We have analyzed the change in the period of the ultracompact binary system ZTF J213056.71+442046.5, a source of potentially detectable mHz gravitational waves for planned space laser interferometers. The photometric data cover a time interval of almost 6.5 years and include our own observations carried out with the RC600 telescope at the Caucasus Mountain Observatory of the Sternberg Astronomical Institute of the Moscow State University and data from the ZTF sky survey. The O-C diagram can be described by quadratic light elements that correspond to a rate of period decrease dP/dt=(-2.66± 0.62)× 10^-12 s s ^-1 . This value leads to an almost twofold increase in the expected signal-to-noise ratio for the observations of gravitational waves from this binary system with space laser interferometers.

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 present the results of spectral observations and consequent analysis of six long-period double-lined eclipsing binaries (DLEBs) with main-sequence (MS) components from a sample formed with the aim of testing the ‘‘mass–luminosity’’ relation (MLR) for stars in the M/M_⊙>1.5 mass range. We analyzed all the obtained spectra using a technique that allows one to reveal the binary nature of the system and determine T_eff and log g for each component, as well as the system metallicity [Fe/H] and line-of-sight extinction E(B-V) . We computed the absolute parameters of the systems under consideration. An analysis of the obtained spectra shows that for three of the six objects (V1156 Cyg, EU Gem and V733 Per) we can clearly establish their binary nature and determine the spectral type and class for each component. Both components of the V733 Per system have already left the MS, and therefore the system must be excluded from our sample, whereas studies of V1156 Cyg and EU Gem should continue. OT And did not demonstrate a binary spectrum, however, the main component of the system is a hot A6 V star, and therefore, OT And should remain in our sample. We also revealed no binarity in the IM Del and LX Gem systems. Their brighter components turned out to be a cool giant and a supergiant, and these systems should be excluded from the sample based on the results of our analysis. We used the same technique to analyze the two spectra obtained for systems EU Gem and LX Gem using LAMOST. We have shown that the parameters determined from LAMOST spectra are in good agreement with the parameters determined for spectra obtained at the Caucasian Mountain Observatory (CMO) of SAI MSU. Our analysis allowed us to plot a first approximation of the V1156 Cyg velocity curves and show that the cool component in this system has a larger mass.

Long-period eclipsing binaries (variables) are a valuable source of data for calculating stellar masses. Such objects have a sufficient amount of both photometric and spectral data for determining their parameters and further analysis. We began a project to study long-period massive eclipsing binaries in order to determine their component masses and refine the mass-luminosity relation for stars of high and intermediate masses. We describe our project in general terms, focusing in more detail on the use of large photometric surveys as an important base in our research. We will talk about almost all avaliable large sky surveys, from which we collected all available photometric data on our objects and constructed light curves. We present the results of photometric data analysis for the objects we study using existing and specially constructed software packages. In particular we demonstrate several cases, where application of the surveys’ data to our objects allows us to obtain new orbital period for eclipsing binaries. The paper is based on a talk presented at the astrophysical memorial seminar “Novelties in Understanding the Evolution of Binary Stars”, dedicated to the 90th anniversary of Professor M.A. Svechnikov.

For both periods of the double-mode Cepheid V371 Per and for the Cepheid OGLE-LMC-CEP-2132 we have constructed O-C diagrams spanning a time interval of 126 and 119 years, respectively. The O-C diagrams have the shape of parabolas, which has allowed us for the first time to determine the quadratic light elements and to calculate the rates of evolutionary changes in their periods: dP_Fu/dt=1.085(±0.007) s yr ^-1 and dP_1O/dt=0.923(±0.003) s yr ^-1 for the fundamental mode and the first overtone of V371 Per, respectively, and dP/dt=15.304(±0.048) s yr ^-1 for OGLE-LMC-CEP-2132, in agreement with the results of theoretical calculations for the first crossing of the instability strip. The pulsation stability test proposed by Lombard and Koen has confirmed that the increase in the periods is real.

Evolutionary link between Red Supergiants and Luminous Blue variables is interesting, but still poorly understood. Wepresent the results of study of the Galactic candidate luminous blue variable Wray 15-906, revealed via detection of itsinfrared circumstellar shell (of ≈ 2 pc in diameter) with the Wide-field Infrared Survey Explorer (WISE) and the HerschelSpace Observatory. Using the stellar atmosphere code CMFGEN and the Gaia parallax, we found that Wray 15-906 is arelatively low-luminosity, log(L/L ⊙ ) ≈ 5.4, star of temperature of 25 ± 2 kK. In the framework of single star evolution,the obtained results suggest that Wray 15-906 is a post-red supergiant star with initial mass of ≈ 25 M ⊙ and that beforeexploding as a supernova it could transform for a short time into a WN11h star. The presence of shell with mass 2.9±0.5 M ⊙indicates that Wray 15-906 has suffered substantial mass loss in the recent past.

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.

We propose a new version of the (Baade–Becker–Wesselink) pulsating photospheres method based on direct spectral measurements of the effective temperatures of Cepheids carried out in different pulsation phases. By comparing the effective temperatures calculated using normal color calibrations with real spectroscopic estimates, we were able to not only determine the color excess with an accuracy of the order of $$0\mathop .\limits^{\text{m}} 01$$ mag, but also use all the measured effective temperature values to derive a new color calibration for the effective temperature of high luminosity stars, also taking into account the differences in metallicity $${\text{[Fe/H}}]$$ and surface gravity $$\log {\kern 1pt} g$$ : log Teff = 3.88 – 0.20(B – V)0 + 0.026(B –V) $$_{0}^{2}$$ + 0.009log g – 0.010(B – V)0log g – 0.051[Fe/H] + 0.051(B – V)0[Fe/H], the relative accuracy of which is approximately $$1.1\% $$ . In addition, the complete identity of the two main versions of the Baade–Becker–Wesselink method was proved: the surface brightness method (SB), first proposed by Barnes and Evans in 1976, and the maximum likelihood method (or light-curve modeling method) proposed by Balona in 1977 and later improved by Rastorguev and Dambis in 2010. This approach consists of using significantly nonlinear color calibrations for $$\log {{T}_{{{\text{eff}}}}}$$ and bolometric correction $$BC$$ and is easily applicable to the surface brightness method. This method is also applicable in studies of other types of pulsating variable stars, e.g., RR Lyrae, Mirae and $$\delta $$ Sct type variables with known effective temperature estimates.

Abstract One of the important sources for independent determination of stellar masses is eclipsing binaries with components on the main sequence, and with observable spectral lines of both components. The parameters of such stars are used to construct the mass–luminosity relation for stars of high and intermediate masses. Among them, the type of long-period eclipsing binaries stands out, the parameters of which are currently not fully determined, which is associated with the difficulties caused by the need for long-term observations. In this article, we will review the currently available observational data for such objects and discuss the prospects for their use to determine stellar masses.

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°.

For two classical Cepheids, CEa Cas and CEb Cas, members of the open cluster NGC 7790, we have constructed $$O-C$$ diagrams spanning a time interval of 125 years. The $$O-C$$ diagrams have the shape of parabolas, which has allowed us for the first time to determine the quadratic light elements and to calculate the rates of evolutionary changes in their periods: $$dP/dt={-}0.038({\pm}{0.017})$$ s yr $${}^{-1}$$ for CEa Cas and $$dP/dt={+}0.099({\pm}{0.010})$$ s yr $${}^{-1}$$ for CEb Cas, in agreement with the theoretical calculations for the second and third crossings of the instability strip, respectively. The pulsation stability test proposed by Lombard and Koen has confirmed that the changes in the periods are real.

The reduction of all the available photometry for the Cepheid SU Sct has allowed its $$O-C$$ diagram spanning a time interval of 60 years to be constructed. Six abrupt changes in the period have been detected. The pulsation stability test proposed by Lombard and Koen (1993) has confirmed that the changes in the period are real. The absolute magnitude of SU Sct is $$M_{V}\simeq{-}0\overset{\textrm{m}}{.}32$$ , confirming that it belongs to BL Her-type Population II Cepheids.

The reduction of all the available photometry for the Cepheid V420 Cen has allowed its $$O-C$$ diagram spanning a time interval of 131 years to be constructed. The data obtained provide evidence for the existence of large random fluctuations in the period ( $$\varepsilon/P\approx 0.021$$ ). Fitting the $$O-C$$ residuals by a cubic parabola has made it possible to estimate the rate of secular decrease in the period, $$dP/dt=-353.0({\pm}{3.6})$$ s yr $${}^{-1}$$ . The pulsation stability test proposed by Lombard and Koen in 1993 has confirmed that the decrease in the period is real.

The reduction of all the available photometry for the Cepheid CE Pup has allowed its $$O-C$$ diagram spanning a time interval of 128 years to be constructed. This has made it possible for the first time to calculate the rate of evolutionary increase in the period, $$dP/dt=+155.3(\pm{13.1})$$ s yr $${}^{-1}$$ , in agreement the results of model calculations for the third crossing of the instability strip. The pulsation stability test proposed by Lombard and Koen confirmed that the evolutionary change in the period is real.

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.

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.

The reduction of all the available photometry for the Cepheid EV Aql has allowed its $$O-C$$ diagram spanning a time interval of 130 years to be constructed. This has made it possible to calculate the rate of evolutionary decrease in the period, $$dP/dt=-33.2({\pm}{6.9})$$ s yr $${}^{-1}$$ , in agreement with the results of model calculations for the second crossing of the instability strip. The pulsation stability test proposed by Lombard and Koen has confirmed that the decrease in the period is real.