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\begin{document}
\title{ACT Reference Catalog}
\author{Sean E. Urban, Thomas E. Corbin and Gary L. Wycoff}
\maketitle

\begin{center}
\Large
\vspace*{1.0 in}
Catalog of Positions and Proper Motions Derived from the Combination of
the AC 2000 Catalog and the Positions in the Tycho Catalogue.  Positions and
proper motions are on the Hipparcos System (J2000.0) for the Epoch J2000.0.

\vspace*{1.0 in}
United States Naval Observatory \\
Washington, D. C.
\end{center}
\normalsize
\newpage
\tableofcontents
\listoftables
\newpage

\section{Introduction}
The ACT Reference Catalog contains 988,758 star positions and proper motions
covering the entire sky for the epoch and equinox J2000.0.  The proper motions
are from new reductions of the Astrographic Catalogue 
(AC~2000; Urban et al., 1997) combined with the positions in the Tycho
Catalogue (ESA 1997).  Additional photometric and cross referencing data from  
Tycho are included.  This document briefly describes these two data sets,
and the catalog resulting from their combination.

\section{The AC~2000}

The AC~2000 is a positional catalog recently compiled at The U.S. Naval
Observatory using the plate measures contained in the Astrographic Catalogue (AC).
The AC was an international program designed to photograph and measure the
positions of all stars brighter than magnitude 11.0.  Since observing and
measuring the 22,000 plates needed to cover the sky was too labor intensive for
any one observatory to undertake, the task was spread among several
observatories, each photographing and measuring stars between two parallels
of declination.  In total, 20~observatories participated in the data
gathering and the sky was sectioned into 22~zones.
By the conclusion of the project, positions of 4.6 million stars had been
measured, many as faint as 13th magnitude.  These positions have an extremely
early epoch; the average epoch of an AC plate is 1907.

To compile the AC~2000,
each of the 22 zones making up the Astrographic Catalogue was reduced
independently using the Astrographic Catalog Reference Stars  (ACRS;
Corbin \& Urban 1988, Corbin \& Urban 1990).  The plates of each zone were
analyzed for tilt, radial and tangential distortions, coma, magnitude
equation and non-symmetric field distortions.  Following this analysis, 
reductions of each plate were made to transform the image measures to 
equatorial coordinates.  Following these reductions, the
data were placed on the Hipparcos system and the magnitudes were converted to
be close to those of the Tycho B data.  The resulting data were then combined
into the final catalog.  Detailed information on the reduction methodology and
input data can be found in the INTRO.TEX file on the CD-ROM containing the 
AC~2000.

Although positional accuracies contained in the AC~2000 vary from zone to 
zone and star to star, most are between 150 and 300~mas at the mean epochs 
of observations.  The average epoch for an AC plate is 1907 (although 
this too can vary quite a bit).  The early epochs and
good accuracies make the positions in the AC~2000 extremely valuable for 
determining proper motions when combined with modern observations.

\section{The Tycho Catalogue}
The Hipparcos satellite was a European Space Agency (ESA) funded, astrometric
instrument launched in 1989 and operated until 1993.  The primary mission
was the determination of accurate positions, proper motions and parallaxes
of 118,218 stars. The results of these observations form
the Hipparcos Catalogue (ESA 1997).  The accuracies of the Hipparcos 
astrometric parameters are roughly 1~mas for position, 1~mas/year for proper
motion, and 1~mas for parallax.

Early in the planning stage for Hipparcos, the mission was expanded to include
data from the satellite's star mapper.  The results of the star mapper's
observations are contained in the Tycho Catalogue (ESA 1997) of          
1,058,332 objects.  The accuracies of the Tycho positions and proper motions
are roughly 30~mas for position and 30~mas/year for 
proper motion.  In addition to the positional information, the Tycho Catalogue
contains two-color photometry for the vast majority of its objects.  The
precisions of the Tycho photometric data are generally well under 0.1 magnitude.
A thorough introduction of the Hipparcos and Tycho missions can be found in the
above reference.

\section{The ACT Reference Catalog}
It was recognized many years ago that the data contained in the Astrographic
Catalogue could be combined with modern epoch observations to compute or 
dramatically improve proper motions (Eichhorn 1974) especially with a catalog
such as Tycho (Urban 1993).  Tycho is 
a perfect catalog to combine with the AC~2000 since the Tycho positions make it
the most accurate catalog of comparable size at its epoch of observation, but
its proper motions degrade it to a sub-standard reference catalog in less than
10~years.  The proper motions of the Tycho stars can be improved from about
30~mas/year to about 3~mas/year by recomputing them using the AC~2000 data
(Urban 1997).  This combination of AC~2000 and Tycho, called
ACT Reference Catalog, degrades much more slowly and is a valuable
astronomical dataset for applications spanning many decades.

\subsection{Matching Tycho and AC~2000}
In order to make the ACT Reference Catalog high quality, it was decided that 
some problematic ``stars'' would not be used.  Positions indicated in the Tycho
Catalogue as coming from close multiple stars or those of extremely low
astrometric quality were discarded (No stars with 'D', 'R' or 'S' in the
MultFlag field or stars with '9' in the Q field were used).

To match the two data sets, the Tycho entries were brought to
the AC~2000 epochs by the application of the published Tycho proper
motions.  An area with a radius of 15 arcsec around each Tycho star was
searched.  If there was a one-to-one match, that is 
one AC~2000 entry and one Tycho entry in the search area, then the two are  
identified as the same star.  If there was not a one-to-one match, for example
one Tycho entry and two AC~2000 entries,  then a ratio of the distances between the
Tycho and the closest AC~2000 star and the Tycho and the farther AC~2000 star
was computed.  If the value of the ratio was 0.2 or less, then 
the  Tycho and the closer AC~2000 star were identified as the same.  Otherwise,
the matching was considered ambiguous and no cross identification was made.
For the Tycho stars not matched at this point,  another search was made but
without application of any proper motions.   A search area with a radius
of 20 arcsec was used.  Again, a ratio test of .2 was applied for all 
non-singular matches.  For the Tycho stars still not matched, a search in the
New Luyten's Two Tenths Catalog (Luyten 1979, Luyten and Hughes 1980) was made.
Luyten's proper motions were then
applied to the Tycho stars to bring them to the epoch of the AC~2000 positions.
A search area with a radius of 15~arcsec around each Tycho star was used.
Once again, if more than one star fell within the search area, a ratio test was
used to determine which observations were really the same star. 

\subsection{Computation of proper motions}
Once the identifications between the AC~2000 and Tycho were made, the proper
motions were computed using the differences in position and epoch.  To bring
these proper motions from the mean epoch to J2000.0, the application of 
standard formulae were used.  In the computation of the foreshortening terms,
the radial velocities were taken from the Hipparcos Input Catalogue
(Turon et al. 1991) and the parallaxes were taken from the Hipparcos Catalogue.

\subsection{Computation of standard errors of proper motion}
The computation of the standard error in proper motions is straightforward, 
since only two position proper motions are involved.  The formula used is 
\begin{equation}
\sigma_\mu = \frac {\sqrt{\sigma^2_{ {\rm AC}} + \sigma^2_{ \rm {T}}}} {EP_{ {\rm T}} - EP_{ {\rm AC}}}
\end{equation}
where $\sigma_{{\rm AC}}$ and $\sigma_{{\rm T}}$ are the standard deviations
of the AC~2000 and Tycho positions respectively.  Note that $\sigma_{{\rm AC}}$
was computed by the scatter in positions of the individual images making up
the mean position.  In order not to under estimate $\sigma_\mu$ for stars 
stars with very small values of $\sigma_{{ \rm AC}}$, a lower limit of 80~mas
has been placed on this value.         

\newpage
\section{Description of ACT Reference Catalog}

\subsubsection{Right ascension}

The right ascension for each star as computed from its Tycho position 
(epoch 1991.25) and ACT proper motion, in units of hours, minutes and seconds
of time, referred to the Hipparcos system (J2000.0) at epoch J2000.0.

\subsubsection{Declination}

The declination for each star as computed from its Tycho position
(epoch 1991.25) and ACT proper motion, in units of degrees, minutes and seconds of arc, referred
to the Hipparcos system (J2000.0) at epoch J2000.0.

\subsubsection{Proper motion, right ascension}
The proper motion for each star as computed from the combination of the 
Tycho and AC~2000 positions, referred to the Hipparcos system (J2000.0) at
epoch J2000.0, in units of seconds of time/year.

\subsubsection{Proper motion, declination}
The proper motion for each star as computed from the combination of the 
Tycho and AC~2000 positions, referred to the Hipparcos system (J2000.0) at
epoch J2000.0, in units of seconds of arc/year.

\subsubsection{Standard errors of equatorial coordinates}
The standard errors in right ascension and declination at epoch 1991.25,
in units of mas. This is T14 and T15 in the Tycho Catalogue.

\subsubsection{Standard errors of proper motion}
The standard errors in proper motion computed as described in section
``Computation of standard errors of proper motion'' in this document, in units
of mas/year. 

\subsubsection{BT Magnitude}
The Tycho Blue magnitudes.  This is T32 in the Tycho Catalogue.

\subsubsection{VT Magnitude}
The Tycho Visual magnitudes.  This is T34 in the Tycho Catalogue.

\subsubsection{B-V}
The color index Johnson B-V.  This is T37 in the Tycho Catalogue.

\subsubsection{Flags}
Flags are provided to give additional data to users.  All are from the 
Tycho Catalogue.  A brief meaning
is given below; for a more detailed description, consult SP-1200 Volume~1.
\begin{itemize}
\item{Astrometry Flag (T10 in Tycho)}
\begin{itemize}
\vspace*{-.15in}
\item{blank: a recommended astrometric reference star}
\vspace*{-.1in}
\item{``X'': a dubious astrometric reference star in Tycho}
\end{itemize}
\item{Quality flag (T40 in Tycho)}
\begin{itemize}
\vspace*{-.15in}
\item{1 through 5: very high to medium quality; probably single stars}
\vspace*{-.1in}
\item{6:  perhaps non-single}
\vspace*{-.1in}
\item{7:  low astrometric quality}
\vspace*{-.1in}
\item{8:  perhaps non-stellar}
\vspace*{-.1in}
\item{blank:  unassigned, observed by Hipparcos, not Tycho}
\end{itemize}
\item{Known variability flag (T47 in Tycho)}
\begin{itemize}
\vspace*{-.15in}
\item{``G'':  Star in General Catalogue of Variable Stars, 4th Edition}
\vspace*{-.1in}
\item{``N'':  Star in New Catalogue of Suspected Variable Stars}
\end{itemize}
\item{Variability from Tycho (T48 in Tycho)}
\begin{itemize}
\vspace*{-.15in}
\item{``U'':  Apparent variability in Tycho data; may be due to duplicity}
\vspace*{-.3in}
\item{``V'':  strong evidence of variability in the Tycho data}
\vspace*{-.1in}
\item{``W'':  variability suspected in the Tycho data}
\end{itemize}
\item{Duplicity from Tycho (T49 in Tycho)}
\begin{itemize}
\vspace*{-.15in}
\item{``Y'':  Investigation of duplicity made, no indication of duplicity}
\vspace*{-.1in}
\item{``Z'':  No investigation of duplicity was performed}
\end{itemize}
\end{itemize}

\subsubsection{Cross identifications}
Cross identifications between Tycho, AC~2000, the Bonner, Cordoba and
Cape Durchmusterungs, the Henry Draper Catalog, and Hipparcos Catalogue
are provided.  The identifications of the Durchmusterungs, Henry Draper,
and Hipparcos numbers are from the Tycho Catalogue. 

\newpage
\addcontentsline{toc}{section}{Bibliography}
\begin{thebibliography}{}
\bibitem{Corbin1}
Corbin, T.E. and Urban, S.E., 1988, IAU Symposium 133 Mapping the Sky,
ed. S. Debarbat, J.A. Eddy, H. K. Eichhorn and A. R. Upgren,
Kluwer, Dortrecht, p. 287 
\bibitem{Corbin2}
Corbin, T.E., and Urban, S.E., 1990, IAU Symposium 141 Inertial Coordinate
 System on the Sky, ed. J. Lieske and V.K. Abalakin
 Kluwer, Dortrecht p. 433.
\bibitem{Eichhorn}
Eichhorn, H., 1974, Astronomy of Star Positions, Fredrick Ungar, p. 283
\bibitem{ESA1}
ESA, 1997, The Hipparcos and Tycho Catalogues, SP-1200
\bibitem{Luy1}
Luyten, W.J., 1979, 1980, New Luyten Catalogue of Stars with Proper Motions
Larger than Two Tenths of an Arcsecond (Minneapolis:  University of Minnesota) 
\bibitem{Luy2}
Luyten,  W.J. and Hughes,  H.S., 1980,  Proper Motion Survey with the
Forty-Eight Inch Schmidt Telescope.  LV. First Supplement to the NLTT Catalogue
(Minneapolis: University of Minnesota)
\bibitem{Tur1}
Turon, C., Creze, M., Egret, D., et al., 1992, The Hipparcos Input Catalogue, ESA SP-1136
\bibitem{Urban0}
Urban, S.E., 1993, The U.S. Naval Observatory's Astrographic Catalogue Project,
in Workshop on Databases for Galactic Structure, ed. A.G.D Philip, B. Hauck,
and A.R. Upgren, L. Davis Press p. 145
\bibitem{Urban1}
Urban, S.E., 1997, New Reductions of the Astrographic Catalogue, in Proceedings
of IAU Colloquium 165, ed. Wytrzyszczak, I.M., Lieske, J.H., and Feldman,R.A,
Kluwer Academic Publishers, p. 493
\bibitem{Urban2}
Urban, S.E., Corbin, T.E., Wycoff, G.L., Martin, J.C., Jackson E.S., Hall, D.M,
and Zacharias, M.I., 1997, The AC~2000: The Astrographic Catalogue on the 
Hipparcos System, in preparation.
\end{thebibliography}

\newpage
\begin{table}    
\caption{Byte-by-byte description of ACT Reference Catalog using format
requested by the CDS.}
\begin{flushleft}
\begin{tabular}{lllll}
\hline\noalign{\smallskip}
 Bytes & Format & Units    & Label   &  Explanations        \\
\noalign{\smallskip}
\hline\noalign{\smallskip}
   1- 2& I2   &  h         & RAh     & Right Ascension, Eq. and Epoch J2000.0 (hours)   \\
   4- 5& I2   &  min       & RAm     & Right Ascension, Eq. and Epoch J2000.0 (minutes) \\
   7-13& F7.4 &  s         & RAs     & Right Ascension, Eq. and Epoch J2000.0 (seconds) \\
     15& A1   &  ---       & DE-     & Declination, Eq. and Epoch J2000.0 (sign)  \\
  16-17& I2   &  deg       & DEd     & Declination, Eq. and Epoch J2000.0 (degrees)\\
  19-20& I2   &  arcmin    & DEm     & Declination, Eq. and Epoch J2000.0 (minutes) \\
  22-27& F6.3 &  arcsec    & DEs     & Declination, Eq. and Epoch J2000.0 (seconds) \\
  29-35& F7.5 &  s/yr      & pmRA    & Proper Motion in RA, at J2000.0 (sec of time/yr) \\
  37-43& F7.4 &  arcsec/yr & pmDE    & Proper Motion in Dec, at J2000.0 (arcsec/yr) \\
  45-49& F5.1 &  mas       & e\_RAs  & ?Stand. dev. of RA at 1991.25 (T14 in Tycho) \\
  51-55& F5.1 &  mas       & e\_DEs  & ?Stand. dev. of Dec at 1991.25 (T15 in Tycho) \\
  56-61& F6.2 &  mas/yr    & e\_pmRA & ?Stand. dev. of Proper motion (RA), in mas/yr \\
  62-67& F6.2 &  mas/yr    & e\_pmDE & ?Stand. dev. of Proper motion (RA), in mas/yr \\
  69-74& F6.3 &  mag       & B(mag)  & Blue magnitude from Tycho (T32) \\
  76-81& F6.3 &  mag       & V(mag)  & Visual magnitude from Tycho (T34) \\
  83-88& F6.3 &  mag       & B-V     & Johnson B-V from Tycho (T37) \\
  90-90& A1   &  ---       & Flag1   & Astrometric Quality flag (T10) \\
  91-91& A1   &  ---       & Flag2   & Quality flag (T40) \\
  92-92& A1   &  ---       & Flag3   & Known variability flag (T47) \\
  93-93& A1   &  ---       & Flag4   & Variability from Tycho (T48) \\
  94-94& A1   &  ---       & Flag5   & Duplicity from Tycho (T49) \\
 96-107& A12  &  ---       & TYCHO   & Tycho ID, embedded zeros for blanks\\
109-115& I7   &  ---       & AC2000  & AC 2000 Number \\
117-125& A9   &  ---       & BD      & BD identifier (T54) \\
127-135& A9   &  ---       & CD      & CD identifier (T55) \\
137-145& A9   &  ---       & CPD     & CPD identifier (T56) \\
147-152& I6   &  ---       & HD      & Henry Draper Number (T53) \\
154-159& I6   &  ---       & HIP     & Hipparcos number (T31) \\
\noalign{\smallskip}
\hline
\label{tab:format}
\end{tabular}
\end{flushleft}
\end{table}
\end{document}
