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We combined data from the Two‐Micron All Sky Survey (2MASS) and USNO‐A2.0 catalogues in order to derive the absolute proper motions of about 280 million stars distributed all over the sky excluding a small region near the Galactic Centre, in the magnitude range 12 < B < 19 mag. The proper motions were derived from the 2MASS Point Sources and USNO‐A2.0 catalogue positions with a mean epoch difference of about 45 years for the Northern hemisphere and about 17 years for the Southern one. The zero‐point of the absolute proper motion frame (the ‘absolute calibration’) was specified with the use of about 1.45 million galaxies from 2MASS. Most of the systematic zonal errors inherent in the USNO‐A2.0 catalogue were eliminated before the calculation of proper motions. The mean formal error of absolute calibration is less than 1 mas yr−1. The XPM Catalogue will be available via CDS in Strasbourg during 2010. The generated catalogue contains the International Celestial Reference System positions of stars for the J2000 epoch, original absolute proper motions, as well as B, R, J, H and K magnitudes. A comparison of the proper motions obtained in this work with the data of other recent catalogues of quasars was fulfilled.

We present a catalogue that contains about 420 million absolute proper motions of stars. It was derived from the combination of positions from Gaia DR1 and 2MASS, with a mean difference of epochs of about 15 yr. Most of the systematic zonal errors inherent in the 2MASS Catalogue were eliminated before deriving the absolute proper motions. The absolute calibration procedure (zero-pointing of the proper motions) was carried out using about 1.6 million positions of extragalactic sources. The mean formal error of the absolute calibration is less than 0.35 mas yr−1. The derived proper motions cover the whole celestial sphere without gaps for a range of stellar magnitudes from 8 to 21 mag. In the sky areas where the extragalactic sources are invisible (the avoidance zone), a dedicated procedure was used that transforms the relative proper motions into absolute ones. The rms error of proper motions depends on stellar magnitude and ranges from 2–5 mas yr−1 for stars with 10 mag &lt; G &lt; 17 mag to 5–10 mas yr−1 for faint ones. The present catalogue contains the Gaia DR1 positions of stars for the J2015 epoch. The system of the PMA proper motions does not depend on the systematic errors of the 2MASS positions, and in the range from 14 to 21 mag represents an independent realization of a quasi-inertial reference frame in the optical and near-infrared wavelength range. The Catalogue also contains stellar magnitudes taken from the Gaia DR1 and 2MASS catalogues. A comparison of the PMA proper motions of stars with similar data from certain recent catalogues has been undertaken.

We have developed the dynamical model of a clumpy torus in an active galactic nucleus (AGN) and compared to recent ALMA observations. We present N-body simulations of a torus in the field of a supermassive black hole (SMBH), made of up to N = 105 gravitationally interacting clouds. As initial conditions, we choose random distributions of the orbital elements of the clouds with a cut-off in the inclination to mimic the presence of wind cones produced at the early AGN stage. When the torus reaches an equilibrium, it has a doughnut shape. We discuss the presence of box orbits. We have then constructed the velocity and velocity dispersion maps using the resulting distributions of the clouds at equilibrium. The effects of torus inclination and cloud sizes are duly analyzed. We discuss the obscuration effects of the clouds using a ray tracing simulation matching the model maps to ALMA resolution. By comparing the model with the observational maps of NGC 1068 we find that the SMBH mass is Msmbh = 5 × 106 M⊙ for the range of the torus inclination angles 45○–60○. We also construct the velocity dispersion maps for NGC 1326 and NGC 1672. They show that the peaks in the ALMA dispersion maps are related to the emission of the torus throat. Finally, we obtain the temperature distribution maps with parameters that correspond to our model velocity maps for NGC 1068. They show stratification in temperature distribution with the shape of the high temperature region as in the VLTI/MIDI map.