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).     

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 the velocity field of F and G dwarfs in the solar neighborhood as a function of age

The space velocities from the catalog of Nordstr?m et al. (2004) are used to trace variations of a number of kinematic parameters of single F and G dwarfs as a function of their age. The vertex deviation of disk stars increases from 7° ± 1° to 15° ± 2° as the mean age decreases from 4.3 to 1.5 Gyr. The two-dimensional velocity distributions in the UV, UW, and VW planes are analyzed. The evolution of the main peaks in the velocity distributions can be followed to an average age of ≈9 Gyr. We find that: (1) in the distributions of the UV velocity components, stars of different types are concentrated toward several stable peaks (the Hyades, Pleiades, and Sirius Cluster), suggesting that the stars belonging to these formations did not form simultaneously; (2) the peak associated with the Hyades Cluster dominates in all age intervals; and (3) the Hyades peak is strongest for stars with an average age of 1.5 Gyr, suggesting that this peak contains a considerable fraction of stars from the Hyades cluster. The age dependences of the kinematic parameters exhibit a break near ≈4–5 Gyr, which can be explained as an effect of the different contributions of stars of the thin and thick disks. The Stromberg relation yields a solar LSR velocity of V _⊙LSR = (8.7, 6.2, 7.2) ± (0.5, 2.2, 0.8) km/s.     

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.     

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 activity of the M dwarf KIC 1572802

The photometric variability of the M dwarf KIC 1572802 has been studied using the most complete observational data, obtained by the Kepler Space Telescope. Power spectra constructed from 59 488 single brightness measurements over 1460 days (~4 yr) show complex brightness variations. It is suggested that two peaks corresponding to the periods P = 0.37088^d and P = 0.37100^d are related to the presence of active regions at different latitudes on the differentially rotating star. Maps of the surface temperature inhomogeneities are used to derive the positions of these active regions. Analysis of these maps suggests that a switch in the active latitudes occurred 590 days after the beginning of the observations. The variations of the positions of the active regions are also analyzed. These high-temporal-resolution observations revealed a short time-scale change in the active latitudes lasting about 7^d, followed by a “flip-flop,” for the first time. The fraction of the surface of KIC 1572802 covered by spots is S ~ 7%. Comparison with literature data indicate that this S value for KIC 1572802 is substantially higher than the average spottedness of stars with temperatures of 3500–4500 K. This may indicate enhanced activity of KIC 1572802. The parameters of the differential rotation of the star are estimated; the inferred rotational velocity, Ω = 0.0056 ± 0.0010, is substantially lower than the solar value, but comparable to Ω for the cool dwarfs HK Aqr and EY Dra. The value of the Rossby number Ro = 0.011 suggests that KIC 1572802 is in the saturation region of the diagram of Ro vs. X-ray luminosity. If the Ro value for KIC 1572802 is this low, this implies that its magnetic field is of the order of tens or even hundreds of Gauss.     

The structure of the <Emphasis Type="Italic">AD</Emphasis> diagram for the hyades cluster

The Hyades Cluster is used to analyze details of the AD-diagram method developed in our earlier works and applied to the corona of the Ursa Major stream. Hipparcos data are used to analyze the kinematics of the Hyades Cluster and determine its apex. Evidence for rotation of the cluster is presented.     

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.     

Activity of Young Dwarfs with Planetary Systems: EPIC 211901114 and K2–33

The results of an analysis of the activity of the young stars with planetary systems EPIC 211901114 and K2–33 based on observational data obtained over 70 days with the Kepler Space Telescope are presented. The rotation periods of EPIC 211901114 (8.56±0.60^d) and K2–33 (6.29±0.50^d) have been found. Maps of temperature inhomogeneities on the surfaces of EPIC 211901114 and K2–33 have been constructed. No relative displacements of the active regions on the stellar surface have been foundfor EPIC 211901114. The differential-rotation parameter has been estimated for K2–33, ΔΩ = 0.0039±(0.0020–0.0012) rad/day. The fractional spotted area S on the surface of EPIC 211901114 reaches about 5% of its total visible surface. For K2–33, S is 3.8% of its total visible surface, on average. On the whole, the positions of EPIC 211901114 and K2–33 on S–age, S–rotation period, and S–Rossby number diagrams match the general character of the dependence found earlier for M dwarfs. The flare activity of EPIC 211901114 and K2–33 has been studied, based on 32 flares of EPIC 211901114 and 7 flares of K2–33. The flare frequencies and amplitudes for EPIC 211901114 and K2–33 have been estimated, together with the time scales for their rise and decay. The flare energies have also been estimated, 10^32.1?33.4 and 10^32.2?33.3 erg for EPIC 211901114 and K2–33, respectively.     

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.     

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.     

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.     

The motion of halo stars in dynamical numerical models of open clusters

Equations of motion containing a small parameter μ are derived for stars at the peripheries of open star clusters. The parameter μ is obtained for six numerical open-cluster models. The general analytical solution of these equations of motion for μ = 0 is found. An iterative method is used to derive the frequencies of the stellar motions for first-order expansions in μ of the solutions of the equations of motion for stars at the cluster periphery. Applications of the results are discussed.     

Activity of the M8 Dwarf TRAPPIST-1

The results of an analysis of observations of the cool (M8) dwarf TRAPPIST-1 obtained on the Kepler Space Telescope (the K2 continuation mission) are presented. TRAPPIST-1 possesses a planetary system containing at least seven planets. In all, the observations consist of 105 584 individual brightness measurements made over a total duration of 79 days. Brightness power spectra computed for TRAPPIST-1 exhibit a peak corresponding to P₀ = 3.296 ± 0.007 ^d . There are also two peaks with lower significances at P₁ = 2.908 ^d and P₂ = 2.869 ^d , which cannot be explained by the presence of differential rotation. The observational material available for TRAPPIST-1 is subdivided into 21 datasets, each covering one stellar rotation period. Each of the individual light curves was used to construct a map of the star’s temperature inhomogeneities. On average, the total spotted area of TRAPPIST-1 was S = 5% of the entire visible area. The difference between the angular rotation rates at the equator and at the pole is estimated to be ΔΩ = 0.006. The new results obtained together with data from the literature are used to investigate the properties of this unique star and compare them to the properties of other cool dwarfs. Special attention is paid to the star’s evolutionary status (its age). All age estimates for TRAPPIST-1 based on its activity characteristics (rotation, spot coverage, UV and X-ray flux, etc.) indicate that the star is young.     

Physical Parameters of the Eclipsing System V1176 Cas

The first high-accuracy CCDUBV RI light curves for the recently discovered eclipsing system V1176 Cas (P = 6 _. ^d 33, V = 11 _. ^m 1) have been obtained. A photometric solution for the light curves and physical characteristics of the component stars are derived. The orbital eccentricity is negligible, e = 0.009; both components have physical parameters similar to the Sun, but they are younger and may have an overabundance of metals. The orientation of the orbital ellipse and the low eccentricity make studies of the apsidal motion difficult. Nevertheless, the high accuracy of the available measurements of the timings of minima has enabled derivation of an upper limit for the rate of apsidal rotation, which agrees with a theoretical estimate of this effect.     

Development of a technique for IR spectroscopic determination of nitrogen content and aggregation degree in diamond crystals

A technique for IR spectroscopic determination of the total nitrogen content N _S in the form of A-and B ₁-defects is suggested. It provides for the computer processing and decomposition of IR spectra into constituent bands, calculation of the total absorption band area S _N and individual areas S _A and S _B1 and their normalization with respect to the total area of the diamond intrinsic absorption S ₀, with the normalization coefficients K _S , K _A , and K _B1 being calculated. Based on the analysis of the IR spectra of 60 octahedral diamond crystals from the Mir and Yubileinaya pipes (Sakha-Yakutiya), the empirical functions N _S = 911.85 K _S ^0.9919 ppm (R ² = 0.9859), N _A = 1185.6 K _A ^1.1511 ppm (R ² = 0.8703), and N _B1 = 911.85 K _S ^0.9919 ? 1185.6 K _A ^1.1511 ppm have been defined.     

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).