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3 The astrometric calibration with the USNO-A2.0 Catalog

With the publication of the USNO-A2.0 (Monet et al. 1998), we have been able to, for the first time, make the astrometric calibration of the CCD frame directly, without using secondary catalogs. The USNO-A2.0 catalogue contains more than 526 millions of stars, with magnitudes ranging between 7.5 and 21, referred to the ICRF. Its nominal position error is about 0 $\hbox{$.\!\!^{\prime\prime}$ }$20. The catalogue does not include proper motions and therefore position epochs are given by the date when the plate was taken.

To do the astrometric calibration, the following procedure was employed for every CCD. Preliminarly, any star within the CCD field for which the centering error was larger than 0 $\hbox{$.\!\!^{\prime\prime}$ }$05 had been removed. Then, using the measured positions for the USNO-A2.0 stars in the CCD and the corresponding catalogue positions for them, a four parameters fitting was adjusted. In this way, the position of every star measured on the CCD frame was placed on the ICRF system. As suggested by Monet et al. (1998), the step above was also attempted using locally corrected portions of the USNO-A2.0 catalogue, instead of getting the star positions directly from the catalogue. Three different approaches were used to obtain the local corrections: a simple translation by average, a first degree complete polynomial, and a third degree complete polynomial. In all cases the correction was calculated from the comparison between ACT positions, on the plates epoch, and the USNO-A2.0 catalogue entries. There was no gain in adopting the corrected USNO-A2.0 positions, and thus the original catalog positions were used throughout. Accordingly, the calculated star positions were checked against the catalog ones. Also the calculated plate scale was compared with its nominal value, being found that the difference was smaller than 2%. The calculated minus catalog residuals in equatorial coordinates were, in general, smaller than 0 $\hbox{$.\!\!^{\prime\prime}$ }$8 and the standard deviations $\sigma_x$ and $\sigma_y$ were smaller than 0 $\hbox{$.\!\!^{\prime\prime}$ }$4. For the frames where one of these values was larger than the above upper limits, a further reference star discarding procedure was adopted. Trial reductions were made removing only one of the reference stars. Therefore as many trial reductions as there were reference stars were made. The reduction in which the average residual and the standard deviations resulted largest indicated the reference star to be removed. In half of the cases this procedure was repeated two or more times, till the values fall below the upper limits.


  \begin{figure}\includegraphics[width=8.8cm]{fig1.ps}\end{figure} Figure 3: CCD frame observed at 08/15/1997, $\rm 7^h 0^m 33^s$ UTC. Exposure time $2^{\rm m}$. CCD dimension 770 $\times $ 1200 square pixels

In Fig. 3 a typical CCD frame with Phoebe is presented, to exemplify the reduction procedure. The USNO-A2.0 reference stars are marked by a circle. Those eliminated in the second fitting have cross superimposed. In this frame there were 22 USNO-A2.0 stars, at the beginning. After the first fitting, the following values were found: $0\hbox{$.\!\!^{\prime\prime}$ }2931$ for the plate scale, $2\hbox{$.\!\!^{\prime\prime}$ }08$ for the largest star residual and $0\hbox{$.\!\!^{\prime\prime}$ }229$ and $0\hbox{$.\!\!^{\prime\prime}$ }538$ for $\sigma_x$ and $\sigma_y$. Thus, to comply with the reduction criteria, further rounds of reference stars discarding were made. After the last fitting, there were 19 reference stars and the values found were: $0\hbox{$.\!\!^{\prime\prime}$ }2932$ per pixel for the plate scale, $0\hbox{$.\!\!^{\prime\prime}$ }70$ for the largest value of the residuals and $0\hbox{$.\!\!^{\prime\prime}$ }234$ and $0\hbox{$.\!\!^{\prime\prime}$ }272$ for $\sigma_x$ and $\sigma_y$. The residuals for the Phoebe positions are ( $-0\hbox{$.\!\!^{\prime\prime}$ }06, 0\hbox{$.\!\!^{\prime\prime}$ }03$) and ( $-0\hbox{$.\!\!^{\prime\prime}$ }03$, $-0\hbox{$.\!\!^{\prime\prime}$ }06$), before and after the discarding of reference stars. Along the different observing nights for the 5 missions, Phoebe was imaged on fields of varying star density, as result the number of USNO-A2.0 varied to a large extent in different nights. The number of reference stars in each frame, used in the final reduction, ranges from 5 to 19. In Table 1 all observed positions of Phoebe are presented. The positions are referred to the ICRS, thus tied to the equator and equinox of J2000. The instants of observation are given in universal time. In Table 2 the normal places for each of the twelve nights of observations are presented.


  \begin{figure}\includegraphics[width=8.8cm]{graf3.ps}\end{figure} Figure 4: Observed minus calculated residuals as function of time for Phoebe fitted observations


  \begin{figure}
\includegraphics[width=8.8cm]{graf2.ps}\end{figure} Figure 5: The same as Fig. 4 but referred to the true anomaly


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