Superflares on Giant Stars

The Kepler mission has identified huge flares on various stars, including some solar-type stars. These events are substantially more energetic than solar flares, and are referred to as superflares. Even a low probability of such a superflare occurring on the Sun would be a menace to modern society. A flare comparable in energy to that of superflares was observed on September 24 and 25, 1989 on the binary HK Lac. Unlike the Kepler stars, observations of differential rotation are available for HK Lac. This differential rotation appears to be anti-solar. In the case of anti-solar differential rotation, dynamo models can producemagnetic-activity waves with dipolare symmetry, as well as quasi-stationary magnetic configurations with quadrupolar symmetry. The magnetic energy of such stationary configurations is usually about two orders of magnitude higher than the energy associated with activity waves. We believe that this mechanism could provide sufficient energy to produce superflares on late-type stars. Some simple models in support of this idea are presented.     

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.     

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.     

The character of solar-type activity and the depth of the convective zone

The origin of solar-type activity for low-mass stars of late spectral types is considered. Spectroscopic data were used to study the dependence of the activity level logR′ _HK on the lithium abundance logA(Li) and axial rotation rate. A close correlation between logA(Li) and logR′ _HK is found for two groups of G stars, hotter and cooler than the Sun. This relation is most clearly expressed in the case of high activity, and is somewhat more strongly expressed for G6-K3 dwarfs, which includes many BY Dra variables, than for F8-G5 stars. It is confirmed that, for stars with high activity, both the lithium abundance and the activity level are determined by the rotation rate, which depends on the age. The lithium abundance exhibits different dependences on the chromospheric activity, depending on the level of this activity. Cooler stars, with detectable lithium and solar-like chromospheres, possess much stronger coronas. This change in the relationship between the relative luminosities of the chromosphere and corona can be reliably traced using larger datasets. The different ratios between the activity of the choromosphere and corona for cooler and hotter G stars may reflect the fact that their convective zones become deeper or shallower than some critical value. This is consistent with observations of parameters describing rotational modulation and the correlation and anti-correlation of chromospheric and photospheric activity indices for stars hotter and cooler than the Sun. Physically, this means that the character of the activity could be related to a changing contribution of the large-scale and local magnetic fields to the generation of the activity. The results of this study confirm the earlier idea that there may be different evolution paths associated with solar-type activity. The results can be used to refine methods for estimating ages of stars from their activity levels (gyrochronology).     

Two modes of the differential rotation of the solar corona

The differential rotation of the solar corona is studied using the brightness of the Fe XIV 530.3 nm green coronal line collected over 5.5 solar-activity cycles. The total observed velocity of the coronal rotation is analyzed as a superposition of two modes—fast and slow. A technique for separating two data series composing the initial data set and corresponding to the two differential-rotation modes of the solar corona is proposed. The first series is obtained by averaging the initial data set over six successive Carrington rotations; this series corresponds to long-lived, large-scale coronal regions. The second series is the difference between the initial data and the averaged series, and corresponds to relatively quickly varying coronal component. The coronal rotation derived from the first series coincides with the fast mode detected earlier using the initial data set; i.e., the synodic period of this mode is 27 days at the equator, then weakly increases with latitude, slightly exceeding 28 days at high latitudes. The second series describes a slow rotation displaying a synodic period of about 34 days. This coincides with the period of rotation of the high-latitude corona derived by M. Waldmeier for polar faculae. We expect that coronal objects corresponding to the fast mode are associated with magnetic fields on the scales typical for large activity complexes. The slow mode may be associated with weak fields on small scales.     

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.     

Can Superflares Occur on the Sun? A View from Dynamo Theory

Recent data from the Kepler mission has revealed the occurrence of superflares in Sun-like stars which exceed by far any observed solar flares in released energy. Radionuclide data do not provide evidence for occurrence of superflares on the Sun over the past eleven millennia. Stellar data for a subgroup of superflaring Kepler stars are analysed in an attempt to find possible progenitors of their abnormal magnetic activity. A natural idea is that the dynamo mechanism in superflaring stars differs in some respect from that in the Sun. We search for a difference in the dynamo-related parameters between superflaring stars and the Sun to suggest a dynamo mechanism as close as possible to the conventional solar/stellar dynamo but capable of providing much higher magnetic energy. Dynamo based on joint action of differential rotation and mirror asymmetric motions can in principle result in excitation of two types of magnetic fields. First of all, it is well-known in solar physics dynamo waves. The point is that another magnetic configuration with initial growth and further stabilisation can also be excited. For comparable conditions, magnetic field of second configuration is much stronger than that of the first one just because dynamo does not spend its energy for periodic magnetic field inversions but uses it for magnetic field growth. We analysed available data from the Kepler mission concerning the superflaring stars in order to find tracers of anomalous magnetic activity. As suggested in a recent paper [1], we find that anti-solar differential rotation or anti-solar sign of the mirror-asymmetry of stellar convection can provide the desired strong magnetic field in dynamo models. We confirm this concept by numerical models of stellar dynamos with corresponding governing parameters. We conclude that the proposed mechanism can plausibly explain the superflaring events at least for some cool stars, including binaries, subgiants and, possibly, low-mass stars and young rapid rotators.     

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.     

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.     

Active longitudes and north-south asymmetry of the activity the Sun as manifestations of its relic magnetic field

The distributions of dominant magnetic polarities in synoptic maps of photospheric magnetic fields and their extrapolations to the corona based on Stanford Observatory data are studied. Both dipolar and quadrupolar magnetic patterns are detected in the distributions of dominant polarities in the near-equatorial region of the photosphere for activity cycles 21, 22, and 23. The field in these patterns often has opposite signs on opposite sides of the equator, with this sign changing from cycle to cycle. A longitude-time analysis of variations of the mean solar magnetic field shows that the contribution of the large-scale magnetic patterns to the total field does not exceed 20 µT. The most stable magnetic structures at a quasi-source surface in the solar corona are separated by approximately 180° in heliographic longitude and are close to dipolar. The nature and behavior of these large-scale magnetic patterns are interpreted as a superposition of cyclic dynamo modes and the nonaxially symmetric relic field of the Sun. The contribution of the relic field to the mean solar magnetic field appears as a weak but stable rotational modulation whose amplitude does not exceed 8 µT.     

Long-term variations in the rotation of the solar corona

The characteristic time scales for variations in the differential rotation of the solar corona are determined using measurements of the intensity of the FeXIV 5303 Å coronal line made from 1939–2004. Drift waves of the variations in the rotational speed with an 11-year periodicity can be distinguished. Moving averages with time intervals from two to five years are used to identify torsional waves. In addition, longer-period variations in the rotational speed can be distinguished when longer averaging intervals are used. When the interval used for the moving average is increased to 8–12 years, a quasi-22-year rotational period appears. The low-latitude corona rotates more slowly in odd cycles than in even cycles. Increasing the duration of the averaging interval further shows that rapid rotation at low latitudes was observed in 1940–1950 and 1990–2000, while slow rotation was observed in 1960–1980, possibly suggesting the presence of a 55-year period in the rotational variations. Long-term variations are found in the rotation of polar regions. The rotational variations for high-latitude corona are in antiphase with those for the low-latitude corona. The origins of zones of anomalous coronal rotation and their dynamics in the global activity cycle are discussed.     

Cyclic variations in the differential rotation of the solar corona

The rotation of the solar corona is analyzed using the original database on the brightness of the FeXIV 530.3 nm coronal green line covering six recent activity cycles. The rate of the differential rotation of the corona depends on the cycle phase. In decay phases, there are only small differences in the rotation, which are similar to that of a rigid body. The differences are more significant (though less pronounced than in the photosphere) during rise phases, just before maxima, and sometimes at maxima. The total rate of the coronal rotation is represented as a superposition of two, i.e., fast and slow modes. The synodic period of the fast mode is approximately 27 days at the equator and varies slightly with time. This mode displays weak differences in rotation and is most pronounced in the middle of decay phases. The slow mode is manifested only at high latitudes during the rise phases of activity, and displays a mean period of 31 days. The relative contribution of each mode to the total rotational rate is determined as a function of time and heliographic latitude. These results indicate that the structure of the velocity field in the convective zone must also vary with time. This conclusion can be verified by helioseismology measurements in the near future.     

Search for the general magnetic fields in late-type giants

Surface-averaged longitudinal magnetic-field components (by analogy with the Sun called the general magnetic field) have been measured for 15 late-type giants with an accuracy of several Gauss. Statistically significant fields were detected for nine of these stars. The magnetic-field values obtained suggest the existence of general magnetic fields in these giants.     

Variability of the photospheric radiation of active K-M dwarfs and their X-ray luminosities

Variability of the photospheric radiation of 40 (dKe-dMe) dwarfs in the solar neighborhood due to variations in the spottedness of their surfaces is analyzed based on the behavior of their mean annual brightnesses over long time intervals. The amplitudes and characteristic time scales of the variations of the mean annual brightness are taken to be indicators of photospheric activity and were used to infer the levels of photospheric activity in the stars studied. The influence of axial rotation on the development of cyclic activity in young red dwarfs and F-M main-sequence stars is analyzed. The durations and amplitudes of the photospheric variability of rapidly rotating (dK0e-dK5e) stars testifies to a higher level of photospheric activity among red dwarfs and solar-type stars. The X-ray luminosities of these stars grow with the amplitude of the variations of the mean annual brightness. However, this is not typical of rapidly rotating M dwarfs, for which the X-ray emission varies by more than two orders of magnitude, although their degrees of spottedness are all virtually the same. A linear relationship between the X-ray and bolometric luminosities is observed for young (dKe-dMe) stars, with their ratios log(L _x/L _bol) being about ?3. These properties can be used to determine whether a red dwarf is a young star or is already on the main sequence.     

A search for FK Com candidates using Kepler Space Telescope observations: Analogs of HD 199178

Analysis of collected photometric observations obtained with the Kepler Space Telescope were used to select and study 33 objects with parameters corresponding to those of the FK Com starHD199178; these can be considered candidate stars of this type. In this final study, the four objects with the best light curves, which show the properties of their regular rotational modulation most clearly, were selected for detailed studies. The photometric analysis is based on all data currently available in the Kepler archive (covering almost four years). The rotational periods and estimated parameters of the objects’ differential rotation are determined, and the longitudes of the dominant active regions on the surfaces found. For all four stars, the spot coverage is approximately 1% of the visible stellar surface area. The rotational periods and data on the stars’masses and radii fromtheMAST catalog are used to determine the rotation velocities projected onto the line of sight, which ranged from 12 to 21 km/s. Further studies will enable definite conclusions about how these stars are related to FK Com stars. If they are ultimately classified as FK Com stars, this will considerably increase the number of this rare type of star and the also number of rapidly rotating, single, late-type giants.     

Magnetic fields in the radiative-transport zone and the solar cycle

It is shown that a hypothetical relict magnetic field in the solar radiative-transport zone that penetrates into the convective zone would affect the solar dynamo, resulting in radical changes in the butterfly diagrams. This would transform the traveling waves of activity into standing waves. A comparison of our results with the well-known butterfly diagrams for the Sun gives an upper limit of the order of some tens G for the value of relict magnetic field penetrating into the solar convective zone. At the same time, it is not ruled out that such relict magnetic fields in other solar-type stars are strong enough to make the activity waves become standing waves.     

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.     

On stereoimages of some structures in the solar atmosphere

Three-dimensional structures in the solar chromosphere and corona are considered. It is demonstrated that two photoheliograms separated by ～1 day can be used (using computer-graphics methods) to construct a stereo image of the Sun. The algorithm for this is presented and carried out for H_α images of the total disk. A bulge in the equatorial region resulting from the differential rotation of the Sun can be seen in the stereo image. Structures called Whitney pleats in catastrophe theory are observed in the solar corona. Such structures are encountered in prominences. The well-known helmets (or streamers) are pleats of heliospheric plasma sheets. Isophotes for such a sheet and the degree of polarization of the radiation in the pleat are calculated and compared with observational data.     

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.