Stability of a planet in the HD 41004 binary system

The Hill stability criterion is applied to analyse the stability of a planet in the binary star system of HD 41004 AB, with the primary and secondary separated by 22 AU, and masses of 0.7 M_⊙ and 0.4 M_⊙, respectively. The primary hosts one planet in an S‐type orbit, and the secondary hosts a brown dwarf (18.64 M_J) on a relatively close orbit, 0.0177 AU, thereby forming another binary pair within this binary system. This star‐brown dwarf pair (HD 41004 B+Bb) is considered a single body during our numerical calculations, while the dynamics of the planet around the primary, HD 41004 Ab, is studied in different phase‐spaces. HD 41004 Ab is a 2.6 M_J planet orbiting at the distance of 1.7 AU with orbital eccentricity 0.39. For the purpose of this study, the system is reduced to a three‐body problem and is solved numerically as the elliptic restricted three‐body problem (ERTBP). The Hill stability function is used as a chaos indicator to configure and analyse the orbital stability of the planet, HD 41004 Ab. The indicator has been effective in measuring the planet's orbital perturbation due to the secondary star during its periastron passage. The calculated Hill stability time series of the planet for the coplanar case shows the stable and quasi‐periodic orbits for at least ten million years. For the reduced ERTBP the stability of the system is also studied for different values of planet's orbital inclination with the binary plane. Also, by recording the planet's ejection time from the system or collision time with a star during the integration period, stability of the system is analysed in a bigger phase‐space of the planet's orbital inclination, ≤ 90°, and its semimajor axis, 1.65–1.75 AU. Based on our analysis it is found that the system can maintain a stable configuration for the planet's orbital inclination as high as 65° relative to the binary plane. The results from the Hill stability criterion and the planet's dynamical lifetime map are found to be consistent with each other. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

HD 115781 and HD 116204—two RS CVn binaries

HD 115781 and HD 116204 (BL CVn and BM CVn) are shown to be RS CVn binaries with periods near 20 days. HD 115781 is double-lined; the primary type is about K1III, while the secondary is probably a late-type subgiant. The masses of the two components are equal within observational error. There is substantial photometric variability with a period half the orbital period; it is attributed to ellipsoidal variation. HD 116204 is also of type K1III. It shows exceptionally strong Ca II H and K emission, together with an emission-line spectrum typical of RS CVn stars in theIUE ultraviolet region, but Hα is an absorption line. The secondary star in the HD 116204 system has not been detected. The primary shows photometric variations, presumably due to starspots, with a period 5 per cent longer than the orbital period.     

Numerical Instruments for the Analysis of Secular Dynamics of Exoplanetary Systems

A review is given of modern numerical methods for the analysis of resonant and chaotic dynamics: calculation of the Lyapunov characteristic exponents, the MEGNO method, and the maximum eccentricity method. These methods are used to construct stability diagrams for the planetary systems γ Cep, HD 196885, and HD 41004. The diagrams are analyzed to determine the most probable values taken by the orbital parameters of the exoplanets and obtain estimates for the Lyapunov time of their orbital dynamics. The stability diagrams constructed using the different methods are compared to analyze their effectiveness in the study of secular dynamics of exoplanetary systems.     

Speckle interferometry of magnetic stars with the BTA. I. First results

We present the results of speckle interferometry of a sample of 117 chemically peculiar stars with global magnetic fields. The observations were made in December 2009 at the BTA with a spatial resolution of about 0.02″ in the visual spectral region. Twenty-nine stars were resolved into individual components, 14 of them for the first time (HD965, HD5797, HD8855, HD10783, HD16605, HD21699, HD35502, HD51418, HD64486, HD79158, HD103498, HD108651, HD213918, HD293764). In twelve cases a companion turned out to be 2–4 ^m fainter than the main component—a magnetic star. Young hot Bp stars HD35502 and HD213918 are exceptions, since their companions are fainter by about 1 ^m . In all cases, the linear distance from a star to its companion at the epoch of observations in the picture plane exceeded 10⁹ km. Eighty-eight magnetic CP stars revealed no secondary components within our study. Thus, the fraction of speckle interferometric binaries in our sample amounts to 25%.     

The atmospheres of helium-deficient Bp stars

Based on spectra taken with a 6-m telescope, we analyzed the abundances of chemical elements in the He-weak stars HD 21699 and HD 217833, estimated their surface magnetic fields (B_s = 4000 and 4500 G, respectively) from the magnetic intensification of spectral lines, and determined their microturbulences (V _t = 0.80 and 0.75 km s⁻¹, respectively). The low values of V _t show that the stellar atmospheres are stabilized by a magnetic field, which explains the presence of diffusion processes that lead to chemical anomalies. Helium is strongly underabundant, and its deficiency is −1.50 and −1.81 dex in HD 21699 and HD 217833, respectively. We used model atmospheres to determine the effective temperatures, T _eff = 16 000 and 15 450 K, and surface gravities, log g = 4.15 and 3.88, for the stars from the Hδ line, implying that they lie on the main sequence near the stars of luminosity class V.     

Comprehensive study of the magnetic stars HD 5797 and HD 40711 with large chromium and iron overabundances

We present the results of a comprehensive study of the chemically peculiar stars HD 5797 and HD 40711. The stars have the same effective^temperature, T _eff = 8900 K, and a similar chemical composition with large iron (+1.5 dex) and chromium (+3 dex) overabundances compared to the Sun. The overabundance of rare-earth elements typically reaches +3 dex. We have measured the magnetic field of HD 5797. The longitudinal field component B _e has been found to vary sinusoidally between −100 and +1000 G with a period of 69 days. Our estimate of the evolutionary status of the stars suggests that HD 5797 and HD 40711, old objects with an age t ≈ 5 × 10⁸ yr, are near the end of the core hydrogen burning phase.     

Stability of outer planetary orbits around binary stars: A comparison of Hill's and Laplace's stability criteria

A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m ₂/(m ₁+m ₂). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of .     

THE HILL PROBLEM WITH OBLATE SECONDARY: NUMERICAL EXPLORATION

We introduce a three-dimensional version of Hill’s problem with oblate secondary, determine its equilibrium points and their stability and explore numerically its network of families of simple periodic orbits in the plane, paying special attention to the evolution of this network for increasing oblateness of the secondary. We obtain some interesting results that differentiate this from the classical problem. Among these is the eventual disappearance of the basic family g′ of the classical Hill problem and the existence of out-of-plane equilibrium points and a family of simple-periodic plane orbits non-symmetric with respect to the x-axis.     

Hill stability in the many-body problem

We established a criterion for the Hill stability of motions in the problem of many spherical bodies with a spherical density distribution. The region of Hill stability was determined. The sizes of this region are comparable to the total volume of all of the bodies in the system, which sharply increases the probability of mutual collisions. This result may be considered as a confirmation that a supermassive core can be formed at the center of a globular star cluster. The motions in the n-body problem are shown to be unstable according to Hill.     

Hill stability of the satellite in the elliptic restricted four-body problem

We consider an elliptic restricted four-body system including three primaries and a massless particle. The orbits of the primaries are elliptic, and the massless particle moves under the mutual gravitational attraction. From the dynamic equations, a quasi-integral is obtained, which is similar to the Jacobi integral in the circular restricted three-body problem (CRTBP). The energy constant \(C\) determines the topology of zero velocity surfaces, which bifurcate at the equilibrium point. We define the concept of Hill stability in this problem, and a criterion for stability is deduced. If the actual energy constant \(C_{\mathrm{ac}}\ ( {>} 0 ) \) is bigger than or equal to the critical energy constant \(C_{\mathrm{cr}}\), the particle will be Hill stable. The critical energy constant is determined by the mass and orbits of the primaries. The criterion provides a way to capture an asteroid into the Earth–Moon system.     

Stability of strange dwarfs. I. Static criterion for stability. Statement of the problem

This is a study of the stability of strange dwarfs, superdense stars with a small quark core (M _0core /M _⨀ < 0.017) and an extended crust consisting of atomic nuclei and a degenerate electron gas where the density may be two orders of magnitude greater than the maximum density for white dwarfs. For a given equation of state, the mass, total number of baryons, and radius of strange dwarfs are uniquely determined by the central energy density ρ _c and the energy density ρ _tr of the crust at the surface of the quark core. Thus, the entire range of variation of ρ _c and ρ _tr must be taken into account in studying the stability of these configurations. This can be done by examining a series of configurations with a fixed rest mass M ₀ (total baryon number) of the quark core and different masses of the crust. In each series, ρ _tr ranges from the value for white dwarfs to ρ _drip = 4.3∙10¹¹ g/cm³, at which free neutrons are created in the crust. According to the static criterion for stability, stability is lost in an individual series when the mass of the strange dwarf reaches a maximum as a function of ρ _tr . Translated from Astrofizika, Vol. 52, No. 2, pp. 325–332 (May 2009).     

HD/H<Subscript>2</Subscript> molecular clouds in the early Universe: The problem of primordial deuterium

We have detected new HD absorption systems at high redshifts, z _abs = 2.626 and z _abs = 1.777, identified in the spectra of the quasars J0812+3208 and Q1331+170, respectively. Each of these systems consists of two subsystems. The HD column densities have been determined: log N _HD^A = 15.70 ± 0.07 for z _A = 2.626443(2) and log N _HD^B = 12.98 ± 0.22 for z _B = 2.626276(2) in the spectrum of J0812+3208 and log N _HD^C = 14.83 ± 0.15 for z _C = 1.77637(2) and log N _HD^D = 14.61 ± 0.20 for z _D = 1.77670(3) in the spectrum of Q1331+170. The measured HD/H₂ ratio for three of these subsystems has been found to be considerably higher than its values typical of clouds in our Galaxy.We discuss the problem of determining the primordial deuterium abundance, which is most sensitive to the baryon density of the Universe Ω_b. Using a well-known model for the chemistry of a molecular cloud, we have estimated the isotopic ratio D/H=HD/2H₂ = (2.97 ± 0.55) × 10⁻⁵ and the corresponding baryon density Ω_b h ² = 0.0205_−0.0020^+0.0025. This value is in good agreement with Ω_b h ² = 0.0226_−0.0006^0.0006 obtained by analyzing the cosmic microwave background radiation anisotropy. However, in high-redshift clouds, under conditions of low metallicity and low dust content, hydrogen may be incompletely molecularized even in the case of self-shielding. In this situation, the HD/2H₂ ratio may not correspond to the actual D/H isotopic ratio. We have estimated the cloud molecularization dynamics and the influence of cosmological evolutionary effects on it.     

The RS canum venaticorum binary HD 116204

BV photometry of HD 116204 obtained on 57 nights during 1983–84, 1984–85 and 1986–87 observing season is presented. A photometric period of 21.9 ± 0.2 d and a mean (B-V)= 1.196 ± 0.010 are obtained. It is suggested that the binary HD 116204 has a mass ratio close to unity. Attempts are needed to detect the spectrum of secondary.     

Lithium in chemically peculiar CP stars with magnetic fields

The problem of lithium in chemically peculiar Ap-CP stars has been the subject of debate for many years. The main reason for this is a lack of spectral observations of Ap stars in the neighborhood of the lithium resonance doublet Li I 6708 Å. An international cooperation project on “Lithium in cool CP stars with magnetic fields” was started in 1996. Systematic observations of CP stars in spectral regions of the 6708 Å and 6103 Å lines at the ZTSh (CrAO), CAT (ESO), Feros (ESO), and the 74″ telescope of the Mount Stromlo Observatory (Australia) have been used to analyze spectra of several CP stars studied by the way the 6708 Å lithium line varies with the stars’ rotational phase. Monitoring of the spectra of the oscillating CP stars (group I) HD 83368, HD 60435, and HD 3980, for which significant Doppler shifts of the Li I 6708 Å line are observed led to the discovery of “lithium spots” on the surface of these stars whose positions are related to the magnetic field structure. Models of the surfaces of these stars with the special program “ROTATE” based on the profiles of the Li I 6708 Å line are used to estimate the size of the spots, their positions on the stars’ surface, and the lithium abundances in these spots. A detailed analysis and modelling of the spectra of slowly rotating oscillating CP stars with strong, invariant lithium 6708 Å emission, including blending with lines of the rare earth elements, reveals an enhanced lithium abundance, with the abundance determined from the lithium 6103 Å line being higher than that determined from the 6708 Å line for all the stars. This may indicate vertical stratification of lithium in the atmospheres of CP stars with an anomalous isotopic composition (⁶Li/⁷Li = 0.2–0.5). HD 101065, an ultraslow rotator (vsini ≈ 1.5) visible from the poles and with powerful oscillations which cause pulsating line broadening in its spectrum, is unique among these stars. The amount of lithium in the atmosphere of HD 101065 logN(Li) = 3.1 on a scale of logN(H) = 12.0 and the isotope ratio ⁶Li/⁷Li ≈ 0.3. The high estimates of ⁶Li/⁷Li may be explained by the production of lithium in spallation reactions and the preservation of surface ⁶Li and ⁷Li by strong magnetic fields in the upper layers of the atmosphere near the magnetic poles. __________ Translated from Astrofizika, Vol. 50, No. 3, pp. 463–492 (August 2007).     

Local Stability Criterion for a Self-Gravitating Gaseous Disk of Spiral Galaxies

An improved linear stability theory of small-amplitude oscillations of a self-gravitating, infinitesimally thin gaseous disk of spiral galaxies has been developed by Bertin, Lau, Lin, Mark, Morozov, Polyachenko, and others in the approximation of moderately tightly wound gravity perturbations. In this regime, the generalized Lin–Shu type dispersion relation was also found by including higher order terms in the small parameter 1/kr for wavenumber k and radius r. It was shown that in the differentially rotating disks for nonaxisymmetric (spiral)perturbations Toomre's modified critical Q-parameter is larger than the standard one: the fact that the spiral perturbations in the nonuniformly rotating system are more unstable than the axisymmetric ones is taken into account in this modified local stability criterion. We use hydrodynamical simulations to test the validity of the modified local criterion. This revised version was published online in July 2006 with corrections to the Cover Date.     

Against all odds? Forming the planet of the HD 196885 binary

HD 196885 Ab is the most ??extreme?? planet-in-a-binary discovered to date, whose orbit places it at the limit for orbital stability. The presence of a planet in such a highly perturbed region poses a clear challenge to planet-formation scenarios. We investigate this issue by focusing on the planet-formation stage that is arguably the most sensitive to binary perturbations: the mutual accretion of kilometre-sized planetesimals. To this effect we numerically estimate the impact velocities dv amongst a population of circumprimary planetesimals. We find that most of the circumprimary disc is strongly hostile to planetesimal accretion, especially the region around 2.6 AU (the planet??s location) where binary perturbations induce planetesimal-shattering dv of more than 1 kms^?1. Possible solutions to the paradox of having a planet in such accretion-hostile regions are (1) that initial planetesimals were very big, at least 250 km (2) that the binary had an initial orbit at least twice the present one, and was later compacted due to early stellar encounters (3) that planetesimals did not grow by mutual impacts but by sweeping of dust (the ??snowball?? growth mode identified by Xie et al., in Astrophys J 724:1153, 2010b), or (4) that HD 196885 Ab was formed not by core-accretion but by the concurrent disc instability mechanism. All of these 4 scenarios remain however highly conjectural.     

The influence of mutual perturbations on the eccentricity excitation by jet acceleration in extrasolar planetary systems

We study the influence of mutual planetary perturbations on the process of eccentricity excitation by jet acceleration suggested by Namouni (Astron. J. 130, 280–294). Modeling the jet’s action by a constant-direction acceleration, we solve the linear secular equations of the combined planetary perturbations and the jet acceleration of the host star for a two-planet system. The effects of the acceleration’s strength, relative mass ratio and the relative distance of the two planets are investigated. The model is applied to the extrasolar planetary systems of HD 108874, 47 Uma, and HD 12661.     

The <Emphasis Type="Italic">r</Emphasis>- and <Emphasis Type="Italic">s</Emphasis>-process contributions to heavy-element abundances in the halo star HD 29907

The abundances of 22 heavy elements from Sr to Pb have been determined for the halo star HD 29907 (T _eff = 5500 K, log g = 4.64) with [Fe/H] = −1.55 using high-quality VLT/UVES spectra (ESO, Chile). The star has a moderate enhancement of r-process elements (Eu-Tm) with [r/Fe] = 0.63. In the range from Ba to Yb, the derived abundance pattern agrees well with those for strongly r-process enhanced stars (r-II stars with [Eu/Fe] > 1 and [Ba/Eu] < 0), such as CS 22892-052 and CS 31082-001, as well as with the scaled solar r-process curve and the r-process model HEW. Thus, Ba-Yb in HD 29907 originate in the r-process. Just as other moderately r-process enhanced stars studied in the literature, HD 29907 exhibits higher Sr, Y, and Zr abundances than those for r-II stars. These results confirm the assumption by other authors about the existence of an additional Sr-Zr synthesis mechanism in the early Galaxy before the onset of nucleosynthesis in asymptotic giant branch (AGB) stars. The same mechanism can be responsible for the enhancement of Mo-Ag in the star being investigated compared to r-II stars. There are no grounds to suggest the presence of s-nuclei of lead in the material of the star being investigated, because its measured abundance ratio log ɛ(Pb/Eu) = 1.20 lies within the range for the comparison stars: from log ɛ(Pb/Eu) = 0.17 (CS 31082-001) to < 1.55 (HE 1219-0312). Thus, even if there was a contribution of AGB stars to the heavy-element enrichment of the interstellar medium at the epoch with [Fe/H] = −1.55, it was small, at the level of the abundance error.     

Photometric variability of four coronally active stars

We present photometric observations of four stars that are optical counterparts of soft X-ray/EUV sources, namely 1ES 0829+15.9, 1ES0920-13.6, 2RE J1 10159+223509 and 1ES 1737+61.2. We have discovered periodic variability in two of the stars, viz., MCC 527 (1ES 0829+15.9; Period = 0 ^d .828 ± 0.0047) and HD 81032 (1ES 0920-13.6; Period = ∼ 57.02 ± 0.560 days). HD 95559 (2RE J1 10159+223509) is found to show a period of 3 ^d . HD 160934 (1ES1737+61.2) also shows photometric variability but needs to be monitored further for finding its period. These stars most likely belong to the class of chromospherically active stars.     

Study of the IR-excess supergiant HD 331319

We report the discovery of brightness variability in the IR-excess early F supergiant HD 331319, a candidate post-AGB star. Over three years of systematic U BV observations, the star showed low-amplitude (up to in V) quasi-periodic brightness variations on a time scale of ∼45 days. A preliminary analysis of our photometry indicates that HD 331319 and other typical post-AGBF supergiants have a similar pattern of variability. A study of the extinction toward HD 331319 leads us to conclude that the fraction of the circumstellar extinction is small for this star. We present low-resolution spectroscopy for HD 331319 and discuss the spectral classification of post-AGB F supergiants using HD 331319, HD 161796, HD 187885, and HD 56126 as examples.