Photospheric activity, rotation, and radial velocity variations of the planet-hosting star CoRoT-7
A. F. Lanza, A. S. Bonomo, C. Moutou, I. Pagano, S. Messina, G. Leto, G. Cutispoto, S. Aigrain, R. Alonso, P. Barge, M. Deleuil, M. Auvergne, A. Baglin, A. Collier Cameron
备注：
13 pages, 9 figures, accepted by Astronomy and Astrophysics
The CoRoT satellite has recently discovered the transits of a telluric planet across the disc of a late-type magnetically active star dubbed CoRoT-7, while a second planet has been detected after filtering out the radial velocity (hereafter RV) variations due to stellar activity. We investigate the magnetic activity of CoRoT-7 and use the results for a better understanding of its impact on stellar RV variations. We derive the longitudinal distribution of active regions on CoRoT-7 from a maximum entropy spot model of the CoRoT light curve. Assuming that each active region consists of dark spots and bright faculae in a fixed proportion, we synthesize the expected RV variations. Active regions are mainly located at three active longitudes which appear to migrate at different rates, probably as a consequence of surface differential rotation, for which a lower limit of ΔΩ/ Ω= 0.058 \pm 0.017 is found. The synthesized activity-induced RV variations reproduce the amplitude of the observed RV curve and are used to study the impact of stellar activity on planetary detection. In spite of the non-simultaneous CoRoT and HARPS observations, our study confirms the validity of the method previously adopted to filter out RV variations induced by stellar activity. We find a false-alarm probability < 0.01 percent that the RV oscillations attributed to CoRoT-7b and CoRoT-7c are spurious effects of noise and activity. Additionally, our model suggests that other periodicities found in the observed RV curve of CoRoT-7 could be explained by active regions whose visibility is modulated by a differential stellar rotation with periods ranging from 23.6 to 27.6 days.
The CoRoT satellite has recently discovered a hot Jupiter that transits across the disc of a F9V star called CoRoT-6 with a period of 8.886 days. We model the photospheric activity of the star and use the maps of the active regions to study stellar differential rotation and the star-planet interaction. We apply a maximum entropy spot model to fit the optical modulation as observed by CoRoT during a uninterrupted interval of about 140 days. Photospheric active regions are assumed to consist of spots and faculae in a fixed proportion with solar-like contrasts. Individual active regions have life…
Close-in massive planets interact with their host stars through tidal and magnetic mechanisms. In this paper, we review circumstantial evidence for star-planet interaction as revealed by the photospheric magnetic activity in some of the CoRoT planet-hosting stars, notably CoRoT-2, CoRoT-4, and CoRoT-6. The phenomena are discussed in the general framework of activity-induced features in stars accompanied by hot Jupiters. The theoretical mechanisms proposed to explain the activity enhancements possibly related with hot Jupiter are also briefly reviewed with an emphasis on the possible effects at…
The space experiment CoRoT has recently detected a transiting hot Jupiter in orbit around a moderately active F-type main-sequence star (CoRoT-Exo-4a). This planetary system is of particular interest because it has an orbital period of 9.202 days, the second longest one among the transiting planets known to date. We study the surface rotation and the activity of the host star during an uninterrupted sequence of optical observations of 58 days. Our approach is based on a maximum entropy spot modelling technique extensively tested by modelling the variation of the total solar irradiance. It assu…
I briefly review the current state of the modelling of photospheric activity based on the high-precision optical light curves obtained with MOST, CoRoT, and Kepler. These models can be used to search for active longitudes where activity is preferentially concentrated, estimate the amplitude of stellar differential rotation, and look for short-term activity cycles as, e.g., in the case of CoRoT-2. In the case of a late-type star accompanied by a transiting hot Jupiter, the small light modulations observed during transits when a dark spot is occulted by the disc of the planet are also briefly co…
CoRoT-2a is a young (about 0.5 Gyr) G7V star accompanied by a transiting hot-Jupiter, discovered by the CoRoT satellite (Alonso et al. 2008; Bouchy et al. 2008). An analysis of its photospheric activity, based on spot modelling techniques previously developed by our group for the analysis of the Sun as a star, shows that the active regions on CoRoT-2a arised within two active longitudes separated by about 180 degrees and rotating with periods of 4.5221 and 4.5543 days, respectively, at epoch of CoRoT observations (112 continous days centered at 2007.6). We show that the total spotted area osci…
We analyze variations in the transit lightcurves of CoRoT-2b, a massive hot Jupiter orbiting a highly active G star. We use one transit lightcurve to eclipse-map a photospheric spot occulted by the planet. In this case study we determine the size and longitude of the eclipsed portion of the starspot and systematically study the corresponding uncertainties. We determine a spot radius between $4.5\degr$ and $10.5\degr$ on the stellar surface and the spot longitude with a precision of about $\pm 1$ degree. Given the well-known transit geometry of the CoRoT-2 system, this implies a reliable detect…
Protoplanetary disks, debris disks, and disrupted or evaporating planets can all feed accretion onto stars. The photospheric abundances of such stars may then reveal the composition of the accreted material. This is especially likely in B to mid-F type stars, which have radiative envelopes and hence less bulk--photosphere mixing. We present a theoretical framework (\texttt{CAM}) considering diffusion, rotation, and other stellar mixing mechanisms, to describe how the accreted material interacts with the bulk of the star. This allows the abundance pattern of the circumstellar material to be cal…
Recently, the study of the CoRoT target HD 49933 showed evidence of variability of its magnetic activity. This was the first time that a stellar activity was detected using asteroseismic data. For the Sun and HD 49933, we observe an increase of the p-mode frequencies and a decrease of the maximum amplitude per radial mode when the activity level is higher. Moreover a similar behavior of the frequency shifts with frequency has been found between the Sun and HD 49933. We study 3 other targets of CoRoT as well, for which modes have been detected and well identified: HD 181420, HD 49385, and HD 52…
Spectroscopy across spatially resolved stellar surfaces reveals spectral line profiles free from rotational broadening, whose gradual changes from disk center toward the stellar limb reflect an atmospheric fine structure that is possible to model by 3-D hydrodynamics. Previous studies of photospheric spectral lines across stellar disks exist for the Sun and HD209458 (G0 V) and are now extended to the planet-hosting HD189733A to sample a cooler K-type star and explore the future potential of the method. During exoplanet transit, stellar surface portions successively become hidden and differenti…
The photospheric spot activity of some of the stars with transiting planets discovered by the CoRoT space experiment is reviewed. Their out-of-transit light modulations are fitted by a spot model previously tested with the total solar irradiance variations. This approach allows us to study the longitude distribution of the spotted area and its variations versus time during the five months of a typical CoRoT time series. The migration of the spots in longitude provides a lower limit for the surface differential rotation, while the variation of the total spotted area can be used to search for sh…
Chemical abundances in solar-type stars are a much debated topic. Planet-hosting stars are known to be metal-rich, but whether or not this peculiarity applies also to the chemical composition of the outer stellar atmospheres is still to be clarified. More in general, coronal and photospheric abundances in late-type stars appear to be different in many cases, but understanding how chemical stratification effects work in stellar atmospheres requires an observational base larger than currently available. We obtained XMM-Newton high-resolution X-ray spectra of Tau Bootis, a well known nearby star …
The homogeneous spectroscopic determination of the stellar parameters is a mandatory step for transit detections from space. Knowledge of which population the planet hosting stars belong to places constraints on the formation and evolution of exoplanetary systems. We used the FLAMES/GIRAFFE multi-fiber instrument at ESO to spectroscopically observe samples of stars in three CoRoT/Exoplanet fields, namely the LRa01, LRc01, and SRc01 fields, and characterize their stellar populations. We present accurate atmospheric parameters, Teff, logg, [M/H], and [$α$/Fe]\ derived for 1227 stars in these fie…
Recently, the study of the CoRoT target, HD49933, showed evidence of variability of its magnetic activity. This was the first time that a stellar activity was detected using asteroseismic data. For the Sun and HD49933, we observe an increase of the p-mode frequencies and a decrease of the maximum amplitude per radial mode when the activity level is higher. Moreover, we have been able to determine the variation of the frequency shift as a function of frequency, a premier in a star different from the Sun, showing pretty interesting similarities with the behavior already seen in the Sun. Beside, …
AU Mic is a young, very active M dwarf star with a debris disk and at least one transiting Neptune-size planet. Here we present detailed analysis of the magnetic field of AU Mic based on previously unpublished high-resolution optical and near-infrared spectropolarimetric observations. We report a systematic detection of circular and linear polarization signatures in the stellar photospheric lines. Tentative Zeeman Doppler imaging modeling of the former data suggests a non-axisymmetric global field with a surface-averaged strength of about 90 G. At the same time, linear polarization observation…
Context. Kepler-17 is a G2V sun-like star accompanied by a transiting planet with a mass of ~2.5 Jupiter masses and an orbital period of 1.486 d, recently discovered by the Kepler space telescope. This star is highly interesting as a young solar analogue. Aims. We used about 500 days of high-precision, high-duty-cycle optical photometry collected by Kepler to study the rotation of the star and the evolution of its photospheric active regions. Methods. We applied a maximum-entropy light curve inversion technique to model the flux rotational modulation induced by active regions that consist of d…
The presence of stellar companions around planet hosting stars influences the architecture of their planetary systems. To find and characterise these companions and determine their orbits is thus an important consideration to understand planet formation and evolution. For transiting systems even unbound field stars are of interest if they are within the photometric aperture of the light curve measurement. Then they contribute a constant flux offset to the transit light curve and bias the derivation of the stellar and planetary parameters if their existence is unknown. Close stellar sources are…
CoRoT-2, the second planet-hosting star discovered by the CoRoT satellite, is a young and active star. A total of 77 transits were observed for this system over a period of 135 days. Small modulations detected in the optical light curve of the planetary transits are used to study the position, size, intensity, and temporal evolution of the photospheric spots on the surface of the star that are occulted by the planetary disk. We apply a spot model to these variations and create a spot map of the stellar surface of CoRoT-2 within the transit band for every transit. From these maps, we estimate t…
Tidal dissipation in late-type stars is presently poorly understood and the study of planetary systems hosting hot Jupiters can provide new observational constraints to test proposed theories. We focus on systems with F-type main-sequence stars and find that the recently discovered system CoRoT-11 is presently the best suited for such a kind of investigation. A classic constant tidal lag model is applied to reproduce the evolution of the system from a plausible nearly synchronous state on the ZAMS to the present state, thus putting constraints on the average modified tidal quality factor <Q'_s…
We study the variability of solar activity using new photospheric proxies originally developed for the analysis of stellar magnetism with the CoRoT and Kepler photometric observations. These proxies are obtained by tracking the temporal modulations in the observations associated to the spots and magnetic features as the Sun rotates. We analyze here 21 years, spanning solar cycles 23 and 24, of the observations collected by the space-based photometric VIRGO and radial velocity GOLF instruments on board the SoHO satellite. The photospheric activity proxy Sph is then calculated for each of the th…
A major goal in the discovery and characterisation of exoplanets is to identify terrestrial-type worlds that are similar to (or otherwise distinct from) our Earth. Recent results have highlighted the importance of applying devolatilisation -- i.e. depletion of volatiles -- to the chemical composition of planet-hosting stars to constrain bulk composition and interiors of terrestrial-type exoplanets. In this work, we apply such an approach to a selected sample of 13 planet-hosting Sun-like stars, for which high-precision photospheric abundances have been determined in the first paper of the seri…
HD 46375 is known to host a Saturn-like exoplanet orbiting at 0.04 AU from its host star. Stellar light reflected by the planet was tentatively identified in the 34-day CoRoT run acquired in October-November 2008. We constrain the properties of the magnetic field of HD 46375 based on spectropolarimetric observations with the NARVAL spectrograph at the Pic du Midi observatory. In addition, we use a high-resolution NARVAL flux spectrum to contrain the atmospheric parameters. With these constraints, we perform an asteroseismic analysis and modelling of HD 46375 using the frequencies extracted fro…
The planet-hosting and Sirius-type binary system epsilon Reticulum (HD 27442) is examined from the perspective of its more evolved white dwarf secondary. The stellar parameters are determined from a combination of Balmer line spectroscopy, gravitational redshift, and solid angle. These three methods conspire to yield the most accurate physical description of the companion to date: Teff=15,310 \pm 350 K and M=0.60 \pm 0.02 Msol. Post-main sequence mass loss indicates the current binary separation has increased by a factor of 1.6 from its primordial state when the current primary was forming its…
The CoRoT short asteroseismic runs give us the opportunity to observe a large variety of late-type stars through their solar-like oscillations. We report the observation and modeling of the F5V star HD 175272. Our aim is to define a method for extracting as much information as possible from a noisy oscillation spectrum. We followed a differential approach that consists of using a well-known star as a reference to characterize another star. We used classical tools such as the envelope autocorrelation function to derive the global seismic parameters of the star. We compared HD 175272 with HD 181…
The magnetic activity levels of planet host stars may differ from that of stars not known to host planets in several ways. Hot Jupiters may induce activity in their hosts through magnetic interactions, or through tidal interactions by affecting their host's rotation or convection. Measurements of photospheric, chromospheric, or coronal activity might then be abnormally high or low compared to control stars that do not host hot Jupiters, or might be modulated at the planet's orbital period. Such detections are complicated by the small amplitude of the expected signal, by the fact that the signa…
In this paper, we present new spectropolarimetric observations of the planet-hosting star Tau Bootis, using ESPaDOnS and Narval spectropolarimeters at Canada-France-Hawaii Telescope (CFHT) and Telescope Bernard Lyot (TBL), respectively. We detected the magnetic field of the star at three epochs in 2008. It is a weak magnetic field of only a few Gauss, oscillating between a predominant toroidal component in January and a dominant poloidal component in June and July. A magnetic polarity reversal was observed relative to the magnetic topology in June 2007. This is the second such reversal observe…
The star HD 52265 is a G0V metal-rich exoplanet-host star observed in the seismology field of the CoRoT space telescope from November 2008 to March 2009. The satellite collected 117 days of high-precision photometric data on this star, showing that it presents solar-like oscillations. HD 52265 was also observed in spectroscopy with the Narval spectrograph at the same epoch. We characterise HD 52265 using both spectroscopic and seismic data. The fundamental stellar parameters of HD 52265 were derived with the semi-automatic software VWA, and the projected rotational velocity was estimated by fi…
We present a determination of photospheric parameters and C abundances for a sample of 172 G and K dwarfs, subgiants, and giants with and without detected planets in the solar neighbourhood. The analysis was based on high S/N and high resolution spectra observed with the ELODIE spectrograph, and for which the observational data was publicly available. We intend to contribute precise and homogeneous C abundances in studies that compare the behaviour of light elements in stars, hosting planets or not. This will bring new arguments to the discussion of possible anomalies that have been suggested …
We report here results of spectropolarimetric observations of the classical T Tauri star DN Tau carried out (at 2 epochs) with ESPaDOnS at the Canada-France-Hawaii Telescope within the `Magnetic Protostars and Planets' programme. We infer that DN Tau, with a photospheric temperature of 3,950+-50 K, a luminosity of 0.8+-0.2 Lsun and a rotation period of 6.32 d, is a ~2Myr-old fully-convective 0.65+-0.05 Msun star with a radius of 1.9+-0.2 Dsun, viewed at an inclination of 35+-10degr. Clear circularly-polarized Zeeman signatures are detected in both photospheric and accretion-powered emission li…
We report here results of spectropolarimetric observations of the ~8Myr classical TTauri star (cTTS) TWHya carried out with ESPaDOnS at the Canada-France-Hawaii Telescope (CFHT) in the framework of the `Magnetic Protostars and Planets' (MaPP) programme, and obtained at 2 different epochs (2008 March and 2010 March). Obvious Zeeman signatures are detected at all times, both in photospheric lines and in accretion-powered emission lines. Significant intrinsic variability and moderate rotational modulation is observed in both photospheric and accretion proxies. Using tomographic imaging, we recons…
Photospheric stellar activity might be an important source of noise and confusion in the radial-velocity measurements. RV planet search surveys as well as follow-up of photometric transit surveys require a deeper understanding and characterization of the effects of stellar activities to disentangle it from planetary signals. We simulate dark spots on a rotating stellar photosphere. The variations of the photometry, RV and spectral line shapes are characterized and analyzed according to the stellar inclination, the latitude and the number of spots. The Lomb-Scargle periodograms of the RV variat…
Pre-main sequence stars are variable sources. In diskless stars this variability is mainly due to the rotational modulation of dark photospheric spots and active regions, as in main sequence stars even if associated with a stronger magnetic activity. Aims. We aim at analyzing the simultaneous optical and X-ray variability in these stars to unveil how the activity in the photosphere is connected with that in the corona, to identify the dominant surface magnetic activity, and to correlate our results with stellar properties, such as rotation and mass. Methods. We analyzed the simultaneous optica…
The spectral and magnetic properties and variability of the B2Vnp emission-line magnetosphere star HR7355 were analyzed. The object rotates at almost 90% of the critical value, meaning it is a magnetic star for which oblateness and gravity darkening effects cannot be ignored any longer. A detailed modeling of the photospheric parameters indicate that the star is significantly cooler than suggested by the B2 spectral type, with T_eff=17500K atypically cool for a star with a helium enriched surface. The spectroscopic variability of helium and metal lines due to the photospheric abundance pattern…
We report here results of spectropolarimetric observations of the classical T Tauri star (cTTS) GQ Lup carried out with ESPaDOnS at the Canada-France-Hawaii Telescope (CFHT) in the framework of the "Magnetic Protostars and Planets" (MaPP) programme, and obtained at 2 different epochs (2009 July & 2011 June). From these observations, we first infer that GQ Lup has a photospheric temperature of 4,300+-50Â K and a rotation period of 8.4+-0.3 d; it implies that it is a 1.05+-0.07 Msun star viewed at an inclination of ~30deg, with an age of 2-5 Myr, a radius of 1.7+-0.2 Rsun, and has just started t…
In the stellar forming region NGC 2264 there are objects catalogued as hosting a transitional disk according to spectrum modeling. Four members of this set have optical and infrared light curves coming from the CoRoT and Spitzer telescopes. In this work, we try to simultaneously explain the light curves using the extinction of the stellar radiation and the emission of the dust inside the hole of a transitional disk. For the object Mon-296, we were successful. However, for Mon-314, and Mon-433 our evidence suggests that they host a pre-transitional disk. For Mon-1308 a new spectrum fitting usin…
The characterization of the growing number of newly discovered exoplanets ---nature, internal structure, formation and evolution--- strongly relies on the properties of their host-star, i.e. its mass, radius and age. These latter can be inferred from stellar evolution models constrained by the observed global parameters of the host-star --- effective temperature, photospheric chemical composition, surface gravity and/or luminosity--- and by its mean density inferred from the transit analysis. Additional constraints for the models can be provided by asteroseismic observations of the host-star. …
There have recently been detections of radio emission from low-mass stars, some of which are indicative of star-planet interactions. Motivated by these exciting new results, here we present stellar wind models for the active planet-hosting M dwarf AU Mic. Our models incorporate the large-scale photospheric magnetic field map of the star, reconstructed using the Zeeman-Doppler Imaging method. We use our models to assess if planet-induced radio emission could be generated in the corona of AU Mic, through a mechanism analogous to the sub-Alfvénic Jupiter-Io interaction. In the case that AU Mic ha…
Differences in the elemental abundances of planet hosting stars in binary systems can give important clues and constraints about planet formation and evolution. In this study we performed a high-precision, differential elemental abundance analysis of a wide binary system, HD 80606/80607, based on high-resolution, high signal-to-noise ratio Keck/HIRES spectra. HD 80606 is known to host a four Jupiter mass giant planet while no planet has yet been detected around HD 80607. We determined stellar parameters as well as abundances for 23 elements for these two stars with extremely high precision. Ou…
Studies of the planet abundance as a function of stellar mass have suggested a strong increase in the frequency of planet occurrence around stars more massive than $1.5 M_\odot$, and that such stars are deficit in short period planets. These planet searches have relied on giant stars for a sample of high mass stars, which are hostile to precision Doppler measurements due to rotation and activity while on the main sequence. This paper considers the observed $v\sin i$ and observationally inferred mass for exoplanet hosting giants with the $v\sin i$ of distribution of field stars, which show disc…
Finding solar-analog stars with fundamental properties as close as possible to the Sun and studying the characteristics of their surface magnetic activity is a very promising way to understand the solar variability and its associated dynamo process. However, the identification of solar-analog stars depends on the accuracy of the estimated stellar parameters. Thanks to the photometric CoROT and Kepler space missions, the addition of asteroseismic data was proven to provide the most accurate fundamental properties that can be derived from stellar modeling today. Here, we present our latest resul…
There have recently been detections of radio emission from low-mass stars, some of which are indicative of star-planet interactions. Motivated by these exciting new results, in this paper we present Alfvén wave-driven stellar wind models of the two active planet-hosting M dwarfs Prox Cen and AU Mic. Our models incorporate large-scale photospheric magnetic field maps reconstructed using the Zeeman-Doppler Imaging method. We obtain a mass-loss rate of $0.25~\dot{M}_{\odot}$ for the wind of Prox Cen. For the young dwarf AU Mic, we explore two cases: a low and high mass-loss rate. Depending on the…
Past UV and optical observations of stars hosting hot Jupiters have shown that some of these stars present an anomalously low chromospheric activity, significantly below the basal level. For WASP-13, observations have shown that the apparent lack of activity is possibly caused by absorption from the intervening ISM. Inspired by this result, we study the effect of ISM absorption on activity measurements (S and logR'$_{\rm HK}$ indices) for main-sequence late-type stars. To this end, we employ synthetic stellar photospheric spectra combined with varying amounts of chromospheric emission and ISM …
Aims: We investigate magnetic tracers in the photosphere and the chromosphere of the ultra-rapid rotator ($P\sim0.32d$) V530 Per, a cool member of the open cluster $α$ Persei, to characterize the short-term variability of the magnetic activity and large-scale magnetic field of this prototypical young, rapidly rotating solar-like star. Methods: With time-resolved spectropolarimetric observations spread over four close-by nights, we reconstructed the brightness distribution and large-scale magnetic field geometry of V530 Per through Zeeman-Doppler imaging. Simultaneously, we estimated the short-…
Terrestrial Exoplanet Internal Structure Constraints Enabled by Comprehensive Host Star Characterization Reveal that Terrestrial Planets in Mean-motion Resonances are Water Rich
The wavelet transform has been used for numerous studies in astrophysics, including signal--noise periodicity and decomposition as well as the signature of differential rotation in stellar light curves. In the present work, we apply the Morlet wavelet with an adjustable parameter $a$, which can be fine-tuned to produce optimal resolutions of time and frequency, and the Haar wavelet for decomposition at levels of light curves. We use the WaveLab--package (library of Matlab routines for wavelet analysis) for the decomposition and a modified version of Colorado--package for the wavelet maps of sy…
Overmassive No More: The Case for Little Red Dots Hosting Black Hole Seeds as Massive as Single Supermassive Stars
Institute for Astronomy, University of Hawai‘i（夏威夷大学天文研究所）；Department of Astrophysical Sciences, Princeton University（普林斯顿大学天体物理科学系）；Max-Planck-Institut für Astronomie（马克斯·普朗克天文学研究所）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究院）；Department of Astronomy, The University of Texas at Austin（德克萨斯大学奥斯汀分校天文学系）；Cosmic Frontier Center, The University of Texas at Austin（德克萨斯大学奥斯汀分校宇宙前沿中心）；MIT Kavli Institute for Astrophysics and Space Research（麻省理工学院卡弗里天体物理学与空间研究研究所）；David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto（多伦多大学大卫·A·邓普克天文学与天体物理学系）；Cosmic Dawn Center (DAWN)（宇宙黎明中心）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Department of Astronomy, University of Florida（佛罗里达大学天文学系）
We identify nine young stellar objects (YSOs) in the NGC 2264 star-forming region with optical {\em CoRoT} light curves exhibiting short-duration, shallow, periodic flux dips. All of these stars have infrared (IR) excesses that are consistent with their having inner disk walls near the Keplerian co-rotation radius. The repeating photometric dips have FWHM generally less than one day, depths almost always less than 15%, and periods (3<P<11 days) consistent with dust near the Keplerian co-rotation period. The flux dips vary considerably in their depth from epoch to epoch, but usually persist for…
We introduce a method of measuring a lower limit to the amplitude of surface differential rotation from high-precision, evenly sampled photometric time series. It is applied to main-sequence late-type stars whose optical flux modulation is dominated by starspots. An autocorrelation of the time series was used to select stars that allow an accurate determination of starspot rotation periods. A simple two-spot model was applied together with a Bayesian information criterion to preliminarily select intervals of the time series showing evidence of differential rotation with starspots of almost con…
