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.     

Collision-induced absorption of radiation in the atmospheres of late-type stars

Problems associated with taking into account absorption induced by collisions between hydrogen and helium atoms, helium atoms and hydrogen molecules, and hydrogen molecules, resulting in the formation of short-lived, quasi-molecular complexes are discussed, together with opacity in the atmospheres of late-type stars due to such absorption. There is good agreement between such opacities computed using codes developed by the author and by R. Kurucz. To demonstrate the importance of including collision-induced opacity, theoretical fluxes are compared to the observed spectral energy distribution of the metal-poor L subdwarf SDSS J125637.13-022452.4. The spectral energy distribution of this object can be reproduced with an effective temperature of T_eff = 2600 K only if collision-induced absorption is taken into account.     

Origin of prolonged X-ray flares on active late-type stars

Soft X-ray data for prolonged flares in subgiants in RS CVn binary systems and some other active late-type stars (AB Dor, Algol) are analyzed. During these nonstationary events, a large amount of hot plasma with temperatures exceeding 10⁸ K exists for many hours. Numerical simulations of gas-dynamical processes in the X-ray source—giant loops—can yield reliable estimates of the plasma parameters and flare-source size. This confirms that such phenomena exist while considerable energy is supplied to the top part of a giant loop or system of loops. Refined estimates of the flare energy (up to 10³⁷ erg) and scales contradict the widely accepted idea that prolonged X-ray flares are associated with the evolution of local magnetic fields. The energy of the current component of the large-scale magnetic field arising during the ejection of magnetic field by plasma jets or stellar wind is estimated. Two cases are considered: a global stellar field and fields connecting regions with oppositely directed unipolar magnetic fields. The inferred energy of the current component of the magnetic field associated with distortion of the initial MHD configuration is close to the total flare energy, suggesting that large-scale magnetic fields play an important role in prolonged flares. The flare process encompasses some portion of a streamer belt and may propagate along the entire magnetic equator of the star during the most powerful prolonged events.     

The quiescent X-ray emission of X-ray novae and the coronal emission of late-type stars

The X-ray luminosities and spectra of F-M stars of luminosity classes IV–V are analyzed. In dwarfs with rotational velocities of about 100 km/s, such as the optical components of low-mass X-ray novae with black holes, hot plasma can be confined in coronal loops even in the presence of fairly weak magnetic fields. Thus, the soft X-ray emission of such systems in their quiescent state (to 10³¹ erg/s) could be associated with the coronal emission of the optical component/dwarf. Two systems studied with subgiants (V1033 Sco and V404 Cyg) have X-ray luminosities 2×10³²–2×10³³ erg/s. The X-ray emission of a solar-type corona cannot provide such luminosities. However, a transition to a non-solar corona is possible in rapidly rotating subgiants—a dynamical corona whose X-ray emission can be one to two orders of magnitude higher than observed for more slowly rotating late-type subgiants in the solar neighborhood. This suggests that the quiescent X-ray emission of these two systems is provided by emission from the corona of the subgiant optical component.     

Levels of coronal and chromospheric activity in late-type stars and various types of dynamo waves

We analyze the X-ray emission and chromospheric activity of late-type F, G, and K stars studied in the framework of the HK project. More powerful coronas are possessed by stars displaying irregular variations of their chromospheric emission, while stars with cyclic activity are characterized by comparatively modest X-ray luminosities and ratios of the X-ray to bolometric luminosity L _X/L _bol. This indicates that the nature of processes associated with magnetic-field amplification in the convective envelope changes appreciably in the transition from small to large dynamo numbers, directly affecting the character of the (α-Ω) dynamo. Due to the strong dependence of both the dynamo number and the Rossby number on the speed of axial rotation, earlier correlations found between various activity parameters and the Rossby number are consistent with our conclusions. Our analysis makes it possible to draw the first firm conclusions about the place of solar activity among analogous processes developing in active late-type stars.     

The effects of deviations from LTE in sulphur lines for late-type stars

We analyze the formation of lines of neutral sulfur in the spectra of F-K stars taking into account the effects of deviations from local thermodynamical equilibrium (LTE). Our calculations were carried out for Kurucz model atmospheres with T _eff = 5000–6500 K, log g = 2?4 and [Fe/H] = ?4?0, using a 65-level model of the SI atom. Deviations from LTE affect lines of different multiplets of the sulfur atom differently. Non-LTE corrections, which are relatively small (to ?0.10 dex) for the 6543–6557 Å lines, increase to ?0.26 dex for the 8694 Å line, and reach ?1.1 dex for the 9212–9237 Å IR triplet. The model of the atom was verified by modeling the sulfur lines of the studied multiplets in the spectra of the Sun, two main sequence stars, and two supergiants. Good consistency with the observed line profiles was obtained. Failure to take into account strong non-LTE-effects may explain the large sulfur excesses detected in stars with very low metal abundances.     

Observations of late-type variable stars in the water vapor radio line. The long-period variable R cassiopeia

Observations of circumstellar maser emission from the long-period variable R Cas in the 1.35-cm water-vapor line are reported. The observations were carried out on the 22-m radio telescope of the Pushchino Radio Astronomy Observatory in 1980–2003 (JD=2444409–2452724). Over the 23 years of observations, strong flares in the H₂O line profile were recorded in 1982 (with a peak flux density up to 400 Jy) and 1986–1989 (up to 750 Jy). Subsequently, from 1990 to March 2003, the H₂O line flux was usually below the detection threshold of the radio telescope (<5–10 Jy). Episodic small increases of the emission with peak flux densities of 20–60 Jy were observed. The variations of the H₂O line flux F are correlated with variations in the visual brightness of the star. The phase delay Δ_γ of the F variations relative to the optical light curve of R Cas ranged from 0.2–0.3P during the observations (P=430.46^d is the star's period). A model for the variability of the H₂O maser in R Cas is discussed. If the variations are due to periodic impacts by shock waves driven by the stellar pulsations, the time for the shock to travel from the photosphere to the inner boundary of the H₂O-masing shell may reach 2–4P. The flares could be due to transient episodes of enhanced mass loss by the star or to the propagation of an exceptionally strong shock from the stellar surface.     

The evolution of solar-like activity of low-mass stars

An analysis of data on chromospheric activity obtained in the framework of exoplanet-search programs is presented. Observations of 1334 stars showing that the chromospheric activity of the Sun is clearly higher than for the vast majority of stars in the solar vicinity are used. A comparison of chromospheric and coronal activity led to the identification of a significant group of stars with a low level of chromospheric activity, whose coronal radiation spans wide ranges. There are reasons to believe that the chromospheric and coronal activities of one group of stars decrease simultaneously as the rotation decelerates, while, in stars of the other group, the chromospheric activity diminishes, but their coronas remain stronger than that of the Sun. Features of cyclic activity of the Sun are discussed. This enables us to associate differences in the behavior of the activity with different depths of the convective zones of stars of spectral classes earlier and later than G6. Arguments in favor of a two-layer dynamo and different roles of the large-scale and small-scale magnetic fields in the formation and evolution of activity are formulated. Age estimations based on activity levels (gyrochronology) must be carried out differently for these different groups of stars.     

G0-G5V stars and the Sun in the u vby system

The color indices of the Sun in the u vby system are calculated using the spectral energy distribution of Lockwood, Tug, and White. This allows errors in the absolute calibration to be excluded from the calculated color indices. The normal position of the Sun on the (v-b)?(b-y) and (v-y)?(b-y) color-color diagrams for early G stars testifies to the absence of any significant peculiarities in the Sun compared to other stars of similar spectral type. These diagrams can provide a useful tool in searches for candidate solar analogues among faint stars.     

Patterns of activity in stars with cycles becoming established

Late-type stars with chromospheric and coronal activities exceeding those of the Sun and other stars with well-defined cycles are considered. These rotate more rapidly than stars with well established cycles; for single stars, this appears to be due to their younger ages. The spots on such stars cover several per cent of the total area, which is an order of magnitude higher than for the Sun at its activity maximum. Our wavelet analysis of the chromospheric-emission variability, which has been observed since 1965 in the framework of the HK project, indicates that the period of the axial rotation of some of these starts varies from year to year. This is most pronounced in two “Good” stars according to the classification of Baliunas et al., HD 149661 and HD 115404, and also in a star with a more complex variability, HD 101501. No similar effect is exhibited by the “Excellent” cyclic-activity stars. Such variations in the period can be observed during epochs of appreciable rotational modulations of the chromospheric-emission fluxes, most likely, immediately after the maximum of a long-period wave (cycle?). This seems to provide evidence for the existence of huge activity complexes in the chromospheres of these stars, whose longitudes remain virtually constant over several years; they drift from fairly high latitudes to the equator at speeds close to the value typical of sunspots. The observed period variations are most likely due to differential rotation of the same sign that is known for the Sun. Our results provide independent confirmation of similar conclusions obtained by us previously using zonal models for highly spotted stars. Other activity features of a selected star group and the implications of the results for the theory of stellar and solar dynamos are discussed.     

The large-scale magnetic field on the Sun: The equatorial region

The sector structure and variations in the large-scale magnetic field of the Sun are studied in detail using solar magnetic-field data taken over a long time interval (1915–1990). The two-sector and four-sector structures are independent entities (i.e., their cross correlation is very small), and they are manifest in different ways during the main phases of the 11-year cycle. The contribution of the two-sector structure increases toward the cycle minimum, whereas that of the four-sector structure is larger near the maximum. The magnetic-field sources determining the two-sector structure are localized near the bottom of the convection zone. The well-known 2–3-year quasi-periodic oscillations are primarily associated with the four-sector structure. The variations in the rotational characteristics of these structures have a period of 55–60 years. The results obtained are compared with the latest helioseismology data.     

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.     

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.     

Orbital-period variations of the close binaries with late-type components TY Del and RY Cnc

A detailed study of orbital-period variations was performed for TY Del and RY Cnc, which are both Algol-type eclipsing binaries with late-type second aries; for RY Cnc, this is the first study of this kind. The period variations of both stars can be considered a superposition of a secular period increase and cyclic changes of this period. The secular period increase can be explained as the effect of a uniform transfer of mass from the lower-mass to the higher-mass component, with the total angular momentum conserved. The mass-transfer rate is about 1.25 × 10^⊙ M _⊙/year for TY Del and (0.68?1.02) × 10^?8 M _⊙/year for RY Cnc. The cyclic period variations of the eclipsing binaries TY Del and RY Cnc could be due to either the presence of a third body in the system or the influence of magnetic activity of the secondary.     

The evolution of stars paired with supermassive black holes

A star located in the close vicinity of a supermassive black hole (SMBH) in a galactic nucleus or a globular-cluster core could form a close binary with the SMBH, with the star possibly filling its Roche lobe. The evolution of such binary systems is studied assuming that the SMBH mainly accretes matter from the companion star and that the presence of gas in the vicinity of the SMBH does not appreciably influence variations in the star’s orbit. The evolution of the star–SMBH system is mainly determined by the same processes as those determining the evolution of ordinary binaries. The main differences are that the star is subject to an incident flux of hard radiation arising during the accretion of matter by the SMBH, and, in detached systems, the SMBH captures virtually all the wind emitted by its stellar companion, which appreciably influences the evolution of the major axis of the orbit. Moreover, the exchange between the orbital angular momentum and the angular momentum of the overflowing matter may not be entirely standard in such systems. The computations assume that there will be no such exchange of angular momentum if the characteristic timescale for mass transfer is shorter than the thermal time scale of the star. The absorption of external radiation in the stellar envelope was computed using the same formalism applied when computing the opacity of the stellar matter. The numerical simulations show that, with the adopted assumptions, three types of evolution are possible for such a binary system, depending on the masses and the initial separation of the SMBH and star. Type I evolution leads to the complete destruction of the star. Only this type of evolution is realized for low-mass main-sequence (MS) stars, even those with large initial separations from their SMBHs. Massive MS stars will also be destroyed if the initial separation is sufficiently small. However, two other types of evolution are possible for massive stars, with a determining role in the time variations of the parameters of the star–SMBH system being played by the possible growth of the massive star into a red giant during the time it is located in the close vicinity of the SMBH. Type II evolution can be realized for massive MS stars that are initially farther from the SMBH than in the case of disruption. In this case, the massive star fills its Roche lobe during its expansion, but is not fully destroyed; the star retreats inside its Roche lobe after a period of intense mass loss. This type of evolution is characterized by an increase in the orbital period of the system with time. As a result, the remnant of the star (its former core) is preserved as a white dwarf, and can end up at a fairly large distance from the SMBH. Type III evolution can be realized formassiveMSstars that are initially located still farther from their SMBHs, and also for massive stars that are already evolved at the initial time. In these cases, the star moves away from the SMBH without filling its Roche lobe, due to its intense stellar wind. The remnants of such stars can also end up at a fairly large distances from their SMBHs.     

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.     

Positional evolution of magnetic foci in the polar regions of the Sun with the phase of the solar activity cycle

The behavior of magnetic foci—intersection points of tangents to ray structures in the polar corona of the Sun—is studied. This behavior reflects the evolution of the large-scale magnetic field near the poles, and is one of only a few sources of information on the polar magnetic field of the Sun. For the first time, the positions of the magnetic foci are plotted as a function of the solar-cycle phase for a full cycle, based not only on total-eclipse images but also on daily coronal observations in the FeIX and FeX (171 Å) lines carried out with the EIT telescope on the SOHO satellite. The temporal behavior of the foci over a cycle differs appreciably from that inferred from isolated observations during eclipses. The curve agrees fairly well with the model of the global-field evolution suggested by us previously.     

The evolution of close binary stars

A review of our current understanding of the physics and evolution of close binary stars with various masses under the influence of the nuclear evolution of their components and their magnetic stellar winds is presented. The role of gravitational-wave radiation by close binaries on their evolution and the loss of their orbital angular momentum is also considered. The final stages in the evolution of close binary systems are described. The review also notes the main remaining tasks related to studies of the physics and evolution of various classes of close binaries, including analyses of collisions of close binaries and supermassive black holes in galactic nuclei. Such a collision could lead to the capture of one of the components by the black hole and the acceleration of the remaining component to relativistic speeds.     

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.