Kepler Data Research Articles

Mixed-mode coupling in the red clump

The investigation of global, resonant oscillation modes in red giant stars offers valuable insights into their internal structures. In this study, we investigate in detail the information we can recover on the structural properties of core-helium burning (CHeB) stars by examining how the coupling between gravity- and pressure-mode cavities depends on several stellar properties, including mass, chemical composition, and evolutionary state. Using the structure of models computed with the stellar evolution code MESA, we calculate the coupling coefficient implementing analytical expressions, which are appropriate for the strong coupling regime and the structure of the evanescent region in CHeB stars. Our analysis reveals a notable anti-correlation between the coupling coefficient and both the mass and metallicity of stars in the regime M ≲ 1.8 M⊙, in agreement with Kepler data. We attribute this correlation primarily to variations in the density contrast between the stellar envelope and core. The strongest coupling is expected thus for red-horizontal branch stars, partially stripped stars, and stars in the higher-mass range exhibiting solar-like oscillations (M ≳ 1.8 M⊙). While our investigation emphasises some limitations of current analytical expressions, it also presents promising avenues. The frequency dependence of the coupling coefficient emerges as a potential tool for reconstructing the detailed stratification of the evanescent region.

Vector to matrix representation for CNN networks for classifying astronomical data

Choosing the right classifier is crucial for effective classification in various astronomical datasets aimed at pattern recognition. While the literature offers numerous solutions, the support vector machine (SVM) continues to be a preferred choice across many scientific fields due to its user-friendliness. In this study, we introduce a novel approach using convolutional neural networks (CNNs) as an alternative to SVMs. CNNs excel at handling image data, which is arranged in a grid pattern. Our research explores converting one-dimensional vector data into two-dimensional matrices so that CNNs pre-trained on large image datasets can be applied. We evaluate different methods to input data into standard CNNs by using two-dimensional feature vector formats. In this work, we propose a new method of data restructuring based on a set of wavelet transforms. The robustness of our approach is tested across two benchmark datasets/problems: brown dwarf identification and threshold crossing event (Kepler data) classification. The proposed ensembles produce promising results on both datasets. The MATLAB code of the proposed ensemble is available at https://github.com/LorisNanni/Vector-to-matrix-representation-for-CNN-networks-for-classifying-astronomical-data

Asteroseismic measurement of core and envelope rotation rates for 2006 red giant branch stars

Context. Tens of thousands of red giant stars in the Kepler data exhibit solar-like oscillations. The mixed-mode characteristics of their oscillations enable us to study the internal physics from the core to the surface, such as differential rotation. However, envelope rotation rates have only been measured for about a dozen red giant branch (RGB) stars so far. This limited the theoretical interpretation of angular momentum transport in post-main sequence phases. Aims. We report the measurements of g-mode properties and differential rotation in the largest sample of Kepler RGB stars. Methods. We applied a new approach to calculate the asymptotic frequencies of mixed modes, which accounts for so-called near-degeneracy effects (NDEs) and leads to improved measurements of envelope rotation rates. By fitting these asymptotic expressions to the observations, we obtained measurements of the properties of g modes (period spacing, ΔΠ1, coupling factor, q, g-mode offset term, εg, small separation, δν01) and the internal rotation (mean core, Ωcore, and envelope, Ωenv, rotation rates). Results. Among 2495 stars with clear mixed-mode patterns, we found that 800 show doublets and 1206 show triplets, while the remaining stars do not show any rotational splittings. We measured core rotation rates for 2006 red giants, doubling the size of pre-existing catalogues. This led us to discover an over-density of stars that are narrowly distributed around a well-defined ridge in the plane, showing core rotation rate versus evolution along the RGB. These stars could experience a different angular momentum transport compared to other red giants. With this work, we also increased the sample of stars with measured envelope rotation rates by two orders of magnitude. We found a decreasing trend between envelope rotation rates and evolution, implying that the envelopes slow down with expansion, as expected. We found 243 stars whose envelope rotation rates are significantly larger than zero. For these stars, the core-to-envelope rotation ratios are around Ωcore/Ωenv ∼ 20 and show a large spread with evolution. Several stars show extremely mild differential rotations, with core-to-surface ratios between 1 and 2. These stars also have very slow core rotation rates, suggesting that they go through a peculiar rotational evolution. We also discovered more stars located below the ΔΠ1–Δν degeneracy sequence, which presents an opportunity to study the history of plausible stellar mergers.

Distinctions between TESS and Kepler data of KIC 8462852 and criticism of the circumsolar ring hypotheses

KIC 8462852, an F3 main sequence star, has been observed to undergo deep light curve dips whose origin remains unknown. Since the discovery of these deep dips in 2016, numerous hypotheses have been proposed, including but not limited to dust clouds, a family of disrupted comets, and circumstellar gas. In this paper, the possibility of the circumsolar ring hypothesis is explored by evaluating the flux change of surrounding stars and calculating the possible thickness of the ring. This work also analyzes Kepler data and the new TESS data of KIC 8462852, which presents a symmetric transit-like dip that has never been observed. Speculating this is a planet-star transit. This work yields a transit period of 427 days. The analysis of the latest data set provides further evidence for the study and may weaken some predicted periods and hypotheses.

Rapid multi-band space-based optical timing: revolutionizing accretion physics

Optical timing with rapid, seconds-to-minutes cadences with high photometric precision and gap-free long baselines is necessary for an unambiguous physical picture of accretion phenomena, and is only possible from space. Exoplanet-hunting missions like Kepler and TESS have offered an outstanding new window into detailed jet and accretion physics, but have been severely hampered by incomplete calibration and systematics treatments and, most especially, a monochromatic single wide bandpass. Advances made using Kepler and TESS survey data, when considered alongside detailed, expensive multi-color experiments done from the ground, reveal the enormous potential of a space-based multi-color optical timing mission with a high energy focus.

The GAPS Programme at TNG

Context. The atmospheric characterisation of hot and warm Neptune-size exoplanets is challenging mainly due to their relatively small radius and atmospheric scale height, which reduce the amplitude of atmospheric spectral features. The warm-Neptune HAT-P-11 b is a remarkable target for atmospheric characterisation because of the large brightness of its host star (V = 9.46 mag; H = 7.13 mag). Aims. The aims of this work are to review the main physical and architectural properties of the HAT-P-11 planetary system, and to probe the presence of eight molecular species in the atmosphere of HAT-P-11 b through near-infrared (NIR) high-resolution transmission spectroscopy. Methods. We reviewed the physical and architectural properties of the HAT-P-11 planetary system by analysing transits and occultations of HAT-P-11 b from the Kepler data set as well as HIRES at Keck archival radial-velocity data. We modelled the latter with Gaussian-process regression and a combined quasi-periodic and squared-exponential kernel to account for stellar variations on both (short-term) rotation and (long-term) activity-cycle timescales. In order to probe the atmospheric composition of HAT-P-11 b, we observed four transits of this target with the NIR GIANO-B at TNG spectrograph and cross-correlated the data with template atmospheric transmission spectra. Results. We find that the long-period radial-velocity signal previously attributed to the HAT-P-11 c planet (P ~ 9.3 yr; Mp sin i ~ 1.6 MJ; e ~ 0.6) is more likely due to the stellar magnetic activity cycle. Nonetheless, the HIPPARCOS-Gaia difference in the proper-motion anomaly suggests that an outer-bound companion might still exist. For HAT-P-11 b, we measure a radius of Rp = 0.4466 ± 0.0059 RJ, a mass of Mp = 0.0787 ± 0.0048 MJ, a bulk density of ρp = 1.172 ± 0.085 g cm−3, and an orbital eccentricity of e = 0.2577−0.0025+0.0033. These values are compatible with those from the literature. Probing its atmosphere, we detect the presence of two molecular species, H2O and NH3, with a S/N of 5.1 and 5.3, and a significance of 3.4 σ and 5.0 σ, respectively. We also tentatively detect the presence of CO2 and CH4, with a S/N of 3.0 and 4.8, and a significance of 3.2 σ and 2.6 σ, respectively. Conclusions. We revisit the HAT-P-11 planetary system, confirm the presence of H2O, and report the detection of NH3 in the atmosphere of HAT-P-11 b, also finding hints for the presence of CO2 and CH4 that need to be confirmed by further observations.

Asteroseismology of the young open cluster NGC 2516

Context. Asteroseismic modelling of isolated stars presents significant challenges due to the difficulty in accurately determining stellar parameters, particularly the stellar age. These challenges can be overcome by observing stars in open clusters whose coeval members share an initial chemical composition. The light curves from the all-sky survey by the Transiting Exoplanet Survey Satellite (TESS) allow us to investigate and analyse stellar variations in clusters with an unprecedented level of detail for the first time. Aims. We aim to detect gravity-mode oscillations in the early-type main-sequence members of the young open cluster NGC 2516 to deduce their internal rotation rates. Methods. We selected the 301 member stars with no more than mild contamination as our sample. We analysed the full-frame image light curves, which provide nearly continuous observations in the first and third years of TESS monitoring. We also collected high-resolution spectra using the Fiber-fed Extended Range Optical Spectrograph for the g-mode pulsators, with the aim of assessing the Gaia effective temperatures and gravities and preparing for future seismic modelling. Results. By fitting the theoretical isochrones to the colour-magnitude diagram of a cluster, we determined an age of 102 ± 15 Myr and inferred that the extinction at 550 nm (A0) is 0.53 ± 0.04 mag. We identified 147 stars with surface-brightness modulations: 24 with gravity (g-)mode pulsations (γ Doradus or slowly pulsating B-type stars) and 35 with pressure (p-)mode pulsations (δ Sct stars). When sorted by colour index, the amplitude spectra of the δ Sct stars show a distinct ordering and reveal a discernible frequency-temperature relationship. The near-core rotation rates, measured from period spacing patterns in two slowly pulsating B-type (SPB) stars and nine γ Dor stars, reach up to 3 d−1. This is at the high end of the values found from Kepler data of field stars of similar variability type. The γ Dor stars of NGC 2516 have internal rotation rates as high as 50% of their critical value, whereas the SPB stars exhibit rotation rates close to their critical rate. Although the B-type stars are rotating rapidly, we did not find long-term brightness and colour variations in the mid-infrared, which suggests that there are no disc or shell formation events in our sample. We also discussed the results of our spectroscopic observations for the g-mode pulsators.

A Search for Temporal Atmospheric Variability of Kepler Hot Jupiters

Abstract We perform a systematic search for atmospheric variability in short-period gas-giant planets (hot Jupiters) observed by the Kepler mission, by looking for temporal variability of their secondary eclipse depths. This is motivated by a recent detection of a decrease in the dayside brightness of KELT-1 b between TESS Sectors 17 and 57, separated by about 3 yr. We fit the Kepler light curves of 53 hot Jupiters and measure their secondary eclipse depths during individual Kepler quarters and four-quarter windows. We detect the secondary eclipses in individual quarters or four-quarter windows for 17 out of the 53 systems. In those 17 systems we do not detect statistically significant astrophysical variation in the secondary eclipse depths. We show that the data is sensitive to the variability seen for KELT-1 b in TESS data. Therefore, the absence of detected secondary eclipse variability in Kepler data suggests that the atmospheric variability in KELT-1 b is not common. In addition, several of the 53 targets we investigated display variability in their transit depths with a period of four quarters (1 yr). This instrumental signal is likely present in the light curves of other transiting planets we did not analyze and other variable stars observed by Kepler. Finally, we find that Kepler-488 b has a secondary eclipse depth that is unphysically large for a planet, and thus is likely a misclassified red dwarf.

Search and characterization of third-body candidates around short-period binaries using Kepler and TESS data

ABSTRACT The study of the orbital period variation of short-period binary systems has been important to understand several physical phenomena, such as the emission of gravitational waves, angular momentum loss via magnetic braking, matter transfer between the components, apsidal motion, quadrupole moment variation, and presence of circumbinary bodies. With the advent of large space missions, e.g. Kepler and Transiting Exoplanet Survey Satellite (TESS), an enormous amount of high-precision photometric data with temporal coverage from years to decades has become available. Thus, in this work, we propose to study the orbital period variation of a sample of 253 binary that was observed by both Kepler and TESS and therefore with a temporal coverage of more than 10 yr. The main goal of this paper is the search and characterization of third bodies. Based on the periodicity analysis of the observed minus calculated (O − C) diagram of the sample, 75 of them showed periodic variation and therefore were classified as binary systems with third-body candidates, while the remaining 178 did not show periodic variations. This result is a two-fold increase in tertiary candidates around binary systems compared to the study carried out with only Kepler data. Although our estimated rate of third-body candidates (∼30 per cent) is higher than that obtained only with Kepler data (∼20 per cent), it should be taken as a lower limit.

Predicted asteroseismic detection yield for solar-like oscillating stars with PLATO

Aims. In this work, we determine the expected yield of detections of solar-like oscillations for the targets of the foreseen PLATO ESA mission. Our estimates are based on a study of the detection probability, which takes into account the properties of the target stars, using the information available in the PIC 1.1.0, including the current best estimate of the signal-to-noise ratio (S/N). The stellar samples, as defined for this mission, include those with the lowest noise level (P1 and P2 samples) and the P5 sample, which has a higher noise level. For the P1 and P2 samples, the S/N is high enough (by construction) that we can assume that the individual mode frequencies can be measured. For these stars, we estimate the expected uncertainties in mass, radius, and age due to statistical errors induced by uncertainties from the observations only. Methods. We used a formulation from the literature to calculate the detection probability. We validated this formulation and the underlying assumptions with Kepler data. Once validated, we applied this approach to the PLATO samples. Using again Kepler data as a calibration set, we also derived relations to estimate the uncertainties of seismically inferred stellar mass, radius, and age. We then applied those relations to the main sequence stars with masses equal to or below 1.2 M⊙ belonging to the PLATO P1 and P2 samples and for which we predict a positive seismic detection. Results. We found that we can expect positive detections of solar-like oscillations for more than 15 000 FGK stars in one single field after a two-year observation run. Among them, 1131 main sequence stars with masses of ≤1.2 M⊙ satisfy the PLATO requirements for the uncertainties of the seismically inferred stellar masses, radii, and ages. The baseline observation programme of PLATO consists of observing two fields of similar size (one in the southern hemisphere and one in the northern hemisphere) for two years apiece. Accordingly, the expected seismic yields of the mission amount to over 30 000 FGK dwarfs and subgiants, with positive detections of solar-like oscillations. This sample of expected solar-like oscillating stars is large enough to enable the PLATO mission’s stellar objectives to be amply satisfied. Conclusions. The PLATO mission is expected to produce a catalog sample of extremely well seismically characterized stars of a quality that is equivalent to the Kepler Legacy sample, but containing a number that is about 80 times greater, when observing two PLATO fields for two years apiece. These stars are a gold mine that will make it possible to make significant advances in stellar modelling.

Do Faculae Affect Autocorrelation Rotation Periods in Sun-like Stars?

Rotational periods derived from autocorrelation function (ACF) techniques on stars photometrically similar to the Sun in Kepler data have proven difficult to reliably determine. We investigate various instrumental and astrophysical factors affecting the accuracy of these measurements, including the effects of observational windows and noise, stellar activity and inclination, spectral passbands, and the separate normalization of contiguous segments. We validate that the flux variations due to faculae are very periodic, but starspots are the dominant source of bolometric and visible differential variability in Sun-like stars on rotational timescales. We quantify how much stronger the relative contribution of faculae would have to be to render Sun-like light curves periodic enough to reliably measure with autocorrelation methods. We also quantify how long starspot lifetimes need to be to render pure spot light curves periodic enough. In general, longer observational windows yield more accurate ACF measurements, even when faculae are not present. Due to the enhancement of the relative contribution of faculae, observing stars with intermediate inclinations, during activity minima, and/or through bluer passbands has the effect of strengthening the periodicity of the light curve. We search for other manifestations of faculae in broadband photometry of Sun-like stars and conclude that without absolute flux measurements or restriction to shorter-wavelength passbands, differential light curves are uninformative about faculae.

Perturbative analysis of the effect of a magnetic field on gravito-inertial modes

Context. Magnetic fields have been measured recently in the cores of red giant stars thanks to their effects on stellar oscillation frequencies. The search for magnetic signatures in pulsating stars, such as γ Doradus (γ Dor) or slowly pulsating B stars, requires us to adapt the formalism developed for slowly rotating red giants to rapidly rotating stars. Aims. We perform a theoretical analysis of the effects of an arbitrary magnetic field on high radial order gravity and Rossby modes in a rapidly rotating star. Methods. The magnetic effects were treated as a perturbation. For high radial order modes, the contribution of the radial component of the magnetic field is likely to dominate over the azimuthal and latitudinal components. The rotation is taken into account through the traditional approximation of rotation. Results. General expressions of the frequency shift induced by an arbitrary radial magnetic field are derived. Approximate analytical forms are obtained in the high-order, high-spin-parameter limits for the modes most frequently observed in γ Dor stars. We propose simple methods to detect seismic magnetic signatures and measure possible magnetic fields in such stars. Conclusions. These methods offer new possibilities to look for internal magnetic fields in future observations, such as those of the PLATO mission, or of revisiting existing Kepler or TESS data.

Relations of Rotation and Chromospheric Activity to Stellar Age for FGK Dwarfs from Kepler and LAMOST

The empirical relations between rotation period, chromospheric activity, and age can be used to estimate stellar age. To calibrate these relations, we present a catalog, including the masses and ages of 52,321 FGK dwarfs, 47,489 chromospheric activity index logRHK+ , 6077 rotation periods P rot, and variability amplitudes S ph, based on data from LAMOST DR7, Kepler, and Gaia Data Release 3. We find a pronounced correlation among P rot, age, and [Fe/H] throughout the main-sequence phase for F dwarfs. However, the decrease of logRHK+ over time is not significant except for those with [Fe/H] < −0.1. For G dwarfs, both P rot and logRHK+ are reliable age probes in the ranges ∼2–11 Gyr and ∼2–13 Gyr, respectively. K dwarfs exhibit a prominent decrease in logRHK+ within the age range of ∼3–13 Gyr when the relation of P rot–τ is invalid. These relations are very important for promptly estimating the age of a vast number of stars, thus serving as a powerful tool in advancing the fields of exoplanet properties, stellar evolution, and Galactic archeology.

Detection of Solar-like Oscillations in Subgiant and Red Giant Stars Using 2 minute Cadence TESS Data

Based on all 2 minute cadence TESS light curves from Sector 1 to 60, we provide a catalog of 8651 solar-like oscillators, including frequency at maximum power ( νmax , with its median precision σ = 5.39%), large frequency separation (Δν, σ = 6.22%), and seismically derived masses, radii, and surface gravity values. In this sample, we have detected 2173 new oscillators and added 4373 new Δν measurements. Our seismic parameters are consistent with those from Kepler, K2, and previous TESS data. The median fractional residual in νmax is 1.63%, with a scatter of 14.75%, and in Δν it is 0.11%, with a scatter of 10.76%. We have detected 476 solar-like oscillators with νmax exceeding the Nyquist frequency of Kepler long-cadence data during the evolutionary phases of subgiants and the base of the red giant branch, which provide a valuable resource for understanding angular momentum transport.

Properties of PSR J1023+0038 Based on Kepler, TESS, and FAST

The pulsar system PSR J1023+0038 is a very interesting binary with radio millisecond pulsar and low-mass X-ray binary transitions, which depend on the stellar accretion process. We have used Kepler light curves with 1 minute cadence and TESS light curves with 2 minute cadence to study the flare properties of PSR J1023+0038. We detected 516 flare events in the K2 data and 84 flare events in the TESS survey data. We determined the flare rise and delay times, the flare durations and amplitudes, and flare energies. We obtained a value of the power-law index of 0.359 ± 0.023 between the flare energies and decay times, which is similar to the theoretically predicted value of 1/3. This in turn indicates that PSR J1023+0038 might be exhibiting physical mechanisms described by magnetic reconnection theory. Using the maximum likelihood estimation method, we also calculated the power-law index of the cumulative flare frequency distribution, finding 1.87 ± 0.27 for the Kepler data and 1.74 ± 0.29 for the TESS data. Meanwhile, we reduced six FAST observations of PSR J1023+0038 from 2019–2021 using a standard pulsar search procedure. We report that we detected a prompt signal with a period compatible with that found in previous observations of PSR J1023+0038. However, there are several reasons (statistical, excess DM, pulse shape, etc.) as to why the association is not likely.

Large exomoons unlikely around Kepler-1625 b and Kepler-1708 b

AbstractThere are more than 200 moons in our Solar System, but their relatively small radii make similarly sized extrasolar moons very hard to detect with current instruments. The best exomoon candidates so far are two nearly Neptune-sized bodies orbiting the Jupiter-sized transiting exoplanets Kepler-1625 b and Kepler-1708 b, but their existence has been contested. Here we reanalyse the Hubble and Kepler data used to identify the two exomoon candidates employing nested sampling and Bayesian inference techniques coupled with a fully automated photodynamical transit model. We find that the evidence for the Kepler-1625 b exomoon candidate comes almost entirely from the shallowness of one transit observed with Hubble. We interpret this as a fitting artefact in which a moon transit is used to compensate for the unconstrained stellar limb darkening. We also find much lower statistical evidence for the exomoon candidate around Kepler-1708 b than previously reported. We suggest that visual evidence of the claimed exomoon transits is corrupted by stellar activity in the Kepler light curve. Our injection-retrieval experiments of simulated transits in the original Kepler data reveal false positive rates of 10.9% and 1.6% for Kepler-1625 b and Kepler-1708 b, respectively. Moreover, genuine transit signals of large exomoons would tend to exhibit much higher Bayesian evidence than these two claims. We conclude that neither Kepler-1625 b nor Kepler-1708 b are likely to be orbited by a large exomoon.

Pulsating components of the eclipsing binaries with long period eccentric orbits

Taking into account the results found by analysing the Kepler data together with our photometric observations, we present new findings about KIC 5217733 and KIC 11671429, which are two highly eccentric detached eclipsing binaries. We estimate that the radii of the primary and secondary components should be, respectively, 5.41±0.07 R⊙ and 1.59±0.07 R⊙, while their masses should be 2.59±0.09 M⊙ and 1.66±0.09 M⊙ for KIC 5217733, whose orbital period is 161.252379 days. In the case of KIC 11671429, whose orbital period is 112.463712 days, the radii of the primary and secondary components are estimated as 3.05±0.07 R⊙ and 1.60±0.11 R⊙, and their masses are computed as 1.64±0.09 M⊙ and 1.52±0.14 M⊙, respectively. The frequency analyses of the variations at out-of-eclipses reveal that both targets exhibit pulsations. In these pulsations, the g-modes are dominant for KIC 521773, while the p-modes are dominant for KIC 11671429.

Stellar spectral-type (mass) dependence of the dearth of close-in planets around fast-rotating stars

In 2013 a dearth of close-in planets around fast-rotating host stars was found using statistical tests on Kepler data. The addition of more Kepler and Transiting Exoplanet Survey Satellite (TESS) systems in 2022 filled this region of the diagram of stellar rotation period (Prot) versus the planet orbital period (Porb). We revisited the Prot extraction of Kepler planet-host stars, we classify the stars by their spectral type, and we studied their Prot–Porb relations. We only used confirmed exoplanet systems to minimize biases. In order to learn about the physical processes at work, we used the star-planet evolution code ESPEM (French acronym for Evolution of Planetary Systems and Magnetism) to compute a realistic population synthesis of exoplanet systems and compared them with observations. Because ESPEM works with a single planet orbiting around a single main-sequence star, we limit our study to this population of Kepler observed systems filtering out binaries, evolved stars, and multi-planets. We find in both, observations and simulations, the existence of a dearth in close-in planets orbiting around fast-rotating stars, with a dependence on the stellar spectral type (F, G, and K), which is a proxy of the mass in our sample of stars. There is a change in the edge of the dearth as a function of the spectral type (and mass). It moves towards shorter Prot as temperature (and mass) increases, making the dearth look smaller. Realistic formation hypotheses included in the model and the proper treatment of tidal and magnetic migration are enough to qualitatively explain the dearth of hot planets around fast-rotating stars and the uncovered trend with spectral type.

Prediction of Short Stellar Activity Cycles using Derived and Established Empirical Relations between Activity and Rotation Periods

In our previous work, we investigated the occurrence rate of super-flares on various types of stars and their statistical properties, with a particular focus on G-type dwarfs, using entire Kepler data. The said study also considered how the statistics change with stellar rotation period, which in turn, had to be determined. Using such new data, as a by-product, we found 138 Kepler IDs of F- and G-type main sequence stars with rotation periods less than a day (P rot < 1 day). On one hand, previous studies have revealed short activity cycles in F-type and G-type stars and the question investigated was whether or not short-term activity cycles are a common phenomenon in these stars. On the other hand, extensive studies exist which establish an empirical connection between a star’s activity cycle and rotation periods. In this study, we compile all available Kepler data with P rot < 1 day, and rely on an established empirical relation between P cyc and P rot with the aim to provide predictions for very short 5.09 ≤ P cyc ≤ 38.46 day cases in a tabular form. We propose an observation to measure P cyc using a monitoring program of stellar activity (e.g., activity-related chromospheric emission S-index) or a similar means for the Kepler IDs found in this study in order put the derived empirical relations between P cyc and P rot derived here to the test. We also propose an alternative method for measuring very short P cyc, using flare-detection algorithms applied to future space mission data.

New Cases of Superflares on Slowly Rotating Solar-type Stars and Large Amplitude Superflares in G- and M-type Main Sequence Stars

In our previous work, we searched for superflares on different types of stars while focusing on G-type dwarfs using entire Kepler data to study statistical properties of the occurrence rate of superflares. Using these new data, as a by-product, we found 14 cases of superflare detection on 13 slowly rotating Sun-like stars with rotation periods of 24.5–44 days. This result supports the earlier conclusion by others that the Sun may possibly undergo a surprise superflare. Moreover, we found 12 and seven new cases of detection of exceptionally large amplitude superflares on six and four main sequence stars of G- and M-type, respectively. No large-amplitude flares were detected in A, F or K main sequence stars. Here we present preliminary analysis of these cases. The superflare detection, i.e., an estimation of flare energy, is based on a more accurate method compared to previous studies. We fit an exponential decay function to flare light curves and study the relation between e-folding decay time, τ, versus flare amplitude and flare energy. We find that for slowly rotating Sun-like stars, large values of τ correspond to small flare energies and small values of τ correspond to high flare energies considered. Similarly, τ is large for small flare amplitudes and τ is small for large amplitudes considered. However, there is no clear relation between these parameters for large amplitude superflares in the main sequence G- and M-type stars, as we could not establish clear functional dependence between the parameters via standard fitting algorithms.