All available photometry for the Cepheid KN Cen is analyzed to construct its (O-C) diagram spanning a 134-year long time interval. This made it possible for the first time to compute the rate of evolutionary period increase of the Cepheid, dP/dt=+2.91(±1.68) s yr ^-1 , which is consistent with the results of model computations for the third crossing of the instability strip. The test for stability of pulsations proposed by Lombard and Koen confirmed the reality of the evolutionary period change.

We study the periodic enhancement of either trailing or leading segments of the resonance elliptical rings in the dynamical model of the Galaxy which reproduces distributions of observed velocities derived from Gaia DR3 (EDR3) data along the Galactocentric distance. The model disc forms a nuclear ring, an inner combined ring, and outer resonance rings R-1 and R-2. The backbone of the inner combined ring is banana-type orbits around the Lagrange equilibrium points L-4 and L-5. Orbits associated with the unstable equilibrium points L-1 and L-2 also support the inner ring. We have found the changes of the morphology of the inner ring with a period of P = 0.57 +/- 0.02 Gyr, which is close to the period of revolution along the long-period orbits around the points L-4 and L-5. A possible explanation of these morphological changes is the formation of an overdensity which then begins circulating along the closed contour. In the region of the Outer Lindblad Resonance (OLR), we have found the changes of the morphology of the outer rings with a period of P = 2.0 +/- 0.1 Gyr. Probably, the morphological changes of the outer rings are due to the orbits trapped by the OLR. These orbits exhibit librations of the direction of orbital elongation with respect to the minor axis of the bar as well as the long-term variations in the stellar angular momentum, energy, average radius of the orbit, and eccentricity. Among many librating orbits, we discovered orbits with the libration period of P = 1.91 +/- 0.01 Gyr, which may cause the morphological changes of the outer rings.

A model of the Galaxy with the outer ring R 1 R 2 can reproduce the observed distribution of the radial, V R , and azimuthal,V T , velocity components along the Galactocentric distance, R, derived from the Gaia EDR3 data. The best agreementbetween the model and observed velocities corresponds to the time 1.8 ± 0.5 Gyr after the start of the simulation. Theangular velocity of the bar of Ω b = 55 ± 3 km s −1 kpc −1 and the position angle of the bar of θ b = 45 ± 15 ◦ provide the bestagreement between the model and observed velocities.

ABSTRACT A model of the Galaxy with the outer ring R1R2 can explain the observed distribution of the radial, VR, and azimuthal, VT, velocity components along the Galactocentric distance, R, derived from the Gaia EDR3 data. We selected stars from the Gaia EDR3 catalogue with reliable parallaxes, proper motions, and line-of-sight velocities lying near the Galactic plane, |z| < 200 pc, and in the sector of the Galactocentric angles |θ| < 15° and calculated the median velocities VR and VT in small bins along the distance R. The distribution of observed velocities appears to have some specific features: the radial velocity VR demonstrates a smooth fall from +5 km s−1 at the distance of R ≈ R0 − 1.5 kpc to −3 km s−1 at R ≈ R0 + 1.0 kpc while the azimuthal velocity VT shows a sharp drop by 7 km s−1 in the distance interval R0 < R < R0 + 1.0 kpc, where R0 is the solar Galactocentric distance. We build a model of the Galaxy including bulge, bar, disc, and halo components, which reproduces the observed specific features of the velocity distribution in the Galactocentric distance interval |R − R0| < 1.5 kpc. The best agreement corresponds to the time 1.8 ± 0.5 Gyr after the start of the simulation. A model of the Galaxy with the bar rotating at the angular velocity of Ωb = 55 ± 3 km s−1 kpc−1, which sets the OLR of the bar at the distance of R0 − 0.5 ± 0.4 kpc, provides the best agreement between the model and observed velocities. The position angle of the bar, θb, corresponding to the best agreement between the model and observed velocities is θb = 45 ± 15°.

This paper presents results from photometric and statistical-parallax analysis of a sample of 850 field RR Lyrae (RRL) variables. The photometric and spectroscopic data for our sample of RRLs are obtained from (1) our new spectroscopic observations (for 448 RRLs) carried out with the Southern African Large Telescope; (2) our photometric observations using the 1.0-m telescope of the South African Astronomical Observatory, and (3) literature. These are combined with accurate proper motion data from the second data release of the Gaia mission (DR2). This study primarily determines the velocity distribution of solar neighbourhood RRLs, and it also calibrates the zero-points of the RRLs' visual V-band luminosity-metallicity (LZ or M-V-[Fe/H]) relation and their period-luminosity-metallicity (PLZ) relations in the Wide-field Infrared Survey ExplorerW1 and Two-Micron All-Sky Survey Ks bands. We find the bulk velocity of the halo RRLs relative to the Sun to be (U-0, V-0, W-0)(Halo) =(- 16 +/- 7, -219 +/- 7, -6 +/- 5)kms(-1) in the direction of Galactic centre, Galactic rotation, and North Galactic pole, respectively, with velocity-dispersion ellipsoids (sigma V-R, sigma V-phi, sigma V-theta)(Halo) = (153 +/- 7, 106 +/- 4, 101 +/- 4)kms(-1). The corresponding parameters for the disc component are found to be (U-0, V-0, W-0)(Disc) = (- 19 +/- 5, -46 +/- 5, -14 +/- 3)kms(-1) and (sigma V-R, sigma V-phi, sigma V-theta)(Disc) =(49 +/- 4, 38 +/- 4, 25 +/- 3)kms(-1). The calibrated PLZ in W1-, Ks-, and V-band LZ relations are, < M-Ks > = , and , respectively. The calibrated PLZ and LZ relations are used to estimate the Galactic Centre distance and the distance modulus of the Large Magellanic Cloud (LMC), which are found to be 7.99 +/- 0.49kpc and 18.46 +/- 0.09 mag, respectively. All our results are in excellent agreement with available literature based on statistical-parallax analysis, but are considerably more accurate and precise. Moreover, the zero-points of our calibrated PLZ and LZ relations are quite consistent with current results found by other techniques and yield an LMC distance modulus that is within 0.04 mag of the current most precise estimate.

We estimated the contribution of binary systems to the velocity dispersion inside OB-associations derived from Gaia DR2 proper motions. The maximum contribution to the velocity dispersion is given by the systems with the period of revolution of P=5.9 yr whose components shift by a distance of about the diameter of the system during the base-line time of Gaia DR2 observations. We employed two methods to study the motion of the photocenter of the binary system: the first one uses the total displacement between the initial and final visibility periods and the second one is based on solving a system of n equations defining the displacements at the times t_n. The first and second methods yield very similar sigma_bn values of 0.90 and 0.87 km s-1, respectively. Taking into account the fact that orbits are elliptical slightly decreases the inferred sigma_bn. We estimated the eccentricity-averaged sigma_bn value to be sigma_bn=0.81 km s-1 assuming that the orbital eccentricities of massive binary systems are distributed uniformly in the [0, 0.9] interval. The choice of the exponent gamma in the power-law distribution, p_q ~ q^gamma, of the component-mass ratios q=M_2/M_1 of binary systems appears to have little effect on sigma_bn. A change of gamma from 0 (flat distribution) to -2.0 (preponderance of systems with low-mass components) changes sigma_bn from 0.90 to 1.07 km s-1.

In 2012–2014 we obtained 3296 CCD frames in the $$BVI_{c}$$ photometric system for the RR Lyrae star T Men with the 76-cm telescope of the South African Astronomical Observatory (SAAO, SAR) and the 1-m telescopes of the Las Cumbres Observatory Global Telescope (LCOGT). Our observations showed a slightly increased scatter of data points on the light curve, which allowed the Blazhko effect with a period $${\sim}18\overset{\textrm{d}}{.}49$$ to be detected. To study the variability of the pulsation period, we used all the available observations, including 1325 magnitude estimates from the digitized Harvard Astronomical Plate Collection (the DASCH project). This allowed us to construct an $$O-C$$ diagram spanning a time interval of 125 years and for the first time to detect at least three abrupt changes in the pulsation period.

We study the motions inside 28 OB-associations with the use of Gaia DR2 proper motions. The average velocity dispersion calculated for 28 OB-associations including more than 20 stars with Gaia DR2 proper motion is sigma_v =4.5 km s-1. The median virial and stellar masses of OB-associations are M_vir=8.9 x 10^5 and M_st=8.1 x 10^3 Ms, respectively. The median star-formation efficiency in parent giant molecular clouds appears to be epsilon=1.2 per cent. Gaia DR2 proper motions confirm the expansion in the Per OB1, Car OB1 and Sgr OB1 associations found earlier with Gaia DR1 data. We also detect the expansion in Gem OB1, Ori OB1 and Sco OB1 associations which became possible for the first time now when analyzed with Gaia DR2 proper motions. The analysis of the distribution of OB-stars in the Per OB1 association shows the presence of a shell-like structure with the radius of 40 pc. Probably, the expansion of the Per OB1 association started with the velocity greater than the present-day expansion velocity equal to 5.0 +\- 1.7 km s-1.

We calculated the median parallaxes for 47 OB associations including at least 10 stars with known Gaia DR2 parallaxes. A comparison between trigonometric and photometric parallaxes of OB associations reveals a zero-point offset of $\Delta \varpi=-0.11\pm0.04$ mas indicating that Gaia DR2 parallaxes are, on average, underestimated and the distances derived from them are overestimated. The correction of $\Delta \varpi=-0.11$ mas is consistent with the estimate that Arenou et al. (2018) obtained for bright stars. An analysis of parallaxes of OB associations and high-luminosity field stars confirms our previous conclusion (Dambis et al. 2001) that the distance scale for OB stars established by Blaha and Humphreys (1989) must be reduced by 10–20%. Spurious systematic motions of 10–20 km s−1 at the distances of 2–3 kpc from the Sun are found to arise from the use of the uncorrected Gaia DR2 parallaxes.

We took a total of 635 B-, V-, and Ic-band CCD frames for the RRab Lyr type variable DVMon, which has a close bright visual companion with a separation of about 1.9′. Observations were made with the 76-cm telescope of the South African Astronomical Observatory (SAAO, South Africa) using SBIG CCD ST-10XME. For the first time, we obtained reliable separate PSF-photometry of both stars and determined their coordinates. We used all available data to construct the O — C diagram spanning a 110-year long time interval, which allowed us to reveal at least three sudden changes of the pulsation period around JD 2438000, 2453500, and 2456500. Our high resolution echelle spectra with the Southern African Large Telescope (SALT) showed that DV Mon belongs to type ab RR Lyrae variables of the Galactic thick disk.

A total of 820 magnitude estimates were made for the long-period classical Cepheid V609 Cyg ( $P =31.1$  days) using the photographic plate collections of the Harvard College Observatory and Sternberg Astronomical Institute. Combined with published photometry, the data cover a time baseline of about 129 years on the resulting $O$ – $C$ diagram. That circumstance allowed us to detect an evolutionary increase in the pulsation period at a rate of $21.38 \pm 2.05$  s yr−1, corresponding to $\log (\dot{P} /P) = -5.10$ , which agrees well with theoretical predictions for a star in the third crossing of the instability strip. When reduced using the method introduced by Eddington and Plakidis (Mon. Not. R. Astron. Soc. 90:65, 1929) the available data demonstrate the presence of mild random period fluctuations, which do not mask the evolutionary changes in the $O$ – $C$ residuals.

Based on a sample of RR Lyrae variable stars including more than 9000 objects with proper motions and distances, we have investigated the kinematics of the Galactic halo from the two-dimensional velocity field. We have used both the proper motions deduced independently by us from the positional data taken from all-sky catalogues in a time interval up to 65 years and the proper motions taken from the Gaia DR2 catalogue. In addition, we have also studied the halo kinematics from the three-dimensional velocity field of ~850 RR Lyrae variables with distances, proper motions, and line-of-sight velocities. The kinematic parameters describing the velocity field have been estimated by the maximum-likelihood method; their change with Galactocentric distance has been investigated. The radial velocity dispersion in spherical coordinates σr ≈ 160−170 km s−1 exceeds its values from previous papers approximately by 20 km s−1, while the anisotropy parameter β ≈ 0.68−0.72 agrees satisfactorily with previous studies. When estimating the rotation velocity of the population of RR Lyrae stars, we identified the inner and outer halos with weak prograde and retrograde rotations, respectively.

We cross-match objects from several different astronomical catalogs to determine the absolute proper motions of stars within the 30-arcmin radius fields of 115 Milky-Way globular clusters with the accuracy of 1–2 mas yr−1. The proper motions are based on positional data recovered from the USNO-B1, 2MASS, URAT1, ALLWISE, UCAC5, and Gaia DR1 surveys with up to ten positions spanning an epoch difference of up to about 65 years, and reduced to Gaia DR1 TGAS frame using UCAC5 as the reference catalog. Cluster members are photometrically identified by selecting horizontal- and red-giant branch stars on color–magnitude diagrams, and the mean absolute proper motions of the clusters with a typical formal error of about 0.4 mas yr−1 are computed by averaging the proper motions of selected members. The inferred absolute proper motions of clusters are combined with available radial-velocity data and heliocentric distance estimates to compute the cluster orbits in terms of the Galactic potential models based on Miyamoto and Nagai disk, Hernquist spheroid, and modified isothermal dark-matter halo (axisymmetric model without a bar) and the same model + rotating Ferre’s bar (non-axisymmetric). Five distant clusters have higher-than-escape velocities, most likely due to large errors of computed transversal velocities, whereas the computed orbits of all other clusters remain bound to the Galaxy. Unlike previously published results, we find the bar to affect substantially the orbits of most of the clusters, even those at large Galactocentric distances, bringing appreciable chaotization, especially in the portions of the orbits close to the Galactic center, and stretching out the orbits of some of the thick-disk clusters.

Position data for stars in the vicinities of 119 Galactic globular clusters from the USNOB1, 2MASS, URAT1, and ALLWISE catalogs have been reduced in the system of the UCAC5 reference catalog. The published positions are used together with positions from the UCAC5 and Gaia DR1 catalogs (with a difference in their epochs of 65 years) and photometric data from the 2MASS survey to distinguish cluster members, determine their absolute proper motions with an accuracy of 1–2 milliarcseconds/year (mas/year), and calculate the mean absolute proper motions of the clusters with accuracies of about 0.4 mas/year. The derived proper motions and published distances and radial velocities for the clusters are used to establish the absence of rotation for a sample of metal-poor clusters in the Galactic halo. The mean velocity of the Sun relative to this sample is found to be (Vx(0), Vy(0), Vz(0)) = (−16 ± 16, −231 ± 19, +2± 16) km/s, and the distance of the Sun fromthe Galactic center is estimated to be R0 = 7.6 ±0.7 kpc. This paper is based on a presentation made at the conference “Modern Astrometry 2017,” dedicated to the memory of K.V. Kuimov (Sternberg Astronomical Institute,Moscow State University, October 23–25, 2017).