Is NGC 7006 a globular cluster with a primarily red horizontal branch?

A CCD BV R photometric study of the central region (15″ ≤ r ≤ 100″) of the globular cluster NGC 7006 based on color-magnitude diagrams is presented. We find for the main parameters of the cluster [Fe/H] = ?1.62, Y = 0.21, E _B?V = 0.15 ^m , V _HB = 18.84 ^m , M _V ^HB =+0.56 ^m , R _⊙ = 37.1 kpc). Two previously unknown RR Lyr variables were discovered in the central region of the cluster. The morphological index of the horizontal branch for the entire region studied indicates that the red stellar population dominates, consistent with previous studies: HB _mi = ?0.13. Such anomalously negative morphological indices are possessed by a whole group of Ool clusters with intermediate metallicities, which also display a characteristic distribution of stars along the horizontal branch. There is a radial dependence for the horizontal-branch morphology, with the color becoming primarily blue with approach toward the cluster center. One possible origin for this behavior could be the effect of inner dynamical processes on the spatial distribution of hot stars.     

Logarithmic density range and the percentage of stars in the cores of various subsystems of the globular clusters M56, M12, NGC 6535, NGC 6171, NGC 5466, and M92

Lower limits for the percentages of stars with various luminosities in the cores of six globular clusters are derived using stellar spatial density distributions f(r) to deep limiting B magnitudes obtained earlier. For NGC 6535 and NGC 5466, the logarithmic density range and Kholopov parameters D_f and D_r are also determined. These two parameters are correlated with the mean masses of stars of various subsystems and the total mass (number) of stars in the cluster.     

Dynamical evolution of multiple stars

We have modeled the dynamical evolution of small groups of N=3–18 stars in the framework of the gravitational N-body problem, taking into account possible coalescences of stars and the ejection of single and binary stars from the system. The distribution of states is analyzed for a time equal to 300 initial crossing times of the system. The parameters of the binaries and stable triple systems formed, as well as those of ejected single stars, are studied. In most cases, the evolution of the group results in the formation of a binary or stable triple system. The orbital eccentricities of the binaries formed are distributed according to the law f(e)=2e. As a rule, stable triple systems display pronounced hierarchy (the mean ratio of the semimajor axes of the outer and inner binaries is about 20:1). Stars are ejected with velocities from several km/s to several tens of km/s. The results of the modeling are compared with the parameters of observed wide binaries and triple systems.     

The chemical evolution of globular clusters

The sequence of events determining the initial stages of star formation is analyzed in framework of the self-enrichment scenario. The computations are based on a single-zone chemo-dynamical model. It is shown that the first episode of star formation was characterized by an initial mass function shifted toward massive stars (M ≥ 8M_⊙). We argue that the transition to a star formation with a normal (Salpeter) initial mass function was due to more efficient radiative cooling of the proto-globular cluster gas after its enrichment to a metallicity of Z ～ 0.02 Z_⊙ in agreement with those observed in globular clusters.     

Dynamical evolution of multiple stars: Influence of the initial parameters of the system

We have modeled the dynamical evolution of small stellar groups with N=6 components in the framework of the gravitational N-body problem, taking into account possible mergers of stars and ejection of single and binary stars. We study the influence of the initial global parameters of the systems (the mass spectrum, average size, virial factor) on their dynamical evolution. The distribution over states is analyzed for a time equal to 300 initial crossing times of the system. The parameters of binary and stable triple systems that form are studied, as well as the properties of ejected single and binary stars. The rate of dynamical evolution in both expanding and contracting groups is higher than in systems in a state of virial equilibrium. The dynamical evolution is more intense in the case of unequal masses than when the system initially consists of equal-mass stars. In most cases, the evolution of a group ends with the formation of a binary or stable triple system. The semimajor axes of the binaries range from several hundredths to several times the initial size of the system. The distribution of the eccentricities of the binaries formed is consistent with an f(e)=2e law. When the initial size of the group is small, the number of final binaries with large eccentricities, and also of stable triple systems with elongated inner-binary orbits, decreases due to merging. As a rule, stable triple systems are substantially hierarchical (the average ratio of the semimajor axes of the inner and outer binaries is 1: 20). On average, the eccentricities of the inner binaries exceed those of the outer binaries: they are equal to \(\overline {e_{in} } \approx 0.7\) and \(\overline {e_{ex} } \approx 0.5\), respectively. The velocities of ejected stars are from several to several tens of km/s, and tend to increase as the initial size of the system, and hence its virial coefficient, decreases.     

Wolf-Rayet stars,black holes,and gamma-ray bursters in close binaries

We consider the evolutionary status of observed close binary systems containing black holes and Wolf-Rayet (WR) stars. When the component masses and the orbital period of a system are known, the reason for the formation of a WR star in an initial massive system of two main-sequence stars can be established. Such WR stars can form due to the action of the stellar wind from a massive OB star (M_OB≥50M_⊙), conservative mass transfer between components with close initial masses, or the loss of the common envelope in a system with a large (up to ～25) initial component mass ratio. The strong impact of observational selection effects on the creation of samples of close binaries with black holes and WR stars is demonstrated. We estimate theoretical mass-loss rates for WR stars, which are essential for our understanding the observed ratio of the numbers of carbon and nitrogen WR stars in the Galaxy \(\dot M_{WR} (M_ \odot yr^{ - 1} ) = 5 \times 10^{ - 7} (M_{WR} /M_ \odot )^{1.3} \). We also estimate the minimum initial masses of the components in close binaries producing black holes and WR stars to be ～25M_⊙. The spatial velocities of systems with black holes indicate that, during the formation of a black hole from a WR star, the mass loss reaches at least several solar masses. The rate of formation of rapidly rotating Kerr black holes in close binaries in the Galaxy is ～3×10^?6 yr^?1. Their formation may be accompanied by a burst of gamma radiation, possibly providing clues to the nature of gamma-ray bursts. The initial distribution of the component mass ratios for close binaries is dN～dq=dM₂/M₁ in the interval 0.04?q₀≤1, suggesting a single mechanism for their formation.     

The Initial Mass Spectra of Astronomical Objects

The fundamental premises concerning the existence of a universal basic distribution describing the initial mass functions (IMFs) of various astronomical objects on scales from brown dwarfs to clusters of galaxies are considered. This distribution has the form dN ∝ M^?2dM, where M is the mass of an object and N the number of objects with a given mass. It is shown that, at least for objects forming as a result of fragmentation (e.g., stars, star clusters), the basis of this distribution may correspond to a white-noise model. The classical problem of the formation of the IMF for stars is discussed in this context, incuding the relationship between the mass function of protostellar clouds and the stellar IMF. The main factors determining the mass functions of galaxies and galaxy clusters are also considered.     

Abundances of carbon,nitrogen, oxygen,and other elements in the atmospheres of the giants 25 Mon and HR 7389

An analysis of high-resolution CCD spectra of the giant 25 Mon, which shows signs of metallicity, and the normal giant HR 7389 is presented. The derived effective temperatures, gravitational accelerations, and microturbulence velocities are T_eff = 6700 K, log g = 3.24, and ξ _t = 3.1 km/s for 25 Mon and T_eff = 6630 K, log g = 3.71, and ξ _t = 2.6 km/s for HR 7389. The abundances (log ε) of nine elements are determined: carbon, nitrogen, oxygen, sodium, silicon, calcium, iron, nickel, and barium. The derived excess carbon abundances are 0.23 dex for 25 Mon and 0.16 dex for HR 7389. 25 Mon displays a modest (0.08 dex) oxygen excess, with the oxygen excess for HR 7389 being somewhat higher (0.15 dex). The nitrogen abundance is probably no lower than the solar value for both stars. The abundances of iron, sodium, calcium (for HR 7389), barium, and nickel exceed the solar values by 0.22–0.40 dex for both stars. The highest excess (0.62 dex) is exhibited by the calcium abundance for 25 Mon. Silicon displays a nearly solar abundance in both stars—small deficits of ?0.03 dex and ?0.07 dex for 25 Mon and HR 7389, respectively. No fundamental differences in the elemental abundances were found in the atmospheres of 25 Mon and HR 7389. Based on their T_eff and log g values, as well as theoretical calculations, A. Claret estimated the masses, radii, luminosities, and ages of 25 Mon (M/M_⊙ = 2.45, log(R/R_⊙) = 0.79, log(L/L_⊙) = 1.85, t = 5.3 × 10⁸ yr) and HR 7389 (M/M_⊙ = 2.36, log(R/R_⊙) = 0.50, log(L/L_⊙) = 1.24, t = 4.6 × 10⁸ yr), and also of the stars 20 Peg (M/M_⊙ = 2.36, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.79, t = 4.9 × 10⁸ yr) and 30 LMi (M/M_⊙ = 2.47, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.88, t = 4.8 × 10⁸ yr) studied by the author earlier.     

Magnetic field models for HD 116458 and HD 126515

We have modeled the magnetic fields of the slowly rotating stars HD 116458 and HD 126515 using the “magnetic charge” technique. HD 116458 has a small angle between its rotation axis and dipole axis (β = 12°), whereas this angle is large for HD 126515 (β = 86°). Both stars can be described with a decentered-dipole model, with the respective displacements being r = 0.07 and r = 0.24 in units of the stellar radius. The decentered-dipole model is able to satisfactorily explain the phase relations for the effective field, B_e(P), and the mean surface field, B_s(P), for both stars, along with the fact that the B_e(P) phase relation for HD 126515 is anharmonic. We discuss the role of systematic measurement errors possibly resulting from instrumental or methodical effects in one or both of the phase relations. The displacement of the dipole probably reflects real asymmetry of the stellar field structure, and is not due to measurement errors. Using both phase relations, B_e(P) and B_s(P), in the modeling considerably reduces the influence of the nonuniform distribution of chemical elements on the stellar surface.     

Orthogonal test and regression analysis of the strain on silty soil in Shanghai under metro loading

Cyclic triaxial test by means of the geotechnical digital system is conducted for the soil near the Guoquan Road Station of Metro Line 10 in Shanghai to analyze the strain characteristics and the variation law of saturated silty soil under subway loading. Orthogonal design method is used to arrange the experiment, considering the following factors: frequency ratio f _R, cyclic stress ratio σ _R, vibration time ratio N _R, and the interaction function among them. Results show that the cyclic stress ratio σ _R, the frequency ratio f _R, the vibration time ratio N _R, and the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R have a significant effect on the axial strain of the subway tunnel. The effect of the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R is also significant. From the analysis of variance and regression theory, the nonlinear regression equation of the cumulative plastic strain of silty soil under subway loading is established. Residual analysis proves that the equation is ideal and credible. The results have important value for the design of subway tunnels.     

A model for the population of helium stars in the Galaxy: Low-mass stars

We model the Galactic ensemble of helium stars using population synthesis techniques, assuming that all helium stars are formed in binaries. In this picture, single helium stars are produced by mergers of helium remnants of the components of close binaries (mainly, the merging of helium white dwarfs) or in the disruption of binaries with helium components during supernova explosions. The estimated total birthrate of helium stars in the Galaxy is 0.043 yr^?1; the total number is 4 × 10⁶; and the binarity rate is 76%. We construct a subsample of low-mass (M_He ? 2M_⊙) helium stars defined by observational selection effects: the limiting magnitude (V_He ≤ 16), ratio of the magnitudes of the components in binaries (V_He ≤ V_comp), and lower limit for the semiamplitude of the radial velocity required for detecting binarity (K_min = 30 km s^?1). The parameters of this subsample are in satisfactory agreement with observations of helium subdwarfs. In particular, the binarity rate in the selection-limited sample is 58%. We analyze the relations between the orbital periods and masses of helium subdwarfs and their companions in systems with various combinations of components. We predict that the overwhelming majority (～97%) of unobserved companions to helium stars will be white dwarfs, predominantly, carbon-oxygen white dwarfs.     

Abundances of carbon,nitrogen, oxygen,and other elements in the atmospheres of the giants 15 ori and 22 <Emphasis Type="Italic">ɛ</Emphasis> sex

We have used high-resolution spectra to study the giants 15 Ori and 22 ? Sex. The effective temperature T _eff = 7060 K, gravity log g = 3.16, and microturbulence velocity ξ _t = 3.5 km/s were determined for 15 Ori, with T _eff = 7350 K and log g = 3.90 for 22 ? Sex (the microturbulence velocity for 22 ? Sex was assumed to be ξ _t = 2.7 km/s). We estimated the abundances of C, N, O, Na, Si, Ca, Fe, and Ba (N and Ba, for 15 Ori only). The abundances of carbon, iron, and oxygen in 22 ? Sex are higher than the solar values by +0.31 dex, +0.33 dex, and +0.18 dex, respectively, while the calcium abundance is ?0.19 dex below the solar level. For 15 Ori, we find a slight carbon excess (+0.19 dex), a slight nitrogen deficiency (?0.13 dex), and a considerable deficiency of silicon (?0.42 dex). The abundances of the remaining elements in both stars are near-solar. We find no substantial differences between the abundances derived for 15 Ori and 22 ? Sex and the results of earlier studies of giants by both ourselves and Erspamer and North. A comparison of the atmospheric elemental abundances of giants and δ Scuti stars indicates that the abundances of some lighter elements (oxygen, sodium, silicon, and possibly nitrogen) are somewhat lower for δ Scuti stars than for A-F giants. We determined the masses, radii, luminosities, and ages for 15 Ori and 22 ? Sex.     

Spots and the activity of M dwarfs from observations with the Kepler Space Telescope

A method for estimating the spottedness parameter S (the spotted area as a fraction of the surface of an active star) proposed earlier is applied to an analysis of activity in 1570 M dwarf stars. The analysis is based on observational material obtained with the Kepler Space Telescope, as well as data on the fluxes of the studied objects in the near and far ultraviolet (NUV and FUV) based on data from the GALEX space telescope. The variations of S with the ages of the stars are studied (four groups with different ages are distinguished), as well as variations of S with their rotational periods. A diagram characterizing the relationship between S and the Rossby number Ro resembles the classical dependence of the X-ray luminosities of active stars on Ro, and a saturation regime is attained at the same value, Ro = 0.13. Moreover, objects with ages of more than 100 million years do not form a single sequence (and stars older than 900 million years possess surface spottednesses of order 1%). The S?Ro dependence obtained could expand possibilities for analyzing the dependence of the X-ray luminosities of active stars on their Rossby numbers, and could also be applied to refine parameters characterizing the action of dynamo mechanisms, such as the dynamo number N _D . A comparison of the GALEX NUV and FUV brightness estimates with the activity parameters of the stars suggests that younger, more rapidly rotating active stars are brighter in the NUV, and that the FUV flux grows and the difference of the FUV and NUV brightnesses decreases with increasing spottedness S.     

Fractionation of Rare-Earth Elements in the Processes of Hydrothermal Ore Formation

The data on the distribution of elements in the Pb–Zn cross-section of the Gatsirovskaya vein (the Upper Zgid deposit, North Ossetia, Russia) have shown that the spectra of rare-earth elements (REEs) changed significantly in the ore samples during the vein formation. The sharp growth of the La_N/Yb_N, La_N/Nd_N, Gd_N/Ho_N, and Gd_N/Yb_N ratios is confined to the vein intervals, where the maximum amount of ore components is deposited. The comparison of the REE spectra of ores to the characteristics of the spectra of the rocks surrounding the vein and the host rocks suggests that the vein material deposited from the solutions in which the REE ratio changed with time. REE fractionation occurred due to the mobilization of components by hydrothermal solutions during their interaction with the Paleozoic host granites.     

Calculation of profiles of CIV,NV, OVI,and SiIV resonance lines formed in accretion shocks in T Tauri stars: A plane layer

We have calculated profiles of the CIV 1550, NV 1240, OVI 1035, and SiIV 1400 resonance doublets for a plane-parallel shock viewed at various angles. Calculations were performed for the range of preshock gas velocities V₀ and gas densities ρ₀ appropriate for classical T Tauri stars. The parameters of accretion shocks in young stars can be determined by comparing the calculated and observed profiles of the studied lines and their relative intensities. It is not possible to derive the parameters of the accreting gas from the line profiles without knowing the geometry of the accretion zone. The relation I _v (µ,V₀,ρ₀) for a plane shock, where I _v is the intensity μ=cosθ, can be used to determine the accretion parameters by either choosing a geometry for the radiating region or using a technique similar to Doppler tomography. The results obtained for DR Tau, T Tau, and RY Tau indicate that, in contrast to current concepts, the inner regions of the accretion disk are not disrupted by the magnetic field of the star, and the disk reaches the stellar surface. As a result, only a small fraction of the accreted matter passes through the shock and falls onto the star.     

Separation of chemical elements in the atmospheres of CP stars under the action of light induced drift

A mechanism for the separation of chemical elements and isotopes in the atmospheres of chemically peculiar (CP) stars due to light-induced drift (LID) of ions is discussed. The efficiency of separation due to LID is proportional to the relative difference of the transport frequencies for collisions of ions of heavy elements located in the excited state (collision frequency ν _e ) and ground state (collision frequency ν _g ) with neutral buffer particles (hydrogen and helium), (ν _e ? ν _g )/ν _g . The known interaction potentials are used to numerically compute the relative difference (ν _e ^H ? ν _g ^H )/νg H for collisions between the ions Be⁺, Mg⁺, Ca⁺, Sr⁺, Cd⁺, Ba⁺, Al⁺, and C⁺ and hydrogen atoms. These computations show that, at the temperatures characteristic of the atmospheres of CP stars, T = 7000?20 000 K, values of |ν _e ^H ?ν _g ^H |/ν _g ^H ≈ 0.1?0.4 are obtained. With such relative differences in the transport collision frequencies, the LID rate of ions in the atmospheres of coolCP stars (T < 10000 K) can reach ~0.1 cm/s,which exceeds the drift rate due to light pressure by an order of magnitude. This means that, under these conditions, the separation of chemical elements under the action of LID of ions could be an order of magnitude more efficient than separation due to light pressure. Roughly the same manifestations of LID and light pressure are also expected in the atmospheres of hotter stars (20 000 > T > 10 000 K). LID of heavy ions is manifest only weakly in very hot stars (T > 20 000 K).     

Radial pulsations of helium stars and a model for BX CIR

The results of hydrodynamical calculations of radially pulsating helium stars with masses 0.5M_⊙≤M≤0.9M_⊙, bolometric luminosities 600L_⊙≤5×10³L_⊙, and effective temperatures 1.5×10⁴ K≤T_eff≤3.5×10⁴ K are presented. The pulsation instability of these stars is due to the effects of ionization of iron-group elements in layers with temperatures T～2×10⁵ K. The calculations were carried out using opacities for the relative mass abundances of hydrogen and heavy elements X=0 and Z=0.01, 0.015, and 0.02. Approximate formulas for the pulsation constant Q over the entire range of pulsation instability of the hot helium stars in terms of the mass M, radius R, effective temperature T_eff, and heavy-element abundance Z are derived. The instability of BX Cir to radial pulsations with the observed period Π=0.1066 d occurs only for a mass M≥0.55M_⊙, effective temperature T_eff≥23000 K, and heavy-element abundance Z≥0.015. The allowed mass of BX Cir is in the range 0.55M_⊙≤M≤0.8M_⊙, which corresponds to luminosities 800L_⊙≤M≤1400L_⊙ and mean radii 1.7R_⊙?R?2.1R_⊙.     

Spots and activity of Pleiades stars from observations with the Kepler Space Telescope (K2)

Observations of the K2 continuation of Kepler Space Telescope program are used to estimate the spot coverage S (the fractional spotted area on the surface of an active star) for stars of the Pleiades cluster. The analysis is based on data on photometric variations of 759 confirmed clustermembers, together with their atmospheric parameters, masses, and rotation periods. The relationship between the activity (S) of these Pleiades stars and their effective temperatures shows considerable change in S for stars with temperatures T _eff less than 6100 K (this can be considered the limiting value for which spot formation activity begins) and a monotonic increase in S for cooler objects (a change in the slope for stars with Teff ~ 3700 K). The scatter in this parameter ΔS about its mean dependence on the (V ?Ks)0 color index remains approximately the same over the entire (V?K _s )0 range, including cool, fully convective dwarfs. The computated S values do not indicate differences between slowly rotating and rapidly rotating stars with color indices 1.1 < (V?K _s )0 < 3.7. The main results of this study include measurements of the activity of a large number of stars having the same age (759 members of the Pleiades cluster), resulting in the first determination of the relationship between the spot-forming activity and masses of stars. For 27 stars with masses differing from the solarmass by nomore than 0.1M⊙, themean spot coverage is S = 0.031±0.003, suggesting that the activity of candidate young Suns is more pronounced than that of the present-day Sun. These stars rotate considerably faster than the Sun, with an average rotation period of 4.3^d. The results of this study of cool, low-mass dwarfs of the Pleiades cluster are compared to results from an earlier study of 1570 M stars.     

Analysis of Photometric Observations of the New Cataclysmic Variable ASASSN-13cx

Photometric observations of the variable star ASASSN-13cx acquired in the course of a program of studies of cataclysmic variables and their parameters recently carried out at the Sternberg Astronomical Institute (SAI) are presented. The star was observed with the 50-cm and 60-cm telescopes of the SAI Crimean Astronomical Station and a CCD photometer (～1800 images in the V and Rc filters) during the variable’s outburst of August–September 2014 and in a period of quiescence in October–November 2016. The ASASSN-13cx system is confirmed to be a SU UMa variable. Parameters of the system are derived from eight light curves using a “composite” model that takes into account the presence of a hot spot on the lateral surface of the geometrically thick disk and of a region of enhanced energy release near the disk edge, at the base of the gas flow (the so-called “hot line”). Parameters of the system for three light curves during the outburst were obtained in the framework of a “spiral” model that additionally takes into account the presence of geometric perturbations on the accretion-disk surface. The parameters of ASASSN-13cx determined using these models provide good accuracy in reproducing the system’s light curves in both states. The basic parameters of the system have been determined for the first time: the component mass ratio q = M₁/M₂ = 7.0 ± 0.2, the orbital inclination i = 79.9°?80.1°, the distance between the components’ centers of mass a₀ = 0.821(1) R_?, and the sizes and temperatures of the stars: R₁ = 0.0124(5)a₀ = 0.0102(4) R_?, T₁ = 12 500 ± 280 K, 〈R₂〉 = 0.236(4)a₀ = 0.194(3) R_?, T₂ = 2550 ± 400 K, corresponding to M4–9V for the spectral type of the secondary. Parameters of the accretion disk have been derived for both activity states. The mass of matter in the accretion disk increased by almost a factor of two during ～400 orbital periods in quiescence.