Comparison of the XPM and UCAC4 catalogs

Abstract

The systematic differences between the stellar positions and proper motions of the XPM and UCAC4 catalogs have been obtained in the form of decompositions into vector spherical harmonics by taking into account the magnitude equation. The systematic components have been extracted with a probability of at least 0.98 by dividing 41 316 676 stars into groups corresponding to 12 J magnitude bins with a width of 0.5m for mean values from 10m.25 to 15m.75. A study of the systematic differences between the equatorial coordinates suggests that the range of systematic differences between the XPM and UCAC4 positions exceeds the corresponding range of differences between PPMXL and UCAC4 by a factor of 5, especially for bright stars in the range being investigated. Analysis of the orientation of the XPM and UCAC4 reference frames has shown that their mutual rotation is 2–4 mas around the X axis and 7–10 mas around the Z axis. These angles depend on the magnitude of stars. Since two systems of proper motions are given in the XPM catalog, XPMx and XPMp, we have decomposed the proper motion differences XPMx–XPMp into vector spherical harmonics and found these differences to be free from the magnitude equation. An important fact is that the first-order zonal coefficients have turned out to be greatest in absolute value. The toroidal coefficient t1,0,1,0 found has shown that the XPMx and XPMp reference frames of proper motions rotate relative to each other around the Z axis with an angular velocity of 0.45 mas yr−1. It should be added that the range of systematic differences XPMx–XPMp is 2.1 mas yr−1 in right ascension and 1.7 mas yr−1 in declination. The angular velocities of mutual rotation of the XPMp and UCAC4 reference frames change within the range from 0.6 to 2.2 mas yr−1, while the analogous range for the XPMх and UCAC4 catalogs is 0.3–1.8 mas yr−1. The angular velocity and coordinates of the pole of the mutual rotation axis depend on the magnitude of stars. The parameters of the mutual rotation around the Z axis derived from the differences XPMx–UCAC4 and XPMp–UCAC4 change from 0.03 ± 0.06 to 1.73 ± 0.06 mas yr−1 and from 0.49 ± 0.06 to 2.19 ± 0.06 mas yr−1, respectively. Based on our analysis, we have shown that the XPMcatalog actually comprises two catalogs, XPM(XSC) and XPM(PSC), in which the stellar positions coincide at the standard epoch J2000 and differ at any other epoch. The decomposition coefficients of the systematic differences XPM–UCAC4 we obtained allow the stellar positions and proper motions from one catalog to be reduced to the system of the other catalog by taking into account this duality.