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.     

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.     

Starspots and Activity of the Flare Star GJ 1243

The photometric variability of the uniqueMdwarf flare star GJ 1243 (KIC 9726699) is investigated using the most complete set of observationalmaterial obtained with the Kepler Space Telescope. The analysis is based on 49 487 individual brightness measurements obtained during an interval of 1460 days (nearly four years). The periodicity of the brightness variations with the period P_phot = 0.59261 ± 0.00060^d is confirmed. The temperature inhomogeneities on the stellar surface reconstructed from the light curve are used to drive maps of these surface-temperature inhomogeneities (of the filling factor f). The resulting maps are used to determine the positions of active regions. Analysis of the surface-temperature maps for GJ 1243 led to the conclusion that the positions of spots on the stellar surface displayed appreciable evolution during the analyzed time interval. The maximum value for the lower limit on the differentialrotation parameter ΔΩ is 0.0022 rad/day. This more accurate estimate of ΔΩ is lower than the values presented earlier by Davenport et al. [1] (0.0058 and 0.0036 rad/day), due to the more accurate account of variations in the positions of the most active longitude in the current study. However, the differentialrotation estimate obtained in [1] using a method based on fitting the evolution of spots using twodimensional Gaussian functions essentially coincides with the new estimate presented here. The fractional area of the total spotted surface S of the star during the observing interval considered varied from 7 to 2%. The amplitude of the brightness variability of the star slowly decreased, varying in the range 1.6?0.5%. Overall, the position of GJ 1243 in spottedness–age, spottedness–rotation period, and spottedness–Rossby number diagrams agrees very well with the general character of the dependences displayed in earlier studies of M dwarfs.     

Broad-band multicolor photometry and polarimetry of spotted stars

We have confirmed the BY Dra-type variability of the active spotted stars MS Ser, LQ Hya, VY Ari, and EK Dra using simultaneous UBVRI photometric and polarimetric observations. We have also reliably detected the intrinsic linear polarization of their radiation and its rotational modulation in U due to the inhomogeneous distribution of active magnetized regions over the surfaces of the stars. Modeling of the linear polarization based on the Zeeman effect indicates that all the stars display strong local magnetic fields (about 2 kG, similar to those in sunspots), with filling factors of up to 40% of the total stellar surface. The magnetized regions coincide with cool photospheric spots detected in photoelectric observations.     

Analysis of MOST light curves of the active stars <Emphasis Type="Italic">ɛ</Emphasis> Eri AND <Emphasis Type="Italic">κ</Emphasis> Cet

We have analyzed light curves from the MOST satellite for the two active dwarfs ? Eri and κ Cet. Our maps of the stellar surface-temperature inhomogeneities were obtained with no a priori assumptions about the shape, configuration, and number of spots. We find variations of the surface-temperature inhomogeneities with time, also on time scales about equal to their rotation periods. We consider a model of a spotted star with two types of surface inhomogeneities—spots and related plage fields—and demonstrate that the best agreement between the theoretical and observed light curves is achieved for small ratios of the plage-field area to the area of cool spots. This conclusion indicates that long-term brightness variations of stars younger than the Sun are mainly due to variable spots on their surfaces, while the contribution from plage fields becomes more significant for older stars.     

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 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.     

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.     

Statistics of BY Draconis variables

A statistical survey of 113 spotted red dwarf stars that are known or suspected BY Draconis variables is presented. Typical indicators of stellar photometric activity—the amplitudes of the rotational modulation and seasonal mean brightness variations ΔV and Δ〈V〉—are compared to the global parameters of the stars. First, photometric variability shows a weak dependence on spectral type; second, ΔV and Δ〈V〉 grow with increasing stellar rotational velocity and decreasing Rossby number, with the dependences saturating at the critical values V _crit～15–20 km/s and Ro_crit～0.2–0.3; and third, the Sun as a star fits well into the derived relations. Thus, the spottedness of stars, like other indicators of stellar activity, depends on their global parameters.     

Spots on the surfaces of late-type stars

The spottedness of two stars characterized by significant photometric variability is studied using published data: the recently discovered variable ASAS 063656-0521.0, whose V variability reaches 0.8 ^m , and XXTri (HD12545), which is among the most active RSCVn stars (in 1997–1998, the amplitude of its V variability was 0.63 ^m ). The spots cover up to 44% of the total visible surface S of ASAS 063656-0521.0. The mean estimated spottedness of XX Tri was 32%, and varied from29% to 36%. An analysis of the dependence of the spottedness on the properties of spotted stars, primarily their effective temperatures, is also presented. A modification of a simplifiedmethod for estimating the spottedness S, i.e., the fractional surface area of the spots, is applied to a sample of 48 late-type stars. The dependences of the spottedness on the effective temperature of the stars and the rotational velocity projected onto the line of sight are derived. Two groups of objects can be distinguished. The first contains stars displaying the typical dependence of S on the effective temperature (their maximum value of S is 20–25% for stars with temperatures 4500–5000 K, and S decreases for solar-type stars and cool M dwarfs). The second group is formed of the most active stars, which have temperatures of 3700–5200 K and S values from 25% to 50%. Our preliminary conclusion is that spottedness is not related to the period of the stellar rotation. The previously studied variable V410 Tau is used to consider the shortcomings of the method applied compared to the results of light-curve modeling.     

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.     

Photometric activity of UX orionis stars and related objects in the near infrared and optical: CO Ori,RR Tau,UX Ori,and VV Ser

This paper continues a study of the photometric activity of UX Ori stars in the optical and near-infrared (JHKLM bands) initiated in 2000. For comparison, the list of program stars contains two Herbig Ae stars that are photometrically quiet in the optical: MWC480 andHD179218. Fadings ofUXOri stars in the optical (V band) due to sporadic increases of the circumstellar extinction are also observed in the infrared (IR), but with decreasing amplitude. Two stars, RR Tau and UX Ori, displayed photometric events when V -band fadings were accompanied by an increase in IR fluxes. Among the two Herbig Ae stars that are photometrically quiet in the optical, MWC 480 proved to be fairly active in the IR. Unlike the UX Ori stars, the variation amplitude of MWC 480 increases from the J band to the M band. In the course of the observations, no deep fadings in the IR bands were detected. This indicates that eclipses of the program stars have a local nature, and are due to extinction variations in the innermost regions of the circumstellar disks. The results presented testify to an important role of the alignment of the circumstellar disks relative to the direction towards the observer in determining the observed IR variability of young stars.     

Butterfly diagram for starspots on LQ Hya

Information on the latitude distribution of starspots and changes in this distribution from year to year is very important for our understanding of the nature of stellar activity and for developing dynamo theory. The concept of butterfly diagrams is introduced for highly spotted stars of late spectral types, by analogy to the Maunder diagrams for the Sun. Our approach is based on the zonal spottedness models constructed by Alekseev and Gershberg. A detailed analysis is given for the single active star LQ Hya, and a comparison is made to similar analyses for several stars with two well-separated spot belts—EK Dra, VY Ari, V775 Her, and V833 Tau. The lower boundary of the butterfly diagram drifts toward the equator during the activity-rise phase, i.e., during years when the relative spotted area increases. This effect is clearly expressed for LQ Hya and other stars whose orientation enables observation of both hemispheres and virtually vanishes for V833 Tau, which is viewed nearly pole-on. The upper boundary of the diagram is virtually unchanged for all the considered spotted stars except V775 Her, for which it moves toward the pole. The drift rate of the lower boundary is ?1 to ?2 deg/yr, a factor of two to three smaller in magnitude than the corresponding solar value. Our analysis provides an independent confirmation of the occurrence of high-latitude spots on stars that are younger than the Sun and whose activity is high but less regular than the solar activity; it also enables the identification of the starting times of stellar cycles.     

The evolutionary status of ultraluminous X-ray sources

We analyze models for quasi-stationary, ultraluminous X-ray sources (ULXs) with luminosities 10³⁸–10⁴⁰ erg/s exceeding the Eddington limit for a ～1.4M_⊙ neutron star. With the exception of relatively rare stationary ULXs that are associated with supernova remnants or background quasars, most ULXs are close binary systems containing a massive stellar black hole (BH) that accretes matter donated by a stellar companion. To explain the observed luminosities of ～10⁴⁰ erg/s, the mass of the BH must be ～40M_⊙ if the accreted matter is helium and ～60M_⊙ if the accreted matter has the solar chemical composition. We consider donors in the form of main-sequence stars, red giants, red supergiants, degenerate helium dwarfs, heavy disks that are the remnants of disrupted degenerate dwarfs, helium nondegenerate stars, and Wolf-Rayet stars. The most common ULXs in galaxies with active star formation are BHs with Roche-lobe-filling main-sequence companions with masses ～7M_⊙ or close Wolf-Rayet companions, which support the required mass-exchange rate via their strong stellar winds. The most probable candidate ULXs in old galaxies are BHs surrounded by massive disks and close binaries containing a BH and degenerate helium-dwarf, red-giant, or red-supergiant donor.     

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.     

Photometric period and rotational brightness modulation of V833 Tau

Photometric data covering 1994–2009, obtained at the Crimean Astrophysical Observatory or retrieved from the ASAS and SuperWASP catalogs, were used to analyze the brightness variations of the rapidly rotating star V833 Tau, whose activity level is close to saturation. Combined with previously published results, these data represent for the first time all stages in the development of the star’s 19- year activity cycle. The photometric period and rotational-modulation amplitude for different epochs are determined, and the qualitative pattern of the spots is considered. The photometric period is close to the orbital period, but always exceeds it, indicating that surface inhomogeneities are located far from the equatorial plane. With the high spottedness of the star, reaching 28% at the cycle maximum, the rotationalmodulation amplitude is 0.05?0.1 ^m , and increases during the growth and decline phases of the 19-year cycle. The rotational modulation is due to spots with higher latitudes than in the case of the Sun, and concentrating on active longitudes.     

The formation and evolution of the most massive stars

We consider the formation of massive stars under the assumption that a young star accretes material from the protostellar cloud through its accretion disk while losing gas in the polar directions via its stellar wind. The mass of the star reaches its maximum when the intensity of the gradually strengthening stellar wind of the young star becomes equal to the accretion rate. We show that the maximum mass of the forming stars increases with the temperature of gas in the protostellar cloud T ₀, since the rate at which the protostellar matter is accreted increases with T ₀. Numerical modeling indicates that the maximum mass of the forming stars increases to ～900 M _⊙ for T ₀ ～ 300 K. Such high temperatures of the protostellar gas can be reached either in dense star-formation regions or in the vicinity of bright active galactic nuclei. It is also shown that, the lower the abundance of heavy elements in the initial stellar material Z, the larger the maximum mass of the star, since the mass-loss rate due to the stellar wind decreases with decreasing Z. This suggests that supermassive stars with masses up to 10⁶ M _⊙ could be formed at early stages in the evolution of the Universe, in young galaxies that are almost devoid of heavy elements. Under the current conditions, for T ₀ = (30–100) K, the maximum mass of a star can reach ～100M _⊙, as is confirmed by observations. Another opportunity for the most massive stars to increase their masses emerges in connection with the formation and early stages of evolution of the most massive close binary systems: the most massive stars can be produced either by coalescence of the binary components or via mass transfer in such systems.     

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.     

The activity of late-type stars: the Sun among stars with cyclic activity

The coronal and chromospheric emission of several hundred late-type stars whose activity was recently detected are analyzed. This confirms the previous conclusion for stars of HK project that there exist three groups of objects: active red M dwarfs, G-K stars with cyclic activity, and stars exhibiting high but irregular activity. The X-ray fluxes, EUV-spectra, and X-ray cycles can be used to study the main property of stellar coronas—the gradual increase in the number of high-temperature (T ≥ 10 MK) regions in the transition from the Sun to cyclically active K dwarfs and more rapidly rotating F and G stars with irregular activity. The level of X-ray emission is closely related to the spottedness of the stellar surface. The correlation between the chromospheric and coronal emission is weak when the cycles are well-defined, but becomes strong when the activity is less regular. Unexpectedly, stars whose chromospheric activity is even lower than that of the Sun are fairly numerous. Common and particular features of solar activity among the activity of other cyclically active stars are discussed. Our analysis suggests a new view of the problem of heating stellar coronas: the coronas of stars with pronounced cycles are probably heated by quasistationary processes in loops, while prolonged nonstationary coronal events are responsible for heating the coronas of F and G stars with high but irregular activity.     

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.