Photometric elements,apsidal motion,and a third body in the eclipsing binary HP Aur

Highly accurate W BV R photometric measurements of the eclipsing binary HP Aur were performed in 2002–2003 with the 48-cm AZT-14 reflector at the Tien-Shan High-Altitude Observatory to determine the rate of apsidal motion. A consistent system of physical and geometrical parameters of the components and the binary as a whole has been constructed for the first time by analyzing these new measurements together with other published data: we determined their radii (R₁ = 1.05R_⊙, R₂ = 0.82R_⊙) and luminosities (L₁ = 1.10L_⊙, L₂ = 0.46L_⊙), spectral types (G2V + G8V) and surface gravities (log g₁ = 4.38, log g₂ = 4.51), age (t = 9.5 × 10⁹ yr), and the distance to the binary (d = 197 pc). We detected an ultraviolet excess in the spectra of both components, \(\Delta (W - B) \simeq - 0\mathop .\limits^m 25\), that is probably attributable to a metal deficiency in the atmospheres of these stars. In this system of two solar-type stars, we found a third body with the mass M₃ sin i ₃ ³ = 0.17_M⊙ that revolved with the period P₃ = 13.7 yr around the eclipsing binary in a highly eccentric elliptical orbit: e₃ = 0.70 and A₃ sin i₃ ? 7 AU. The orbit of the eclipsing binary itself was shown to be also elliptical, but with a low eccentricity (e = 0.0025(5)), while apsidal motion with a period U_obs > 80 yr was observed at a theoretically expected period U_th ≈ 92 yr. At least 20 to 30 more years of photoelectric measurements of this star will be required to reliably determine U_obs.     

Close binary systems in multiple stars: III. Eclipsing variables with LITE effect

The list of 240 eclipsing variables with the light equation (LITE effect) has been compiled. Some characteristics of multiple systems have been determined assuming that those stars may contain extra components. Quantity distributions have been obtained for Close Binary Systems (CBSs) with LITE effect and for those without it. The observed excess of short period stars (<0.3 days) is shown to be realistic. The eccentricities of Long Periodic Orbits (LPOs) have a parabolic distribution with a weak maximum at e = 0.28. The ratios of LPO to CBS periods cannot be considered to be random. The dependence of those values on LPO periods has been revealed. The distributions of periods and semimajor axes of LPOs are shown to have maxima at P ₃ = 32 yrs and a = 16 AU, respectively. The latter distribution can be described by the Gaussian function. Approximately 85% of tertiary companions in stellar systems have a mass which is half as much as the total CBS mass. Except for one CBS (RR Lyn), all multiple systems of the obtained list are dynamically stable configurations. The possibilities to detect tertiary companions using speckle interferometry observations and proper motions of CBSs, as well as by extra light contribution when analyzing light curves and radial velocity changes of the CBS center of mass are discussed. Other causes are considered which may be a reason for the LITE effect, such as the mass exchange in CBSs and the influence of the magnetic field of components. Certain difficulties may arise when interpreting the LITE effect caused by the magnetic field of components. The most promising research directions in detecting tertiary companions in CBSs with the LITE effect are suggested.     

Study of the apsidal motion in the eclipsing binary MZ Lac

A series of highly accurate photoelectric observations of the eclipsing binary MZ Lac was obtained with a 48-cm AZT-14 reflector at the Tien-Shan High-Altitude Station of the Sternberg Astronomical Institute from 1985 to 2004 to study its apsidal motion. We constructed a consistent system of physical and geometrical parameters of the components and the binary’s orbit: we determined their masses (M₁ = 1.50M_⊙, M₂ = 1.29M_⊙), radii (R₁ = 1.86R_⊙, R₂ = 1.35R_⊙), luminosities (L₁ = 0.79L_⊙, L₂ = 0.45L_⊙), surface gravities (log_g1 = 4.06, log_g2 = 4.27), age (t = 1.9 × 10⁹ yr), and the distance to the binary (d = 510 pc). The binary exhibits apsidal motion with the period U_obs = 480 ± 40 yr, while its theoretically expected value is U_th = 450 ± 40 yr. Spectroscopic studies of MZ Lac and calculations of the absolute parameters of the components are required to test our conclusions.     

Effects of stellar wind,dynamical friction,and star mergers on the dynamical evolution of multiple stars

The dynamical evolution of small stellar groups composed of N=6 components was numerically simulated within the framework of a gravitational N-body problem. The effects of stellar mass loss in the form of stellar wind, dynamical friction against the interstellar medium, and star mergers on the dynamical evolution of the groups were investigated. A comparison with a purely gravitational N-body problem was made. The state distributions at the time of 300 initial system crossing times were analyzed. The parameters of the forming binary and stable triple systems as well as the escaping single and binary stars were studied. The star-merger and dynamical-friction effects are more pronounced in close systems, while the stellar wind effects are more pronounced in wide systems. Star-mergers and stellar wind slow down the dynamical evolution. These factors cause the mean and median semimajor axes of the final binaries as well as the semimajor axes of the internal and external binaries in stable triple systems to increase. Star mergers and dynamical friction in close systems decrease the fraction of binary systems with highly eccentric orbits and the mean component mass ratios for the final binaries and the internal and external binaries in stable triple systems. Star mergers and dynamical friction in close systems increase the fraction of stable triple systems with prograde motions. Dynamical friction in close systems can both increase and decrease the mean velocities of the escaping single stars, depending on the density of the interstellar medium and the mean velocity of the stars in the system.     

Searching for Binary Systems Among Nearby Dwarfs Based on Pulkovo Observations and SDSS Data

Our goal is to find previously unknown binary systems among low-mass dwarfs in the solar neighborhood and to test the search technique. The basic ideas are to reveal the images of stars with significant ellipticities and/or asymmetries compared to the background stars on CCD frames and to subsequently determine the spatial parameters of the binary system and the magnitude difference between its components. For its realization we have developed a method based on an image shapelet decomposition. All of the comparatively faint stars with large proper motions (V >13 ^m , μ > 300 mas yr^?1) for which the “duplicate source” flag in the Gaia DR1 catalogue is equal to one have been included in the list of objects for our study. As a result, we have selected 702 stars. To verify our results, we have performed additional observations of 65 stars from this list with the Pulkovo 1-m “Saturn” telescope (2016–2017). We have revealed a total of 138 binary candidates (nine of them from the “Saturn” telescope and SDSS data). Six program stars are known binaries. The images of the primaries of the comparatively wide pairs WDS 14519+5147, WDS 11371+6022, and WDS 15404+2500 are shown to be resolved into components; therefore, we can talk about the detection of triple systems. The angular separation ρ, position angle, and component magnitude difference Δm have been estimated for almost all of the revealed binary systems. For most stars 1.5′′ < ρ < 2.5′′, while Δm <1.5^m.     

Properties of Wolf-Rayet stars in eclipsing binary systems

The results of investigations of a number of eclipsing Wolf-Rayet binaries are presented. The ‘core’ radiuses, the ‘core’ temperatures and masses of WR stars in the eclipsing WR+OB binary systems V 444 Cyg, CX Cep, CQ Cep, and CV Ser are obtained (see Table I). The results obtained from the light curves analysis of the V 444 Cyg in the range λλ2460 Å-3.5μ give strong evidence for the Beals (1944) model of WR phenomenon. The chromospheric-coronal effects in the WN5 extended atmosphere are not observed up to a distance ofr?20R _⊙. In the Hertzsprung—Russell diagram all the WR stars lie on the left side from the main sequence between the main sequence and the sequence of uniform helium stars (see Figure 9). Their locations are close to those of the helium remnants formed as a result of mass exchange in massive close binary systems. The period variations in the systems V 444 Cyg and CQ Cep have been discovered and a reliable value of the mass loss rateM=10^?5 M _⊙yr^?1 is obtained, for the two WR stars. The results of the photometric and spectroscopic investigations of the WR stars with low mass companions (post X-ray binary stage?) are presented too (see Table II). The masses of the companions are (1–2)M _⊙, their optical luminosity is ～10³⁶, erg s^?1 which implies that these companions cannot be the normal stars. It is possible that these companions are neutron stars accreting from the stellar wind of the WR stars. Low values of the X-ray luminosities of such WR stars with low mass companions imply that the accretion of matter in such systems is distinct from the accretion process in classical X-ray binary systems. It is noted also that the parameters of low massive companions coupled with WR stars are close to those of helium stars.     

New orbits of wide visual double stars

Based on photographic and CCD observations with the Pulkovo 26-inch refractor, radial velocity measurements with the 1.5-m RTT-150 telescope (TUBITAK National Observatory, Turkey), and highly accurate observations published in the WDS catalog, we have obtained the orbits of ten wide visual double stars by the apparent motion parameter method. The orientation of the orbits in the Galactic coordinate system has been determined. For the outer pair of the multiple star HIP 12780 we have calculated a family of orbits with a minimum period P = 4634 yr. Two equivalent solutions with the same period have been obtained for the stars HIP 50 (P = 949 yr) and HIP 66195 (P = 3237 yr). We have unambiguously determined the orbits of six stars: HIP 12777 (P = 3327 yr), HIP 15058 (P = 420 yr), HIP 33287 (P = 1090 yr), HIP 48429 (P = 1066 yr), HIP 69751 (P = 957 yr), and HIP 73846 (P = 1348 yr). The orbit of HIP 55068 is orientated perpendicularly to the plane of the sky, P >1000 yr. The star HIP 48429 is suspected to have an invisible companion.     

Detection of the binarity of the star J1158+4239

One of the goals of the Pulkovo program of research on stars with large proper motions is to reveal among the low-luminosity stars those that have evidence of binarity. Twelve astrometric binary candidates from the Pulkovo list have been included in the program of speckle observations with the BTA telescope at the Special Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS) and the 2.5-m telescope at the Caucasus Observatory (CO) of the Sternberg Astronomical Institute of the Moscow State University to confirm their binarity and then to determine the parameters of the revealed stellar pairs. The binarity of the brightest of these stars, J1158+4239 (GJ 3697), has been confirmed. Four sessions of speckle observations with the BTA SAO RAS telescope and one session with the 2.5-m CO telescope have been carried out in 2015–2016. The weighted mean estimates of the pair parameters are ρ = 286.5 ± 1.2 mas and θ = 230.24? ± 0.16? at the epoch B2015.88248. The magnitude difference between the pair stars is Δm = 0.55 ± 0.03 (a filter with a central wavelength of 800 nm and a FWHM of 100 nm) and Δm = 0.9 ± 0.1 (an R filter).     

Close binaries in multiple-star systems. I. Eclipsing variables in Orbital Visual Binaries

We made up a list of eclipsing variables from The Sixth Catalog of Orbits of Visual Binary Stars and supplemented it with physical parameters and some orbital elements of triple stars. A histogram of the angles between the orbital planes of close and wide pairs was built. These angles were shown to be no greater than 20° in two-thirds of cases, and the difference between the angles was shown to increase with semimajor axis of visual orbit. The distribution of the ratios between long and short periods has local maxima in certain intervals. The dynamical sum of the masses of triple-system components turned out to be in good agreement with the sum of the masses of close binary components estimated by precise methods and the mass of the tertiary component determined from the mass-luminosity relation. Most of tertiary components were found to have masses half as large as the sums of the masses of close pair components. Our estimates suggest that the precession periods of the orbits of close binary systems range from several thousand to several tens of million years.     

New photometric investigation of the Herbig Ae/Be star HD 52721, a close binary system: Evidence for the existence of large-scale azimuthal inhomogeneities

We present new results of our photometry for the Herbig Be star HD 52721 obtained from January 16 to March 25, 2013. A new data reduction technique is used. Using this technique, we have also reanalyzed the previous results of our photometry for this object pertaining to the period from March 7 to March 28, 2010. The Be star HD 52721 is known as an eclipsing variable with the period P = 1^d. 610. Two photometric minima observed during one period are a peculiarity of its photometric variability. They are separated in phase of the period P by 0.5 and differ from one another in depth by 0 ^m . 04. We have also detected additional minima observed at the phases of maximum brightness. We hypothesize that they can be associated with the existence of local azimuthal inhomogeneities rotating synchronously with the orbital motion of the binary component stars in the circumstellar envelope. When processing our CCD frames, we have applied an efficient CCD-frame rejection method that has allowed the accuracy of observations to be increased considerably. The CCD frames have been further processed using the Apex II software package, which is a universal software platform for astronomical image processing. We justify the need for additional photometric observations of HD 52721 in various color bands to confirm the hypothesis about the existence of azimuthal inhomogeneities in the program binary system and to analyze their physical properties.     

Radial and rotational velocities for a sample of magnetic CP stars

The spectra taken with the Main Stellar Spectrograph (MSS) of the 6-m telescope with a resolution of R ～ 15000 and a signal-to-noise ratio of 200–300 are used to determine the radial velocities and projected rotational velocities (υ _e sin i) for 32 magnetic CP stars. Measured υ _e sin i values range from 18 km/s (the lower boundary determined by the instrumental profile) to 65 km/s. Measurements of standard stars demonstrate the absence of systematic differences between our and published data. Eight of the 32 magnetic stars are found or confirmed to be binary and binarity is suspected for another four stars. The components of tangential velocity are determined for 27 stars with known parallaxes.     

The mass-radius relation in binary systems

The mass-radius relation is determined for Main-Sequence stars from observational data of well-detached binary systems. The results are compared to previous empirical relations and we discuss their application to the study of the light curves of eclipsing binaries. A comparison with theoretical Main-Sequence models has been carried out.     

Orbital stability of systems of closely-spaced planets,II: configurations with coorbital planets

We numerically investigate the stability of systems of 1 \({{\rm M}_{\oplus}}\) planets orbiting a solar-mass star. The systems studied have either 2 or 42 planets per occupied semimajor axis, for a total of 6, 10, 126, or 210 planets, and the planets were started on coplanar, circular orbits with the semimajor axes of the innermost planets at 1 AU. For systems with two planets per occupied orbit, the longitudinal initial locations of planets on a given orbit were separated by either 60° (Trojan planets) or 180°. With 42 planets per semimajor axis, initial longitudes were uniformly spaced. The ratio of the semimajor axes of consecutive coorbital groups in each system was approximately uniform. The instability time for a system was taken to be the first time at which the orbits of two planets with different initial orbital distances crossed. Simulations spanned virtual times of up to 1 × 10⁸, 5 × 10⁵, and 2 × 10⁵ years for the 6- and 10-planet, 126-planet, and 210-planet systems, respectively. Our results show that, for a given class of system (e.g., five pairs of Trojan planets orbiting in the same direction), the relationship between orbit crossing times and planetary spacing is well fit by the functional form log(t _c /t ₀) = b β + c, where t _c is the crossing time, t ₀ = 1 year, β is the separation in initial orbital semimajor axis (in terms of the mutual Hill radii of the planets), and b and c are fitting constants. The same functional form was observed in the previous studies of single planets on nested orbits (Smith and Lissauer 2009). Pairs of Trojan planets are more stable than pairs initially separated by 180°. Systems with retrograde planets (i.e., some planets orbiting in the opposite sense from others) can be packed substantially more closely than can systems with all planets orbiting in the same sense. To have the same characteristic lifetime, systems with 2 or 42 planets per orbit typically need to have about 1.5 or 2 times the orbital separation as orbits occupied by single planets, respectively.     

Planetary system formation through binary star merging

A scenario is considered for the formation of a planetary system through the merging of a binary star comprised of low-mass (0.5–1 M _⊙) stars in the stage of contracting towards the main sequence. According to our previous computations (Sirotkin and Karetnikov, 2006), under certain conditions, the destruction of the more massive component can result in the formation of a central star, an accretion disk, and an extended arm. The extended arm is fragmented to form clouds of planetary masses (<5M _J). The formed disk and clouds rotate in the same direction as the central star. The clouds are in elongated orbits (e > 0.3) lying in the orbital plane of the initial binary system. To test these earlier results, we repeated computations for the same system parameters but with higher accuracy. The new computations confirmed the earlier results and gave new information about the cloud and disk structure.     

The angular momentum-vs-mass relation and the distribution of mass ratios for visual binary systems

The investigation of the angular momentum vs mass relation for binary stars is completed with a study of the 847 systems contained in theFourth Catalog of Orbits of Visual Binary Stars. Because bothJ andM of a visual binary depend steeply on the distance to the system (5th and 3rd powers, respectively), and many of the distances are not well known, the study makes use of an auxiliary parameterR which is independent of distance and proportional toJM ^–5/3.R appears to be uncorrelated withM for the 789 systems for which both can be determined. The non-correlation implies thatJ M ^5/3, expected from Kepler's third law, provides a better fit to the visual binaries than doesJ M ², predicted by some more complex considerations.The distribution functionf(q=M ₂/M₁) of mass ratios for the visual binaries results as a byproduct of the investigation. It peaks extremely sharply towardq=1.0 (much more so than for spectroscopic binaries). Because most visual binaries are wide enough to consist of stars that condensed independently (and so that can be thought of as chosen at random from an initial mass function), one expects the realf(q) to rise toward low ratios. Observational selection against the discovery and study of systems with large magnitude differences between the components must be very large indeed to account for the discrepancy between expectation and observation. The alternative is a mechanism for formation of wide binaries that favours equal components. The distribution of mass ratios for eclipsing binaries is given in an appendix. It peaks strongly atq=0.6–0.75 and largely reflects processes of angular momentum, mass, and energy exchange between the stars in contact systems.     

Results of a long-term monitoring of the multiple system SZ Cam

We present the results of the reduction of our photometric and spectroscopic observations for the eclipsing binary SZ Cam performed with the telescopes at the Astronomical Observatory of the Ural Federal University and the Special Astrophysical Observatory of the Russian Academy of Sciences in 1996–2014. Based on an 11-year-long photometric monitoring of SZ Cam, we have obtained new elements of its photometric orbit and parameters of its components. We have detected low-amplitude periodic light variations in SZ Cam that are possibly related to the ellipsoidal shape of the components of the spectroscopic binary third body. Based on published data and our new spectroscopy, we have found new values for the mass ratio, q = 0.72 ± 0.01, and parameters of the radial velocity curves of the components, V ₀ = ?3.6 ± 1.7 km s^?1, K ₁ = 190.2 ± 1.9 km s^?1, and K ₂ = 263.0 ± 2.4 km s^?1. The component masses have been estimated to be M ₁ = 16.1 M _⊙ and M ₂ = 11.6 M _⊙. We have obtained new light elements and parameters of the radial velocity curves for the third body, V ₀ ^3b = 4.2 ± 0.6 km s^?1 and K ₁ ^3b = 26.6 ± 0.8 km s^?1. We have improved the period of the relative orbit of SZ Cam and the third body, P _orb = 55.6 ± 1.5 yr.     

Chemical composition of the atmosphere and evolutionary status of the spectroscopic and speckle-interferometric binary 12 Persei

The system 12 Per is a spectroscopic and speckle-interferometric binary with the components of similar spectral classes. The parameters of its orbit were determined quite accurately over nearly a century of observations. To refine the atmospheric abundances of its components and their evolutionary status, we obtained the spectra of the star in the 3500–9600 Å spectral region using the echelle spectrometers of the 6-m BTA telescope of the SAO RAS and 2-m Zeiss-2000 telescope at Terskol Peak. Based on the luminosities (L ₁ = 3.02 L _⊙, L ₂ = 1.86 L _⊙) and effective temperatures (T _eff1 = 6195 K and T _eff2 = 6000 K) we have estimated the evolutionary status of the system’s components. The age of the system is 12.1 Byr, the components are at the stage of hydrogen burning near the zero-age main sequence. The resulting element abundances in the atmospheres of 12 Per components indicate enhanced metallicity of both stars: [Fe/H] ≥ 0.35. We consider a scenario in which the initially circular short-period orbit of the pair turns into an eccentric large-period orbit due to the transfer of angular momentum of the components to the angular momentum of orbital motion over one billion years.     

Infrared photometry for five close binary systems

We present the JHKLM photometry for five close (W Ser) binary systems obtained in the period 1996–2004. Positive phase shifts (with respect of the adopted ephemerides) have been found in the orbital infrared light curves for three binaries, RX Cas, KX And, and β Lyr; the rates of increase in their periods are ～3.5 × 10^?4, ～1.6 × 10^?3, and ～1.4 × 10^?4 days yr^?1, respectively. We have performed the spectral classification of the components of the binaries under study and estimated their parameters.     

Gamma-ray binaries and related systems

After initial claims and a long hiatus, it is now established that several binary stars emit high- (0.1–100 GeV) and very high-energy (>100 GeV) gamma rays. A new class has emerged called “gamma-ray binaries”, since most of their radiated power is emitted beyond 1 MeV. Accreting X-ray binaries, novae and a colliding wind binary (η Car) have also been detected—“related systems” that confirm the ubiquity of particle acceleration in astrophysical sources. Do these systems have anything in common? What drives their high-energy emission? How do the processes involved compare to those in other sources of gamma rays: pulsars, active galactic nuclei, supernova remnants? I review the wealth of observational and theoretical work that have followed these detections, with an emphasis on gamma-ray binaries. I present the current evidence that gamma-ray binaries are driven by rotation-powered pulsars. Binaries are laboratories giving access to different vantage points or physical conditions on a regular timescale as the components revolve on their orbit. I explain the basic ingredients that models of gamma-ray binaries use, the challenges that they currently face, and how they can bring insights into the physics of pulsars. I discuss how gamma-ray emission from microquasars provides a window into the connection between accretion–ejection and acceleration, while η Car and novae raise new questions on the physics of these objects—or on the theory of diffusive shock acceleration. Indeed, explaining the gamma-ray emission from binaries strains our theories of high-energy astrophysical processes, by testing them on scales and in environments that were generally not foreseen, and this is how these detections are most valuable.