2 Systematic errors of SIPA1

SIPA1 consists of 200 stars, including 97 FK5 stars and 103 FK5 Extension stars with $9\hbox{$.\!\!^\circ$}6 < \delta<74\hbox{$.\!\!^\circ$}4$. To determine the systematic errors of SIPA1, 199 common stars between SIPA1 and Hipparcos catalogs were used. The positions of Hipparcos stars were reduced to the observational epoch of SIPA1 and the difference $\Delta\alpha\cos\delta,\Delta\delta$ were obtained in the sense of SIPA1 - Hipparcos, which are shown in Figs. 1a,b. The systematic differences as a function of right ascension, $\alpha , \Delta\alpha_\alpha$ and $\Delta\delta_\alpha$,are negligible.

  

Figure 1: a-b) The difference between SIPA1 and the Hipparcos catalog. a) $\Delta\alpha\cos\delta$ vs. $\delta$. b) $\Delta\delta$ vs. $\delta$

  

Figure 2: The difference $\Delta\delta$ between the SIPA1 Input catalog and the Hipparcos catalog at the epoch of SIPA1 observations

The adopted values of latitude and instrument zenith distance in the reduction of SIPA1 are based on the FK5 system. As is well known, the FK5 catalog, especially the FK5 Extension stars, have zonal systematic difference relative to the Hipparcos catalog. The difference $\Delta\delta$ between the SIPA1 input catalog, which consists of FK5 and FK5 Extension stars, and the Hipparcos catalog at the epoch of SIPA1 observations are shown in Fig. 2. The systematic errors of FK5 may be introduced into SIPA1 in the following form [, (Li et al. 1983)]:

  

Table 1: Comparison of the precision of SIPA1 and Meridian catalogs

$$\Delta\delta = \Delta\varphi\sec z\sec\varphi\cos\delta - (\Delta z + \Delta \varphi \tan \varphi \tan z)/\cos q$$ (1)

where q is the parallactic angle, $\varphi$ is the latitude and z is the zenith distance. With a least squares fit to the $\Delta\delta$values of Fig. 1b, the systematic differences in 0$.\!\!^{\prime\prime}$01 in declination between SIPA1 and Hipparcos are derived as:

$$\Delta\delta = 0.464/\cos q + 35.40\cos\delta - 28.0\,.$$ (2)

It can be seen from Fig. 3 that there exists a significant magnitude equation in the right ascension system of SIPA1, which can be expressed with a forth order polynomial:

$$\begin{eqnarray} \Delta\alpha\cos\delta = 187.8 - 122.72V +29.399V^2 \nonumber \\ -3.0939V^3 + 0.12084V^4\end{eqnarray}$$ (3)

where V is the visual magnitude of stars. The unit in Eq. (3) is in 0$.\!\!^{\prime\prime}$01.

  

Figure 3: Magnitude equation of SIPA1, in which the solid line is calculated from Eq. (3)