Magnetic features on the surfaces of cool stars cause variations of their brightness. Such variations have been extensively studied for the Sun. Recent planet-hunting space telescopes allowed measuring brightness variations in hundred thousands of other stars. The new data posed the question of how typical is the Sun as a variable star. Putting solar variability into the stellar context suffers, however, from the bias of solar observations being made from its near-equatorial plane, whereas stars are observed at all possible inclinations. We model solar brightness variations at timescales from days to years as they would be observed at different inclinations. In particular, we consider the effect of the inclination on the power spectrum of solar brightness variations. The variations are calculated in several passbands routinely used for stellar measurements. We employ the Surface Flux Transport Model (SFTM) to simulate the time-dependent spatial distribution of magnetic features on both near- and far-sides of the Sun. This distribution is then used to calculate solar brightness variations following the SATIRE (Spectral And Total Irradiance REconstruction) approach. We have quantified the effect of the inclination on solar brightness variability at timescales down to a day. Thus, our results allow making solar brightness records directly comparable to those obtained by the planet-hunting space telescopes. Furthermore, we decompose solar brightness variations into the components originating from the solar rotation and from the evolution of magnetic features.
The solar brightness varies on timescales from minutes to decades. A clear identification of the physical processes behind such variations is needed for developing and improving physics-based models of solar brightness variability and reconstructing solar brightness in the past. This is, in turn, important for better understanding the solar-terrestrial and solar-stellar connections. We estimate the relative contributions of the continuum, molecular, and atomic lines to the solar brightness variations on different timescales. Our approach is based on the assumption that variability of the solar…
The plethora of photometric data collected by the Kepler space telescope has promoted the detection of tens of thousands of stellar rotation periods. However, these periods are not found to an equal extent among different spectral types. Interestingly, early G-type stars with near-solar rotation periods are strongly underrepresented among those stars with known rotation periods. In this study we investigate whether the small number of such stars can be explained by difficulties in the period determination from photometric time series. For that purpose, we generate model light curves of early G…
The solar brightness varies on timescales from minutes to decades. Determining the sources of such variations, often referred to as solar noise, is of importance for multiple reasons: a) it is the background that limits the detection of solar oscillations, b) variability in solar brightness is one of the drivers of the Earth's climate system, c) it is a prototype of stellar variability which is an important limiting factor for the detection of extra-solar planets. Here we show that recent progress in simulations and observations of the Sun makes it finally possible to pinpoint the source of th…
Regular spaceborne measurements have revealed that solar brightness varies on multiple timescales, variations on timescales greater than a day being attributed to surface magnetic field. Independently, ground-based and spaceborne measurements suggest that Sun-like stars show a similar, but significantly broader pattern of photometric variability. To understand whether the broader pattern of stellar variations is consistent with the solar paradigm we assess relative contributions of faculae and spots to solar magnetically-driven brightness variability. We investigate how the solar brightness va…
Context. Comparison studies of Sun-like stars with the Sun suggest an anomalously low photometric variability of the Sun compared to Sun-like stars with similar magnetic activity. Comprehensive understanding of stellar variability is needed, to find a physical reasoning for this observation. Aims. We investigate the effect of metallicity and effective temperature on the photometric brightness change of Sun-like stars seen at different inclinations. The considered range of fundamental stellar parameters is sufficiently small so the stars, investigated here, still count as Sun-like or even as so…
Images of the Sun at millimeter wavelengths obtained by ALMA show a significant correspondence with the magnetograms. In this paper, we investigate this correspondence by comparing ALMA full-disk solar image taken at 1.2 mm with a SDO/HMI magnetogram and analyze their correlation. It is found that chromospheric network and active regions show a positive correlation where brightness temperature is increasing with the line-of-sight magnetic field strength, while sunspots have a negative correlation. Quiet Sun regions do not show any dependence of the brightness temperature with the magnetic fiel…
The unprecedented precision of broadband stellar photometry achieved with the planet-hunting missions CoRoT and \textit{Kepler} initiated a new era in examining the magnetically-driven brightness variations of hundreds of thousands of stars. Such brightness variations are well studied and understood for the Sun. The plethora of data allows to accurately compare solar and stellar brightness variations. An intriguing question is whether the observed trends in the stellar photometric variability (e.g. the dependence of the variability on the stellar rotation period) can be explained by utilising …
Reconstructing solar magnetic fields from historical observations X. Effect of magnetic field inclination and boundary structure on AIA 1600 Å emission
We consider a model for the cyclic brightness variations of a young star with a low-mass companion that accretes matter from the remnants of a protostellar cloud. At small inclinations of the binary orbit to the line of sight, the streams of matter and the density waves excited in the circumbinary disk can screen the primary component of the binary from the observer. To study these phenomena, we have computed grids of hydrodynamic models for binary systems by the SPH method based on which we have constructed the phase light curves as a function of the rotation angle of the apsidal line relativ…
Comparing solar and stellar brightness variations is hampered by the difference in spectral passbands used in observations as well as by the possible difference in the inclination of their rotation axes from the line of sight. We calculate the rotational variability of the Sun as it would be measured in passbands used for stellar observations. In particular, we consider the filter systems used by the CoRoT, $Kepler$, TESS, and $Gaia$ space missions. We also quantify the effect of the inclination of the rotation axis on the solar rotational variability. We employ the Spectral And Total Irradian…
Kepler observations revealed that hundreds of stars with near-solar fundamental parameters and rotation periods have much stronger and more regular brightness variations than the Sun. Here we identify one possible reason for the peculiar behaviour of these stars. Inspired by solar nests of activity, we assume that the degree of inhomogeneity of active-region (AR) emergence on such stars is higher than on the Sun. To test our hypothesis, we model stellar light curves by injecting ARs consisting of spots and faculae on stellar surfaces at various rates and nesting patterns, using solar AR proper…
For the future development of Chinese Giant Solar Telescope (CGST) in Western China, a new sky brightness monitor (SBM) has been produced for the site survey for CGST. To critically examine the performance and sensitivity of SBM, we used it in the observation of the annular solar eclipse in Dali City, Yunnan, on 15 January 2010. The observation met good weather condition with almost clear sky during the eclipse. The SBM measurement translates into the solar illuminance changes at a level of 2.4 \times 10-4I s-1 during the eclipse. The time of the minimal sky brightness in the field of view (FO…
We report the discovery of a brightness enhancement in the center of a large sunspot umbra at a wavelength of 3 mm using the Atacama Large Millimeter/sub-millimeter Array (ALMA). Sunspots are amongst the most prominent features on the solar surface, but many of their aspects are surprisingly poorly understood. We analyzed a λ=3 mm (100 GHz) mosaic image obtained by ALMA, which includes a large sunspot within the active region AR12470 on December 16, 2015. The 3 mm map has a field-of-view and spatial resolution, which is the highest spatial-resolution map of an entire sunspot in this frequency …
The solar-like latitudinal distribution of flaring activities revealed by TESS, APOGEE and GALAH
Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台光学天文重点实验室）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿科学研究院）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）
By using high-resolution observations of nearly co-temporal and co-spatial Solar Optical Telescope spectropolarimeter and X-Ray Telescope coronal X-ray data onboard Hinode, we revisit the problematic relationship between global magnetic quantities and coronal X-ray brightness. Co-aligned vector magnetogram and X-ray data were used for this study. The total X-ray brightness over active regions is well correlated with integrated magnetic quantities such as the total unsigned magnetic flux, the total unsigned vertical current, and the area-integrated square of the vertical and horizontal magnetic…
Coronal density, temperature and heat flux distributions for the equatorial and polar corona have been deduced by Lemaire [2012] from Saito's model of averaged coronal white light (WL) brightness and polarization observations. They are compared with those determined from a kinetic collisionless/exospheric model of the solar corona. This comparison indicates rather similar distributions at large radial distances (> 7 Rs) in the collisionless region. However, rather important differences are found close to the Sun in the acceleration region of the solar wind. The exospheric heat flux is directed…
We present the spatially resolved absolute brightness of the Fe X, Fe XI and Fe XIV visible coronal emission lines from 1.08 to 3.4 $R_\odot$, observed during the 2019 July 2 total solar eclipse (TSE). The morphology of the corona was typical of solar minimum, with a dipole field dominance showcased by large polar coronal holes and a broad equatorial streamer belt. The Fe XI line is found to be the brightest, followed by Fe X and Fe XIV (in disk $B_\odot$ units). All lines had brightness variations between streamers and coronal holes, where Fe XIV exhibited the largest variation. However, Fe X…
Total solar eclipses (TSEs) provide a unique opportunity to quantify the properties of the K-corona (electrons), F-corona (dust) and E-corona (ions) continuously from the solar surface out to a few solar radii. We apply a novel inversion method to separate emission from the K- and F-corona continua using unpolarized total brightness (tB) observations from five 0.5 nm bandpasses acquired during the 2019 July 2 TSE between 529.5 nm and 788.4 nm. The wavelength dependence relative to the photosphere (i.e., color) of the F-corona itself is used to infer the tB of the K- and F-corona for each line-…
Science Verification (SV) data of solar observations with Atacama Large Millimeter-submillimeter Array (ALMA) telescope were released to the scientific community. Understanding the centre to limb brightness function is necessary to compare features in full disk images. Our goals are to find the empirical centre to limb brightness functions in two available spectral bands and create flattened images with centre to limb brightness variations removed. We used second-order polynomial fit of the cosine of incidence angle to data points as a function of radial distance to the centre of the solar dis…
The evaluation of sky characteristics plays a fundamental role for many astrophysical experiments and ground-based observations. In solar physics, the main requirement for such observations is a very low sky brightness value, that is, less than one-millionth of the solar disk brightness. Few places match such requirement for ground-based, out-of-eclipse coronagraphic measurements. A candidate coronagraphic site is the Dome C plateau in Antarctica. In this paper, we show the first results of the sky brightness measurements at Dome C with the Extreme Solar Coronagraphy Antarctic Program Experime…
We report the temporal evolution of the excess brightness temperature above solar active regions (ARs) observed with the Solar Submillimeter Telescope (SST) at 212 (λ = 1.4 mm) and 405 GHz (λ = 0.7 mm) during Cycles 23 and 24. Comparison with the sunspot number (SSN) yields a Pearson's correlation coefficient R = 0.88 and 0.74 for 212 and 405 GHz, respectively. Moreover, when only Cycle 24 is taken into account the correlation coefficients go to 0.93 and 0.81 for each frequency. We derive the spectral index α between SST frequencies and found a slight anti-correlation with the SSN (R = -0.25);…
The paper presents the results of the analysis of the geometric characteristics of sunspots for the period of 19-24 cycles of activity. The shape of sunspots was studied on the basis of the method of normalization of images of sunspots to study the average profile of the spot. The deviation of the shape of sunspots from the axisymmetric configuration is investigated. It was found that the spots, as a rule, have an ellipsoid shape, and the major axis of the ellipse has a predominant inclination to the equator, opposite in the Northern and Southern hemispheres. The angle of inclination of the su…
We present the construction of a new white-light coronal brightness index (CBI) from the entire archive of observations recorded by the Large Angle Spectrometric Coronagraph (LASCO) C2 camera between 1996 and 2017, comprising two full solar cycles. We reduce all fully calibrated daily C2 observations of the white light corona into a single daily coronal brightness observation for every day of observation recorded by the instrument, with mean daily brightness values binned into 0.1 Rsun radial x 1 degree angular regions from 2.4 -- 6.2 Rsun for a full 360-degrees. As a demonstration of the util…
A challenge in characterizing active region (AR) coronal heating is in separating transient (bursty) loop heating from the diffuse background (steady) heating. We present a method of quantifying coronal heating's bursty and steady components in ARs, applying it to FeXVIII (hot94) emission of an AR observed by SDO/AIA. The maximum, minimum, and average brightness values for each pixel, over a 24 hour period, yield a maximum-brightness map, a minimum-brightness map, and an average-brightness map of the AR. Running sets of such three maps come from repeating this process for each time step of run…
We analyze the effect of solar features on the variability of the solar irradiance in three different spectral ranges. Our study is based on two solar-cycles' worth of full-disk photometric images from the San Fernando Observatory, obtained with red, blue and Ca II K-line filters. For each image we measure the photometric sum, Sigma, which is the relative contribution of solar features to the disk-integrated intensity of the image. The photometric sums in the red and blue continuum, Sigma_r and Sigma_b, exhibit similar temporal patterns: they are negatively correlated with solar activity, with…
It has so far proven impossible to reproduce all aspects of the solar plage chromosphere in quasi-realistic numerical models. The magnetic field configuration in the lower atmosphere is one of the few free parameters in such simulations. The literature only offers proxy-based estimates of the field strength, as it is difficult to obtain observational constraints in this region. Sufficiently sensitive spectro-polarimetric measurements require a high signal-to-noise ratio, spectral resolution, and cadence, which are at the limit of current capabilities. We use critically sampled spectro-polarime…
Continuum intensity observations obtained with the Michelson Doppler Imager (MDI) on-board the SoHO mission provide long time series of filtergrams that are ideal for studying the evolution of large-scale phenomena in the solar atmosphere and their dependence on solar activity. These filtergrams, however, are not taken in a pure continuum spectral band, but are constructed from a proxy, namely a combination of filtergrams sampling the Ni I 676.8 nm line. We studied the sensitivity of this continuum proxy to the shape of the nickel line and to the degradation in the instrumental transmission pr…
Using magnetic and microwave butterfly diagrams, we compare the behavior of solar polar regions to show that (i) the polar magnetic field and the microwave brightness temperature during the solar minimum substantially diminished during the cycle 23/24 minimum compared to the 22/23 minimum. (ii) The polar microwave brightness temperature (b) seems to be a good proxy for the underlying magnetic field strength (B). The analysis indicates a relationship, B = 0.0067Tb - 70, where B is in G and Tb in K. (iii) Both the brightness temperature and the magnetic field strength show north-south asymmetry …
The emission in the near ultraviolet Ca II H & K lines is modulated by stellar magnetic activity. Although this emission, quantified via the S-index, has been serving as a prime proxy of stellar magnetic activity for several decades, many aspects of the complex relation between stellar magnetism and Ca II H & K emission are still unclear. The amount of measured Ca II H & K emission is suspected to be affected not only by the stellar intrinsic properties but also by the inclination angle of the stellar rotation axis. Until now such an inclination effect on S-index has remained largely unexplore…
Our aim is to test potential solar prominence plasma diagnostics as obtained with the new solar capability of the Atacama Large Millimeter / submillimeter Array (ALMA). We investigate the thermal and plasma diagnostic potential of ALMA for solar prominences through the computation of brightness temperatures at ALMA wavelengths. The brightness temperature, for a chosen line of sight, is calculated using densities of hydrogen and helium obtained from a radiative transfer code under non local thermodynamic equilibrium (NLTE) conditions, as well as the input internal parameters of the prominence m…
We use microwave imaging observations from the Nobeyama Radioheliograph at 17 GHz for long-term studies of solar activity. In particular, we use the polar and low-latitude brightness temperatures as proxies to the polar magnetic field and the active-regions, respectively. We also use the location of prominence eruptions as a proxy to the filament locations as a function of time. We show that the polar microwave brightness temperature is highly correlated with the polar magnetic field strength and the fast solar wind speed. We also show that the polar microwave brightness at one cycle is correl…
The absolute brightness temperature of the Sun at millimeter wavelengths is an important diagnostic of the solar chromosphere. Because the Sun is so bright, measurement of this property usually involves the operation of telescopes under extreme conditions and requires a rigorous performance assessment of the telescope. In this study, we establish solar observation and calibration techniques at 2.6-mm wavelength for the Nobeyama 45-m telescope and derive the absolute solar brightness temperature accurately. We tune the superconductor-insulator-superconductor (SIS) receiver by inducing different…
[Abridged] Distant stars and planets will remain spatially unresolved for the foreseeable future. It is nonetheless possible to infer aspects of their brightness markings and viewing geometries by analyzing disk-integrated rotational and orbital brightness variations. We compute the harmonic lightcurves, F_l^m(t), resulting from spherical harmonic maps of intensity or albedo, Y_l^m(theta,phi), where l and m are the total and longitudinal order. Notably, odd m>1 are present in an inclined lightcurve, but not seen by an equatorial observer. We therefore suggest that the Fourier spectrum of a the…
The irradiance of the Sun is modulated on all time scales. Small-scale solar magnetic elements composed of quiet-Sun network and active region plages contribute to this modulation on solar cycle time scales. The evaluation of their contrast as a function of their magnetic field strength is an important constraint for models of solar irradiance variation. In this thesis, we improve and extend the results of earlier contrast studies taking advantage of the high resolution data delivered by the balloon-borne solar observatory Sunrise during its science flights in 2009 and 2013. In addition to the…
We present the first observation of a solar prominence at $84-116$ GHz using the high resolution interferometric imaging of ALMA. Simultaneous observations in H$α$ from Białkaw Observatory and with SDO/AIA reveal similar prominence morphology to the ALMA observation. The contribution functions of 3 mm and H$α$ emission are shown to have significant overlap across a range of gas pressures. We estimate the maximum millimetre-continuum optical thickness to be $τ_\mathrm{3mm}\approx 2$, and the brightness temperature from the observed H$α$ intensity. The brightness temperature measured by ALMA is …
We carried out polarimetric observations of the white-light corona during the total solar eclipses that occurred on 2017 August 21 and 2019 July 2, and successfully obtained data at two different sites for both eclipses. After eliminating the sky background, we derived the brightness, polarization brightness, and degree of the polarization of the K+F corona from just above the limb to approximately 4 $R_\odot$. Furthermore, we isolated the K- and F-corona with plausible degree of polarization of the K-corona. The field of view covering up to approximately 4 $R_\odot$ enabled us to compare the …
This paper presents time series observations and analysis of broadband night sky airglow intensity 4 September 2018 through 30 April 2020. Data were obtained at 5 sites spanning more than 8500 km during the historically deep minimum of Solar Cycle 24 into the beginning of Solar Cycle 25. New time series observations indicate previously unrecognized significant sources of broadband night sky brightness variations, not involving corresponding changes in the Sun's 10.7cm solar flux, occur during deep solar minimum. Even during a deep solar minimum the natural night sky is rarely, if ever, constan…
We carried out spectroscopic observations with Subaru/HDS of 50 solar-type superflare stars found from Kepler data. More than half (34 stars) of the target stars show no evidence of the binary system, and we confirmed atmospheric parameters of these stars are roughly in the range of solar-type stars. We then conducted the detailed analyses for these 34 stars. First, the value of the "$v\sin i$" (projected rotational velocity) measured from spectroscopic results is consistent with the rotational velocity estimated from the brightness variation. Second, there is a correlation between the amplitu…
In addition to the `facular' brightening of active regions, the quiet Sun also contains a small scale magnetic field with associated brightenings in continuum radiation. We measure this contribution of quiet regions to the Sun's brightness from high spatial resolution (0"16-0"32) observations of the Swedish 1-m Solar Telescope (SST) and Hinode satellite. The line-of-sight magnetic field and continuum intensity near \ion{Fe}{i} 6302.5 Å are used to quantify the correlation between field strength and brightness. The data show that magnetic flux density contains a significant amount of intrinsica…
Young and active stars generally have regular, almost sinusoidal, patterns of variability attributed to their rotation, while the majority of older and less active stars, including the Sun, have more complex and non-regular light-curves which do not have clear rotational-modulation signals. Consequently, the rotation periods have been successfully determined only for a small fraction of the Sun-like stars observed by transit-based planet-hunting missions, such as CoRoT, Kepler, and TESS. This suggests that only a small fraction of such systems have been properly identified as solar-like analog…
High-precision time series have recently become available for many stars as a result of data from CoRoT, Kepler, and TESS and have been widely used to study stellar activity. They provide information integrated over the stellar disk, hence many degeneracies between spots and plages or sizes and contrasts. Our aim is to understand how to relate photometric variability to physical parameters in order to help the interpretation of these observations. We computed a large number of synthetic time series of brightness variations for old MS stars within the F6-K4 range, using consistent modeling for …
The intensity of radiation at millimeter wavelengths from the solar atmosphere is closely related to the plasma temperature and the height of formation of the radiation is wavelength dependent. From that follows that the slope of the brightness temperature (T$_\mathrm{b}$) continuum, samples the local gradient of the gas temperature of the sampled layers in the solar atmosphere. We use solar observations from the Atacama Large Millimeter/sub-millimeter Array (ALMA) and perform estimations and prediction of the slope of the T$_\mathrm{b}$ continuum based on differences between synthetic observa…
The star S CrA is a tight visual binary consisting of two classical T Tauri stars, both with outstanding spectral characteristics and brightness variations. High-resolution spectra were collected at ESO and photometric observations with the SMARTS telescope. Both stars undergo large variation in brightness caused mainly by variable foreground extinction. From the stellar parameters we conclude that the two stars are remarkably similar, and that S CrA can be regarded as a T Tauri twin. Rotational periods and inclinations are also similar. The stars differ, however, in terms of degree of veiling…
Early Planet Formation in Embedded Disks (eDisk). XXV. Inclination-Induced Minor-Axis Brightness Asymmetries Reveal Limited Dust Settling in Embedded Protostellar Disks
University of Virginia（弗吉尼亚大学）；Virginia Institute of Theoretical Astronomy, University of Virginia（弗吉尼亚大学理论天文研究所）；National Radio Astronomy Observatory（国家射电天文台）；Kagoshima University（鹿儿岛大学）
Stellar activity induced by active structures (eg, spots, faculae) is known to strongly impact the radial velocity time series. It then limits the detection of small planetary RV signals (eg, an Earth-mass planet in the habitable zone of a solar-like star). In previous papers, we studied the detectability of such planets around the Sun seen as an edge-on star. For that purpose, we computed the RV and photometric variations induced by solar magnetic activity, using all active structures observed over one entire cycle. Our goal is to perform similar studies on stars with different physical and g…
Limb Observations of Global Solar Coronal Extreme-ultraviolet Wavefronts: The Inclination, Kinematics, Coupling with the Expanding Coronal Mass Ejections, and Connection with the Coronal Mass Ejection Driven Shocks
We present the first high-resolution Atacama Large Millimeter/Submillimeter Array (ALMA) observations of a sunspot at wavelengths of 1.3 mm and 3 mm, obtained during the solar ALMA Science Verification campaign in 2015, and compare them with the predictions of semi-empirical sunspot umbral/penumbral atmosphere models. For the first time millimeter observations of sunspots have resolved umbral/penumbral brightness structure at the chromospheric heights, where the emission at these wavelengths is formed. We find that the sunspot umbra exhibits a radically different appearance at 1.3 mm and 3 mm,…
We studied the physical parameters of the penumbra in a large and fully-developed sunspot, one of the largest over the last two solar cycles, by using full-Stokes measurements taken at the photospheric Fe I 617.3 nm and chromospheric Ca II 854.2 nm lines with the Interferometric Bidimensional Spectrometer. Inverting measurements with the NICOLE code, we obtained the three-dimensional structure of the magnetic field in the penumbra from the bottom of the photosphere up to the middle chromosphere. We analyzed the azimuthal and vertical gradient of the magnetic field strength and inclination. Our…
Aims. We use advanced 3D NLTE radiative magnetohydrodynamic simulations of the solar atmosphere to carry out detailed tests of chromospheric diagnostics at millimeter and submillimeter wavelengths. Methods. We focused on the diagnostics of the thermal structure of the chromosphere in the wavelength bands from 0.4 mm up to 9.6 mm that can be accessed with the Atacama Large Millimeter/Submillimeter Array (ALMA) and investigated how these diagnostics are affected by the instrumental resolution. Results. We find that the formation height range of the millimeter radiation depends on the location in…
What Determines the Brightness of the Magnetically Open Solar Corona?: Insights from Three-dimensional Radiative Magnetohydrodynamic Simulations and Observations
Advances in asteroseismology of solar-like stars, now provide a unique method to estimate the stellar inclination $i_{\star}$. This enables to evaluate the spin-orbit angle of transiting planetary systems, in a complementary fashion to the Rossiter-McLaughlin effect, a well-established method to estimate the projected spin-orbit angle $λ$. Although the asteroseismic method has been broadly applied to the Kepler data, its reliability has yet to be assessed intensively. In this work, we evaluate the accuracy of $i_{\star}$ from asteroseismology of solar-like stars using 3000 simulated power spec…
We performed simple spot-model calculations for quasi-periodic brightness variations of solar-type stars showing superflares, by using Kepler photometric data. Most of superflare stars show quasi-periodic brightness modulations with the typical period of one to a few tens of days. Our results indicate that these brightness variations of superflare stars can be explained by the rotation of the star with fairly large starspots. Using the result of the period analysis, we investigated the relation between the energy and frequency of superflares and the rotation period. Stars with relatively slowe…
