Butterfly diagrams of strongly spotted late type stars

At present, long-term (over 30 years) multicolor photometric observations give the possibility to determine general properties of spotted areas on late-type stars. Star-spot modeling from broadband photometric data has been carried out by Alekseev and Gershberg since 1996 under the assumption that spots are situated in two latitudinal zones. Here we propose a new analysis of their results for several G and K dwarf stars with high irregular activity. On these stars, EK Dra, VY Ari, V775 Her, and V833 Tau, two spot belts exist separately and do not merge into a single equatorial active region, as occurs on cooler red-dwarf stars. The zonal spottedness models allow us to fit simultaneously both rotational modulation and long-term variability of stellar brightness. These models give evidence for an equatorward drift of the lower latitude boundary of the spotted region, φ₀, during the rising phase of activity, beyond any possible errors concerned with our methodology. In order to evaluate the drift rate we introduce the concept of `effective' spot belt, whose width is independent of longitude. This permits us to construct butterfly diagrams for stellar spots. The equatorward drift rates of the lower boundary of the spotted region D=dφ_low/dt are (− 1)–(− 2) deg year⁻¹ in the years of increasing spottedness. These values are less than the analogous solar one D≈−4 deg year⁻¹ for the rising phase of the cycle. Thus, cyclic activity can be revealed from butterfly diagrams and derived drifts of starspots prior to a possible detection from the spectral analysis of photometric variability. Finally, we briefly discuss a possible explanation of high-latitude activity and surface drifts of starspots in the framework of the current state of dynamo theory.     

The optical continuum of solar and stellar flares

A further development of the Kostyuk-Pikelner's model is presented. The response of the chromosphere heated by non-thermal electrons of the power-law energy spectrum has been studied on the basis of the numerical solution of the one-dimensional time-dependent equations of gravitational gas dynamics. The ionization and energy loss for the emissions in the Lyman and Balmer lines have been determined separately for the optically thin and thick L-line layers. Due to the initial heating, a higher-pressure region is formed. From this region, disturbances propagate upwards (a shock wave with a velocity of more than 1000 km s^-1) and downwards. A temperature jump propagates downwards, and a shock is formed in front of the thermal wave. During a period of several seconds after the beginning of this process, the temperature jump intensifies the downward shock wave and the large radiative loss gives rise to the high density jump ( ₂/ ₁ 100). The numerical solution has been analyzed in detail for the case heating of the ionized and neutral plasma, and a value of this heating is close to the upper limit of the admissible values. In this case, the condensation located between the temperature jump and the shock wave front, may emit in the observed optical continuum.In their essential features, the gas dynamic processes during the flares in red dwarf atmospheres are the same as those in the solar atmosphere. However, the high atmospheric densities, smaller height scale in red dwarf atmospheres, and greater energy of this processes in stellar flares, give rise, in practice, to the regular generation of optical continuum. The photometric parameters of a source with n 0¹⁵ cm^-3, T 9000 K, and _z 10 km are in a good agreement with observations.     

Helium emission in the middle chromosphere

Slitless spectrograms obtained during the eclipse of 10 June 1972 have been analyzed to determine the height distribution of the D₃ He line intensity.For undisturbed regions the maximum of D₃ line intensity is confirmed to exist at about 1700km above the limb. Besides the above mentioned maximum, in plages a considerable intensity may be observed at low heights (h < 1000 km).An analysis of these observations for h > 1000 km has been carried out within the low temperature mechanism of triplet helium emission taking into account the helium ionization by XUV radiation. The density dependence of the 2³ S level population at different XUV flux values has been calculated. Our observations give N _e 2 × 10¹⁰ cm^–3 in the chromosphere at h = 2000 km. The probable coincidence of the H and He emission small filaments in the middle chromosphere is discussed.     

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.     

When and where are solar cosmic rays accelerated most efficiently?

The acceleration of particles by solar flares with extremely large proton fluxes whose energies exceed 100 MeV is considered. Most importantly, the location of the source of such acceleration in the flare of July 14, 2000, is determined assuming that the acceleration time coincides with the observed burst of hard line and continuous gamma-ray emission. The onset of this event corresponds to 10:19 UT, when data taken by the TRACE space observatory show that one of the flare ribbons reached a large sunspot in a group. The time interval for the development of the flare, 10:20–10:28 UT, is associated with the beginning of an increasing proton flux at the Earth. The region of efficient acceleration is estimated to be approximately two to three times higher than the height where the hard X-ray pulse usually originates (about 7000 km). The results are generalized for 28 powerful flares with extremely efficient acceleration of relativistic particles—in particular, for the well-studied events of June 15, 1991, and May 24, 1990—and are compared with the results of a statistical analysis of over 1100 increasing-proton-flux events. Efficient particle acceleration seems to be associated with the powerful impulsive episodes of the large flares analyzed. The results suggest that, along with sources of local (as in impulsive flares) and post-eruptive acceleration, there is an additional, very efficient, moderate-scale “accelerator” in tenuous regions with fairly strong magnetic fields and magnetic-field gradients.     

Change in the activity character of the coronae of low-mass stars of various spectral types

We study the dependence of the coronal activity index on the stellar rotation velocity. This question has been considered previously for 824 late-type stars on the basis of a consolidated catalogue of soft X-ray fluxes. We carry out a more refined analysis separately for G, K, and M dwarfs. Two modes of activity are clearly identified in them. The first is the saturation mode, is characteristic of young stars, and is virtually independent of their rotation. The second refers to the solar-type activity whose level strongly depends on the rotation period. We show that the transition from one mode to the other occurs at rotation periods of 1.1, 3.3, and 7.2 days for stars of spectral types G2, K4, and M3, respectively. In light of the discovery of superflares on G and K stars from the Kepler spacecraft, the question arises as to what distinguishes these objects from the remaining active late-type stars. We analyze the positions of superflare stars relative to the remaining stars observed by Kepler on the “amplitude of rotational brightness modulation (ARM)—rotation period” diagram. The ARM reflects the relative spots area on a star and characterizes the activity level in the entire atmosphere. G and K superflare stars are shown to be basically rapidly rotating young objects, but some of them belong to the stars with the solar type of activity.     

The flux deficits in star spots

The bolometric flux deficits of the photospheres of spotted stars are derived for the first time in the framework of zonal spottedness models for red dwarfs computed at the Crimean Astrophysical Observatory. The resulting flux deficits are compared to the estimated radiative losses from the chromospheres and coronas measured during quasi-simultaneous observations. A linear correlation is found between the logarithms of these quantities, with the Sun fitting these relations. Radiative losses from the outer stellar atmospheres in quiescence and during individual sporadic flares are significantly lower than the bolometric deficits of the spotted photospheres of active stars. This suggests that the flux deficit due to spots leads to global reconstruction of the atmospheres of red dwarfs, analogous to the local atmospheric reconstruction that occurs during solar and stellar flares. This process may be realized via the superposition of a large number of weak impulsive flares and other dynamic events, which develop on these stars and heat their coronas (i.e., in this view, microflaring is favored as the principal coronal heating mechanism for these stars). A brief analysis of the long-term variations in the chromospheric and photospheric radiation of F-K stars from the HK project and of the Sun suggests that such dynamical reconstruction of the outer atmosphere by energy associated with the flux deficit of the spotted photosphere occurs at times of increased surface activity in all F-M stars.     

Differential rotation of some HK-Project stars and the butterfly diagrams

We analyze the long-term variability of the chromospheric radiation of 20 stars monitored in the course of the HK-Project at the Mount Wilson Observatory. We apply the modified wavelet algorithm for this set of gapped time series. Besides the mean rotational periods for all these stars, we find reliable changes of the rotational periods from year to year for a few stars. Epochs of slower rotation occur when the activity level of the star is high, and the relationship repeats again during the next maximum of an activity cycle. Such an effect is traced in two stars with activity cycles that are not perfectly regular (but labeled “Good” under the classification in [Baliunas, S.L., Donahue, R.A., Soon, W.H., Horne, J.H., Frazer, J., Woodard-Eklund, L., Bradford, M., Rao, L.M., Wilson, O.C., Zhang, Q. et al., 1995. ApJ 438, 269.]) but the two stars have mean activity levels exceed that of the Sun. The averaged rotational period of HD 115404 is 18.5 days but sometimes the period increases up to 21.5 days. The sign of the differential rotation is the same as the Sun’s, and the value ΔΩ/Ω=-0.14. For the star HD 149661, this ratio is −0.074. Characteristic changes of rotational periods occur over around three years when the amplitude of the rotational modulation is large. These changes can be transformed into latitude-time butterfly diagrams with minimal a priori assumptions. We compare these results with those for the Sun as a star and conclude that epochs when surface inhomogeneities rotate slower are synchronous with the reversal of the global magnetic dipole.     

Evidence for a relationship between emerging magnetic fields,electric currents,and solar flares observed on May 10, 2012

Multi-wavelength observations and magnetic-field data for the solar flare of May 10, 2012 (04: 18 UT) are analyzed. A sign change in the line-of-sight magnetic field in the umbra of a small spot has been detected. This is at least partly associated with the emergence of a new magnetic field. A hard X-ray flare was recorded at almost the same time, and a “sunquake” was generated by the impact of the disturbance in the range of energy release on the photosphere. A sigmoid flare was recorded at the beginning of the event, but did not spread, as it usually does, along the polarity inversion (neutral) line. SDO/HMI full vectormagnetic-fieldmeasurements are used to extrapolate the magnetic field of AR 11476 into the corona, and to derive the distribution of vertical currents jz in the photosphere. The relationship between the distribution of currents in the active region and the occurrence of flares is quite complex. The expected “ideal” behavior of the current system before and after the flare (e.g., described by Sharykin and Kosovichev) is observed only in the sigmoid region. The results obtained are compared with observations of two other flares recorded in this active region on the same day, one similar to the discussed flare and the other different. The results confirm that the formation and eruption of large-scale magnetic flux ropes in sigmoid flares is associated with shear motions in the photosphere, the emergence of twisted magnetic tubes, and the subsequent development of the torus instability.