Systematic Differences between the Positions and Proper Motions of Stars from the PPMXL and UCAC4 Catalogs

The PPMXL and UCAC4 catalogs are compared by representing the differences between the positions and proper motions of stars as decompositions into a set of orthogonal vector harmonics with allowance made for the magnitude equation. A list of 41 316 676 common stars has been compiled using the star identification procedure in the J band (2MASS photometric system). The mean differences between the stellar positions and proper motions have been referred to the centers of 1200 HealPix pixels on the sphere. These data have been generated in the equatorial coordinate system for the stars belonging to 12 J magnitude bins with a width of 0.5(m) for mean values from 10.(m)25 to 15.(m)75. For each sample of stars, the differences have been approximated by vector spherical harmonics. A new statistical criterion that is oriented to using HealPix data pixelization and that allows the significance of all the accessible harmonics to be determined is proposed to extract the signal from noise. An analytical method that includes the effects dependent on the magnitude of the stars has been proposed for the first time in the vector spherical harmonics technique, i.e., a new model of systematic differences based on a system of basis functions that are the products of vector spherical harmonics and Legendre polynomials has been generated. The influence of the magnitude equation on the determination of the mutual orientation and rotation of the PPMXL and UCAC4 reference frames has been studied. It has been established that the extreme systematic differences do not exceed in absolute value 20 mas and 4 mas yr(-1) for the positions and proper motions, respectively. The largest differences between the PPMXL and UCAC4 catalogs are shown to be explained by their random rather than systematic errors.