Surface Temperature Inhomogeneities Research Articles

Secondary flows induced by two-dimensional surface temperature heterogeneity in stably stratified channel flow

The structure and impact of thermally induced secondary motions in stably stratified channel flows with two-dimensional surface temperature inhomogeneities is studied using direct numerical simulation (DNS). Starting from a configuration with only spanwise varying surface temperature, where the streamwise direction is homogeneous (Bon & Meyers, J. Fluid Mech., 2022, pp. 1–38), we study cases where the periodic temperature strip length $l_x/h$ (with $h$ the half-channel height) assumes finite values. The patch width ( $l_y/h =\{{\rm \pi} /4, {\rm \pi}/8$ }) and length are varied at fixed stability and two different Reynolds numbers. Results indicate that for the investigated patch widths, the streamwise development of the secondary flows depends on the patch aspect ratio ( $a=l_x/l_y$ ), while they reach a fully developed state after approximately $25l_y$ . The strength of the secondary motions, and their impact on momentum and heat transfer through the dispersive fluxes, is strongly reduced as the length of the temperature strips decreases, and becomes negligible when $a\lesssim 1$ . We demonstrate that upward dispersive and turbulent heat transport in locally unstably stratified regions above the high-temperature patches lead to reduced overall downward heat transfer. Comparison to local Monin–Obukhov similarity theory (MOST) reveals that scaled velocity and temperature gradients in homogeneous stably stratified channel flow at $Re_\tau =550$ agree reasonably well with empirical correlations obtained from meteorological data. For thermally heterogeneous cases with strips of finite length, the similarity functions only collapse higher above the surface, where dispersive fluxes are negligible. Lastly, we show that mean profiles of all simulations collapse when using outer-layer scaling based on displacement thickness.

Use of the reflective background oriented schlieren technique to measure free surface deformations in a thin liquid layer non-uniformly heated from below

To measure liquid film surface deformations, we use the Background Oriented Schlieren (BOS) technique with a reflective optical scheme, which includes a random dot pattern located above the liquid surface, and a camera that captures its reflection from the liquid interface. The substrate was covered with a special black coating to minimize stray light reflection, which allowed to provide clear visualization of the dot pattern reflected from the free surface even for very thin liquid films. Local slopes of the film surface cause the dot displacement on the pattern image relative to the pattern image captured in the absence of any free-surface deformations. Hence, the topography of the liquid film surface is encoded by the apparent displacement of the dot pattern. Using the cross correlation image processing, the displacement vector field was determined, which was then substituted in Poisson equation to reconstruct the free-surface profile of the liquid film. The main advantages of this technique are: applicability for liquids with surface temperature inhomogeneities, experimental simplicity, sensitivity and applicability for both transparent and opaque liquids. Using the reflective BOS technique and using substrate with black coating we measure the free-surface deformation field of a thin layer of silicone oil non-uniformly heated from below. Despite the fact that thermocapillary shear stresses tend to decrease the thickness of the liquid layer in hotter regions, in the experiment, a convex deformation of the liquid film surface was observed above the heater for a few seconds immediately after the start of heating. This phenomenon is explained by the expansion of the liquid induced by the heating, due to the dependence of the liquid density on temperature. The measurement results are compared with those obtained in a single point using the confocal sensor. A good agreement is achieved.

Spectral analysis of the quiescent low-mass X-ray binary in the globular cluster M30

ABSTRACT We present a recent Chandra observation of the quiescent low-mass X-ray binary containing a neutron star (NS), located in the globular cluster M30. We fit the thermal emission from the NS to extract its mass and radius. We find no evidence of flux variability between the two observations taken in 2001 and 2017, nor between individual 2017 observations, so we analyse them together to increase the signal-to-noise ratio. We perform simultaneous spectral fits using standard light-element composition atmosphere models (hydrogen or helium), including absorption by the interstellar medium, correction for pile-up of X-ray photons on the detector, and a power law for count excesses at high photon energy. Using a Markov chain Monte Carlo approach, we extract mass and radius credible intervals for both chemical compositions of the atmosphere: $\mbox{$R_{\rm NS}$}=7.94\mbox{{$\scriptstyle ^{ + 0.76}_{- 1.21}$}}$ km and $\mbox{$M_{\rm NS}$}\lt 1.19$ M⊙ assuming pure hydrogen, and $\mbox{$R_{\rm NS}$}=10.50\mbox{{$\scriptstyle ^{ + 2.88}_{- 2.03}$}}$ km and $\mbox{$M_{\rm NS}$}\lt 1.78$ M⊙ for helium, where the uncertainties represent the 90 per cent credible regions. For H, the small radius is difficult to reconcile with most current nuclear physics models (especially for nucleonic equations of state) and with other measurements of NS radii, with recent preferred values generally in the 11–14 km range. Whereas for He, the measured radius is consistent with this range. We discuss possible sources of systematic uncertainty that may result in an underestimation of the radius, identifying the presence of surface temperature inhomogeneities as the most relevant bias. According to this, we conclude that either the atmosphere is composed of He or it is anH atmosphere with a significant contribution of hotspots to the observed radiation.

Activity of a Young Solar Analog—the Star with an Exoplanet DS Tuc

We present the results of our analysis of the photospheric and chromospheric activity of the star DS Tuc (DS Tuc A, HD 222259A), which is a member of the Tucana–Horologium (Tuc–Hor) group with an age of 45 Myr. The star DS Tuc may be considered as the prototype of a young Sun, while its planetary system may be considered as the prototype of a young Solar system. Using data from the archive of TESS observations, we have analyzed the activity of this star. According to our estimate, the stellar rotation period is $$P=2.85\pm 0.18$$ days, which coincides with its known estimates. The light curve has been analyzed by the method of solving the inverse problem of reconstructing the maps of surface temperature inhomogeneities. We show that there are concentrations of spots at two longitudes on these maps. The spot positions undergo changes. The fraction $$S$$ of the spotted stellar surface is about 3.3 $$\%$$ . We have studied the object’s position on the $$S$$ –age, $$S$$ –rotation period, and $$S$$ –Rossby number diagrams and concluded that it corresponds to the general pattern of the dependences established previously for young stars with planetary systems and solar-type stars. Based on All Sky Automated Survey observations, we have estimated for the first time the possible activity cycle of DS Tuc to be 1610 days (4.4 years).

Activity of the Red Dwarf FR Cnc from Observations with a Robotic IRT-20 Telescope at the Zvenigorod Observatory of INASAN

We present the results of our new photometric observations of the chromospherically active star FR Cnc performed with a robotic telescope at the Zvenigorod Observatory of INASAN in March 2019. The observations were carried out from March 2 to 13, 2019, in the period of time that coincided most closely in time interval with the observations of this star with the Astrosat space telescope. A total of 450 magnitude estimates were obtained in each of the B, V, and R photometric bands over 12 days (from HJD 2458545.2 to HJD 2458556.5). Based on the V-band photometric variability of the star, we have constructed a map of surface temperature inhomogeneities. According to our estimate, the spot area on the surface of the star was ~12% of its total surface area in early 2019. On March 3, 2019, a flare on FR Cnc was detected during our observations at a time corresponding to HJD = 2458554.25891447 or rotation phase 0.8. The data for the flare suggest a rapid brightening of the star by 0.19m in the B band and by 0.09m in the V band; the flare lasted for about 60 min. The energy radiated in the flare was ITEB = 2.17 × 1033 erg and Ey = 1.40 × 1033 erg in the B and V bands, respectively.

Activity of the Star ET Dra

V-band photometric observations of the FK Com type star ET Dra were made at the Zvenigorod observatory (INASAN) during March-April 2018. The new data were used in a solution of the inverse problem of recovering the surface temperature inhomogeneities for ET Dra to study the position of cold regions on its surface which were compared with photometric observations made in 1990.

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 Pphot = 0.59261 ± 0.00060d 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.

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.

Activity and cool spots on the surfaces of G-type stars with superflares from observations with the Kepler Space Telescope

The properties of active regions (cool spots) on the surfaces of 279 G-type stars in which more than 1500 superflares with energies of 1033-1036 erg were detected are analyzed. Diagrams plotting the superflare energy against activity parameters of the stars (the area of their magnetic spots) are considered, and a more extensive study of the activity of two stars with the highest numbers of flares is presented. The range of variation of the superflare energies (up to two orders of magnitude) is realized over the entire interval of rotation periods. It is proposed that the plot of superflare energy vs. rotational period is bimodal. There are probably no appreciable differences in the maximum flare energies for the two groups of objects, which have rotational periods of more than and less than 10 days. Three groups of stars with different surface spottednesses can be distinguished in a plot of superflare energy vs. cool-spot area. The range of variation of the flare energy within a group is roughly the same for these three groups. Most of the points on this diagram lie to the right of the dependence corresponding to B = 3000Gand an inclination i = 90° (the first two groups of objects). It is confirmed that the flare activity is not related directly to circumpolar active regions, since the majority of the points on the diagram lie to the right of the dependence for B = 1000 G and i = 3°. Analysis of stars from the sample, including objects with more than 20 superflares, shows that large variations of the energy (by up to two orders of magnitude) can be reached with small variations of the spottedness parameter S for a single star. Appreciable variability of the spottedness (by factors of five to six) was detected for only two objects from the sample (KIC 10422252 and KIC 11764567). These stars displayed an increase in the flare energy by orders of magnitude for any spottedness level. The activity of KIC 11551430 and KIC 11764567 is analyzed in detail using all available photometric data from the Kepler Space Telescope archives. KIC 11551430 was determined earlier to display the highest number of flares (on average, one flare every 7 days); KIC 11764567 displayed the highest number of flares among stars with rotational periods comparable to the solar period (on average, one flare every 25 days). Maps of surface temperature inhomogeneities of these stars are used to determine the longitudes and other characteristics of their active regions.

Activity of KOI 877 and KOI 896 observed by the Kepler Space Telescope

Observational data obtained by the Kepler Space Telescope are used to investigate the photometric variability of the stars KOI 877 and KOI 896, both of which are multi-planet systems. Surface-temperature inhomogeneities are studied and their evolution traced. 64 810 individual brightness measurements made over 1459.5 days (almost four years) were selected for this analysis. Maps of the surface-temperature inhomogeneities of these stars have been constructed based on fitting to the stellar light curves in a two-temperature approximation. These maps were used to identify the locations of active regions. KOI 877 displayed three states of activity during the observation period. Two active regions were present almost continuously on the surface of KOI 896, with the distance between them in phase being 0.58 at the beginning of the observations and then monotonically decreasing to 0.36. Estimation of the differential-rotation parameters of the stars suggests that KOI 877 is rotating differentially, similar to the Sun, while this parameter is a factor of two higher for KOI 896. Analysis of the variability of the light-curve amplitudes has yielded an independent estimate of the differential-rotation parameters of the two stars. The main properties of KOI 877 and KOI 896 are compared to those of the previously studied star Kepler-32 (KOI 952), whose differential rotation is reanalyzed.

Possibilities for identifying FK com candidates using observations with the Kepler Space Telescope

High-accuracy photometric observations obtained with the Kepler Space Telescope are used to identify candidate FK Com stars-a very rare group of single, rapidly rotating, chromospherically active G-K stars. Published data for more than 40 000 stars are used with available Kepler observations from the Q3 time interval to select four stars with temperature ranges, surface gravities, and rotation periods consistent with those of FK Com stars. These stars also display brightness variations with considerable amplitudes, possibly testifying to the presence of appreciably spotting on their surfaces. The rotation periods of these stars are determined, and the parameters of their differential rotation estimated. The locations (longitudes) of the dominant active regions on the stellar surfaces are identified. In all cases, the active longitude does not remain constant, andmoves across the stellar surface with time. In general, the character of this activeregion movement is the same as that found earlier for FK Com and HD 199178. These displacements are characterized by monotonic motions over hundreds of days, as well as changes in the positions by about 180° (“flip-flops”) or phase shifts not exceeding 0.4 in phase. The number of active-longitude position changes during the studied time interval ranges from one for KIC 11862915 to seven for KIC 5785906 (five phase shifts are also detected for the latter star). The time scale for the position changes of the active longitudes is from 1500 days (about 4 years) to 200 days (0.54 years), comparable to the reported time intervals between flip-flops for FK Com (from 0.8 to 4.4 years). The duration of the stellar activity cycles are estimated by analyzing the amplitude spectrum for changes in the brightness-variation amplitudes for datasets covering a single rotation period. The photometric variations of the stars on various time scales (from the rotation period, which reveals the presence of surface temperature inhomogeneities, to activity cycles lasting for several years) are similar to those derived for FK Com and other stars of this type. The need for spectroscopic observations of the selected candidates to establish whether they are single (do not show signs of binarity), look for emission lines of chromospheric origin, estimate the lithium abundances, and determine the stellar rotation velocities from spectral-line profiles is noted.

Stellar activity observed by the Kepler Space Telescope. The M dwarf of the Kepler-32 system with five orbiting planets

The activity of the central star of the Kepler-32 planetary system is studied using continuous 1141-day observations with the Kepler Space Telescope. The Kepler-32 system includes a slowly rotating Mdwarf (rotational period of 37.8 d) with a mass of 0.54M⊙ and five planets. One of the unique properties of the system is its compactness: the orbits of all five planets are less than a third of the size of the orbit of Mercury; the planet closest to the star is separated from it by only 4.3 stellar radii. Surface-temperature inhomogeneities of the central star are studied using precise photometric observations of Kepler-32, and their evolution traced. In total, 42 624 individual brightness measurements in the 1141-day (3.1-year) observing interval were selected for the analysis. The calculated amplitude power spectra for the first and second halves of the interval of the Kepler-32 observations indicate appreciable variability of the photometric period, corresponding to the evolution of active regions at various latitudes on the stellar surface. Evidence for the existence of two active regions on the stellar surface separated in phase by 0.42 has been found. Time intervals in which the longitudes of the active regions changed (“flip-flops”) with durations of the order of 200–300 days have been established. The spotted area of the star was, on average, about 1% of the total visible surface, and varied from 0.3 to 1.7%. The results for the dwarf Kepler-32 are compared with those from a spectropolarimetric survey of 23 M dwarfs, including both fully convective stars and stars with weakly radiative cores. For a more detailed comparison, temperature inhomogeneities on the surface of one of the survey stars, DS Leo, was reconstructed using the ground-based observations (316 individual measurements of the V-band brightness of the star during seven observing seasons in an all-sky automated survey). The general properties and evolution of the active regions on DS Leo and Kepler-32 are considered. The positions of the active regions on the surface of Kepler-32 yields no evidence for differential rotation of this star. The possibility of detecting the magnetic field of Kepler-32 is proposed. The analysis of the photometric data for Kepler-32 are also compared to the previous results for the fully convective, low-mass M dwarfs GJ 1243 and LHS 6351. This demonstrates that the observed manifestations of activity on Kepler-32 correspond to those for active G-K stars and to M dwarfs with masses of the order of 0.5M⊙, rather than Mdwarfs with masses from 0.2 to 0.5M⊙.

Rotation effects in classical T Tauri stars

Surface temperature inhomogeneities in classical T Tauri stars (CTTS) induced by magnetic activity and mass accretion lead to rotational modulation of both photometric and spectroscopic parameters of these stars. Using the extended photometric catalogue by Grankin et al. (2007), we have derived the periods and amplitudes of the rotational modulation of brightness and color for 31 CTTS; for six of them, the periods have been revealed for the first time. The inclinations of the rotation axis and equatorial rotational velocities of CTTS have been determined. We show that the known periods of brightness variations for some of the CTTS are not the axial rotation periods but are the Keplerian periods near the inner boundary of the dusty disk. We have found that the angular velocity of CTTS with a mass of 0.3 - 3 M_sun in the Taurus-Auriga complex remains constant in the age range 1 - 10 Myr. CTTS on radiative evolutionary tracks rotate faster than completely convective CTTS. The specific angular momentum of CTTS depends on the absolute luminosity in the H\alpha- line.

Activity observed by the Kepler space telescope: The M dwarf LHS 6351 (KIC 2164791)

Continuous 123.87-day observations with the “Kepler” space telescope are used to study the activity of the fully convective, low-mass M dwarf LHS 6351. The axial-rotation period of the star is 3.36 day. High-precision photometric observations of LHS 6351 enabled studies of its surfacetemperature inhomogeneities and their evolution. The difference in the longitudes of active regions increased from 120° at the beginning to 207° at the end of the observations, for i = 60° (and from 156° to 198° for i = 30°). This variation of the locations of the spots on the stellar surface provides evidence for differential rotation of the star. According to our estimates, the rate of displacement of the active regions is (0.006–0.014) ± 0.002 rad/day. Assuming i = 60°, the total area of spots S decreased, on average, from 1.2% to 0.92% of the total visible surface of the star; if i = 30°, this area decreased from 1.8% to 1.0%. We compared manifestations of the magnetic activity of LHS 6351 with the properties of the fully convective M dwarfs V374 Peg and GJ 1243, studied earlier. We derived the dependence of ΔΩ on the Rossby number for these M dwarfs, and identified two groups of stars with differing mass and differential rotation.

Stellar activity from observations with the KEPLER space telescope: The M dwarf GJ 1243

We used continuous observations with the KEPLER space telescope during 44.45 days to study the activity of the fully convective low-mass M dwarf GJ 1243. The star’s rotational period is 0.593 days. Our precision photometry of GJ 1243 made it possible to study its surface temperature inhomogeneities and follow their evolution. We find evidence for two active longitudes on the surface of the star, separated by 203° in longitude or 0.56 in phase. The position of spots on the surface was found to be very stable during the analyzed 74 rotation periods. Assuming that the rotational axis is inclined to the line of sight by i = 60°, the total spotted area S is, on average, 3.2% of the total visible stellar surface, and increased by 0.7% in 100 days; if i = 30°, the area is S = 5.6%. The change in S is due to an increase in the area of the smaller active region. We compare the magnetic-activity features of GJ 1243 and another fully convective star, V374 Peg.

Stellar activity as observed by the KEPLER space telescope: The K Dwarf KIC 8429280

The activity of the K dwarf KIC 8429280 (TYC 3146-35-1) has been studied. Unique high-precision photometric observations of this object obtained with the KEPLER space telescope suggest a pronounced amplitude modulation of the brightness of the star, and have made possible the analysis of surface-temperature inhomogeneities. The evolution of active regions on the surface of KIC 8429280 has been traced during 105 rotation periods. Evidence has been found for the existence of two active longitudes on the surface of KIC 8429280, separated by approximately 180°. The motion of the active longitudes on the surface of KIC 8429280 is complex and unstable. At some times, the active regions moved together in longitude with the rotation of the star, while they moved in opposite directions at other time. The less active region sometimes disappeared completely, and only one active region was observed on the stellar surface. The area of the spotted surface S is 4% of the visible stellar surface for the adopted inclination of the rotation axis of the star to the line of sight, i = 60°. The periodicity for variations in S is no less than 90 d. The timescale for the change in the amplitude of the brightness variations is 30 d. Three epochs of alternation of the active longitudes are close in time to three of four firmly established minima in the amplitudes of the brightness variations. The results of the light-curve analysis for KIC 8429280 are compared to results obtained for the young active solar-type star Corot-Exo-2, which has a similar light curve with a pronounced modulation.

Spots on the surfaces of the chromospherically active stars GSC 08923-01147 and GSC 08933-01802: Observational data of the ASAS-3 project

Active regions on the surfaces of the chromospherically active stars GSC 08923-01147 and GSC 08933-01802 are found by reconstructing the surface-temperature inhomogeneities using the V light curves, obtained from observations performed during the ASAS-3 project. Up to one-third of the total observed area of the stellar surfaces was covered by spots. In GSC 08923-01147, the spotted fraction decreased from 0.31 to 0.05 during the observation period, while it varied within 0.2–0.3 during four years in GSC 08933-01802. The detected phases of active longitudes tend to concentrate near two positions separated by about half a period. The active regions in GSC 08933-01147 became closer or further apart on a time scale of 4.8 years. The maximum separations of the longitudes Δφlong were maximum when the amplitude of the brightness variability reached a minimum. During the transition of the star from a minimum-brightness to an enhanced-brightness state, the longitude of the more active region switched. The brightness variability of GSC 08933-01802 was more substantial (ΔV }~ 0.55m−0.06m). For some time, only one extended active region was present on the stellar surface, while two regions were usually present. No switch of the active longitudes was detected. The more active region monotonically moved over the surface of the star, causing the longitudes of the active regions to drift together. This monotonic change in the position of the more active longitude ceased at the minimum of the brightness-variation amplitude.

Stellar activity observed by the kepler space telescope: The systems with two planets and two active longitudes KOI 877 and KOI 896

Unique high-accuracy 33.5-day continuous photometric observations of the KOI 877 and KOI 896 systems are used to study their surface inhomogeneities and trace the evolution of spots over two to three rotational periods. These systems are two of five candidate multi-planet objects. We found evidence for the existence of two active longitudes on the surfaces of KOI 877 and KOI 896, separated by 165° and 135°, respectively. The fraction of the surface area covered by the spots is similar to the solar one, and comprises about 0.6–1.1% of the total visible surfaces of the stars. A switch of the active longitudes likely occurred in KOI 877 during the observation period. Calculated maps of surface temperature inhomogeneities may be helpful for more accurate derivations of the parameters of planetary systems.

Magnetic activity of the star Corot-Exo-2a

Continuous photometric observations of the young active solar-type star Corot-Exo-2a using the “Corot” space telescope obtained over 142 days were used to analyze the star’s surface temperature inhomogeneities and to monitor their continuous evolution. This analysis was based on the iPH code, which reconstructs the distribution of temperature inhomogeneities on the surface of a star based on its light curve in a two-temperature approximation. We identified five time intervals in the positions of active areas, with corresponding flip-flop events, interpreted as activity periods. Their durations were between 55 and 15 days. The time scale for the active-longitude flip-flops of Corot-Exo-2a is a few tens of days, rather than years, as for other stars studied earlier. We detected motions of the active longitudes, possibly indicating differential rotation of the star. The phenomenon of flip-flops in the positions of active longitudes has a complex character. This is the first case apart fromthe Sun where we are able to follow the appearance and development of temperature inhomogeneities on a stellar surface in such detail. We determined typical timescales for variations of the activity parameter of the star in the ranges 17–20, 28–32, 33–38, and 51–55 days, which characterize changes of the brightness variation amplitude, the spotted surface area, positions of active areas, and brightness variations.

Analysis of MOST light curves of the active stars ɛ Eri AND κ Cet

We have analyzed light curves from the MOST satellite for the two active dwarfs ɛ 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.