Eigenfrequencies of rotationally and tidally distorted white dwarf models of stars

In the present paper we have studied the eigenfrequencies of small adiabatic barotropic pseudo-radial and nonradial modes of oscillations of the white dwarf models of rotating stars in binary systems. In this work the methodology of Mohan and Saxena (in Astrophys. Space Sci. 113:155, 1985) has been used that utilizes the averaging technique of Kippenhahn and Thomas (in Proc. IAU Colloq., vol. 4, p. 20, 1970) and certain results on Roche equipotential as that given by Kopal (in Advances in Astronomy and Astrophysics, Academic Press, 1972). The objective of this study is to investigate the effects of rotation and/or tidal distortion on the periods of oscillations of rotationally and/or tidally distorted white dwarf models of stars assuming it to be the primary component of the binary system and rotating uniformly. The results of present study show that the eigenfrequencies (both radial and nonradial modes) of the rotationally distorted and rotationally and tidally distorted white dwarf model of stars in binary systems tend to decrease under the influence of rotational distortions and rotational and tidal distortions, respectively. However, results are contrary for tidally distorted white dwarf model of stars.     

The two-body interaction potential in the STF tensor formalism: an application to binary asteroids

The symmetric trace free (STF) tensor formalism, developed by Hartmann et al. (Celest Mech Dyn Astron 60:139–159. doi:10.1007/BF00693097, 1994), is a nice tool, not much used in Celestial Mechanics. It is fully equivalent to the usual spherical harmonics but permits more elegant and compact formulations. The coupling between the gravitational fields of extended bodies with this formalism has been used in Mathis and Le Poncin-Lafitte (Astron Astrophys 497:889–910. doi:10.1051/0004-6361/20079054, 2009) for binary stars or planetary systems, but not yet applied to binary asteroids. However, binary asteroids are common in the Solar System and usually their study requires a full two rigid body approach. The formulation of the two-body interaction potential in the STF formalism in the full two rigid body problem is detailed and completed in this article. An application to the binary asteroid (66391) 1999 KW4 is presented with a comparison of our results with other results of the literature for validation.     

Stellar dynamics in young clusters: the formation of massive runaways and very massive runaway mergers

In the present paper we combine an N-body code that simulates the dynamics of young dense stellar systems with a massive star evolution handler that accounts in a realistic way for the effects of stellar wind mass loss. We discuss two topics.

1. The formation and the evolution of very massive stars (with masses >120 M_⊙) is followed in detail. These very massive stars are formed in the cluster core as a consequence of the successive (physical) collisions of the 10–20 most massive stars in the cluster (this process is known as ‘runaway merging’). The further evolution is governed by stellar wind mass loss during core hydrogen and core helium burning (the WR phase of very massive stars). Our simulations reveal that, as a consequence of runaway merging in clusters with solar and supersolar values, massive black holes can be formed, but with a maximum mass ≈70 M_⊙. In low-metallicity clusters, however, it cannot be excluded that the runaway-merging process is responsible for pair-instability supernovae or for the formation of intermediate-mass black holes with a mass of several 100 M_⊙.
2. Massive runaways can be formed via the supernova explosion of one of the components in a binary system (the Blaauw scenario), or via dynamical interaction of a single star and a binary or between two binaries in a star cluster. We explore the possibility that the most massive runaways (e.g. ζ Pup, λ Cep, BD+43°3654) are the product of the collision and merger of two or three massive stars.

     

Fourier analysis of light curves of eclipsing variable stars

The photometric perturbationsB _h ^(l) arising from both tidal and rotational distortion of a close eclipsing binary have been given in two previous papers (Livaniou, 1977; Rovithis-Livaniou, 1977). The aim of the present paper will be to find the eclipse perturbationsB _2m =B _{2m, tid} +B _{2m, rot} of a close binary exhibiting partial eclipses. This will be done giving the suitable combinations of theB _h ^(l) 's and will make easier the application to real stars. After a very brief introduction, Section 2 gives both theB _{2m, tid} andB _{2m, rot} for uniformly bright discs; while in Sections 3 and 4 they are given for linear and quadratic limb-darkening, respectively. Finally, Section 5 gives a brief discussion of the results.     

A family of zero-velocity curves in the restricted three-body problem

The equilibrium points and the curves of zero-velocity (Roche varieties) are analyzed in the frame of the regularized circular restricted three-body problem. The coordinate transformation is done with Levi-Civita generalized method, using polynomial functions of n degree. In the parametric plane, five families of equilibrium points are identified: \(L_{i}^{1}, L_{i}^{2}, \ldots, L_{i}^{n}\) , \(i\in\{ 1,2,\ldots,5 \}, n \in\mathbb{N}^{*}\) . These families of points correspond to the five equilibrium points in the physical plane L ₁,L ₂,…,L ₅. The zero-velocity curves from the physical plane are transformed in Roche varieties in the parametric plane. The properties of these varieties are analyzed and the Roche varieties for n∈{1,2,…,6} are plotted. The equation of the asymptotic variety is obtained and its shape is analyzed. The slope of the Roche variety in \(L_{1}^{1}\) point is obtained. For n=1 the slope obtained by Plavec and Kratochvil (1964) in the physical plane was found.     

Limits on the Orbits of Possible Eccentric and Inclined Moons of Extrasolar Planets Orbiting Single Stars

Limits are placed on the range of orbits and masses of possible moons orbiting extrasolar planets which orbit single central stars. The Roche limiting radius determines how close the moon can approach the planet before tidal disruption occurs; while the Hill stability of the star–planet–moon system determines stable orbits of the moon around the planet. Here the full three-body Hill stability is derived for a system with the binary composed of the planet and moon moving on an inclined, elliptical orbit relative the central star. The approximation derived here in Eq. (17) assumes the binary mass is very small compared with the mass of the star and has not previously been applied to this problem and gives the criterion against disruption and component exchange in a closed form. This criterion was applied to transiting extrasolar planetary systems discovered since the last estimation of the critical separations (Donnison in Mon Not R Astron Soc 406:1918, 2010a) for a variety of planet/moon ratios including binary planets, with the moon moving on a circular orbit. The effects of eccentricity and inclination of the binary on the stability of the orbit of a moon is discussed and applied to the transiting extrasolar planets, assuming the same planet/moon ratios but with the moon moving with a variety of eccentricities and inclinations. For the non-zero values of the eccentricity of the moon, the critical separation distance decreased as the eccentricity increased in value. Similarly the critical separation decreased as the inclination increased. In both cases the changes though very small were significant.     

Structure and evolution of single WR stars

New computations of massive stars follow the evolution up to advanced stages and include:

-A large and flexible nuclear network consisting of 174 nuclear species that are linked by 1742 nuclear reactions.

-Semiconvection, overshooting and mass loss.

-Modern rates for both strong and weak interaction processes as well as the latest rates for the neutrino processes.

-Improved grid distribution and a large number of grid points.

The nuclear network and the diffusion equation are solved for each time step during the whole evolution. In this way the accuracy of nuclear yields and chemical abundances are mainly limited by uncertainties in the diffusion coefficient found from the convection theories. Several instability mechanisms may affect the mass loss rates of massive stars and thereby the structure and abundances of WR stars. Due to heavy mass loss at the LBV and WR stages, the masses at the pre-SN stage may be less than 5M _⊙. Yields and abundances throughout the stars are discussed together with the amount of all elements expelled.     

EXOTIME: searching for planets around pulsating subdwarf B stars

In 2007, a companion with planetary mass was found around the pulsating subdwarf B star V391 Pegasi with the timing method, indicating that a previously undiscovered population of substellar companions to apparently single subdwarf B stars might exist. Following this serendipitous discovery, the EXOTIME (http://www.na.astro.it/~silvotti/exotime/) monitoring program has been set up to follow the pulsations of a number of selected rapidly pulsating subdwarf B stars on time scales of several years with two immediate observational goals:

1. determine $\dot{P}$ of the pulsational periods P
2. search for signatures of substellar companions in O–C residuals due to periodic light travel time variations, which would be tracking the central star’s companion-induced wobble around the centre of mass

These sets of data should therefore, at the same time, on the one hand be useful to provide extra constraints for classical asteroseismological exercises from the $\dot{P}$ (comparison with “local” evolutionary models), and on the other hand allow one to investigate the preceding evolution of a target in terms of possible “binary” evolution by extending the otherwise unsuccessful search for companions to potentially very low masses. While timing pulsations may be an observationally expensive method to search for companions, it samples a different range of orbital parameters, inaccessible through orbital photometric effects or the radial velocity method: the latter favours massive close-in companions, whereas the timing method becomes increasingly more sensitive toward wider separations. In this paper we report on the status of the on-going observations and coherence analysis for two of the currently five targets, revealing very well-behaved pulsational characteristics in HS?0444+0458, while showing HS?0702+6043 to be more complex than previously thought.     

Photometric elements and apsidal motion of the eclipsing binary NSV 18773

The photometric elements of the eclipsing binary NSV 18773 (HD 99898) have been determined for the first time by analyzing its V-and I-band light curves from the ASAS-2 and ASAS-3 catalogs. Based on these elements and using other published spectroscopic and photometric data, we constructed a consistent system of geometrical and physical parameters for the system that consists of two stars (M ₁ = 20M _⊙, Sp₁=B0V, R ₁ = 5.0R _⊙ and M ₂ = 14M _⊙, Sp₂ = B1V, R ₂ = 6.5R _⊙) in elliptical orbits (P = 5 _. ^d 049, e = 0.365, a = 40.1R _⊙). The distance to the system is d = 3.3 kpc, the interstellar extinction is A _V = 2 _. ^m 0, and the age is t = 2.8 × 10⁶ yr. NSV 18773 is a visual binary with components V _A = 9 _. ^m 9 and V _B = 10 _. ^m 3 separated by 0 _. ^" 8. The third light (L ₃ = 0.61) that we found by analyzing the light curves shows that the eclipsing binary is the system’s fainter component B. We confirmed the rapid apsidal motion of the star detected by Otero and Wils (2006) and refined its observed period: U _obs = 150 ± 6 yr. Our photometric elements and physical parameters allowed the apsidal parameter $\bar k_2^{obs} = 0.0135(14)$ , which reflects the density distribution along the radii of the component stars, to be determined. Within the error limits, the derived parameter agrees with its theoretically expected value, $\bar k_2^{th} = 0.0119(8)$ , from current evolutionary models of stars of the corresponding masses and ages.     

Evolution of low-mass helium stars in semidetached binaries

We systematically investigate the evolution of low-mass (0.35, 0.40, and 0.65M _⊙) helium donors in semidetached binaries with white-dwarf accretors. The initial periods of the binaries are chosen in such a way that the helium abundance in the center of the models at the time of Roche lobe overflow varies between Y _c = 0.98 and Y _c ? 0.1. The results of our calculations can be used to analyze the formation scenarios and evolutionary status of AM CVn stars. We show that the minimum orbital periods of the semidetached binaries depend weakly on the total mass of the components and the evolutionary phase of the donor at the time of Roche lobe overflow and are 9–10 min. The differences in the mass transfer rates after P _orb reaches its minimum in the range P _orb ≈ 10–40 min do not exceed a factor of ～2.5. For P _orb ? 20 min, the mass-losing stars are weakly degenerate homogeneous cooling objects; the He, C, N, O, and Ne abundances depend on the evolutionary phase at which Roche lobe overflow occurred. For the binaries that are currently believed to be the most probable candidates for AM CVn stars with helium donors, Y ? 0.4, X _C ? 0.3, X _O ? 0.25, and X _N ? 0.5 × 10^?2. In the binaries under consideration, once P _orb ≈ 40 min has been reached, the mass loss time scale begins to exceed the thermal time scale of the donors, the latter begin to contract, their matter becomes degenerate, and the populations of AMCVn stars with white-dwarf and helium-star progenitors of their donors probably merge together.     

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.     

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.     

Stellar chromospheric temperatures

The emission doublet 2800 Mgii of stellar chromospheric origin is always stronger than the emission in the Lα line of hydrogen. At the same time, the ratio of their fluxes,Q=F(Mgii)/F(Lα), varies over a wide range— from 2 up to 20 in stars of one and the same type. Assuming that both emission structures, 2800 Mgii and Lα, are excited in one and the same region of the chromosphere, an attempt is made to represent the ratioQ as a function from one physical parameter only—chromospheric electron temperature. Such an approach explains easily the observed behaviour of the ratioQ in different stars.     

Spatial distribution and kinematics of OB stars

The sample of 37 485 suspected OB stars selected by Gontcharov (2008) from the Tycho-2 catalogue has been cleaned of the stars that are not of spectral types OV-A0V. For this purpose, the apparent magnitude V _T from Tycho-2, the absolute magnitude $M_{V_T }$ calibrated as a function of the dereddened color index (B _T ? V _T )₀, the interstellar extinction $A_{V_T }$ calculated from the 3D analytical model by Gontcharov (2009) as a function of the Galactic coordinates, and the photometric distance r _ph calculated as a function of V _T , $M_{V_T }$ , and $A_{V_T }$ have been reconciled in an iterative process. The 20 514 stars that passed the iterations have (B _T ? V _T )₀ < 0 and $M_{V_T }$ > ?5 and are considered as a sample of OV-A0V stars complete within 350 pc of the Sun. Based on the theoretical relation between the dereddened color and age of the stars, the derived sample has been divided into three subsamples: (B _T ? V _T )₀ < ?0.2, ?0.2 < (B _T ? V _T )₀ < ?0.1, and ?0.1 < (B _T ? V _T )₀ < 0, younger than 100, 100?C200, and 200?C400 Myr, respectively. The spatial distribution of all 20 514 stars and the kinematics analyzed for more than 1500 stars with radial velocities from the PCRV and RAVE catalogues are different for the subsamples, showing smooth rotations, shears, and deformations of the layer of gas producing stars with the formation of the Gould Belt, the Great Tunnel, the Local Bubble, and other structures within the last 200 Myr. The detected temporal variations of the velocity dispersions, solar motion components, Ogorodnikov-Milne model parameters, and Oort constants are significant, agree with the results of other authors, and show that it is meaningless to calculate the kinematic parameters for samples of stars with uncertain ages or with a wide range of ages.     

Roche potentials including radiation effects

A modified Roche potential which incorporates the effects of radiation pressure due to one component of a binary system is mathematically explored. In some cases, the resulting potentials do not exhibit the familiar contact surfaces of the classical Roche potential. The concept of a contact surface, which has been fundamental to the investigations of close binary systems, must be used with discretion for close binaries in which one component is very luminous. A convenient criterion for the existence of a contact surface is given by (1-μ) ? 3δ_c ^3/2 \((1 - 2(\tfrac{2}{3})^4 \delta _c )\) , (δ_c?1) where μ is the mass of the very luminous star in terms of the system mass. For systems of given μ, no contact surface exists if δ is greater than δ_c where δ is the ratio of radiation pressure force to gravitational attraction. Furthermore, energy considerations of the modified Roche potential indicate that binary systems with δ < δ_c should have a greater tendency to form rings than those with δ < δ_c.     

On the infrared observations of stellar flares

In connection with the appearance of the first results of infrared observations of stellar flares, a more elaborate analysis ofnegative infrared flares as a phenomenon, predicted by the fastelectron hypothesis, has been carried out. As a result, the wavelength regions of negative flares are established for the stars of different spectral types as well as the calculated amplitudes of the negative flares (Tables I and II). The analysis of the infrared observations (c.f. Kilyachkoet al., 1978) lead to the following conclusions:

1. The negative infrared flares discovered around 8000 Å is not in agreement with the theory in the case of the flare star UV Cet. Some traces of negative flares have been noted for a number of less powerful flares of EV Lac.
2. The amplitudes of the recorded positive flares of UV Cet and EV Lac on λ8000 Å are in good agreement with the magnitudes predicted by the fast-electron hypothesis (non-thermal bremsstrahlung).
3. In the future the negative flares around 8000 Å should be looked for in early-type flare stars of types M0-K5.
4. For a positive discovery of negative flares, future observations must be carried out in the wavelength region of 1–3 μm.

     

Absolute magnitude calibration for red clump stars

We combined the (K _s , J?K _s ) data in Laney et al. (Mon. Not. R. Astron. Soc. 419:1637, 2012) with the V apparent magnitudes and trigonometric parallaxes taken from the Hipparcos catalogue and used them to fit the $M_{K_{s}}$ absolute magnitude to a linear polynomial in terms of V?K _s colour. The mean and standard deviation of the absolute magnitude residuals, ?0.001 and 0.195 mag, respectively, estimated for 224 red clump stars in Laney et al. (2012) are (absolutely) smaller than the corresponding ones estimated by the procedure which adopts a mean $M_{K_{s}}=-1.613~\mbox{mag}$ absolute magnitude for all red clump stars, ?0.053 and 0.218 mag, respectively. The statistics estimated by applying the linear equation to the data of 282 red clump stars in Alves (Astrophys. J. 539:732, 2000) are larger, $\Delta M_{K_{s}}=0.209$ and σ=0.524 mag, which can be explained by a different absolute magnitude trend, i.e. condensation along a horizontal distribution.     

On the mass-luminosity relation

The results of a least-squares study of the mass-luminosity relation for eclipsing and visual binary stars consisting of main sequence components are presented. Two methods are discussed. In Part A, the values of the coefficientsA andB in the relation logM=A+BM _Bol are determined. Part B presents a technique which permits the determination of α and β in the relationM=αL ^β, when only the sum of the masses, and not the individual masses of each component, is known. The results and a comparison of the two methods are discussed. It is found that the following massluminosity relation represents the observational data satisfactorily: $$log M = 0.504 - 0.103M_{BOL,} {\text{ }} - \leqslant M_{BOL} \leqslant + 10.5$$ . A discussion of the data and of the possibility that separate mass-luminosity relations may exist for visual and eclipsing binaries is given. The possiblity that more than one mass-luminosity relation is required in the range ?8≤M _Bol ≤+13 is also discussed.     

Rosat and EUVE observations of B stars

Recent observations of the X-ray and EUV emission of non-supergiant B stars are summarized. As compared with O stars, the X-rays of most of the near-main-sequence B stars are soft, and the stars show a departure from theL _x = 10^?7 L _bol relation. Using line driven wind models to provide an estimate of the density distribution, it is concluded that a major fraction of the wind emission measure is hot, whereas in shocked wind theory less than 10 percent of the wind emission measure should be hot. The X-ray observations suggest that all of the B stars are X-ray emitters with a basal X-ray luminosity of about 10^?8.5 L _bol . A hard component dominates the X-ray emission of τ Sco, and possible causes are discussed. For the Be stars, the X-ray emission is that which is expected from a normal B-star wind coming from the poles, as in the Wind Compressed Disk (WCD) model of Be stars. None of the stars, including theβ Cep stars, show noticeable variability in their X-rays.EUVE observations of∈ CMa B2 II, find it to be the brightest object in the EUV sky at 500 to 700 Å. It shows a Lyman continuum flux that is a factor of 30 higher than line blanketed model atmospheres. The continuum is seen on both sides of the He I 504 Å edge, and the discrepancy with model atmospheres is even greater shortward of 504 Å. TheEUVE spectra show emission lines both from high stages of ionization ( Feix to Fexvi) and from low stages (Heii and Oiii). The Heii Lymanα results from recombination following X-ray photoionization in the wind, and the Oiii resonance line is found to be present because of the Bowen fluorescence mechanism. Thus, there is and interesting coupling between the wind production by the EUV photospheric emission, the production of X-ray and line EUV emission by winds, and the production of fluorescence by recombination in the wind; all of these processes are now observable in B stars.