Spots and activity of solar-type stars from Kepler observations

The spot coverages S for 2846 solar-type stars with effective temperatures from 5700 K to 5800 K and gravities from 4.4 to 4.5 have been measured. An analysis based on the MAST catalog, which presents photometric measurements obtained with the Kepler Space Telescope during Q9 is presented. The existence of two groups of solar-type stars, with S values between 0.001 and 0.007 and with S > 0.007, is inferred. The second group (active stars) contains 279 stars (about 10% of the total number of stars analyzed). The mean S parameter for the entire sample is 0.004, comparable to the mean spot coverage of the Sun. In general, the dependence of S on the rotation period for solar-type stars has characteristics similar to those found earlier for stars with exoplanets. For the vast majority of the stars in the sample, the activity is constant, and independent of age. The activity of the small number of active stars with S > 0.007 decreases with age. The age variations of the chromospheric activity index R′_HK are compared to variations of the spot coverage S. The relations analyzed have common characteristic features. It is likely that both the spot activity level and the chromospheric activity level abruptly decrease for stars older than 4 billion yrs.     

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.     

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.     

Photometric elements and apsidal motion of the eclipsing binary ES Lac

We have obtained high-accuracy photoelectric measurements of ES Lac, an eclipsing binary with an elliptical orbit (B9III + B9III; P = 4.459^d, e = 0.198) in 1985–2004 at the Sternberg Astronomical Institute’s Tien Shan High-Altitude Observatory. Our detailed analysis of the 19-year uniform series of measurements has yielded the first photometric elements for this system, as well as a self-consistent set of physical and geometrical parameters for the binary. The virtually identical components (M ₁ = M ₂ = 3.0 M _⊙; R ₁ = R ₂ = 4.12 R _⊙) are appreciably separated from the main sequence, and are located on the giant branch: their age is t = (3.5 ± 0.2) × 10⁸ yrs. An analysis of our observations together with previously published times of minima has enabled a considerable refinement of the period of the apsidal motion, U = 355 ± 20 years, and a first determination of the apsidal parameter reflecting the radial density distributions for the components stars: k ₂ ^obs = 0.00213(18). This value is in a good agreement with the value expected theoretically for current evolutionary models of such stars: k ₂ ^th = 0.00257(15).     

Physical parameters of the eclipsing binary V798 Cep

The first high-accuracy CCD UBV RI(RI)_C light curves for the recently discovered eclipsing binary V798 Cep (P = 16 ^d .08, V = 11 ^m . 8) are presented; this star is included in our program of eclipsing systems with considerable eccentricities. A photometric solution for the light curves and physical characteristics of the component stars are derived. The orbital eccentricity is quite high, e = 0.437. The longitude of periastron is close to 180°, making studies of the apsidal motion difficult. V798 Cep may be a hierarchical system.     

The Spots and Activity of Stars in the Beehive Cluster Observed by the Kepler Space Telescope (K2)

The spottedness parameters S (the fraction of the visible surface of the star occupied by spots) characterizing the activity of 674 stars in the Beehive Cluster (age 650 Myr) are estimated, together with variations of this parameter as a function of the rotation period, Rossby number Ro and other characteristics of the stars. The activity of the stars in this cluster is lower than the activity of stars in the younger Pleiades (125 Myr). The average S value for the Beehive Cluster stars is 0.014, while Pleiades stars have the much higher average value 0.052. The activity parameters of 61 solar-type stars in the Beehive Cluster, similar Hyades stars (of about the same age), and stars in the younger Pleiades are compared. The average S value of such objects in the Beehive Cluster is 0.014± 0.008, nearly coincident with the estimate obtained for solar-type Hyades stars. The rotation periods of these objects are 9.1 ± 3.4 day, on average, in agreement with the average rotation period of the Hyades stars (8.6 ^d ). Stars with periods exceeding 3–4 ^d are more numerous in the Beehive Cluster than in the Pleiades, and their periods have a larger range, 3–30 ^d . The characteristic dependence with a kink at Ro (saturation) = 0.13 is not observed in the S–Rossby number diagram for the Beehive and Hyades stars, only a clump of objects with Rossby numbers Ro > 0.7. The spottedness data for the Beehive Cluster and Hyades stars are in good agreement with the S values for dwarfs with ages of 600–700 Myr. This provides evidence for the reliability of the results of gyrochronological calibrations. The data for the Beehive and Pleiades stars are used to analyze variations in the spot-forming activity for a large number of stars of the same age that are members of a single cluster. A joint consideration of the data for two clusters can be used to draw conclusions about the time evolution of the activity of stars of different masses (over a time interval of the order of 500 Myr).     

Analysis of magnetic activity of the rapidly rotating stars He 373 and AP 225

Spectroscopic and photometric data for the two rapidly rotating members of the α Persei cluster He 373 and AP 225 are analyzed. Improved estimates have been obtained for the projected equatorial rotation velocities: v sin i = 164 km/s for He 323 and v sin i = 129 km/s for AP 225. Multi-band photometric mapping is used to map the spot distributions on the surfaces of the two stars. The fractional spotted areas S and mean temperature difference ΔT between the unspotted photosphere and the spots are estimated (S = 7% and ΔT = 1000 K for He 373; S = 9% and ΔT = 800 K for AP 225). The H _α line profiles of both stars have variable emission components whose widths are used to deduce the presence of extended regions of emission reaching the corotation radius.     

Spots and the Activity of Stars in the Hyades Cluster from Observations with the Kepler Space Telescope (K2)

Observations of the K2 mission (continuing the program of the Kepler Space Telescope) are used to estimate the spot coverage S (the fractional area of spots on the surface of an active star) for stars of the Hyades cluster. The analysis is based on data on the photometric variations of 47 confirmed single cluster members, together with their atmospheric parameters, masses, and rotation periods. The resulting values of S for these Hyades objects are lower than those stars of the Pleiades cluster (on average, by ΔS ~ 0.05?0.06). A comparison of the results of studies of cool, low-mass dwarfs in the Hyades and Pleiades clusters, as well as the results of a study of 1570 M stars from the main field observed in the Kepler SpaceMission, indicates that the Hyades stars are more evolved than the Pleiades stars, and demonstrate lower activity. The activity of seven solar-type Hyades stars (S = 0.013 ± 0.006) almost approaches the activity level of the present-day Sun, and is lower than the activity of solar-mass stars in the Pleiades (S = 0.031 ± 0.003). Solar-type stars in the Hyades rotate faster than the Sun (〈P〉 = 8.6 ^d ), but slower than similar Pleiades stars.     

Evolutionary connection between low-mass detached binaries,contact W UMa systems,and blue stragglers

We analyze the distribution of close binary stars in the orbital semimajor axis—primary mass plane. The reduced spatial density of stars with semimajor axes below 10R_⊙ is confirmed. We identify the area in this plane occupied by precursors of W UMa stars, assuming that the driving force causing the components to approach each other is their magnetic stellar wind. This scenario enables us to estimate the rate of formation (0.02/year) and lifetime (10⁸ yr) of W UMa stars. We derive a theoretical estimate of the ratio of the number of blue stragglers, N _BS , and of horizontal-branch stars, N _HB , in globular clusters based on the hypothesis that all blue stragglers are the result of component mergers in W UMa contact binaries. This ratio is N _BS /N _HB =0.4, close to the observed value for 62 Galactic globular clusters. We discuss possible reasons for the considerable dispersion of the observed estimates of this ratio for different clusters in our Galaxy.     

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.     

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_⊙.     

Long-term Spot-Coverage Variations of 13 BY Dra G–K Dwarfs

The results of spot-coverage modeling for 13 active G–K dwarf stars based on many-year photometric observations are presented. The results of UBVRI observations of eight stars performed at the Crimean Astrophysical Observatory were used together with data from the literature in this analysis. The spot-coverage parameters for 13 selected BY Dra active red dwarfs have been redetermined to improve the zonal spot-coverage model for the stellar photospheres, which currently allows for the presence of two active longitudes. Time variations of the spot-activity characteristics of these systems were analyzed with the aim of searching for possible cyclic variations. All the stars, with the exception of OU Gem and BE Cet, show fairly strong correlations between variations in the spot latitudes and spot areas, with absolute values of the correlation coefficients, R(〈?〉, S), ranging from 0.38 to 0.92. For five stars, an anti-correlation between the mean latitude and area of the spots was found (R(〈?〉, S) from–0.24 to–0.73). This behavior may reflect the drift of spots toward the equator in the course of their development. Eight stars feature positive correlations, i.e. the spots drift towards the pole as their areas increase. Nine stars demonstrate activity cycles, which are reflected in photometric variations as well as variations of the spot areas and mean latitudes. The periods of the latitude drift of the spots are found for five stars; the magnitudes of the spot-latitude drift rates are lower than the corresponding value for sunspots by a factor of 1.5–3.     

IR photometry and models for the dust envelopes of two carbon stars

The results of JHKLM photometry of two carbon stars are presented: the irregular variable NQ Cas and the Mira star BD Vul. Data on the mean fluxes supplemented with mid-IR observations with the IRAS, AKARI, andWISE satellites are used to compute spherically symmetrical model dust envelopes for the stars, consisting of particles of amorphous carbon and silicon carbide. The optical depth in the visible for the comparatively cool dust envelope of BD Vul, with a dust temperature at its inner boundary T₁ = 610 K, is fairly low: τ_V = 0.13. The dust envelope of NQ Cas is appreciably hotter (T₁ = 1550 K), and has τ_V = 0.32. The estimated mass-loss rates are 1.5 × 10^?7M_⊙/yr for NQ Cas and 5.9 × 10^?7M_⊙/yr for BD Vul.     

Nonlinear radial pulsations of Wolf-Rayet stars

The evolution of Population I stars with initial masses 60 M _⊙ ≤ M _ZAMS ≤ 120 M _⊙ is computed up to the Wolf-Rayet stage, when the central helium abundance decreases to Y _c ≈ 0.05. Several models from evolutionary sequences in the core helium-burning stage were used as initial conditions when solving the equations of radiative hydrodynamics for self-exciting stellar radial pulsations. The low-density envelope surrounding the compact core during the core helium burning is unstable against radial oscillations in a wide range of effective temperatures extending to T _eff ～ 10⁵ K. The e-folding time of the amplitude growth is comparable to the dynamical time scale of the star, and, when the instability ceases growing, the radial displacement of the outer layers is comparable to the stellar radius. Evolutionary changes of the stellar radius and luminosity are accompanied by a decrease in the amplitude of radial pulsations, but, at the effective temperature T _eff ≈ 10⁵ K, the stellar oscillations are still nonlinear, with a maximum expansion velocity of the outer layers of about one-third the local escape velocity. The period of the radial oscillations decreases from 9 hr to 4 min as stellar mass decreases from M = 28 M _⊙ to M = 6 M _⊙ in the course of evolution. The nonlinear oscillations lead to a substantial increase of the radii of the Lagrangian mass zones compared to their equilibrium radii throughout the instability region. The instability of Wolf-Rayet stars against radial oscillations is due to the action of the κ mechanism in the iron-group ionization zone, which has a temperature of T ～ 2 × 10⁵ K.     

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.     

High-velocity stars as a result of encounters between stars and massive binary black holes in galactic nuclei

Numerical simulations of the motions of stars in the gravitational fields of binary black holes with various component mass ratios have been carried out. Two models are considered: (1) the two-body problem with two fixed centers; (2) the general three-body problem. The first model is applicable only over short times Δt ? T, where T is the period of the binary system. The second model is applicable at all times except for during close encounters of stars with one of the binary components, r ≤ 0.00002 pc, where r is the distance from the star to the nearer black hole. In very close passages, relativistic corrections must be taken into account. Estimates of the probability of formation of high-velocity stars as a result of such interactions are obtained. It is shown that this mechanism is not suitable for the nucleus of our Galaxy due to the probable absence of a second massive black hole in the central region of the Galaxy.     

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.     

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.