (Greisen \& Calabretta 2002, Calabretta \& Greisen
2002) and a software package which utilizes Calabretta's WCSLIB with real images
(Mink 1997, Mink 1999, Mink 2002).

As more and more optical images were matched to catalogs, the question
of the accuracy of the positions of objects in the catalogs arose.
We set out to compare how well various catalogs fit a large set of
images.

\begin{table}
\begin{center}
\caption{Growing Astronomical Catalogs
\label{P2-7:T2.7-tbl-1}}
\scriptsize
\begin{tabular}{clcl}
\tableline
\tableline
Year &Catalog &Number of Sources &Reference\nl
\tableline
1989 &HST Guide Star Catalog (GSC I) &25,541,952 &Lasker et al. 1990 \nl
1996 &USNO-A1.0 Catalog &488,006,860 &Monet 1996 \nl
1998 &USNO-A2.0 Catalog &526,280,881 &Monet 1998 \nl
2001 &GSC II Catalog (2.2.01) &998,402,801 &McLean et al. 2000 \nl
2002 &USNO-B1.0 Catalog	&1,036,366,767 &Monet et al. 2003 \nl
2003 &2MASS Point Source Catalog &470,992,970 &Cutri et al. 2003 \nl
2003 &USNO UCAC2 Catalog &48,366,996 &Zacharias et al. 2000\nl
\tableline
\end{tabular}
\end{center}
\end{table}

\section{Data and Analysis}

As part of the CfA Century Survey of galaxies (Geller et al. 1997),
1728 15 by 30 arcminute CCD images of a portion of the northern sky
over the north galactic pole were taken as 216 exposures by the 8-detector,
one-degree-square MOSAIC camera (Muller et al. 1998) on the KPNO 0.9 m
telescope in 1998 December and 1999 January and processed as described
in Brown et al. 2001.  A correction was made for distortion across
the wide field and a world coordinate system was fit to objects in the images
found by SExtractor (Bertin \& Arnouts 1998) using WCSTools and the GSC-I
catalog.  The resulting image catalogs, with image coordinates and
approximate right ascension and declination, became the raw data for our study.

The uniformity of the images and the fact that they cover a portion of the
sky well away from the dense star fields of the galactic plane made them
ideal for automatic star matching.  Unix shell scripts written for
each catalog set up an initial FITS header for each of the 1728 images
with the center being the mean position of the objects found in that image.

The WCSTools imwcs program was then run on each image.  The IMWCS program
fits the same number of brightest catalog objects and brightest image
objects limited by whichever there were fewer of; with these wide field
images, the number of catalog objects in the field was usually the limit.
The IMWCS program fit all eight parameters of the FITS WCS tangent plane
projection to all of the catalog-image matches in the field.  The program
made three additional iterations per image following an intial fit.  The
second fit used the refined parameters which might have changed the
position and size of the catalog section to be matched.  In the two final
passes, the tolerance in the catalog-image match was reduced by half each
time to eliminate both bad matches and objects whose catalog positions did
not match their actual positions.  The goodness of a fit for an image is
judged by the mean radial offset between the position of the objects in
the image mapped to sky coordinates through the fit world coordinate
system and the catalog position of the closest object, which is almost
always within one arcsecond.

\section{Results}

The means of the individual image offsets were used to compare how well
each catalog matched the sky as captured by our 1728 CCD images.
The GSC-I was used as a baseline, despite the fact that
it matched 25 or more stars in only 353 of the 1728 images.  Figure 1
shows the distribution of mean Catalog-Image positions in arcseconds.
Table 2 shows how many catalog stars were found in each images as a range
and an average, how many catalog stars were fit to image stars, as a range
and an average for each catalog and the range of mean (Observed-Catalog)
radial offsets per image, and the mean and standard deviation of that
mean for the entire data set.

\begin{figure}
\epsscale{.50}
\plotone{P2-7_f1a.eps}
\plotone{P2-7_f1b.eps}

\plotone{P2-7_f1c.eps}
\plotone{P2-7_f1d.eps}

\plotone{P2-7_f1e.eps}
\plotone{P2-7_f1f.eps}
\caption{Distribution of image-catalog radial offsets.}
\label{P2.7-fig-1}
\end{figure}

\begin{table}[h]
\caption{Fits of Various Catalogs to 1728 Images.
\label{P2.7-tbl-3}}
\begin{center}\scriptsize
\begin{tabular}
{lcrrrrr}
\tableline
\tableline
Catalog &
\multicolumn{2}{c}{Catalog Stars} &
\multicolumn{2}{c}{Matches fit} &
\multicolumn{2}{c}{Image-Catalog (arcsec)} \nl
  &Range &Mean &Range &Mean &Range &Mean(Sigma) \nl
\tableline

GSC-I &26-61 &35.78 &25-64 &34.16 &0.168-0.654 &0.321(0.085) \nl
USNO-A2.0 &119-454 &258.52 &78-353 &189.10 &0.301-0.457 &0.368(0.024) \nl
GSC-II &90-752 &226.73 &87-378 &179.16 &0.123-0.343 &0.196(0.043) \nl
2MASS PSC &93-365 &171.06 &86-331 &153.26 &0.154-0.347 &0.220(0.024) \nl
B1.0/id=2 &136-1125 &586.50 &51-661 &418.47 &0.182-0.523 &0.267(0.030) \nl
B1.0/id=3 &136-957 &528.38 &62-653 &382.16 &0.181-0.479 &0.251(0.029) \nl
B1.0/id=4 &136-654 &365.13 &116-555 &309.98 &0.155-0.430 &0.223(0.023) \nl
B1.0/id=5 &109-409 &227.89 &98-375 &205.14 &0.136-0.326 &0.192(0.021) \nl
UCAC2 &40-72 &51.52 &40-69 &48.80 &0.054-0.159 &0.091(0.015) \nl
\tableline
\end{tabular}
\end{center}
\end{table}

The GSC-I based on plates from the 1980's does better than the USNO-A2.0
which is based on plates from the 1950's, probably
due to the motions of stars in the intervening years, though the shorter
exposures of the GSC-I may also have given better centers.  The more recent
GSC-II, 2MASS PSC, and USNO-B1.0 catalogs all are based on the Tycho-2
astrometric reference catalog (H\o g, et al. 2000), and give similar results.
When the USNO-B1.0 gave worse results than expected, it was filtered by
the number of plates (POSS I red and blue, POSS II red and blue, and N)
on which the object was found.  Thus the most recent catalogs all cluster
around 0$\farcs$2 mean offset.  Only 303 images were fit to the
recently-released UCAC2 catalog which covers our field,  but it is incomplete,
so the automatic matching algorithm does not work perfectly.  The mean offset
was 0$\farcs$1, tightly clustered as the standard deviation and Figure 1
show, half that of the other catalogs.  This shows that detector nonlinearity
is not an issue above 0$\farcs$1, at least for these CCDs, and
that there is room for improvement in the astrometry of current deep
all sky catalogs.

% Finally, we have a little acknowledgments section.

\acknowledgments

This project makes use of several publicly available catalogs.  The
2MASS PSC is from the Two Micron All Sky Survey,
a joint project of the University of Massachusetts and IPAC at Caltech,
funded by NASA and the NSF. The GSC-II is
a joint project of the Space Telescope Science Institute, operated by
AURA for NASA under contract NAS5-26555 and the Osservatorio Astronomico di Torino,
which is supported by the Italian Council for Research in Astronomy, with
additional support is provided by ESO, ST-ECF, the International GEMINI project,
and ESA's Astrophysics Division. 
The GSC-I was produced at the Space Telescope Science
Institute under U.S. Government grants based on photographic data
obtained using the Oschin Schmidt Telescope on Palomar Mountain and
the UK Schmidt Telescope.  The USNO A and B-1.0 catalogs were
provided by Dave Monet and Steve Levine of the U.S. Naval Observatory
at Flagstaff on 21 CDROMs and one 128-gigabyte disk drive, respectively.
A beta version of the UCAC2 and a good discussion of limiting factors
in CCD astrometry were kindly provided by Norbert Zacharias
of the U.S. Naval Observatory at Flagstaff.

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\vspace*{-2ex}	%% TO AVOID last ref. on next page
\begin{references}

\vspace*{-1ex}	%% TO AVOID last ref. on next page
\reference Bertin, E. \& Arnouts, S.  1998, \aaps 117, 393
\reference Brown, W. R. et al. 2001, \aj, 122, 714
\reference Calabretta, M. R. \& Greisen, E. W. 2002, \aap, 395, 1077
\reference Cutri, et al. 2003, VizieR On-line Data Catalog: II/246.
\reference Geller, M. J., et al. 1997, \aj, 114, 2205
\reference Greisen, E. \& Calabretta, M.  2002, \aap, 395, 1061
\reference H\o g, E., et al. 2000, \aap 355, L27	%%% added FO
\reference Lasker, B. M., Sturch, C. R., McLean, B. J., Russell, J. L.,
   Jenkner, H., \& Shara, M. M.  1990, \aj, 99, 2019 
\reference McLean, B. J., Greene, G. R., Lattanzi, M. G., Pirenne, B. 
    2000, \adassix, 145
\reference Mink, D. J. 1997, \adassvi, 249
\reference Mink, D. J. 1999, \adassviii, 498
\reference Mink, D. J. 2002, \adassxi, 169
\reference Monet, D. G.  1996, \baas, 28, 905 (abstract)
\reference Monet, D. G.  1998, \baas, 30, 1427 (abstract)
\reference Monet, D. G. et al.  2003, \aj, 125, 984
\reference Muller, G. P., Reed, R., Armandroff, T., Boroson, T. A., \& Jacoby, G. H. 1998, Proc. SPIE, 3355, 577 
\reference Zacharias, N., et al. 2000, \aj, 120, 2131

\end{references}

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