arXiv subjects

A. F. Lanza

Publications and source records attributed to A. F. Lanza.

At least 127 records · Page 7Linked to original sources

arXiv2017

HADES RV Programme with HARPS-N at TNG. VII. Rotation and activity of M-Dwarfs from time-series high-resolution spectroscopy of chromospheric indicators

We aim to investigate the presence of signatures of magnetic cycles and rotation on a sample of 71 early M-dwarfs from the HADES RV programme using high-resolution time-series spectroscopy of the Ca II H & K and Halpha chromospheric activity indicators, the radial velocity series, the parameters of the cross correlation function and the V-band photometry. We used mainly HARPS-N spectra, acquired over four years, and add HARPS spectra from the public ESO database and ASAS photometry light-curves as support data, extending the baseline of the observations of some stars up to 12 years. We provide log(R'hk) measurements for all the stars in the sample, cycle length measurements for 13 stars, rotation periods for 33 stars and we are able to measure the semi-amplitude of the radial velocity signal induced by rotation in 16 stars. We complement our work with previous results and confirm and refine the previously reported relationships between the mean level of chromospheric emission, measured by the log(R'hk), with the rotation period, and with the measured semi-amplitude of the activity induced radial velocity signal for early M-dwarfs. We searched for a possible relation between the measured rotation periods and the lengths of the magnetic cycle, finding a weak correlation between both quantities. Using previous v sin i measurements we estimated the inclinations of the star's poles to the line of sight for all the stars in the sample, and estimate the range of masses of the planets GJ 3998 b and c (2.5 - 4.9 Mearth and 6.3 - 12.5 Mearth), GJ 625 b (2.82 Mearth), GJ 3942 b (7.1 - 10.0 Mearth) and GJ 15A b (3.1 - 3.3 Mearth), assuming their orbits are coplanar with the stellar rotation.

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arXiv2017

Close-by planets and flares in their host stars

The interaction between the magnetic fields of late-type stars and their close-by planets may produce stellar flares as observed in active binary systems. However, in spite of several claims, conclusive evidence is still lacking. We estimate the magnetic energy available in the interaction using analytical models to provide an upper bound to the expected flare energy. We investigate three different mechanisms leading to magnetic energy release. The first two can release an energy up to $(0.2-1.2) B^{2}_{0} R^{3}/μ$, where $B_{0}$ is the surface field of the star, $R$ its radius, and $μ$ the magnetic permeability of the plasma. They operate in young active stars whose coronae have closed magnetic field lines up to the distance of their close-by planets that can trigger the energy release. The third mechanism operates in weakly or moderately active stars having a coronal field with predominantly open field lines at the distance of their planets. The released energy is of the order of $(0.002-0.1) B^{2}_{0} R^{3}/μ$ and depends on the ratio of the planetary to the stellar fields, thus allowing an indirect measurement of the former when the latter is known. We compute the released energy for different separations of the planet and different stellar parameters finding the conditions for the operation of the proposed mechanisms. An application to eight selected systems is presented. The computed energies and dissipation timescales are in agreement with flare observations in the eccentric system HD 17156 and in the circular systems HD 189733 and HD 179949. This kind of star-planet interaction can be unambiguously identified by the higher flaring frequency expected close to periastron in eccentric systems.

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arXiv2017

The GAPS Project: First Results

The GAPS programme is an Italian project aiming to search and characterize extra-solar planetary systems around stars with different characteristics (mass, metallicity, environment). GAPS was born in 2012, when single research groups joined in order to propose a long-term multi-purpose observing program for the exploitation of the extraordinary performances of the HARPS-N spectrograph, mounted at the Telescopio Nazionale Galileo. Now this group is a concerted community in which wide range of expertise and capabilities are shared in order to reach a more important role in the wider international context. We present the results achieved up to now from the GAPS radial velocity survey: they were obtained in both the two main objectives of the project, the planet detection and the characterization of already known exoplanetary systems. With GAPS we detected, for instance, the first confirmed binary system in which both components host planets (Desidera et al. 2014), the first planetary system around a star in an open cluster (Malavolta et al. 2016), a system of Super-Earths orbiting an M-dwarf star (Affer et al. 2016).

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arXiv2017

The GAPS Programme with HARPS-N@TNG XIV. Investigating giant planet migration history via improved eccentricity and mass determination for 231 transiting planets

We carried out a Bayesian homogeneous determination of the orbital parameters of 231 transiting giant planets (TGPs) that are alone or have distant companions; we employed DE-MCMC methods to analyse radial-velocity (RV) data from the literature and 782 new high-accuracy RVs obtained with the HARPS-N spectrograph for 45 systems over 3 years. Our work yields the largest sample of systems with a transiting giant exoplanet and coherently determined orbital, planetary, and stellar parameters. We found that the orbital parameters of TGPs in non-compact planetary systems are clearly shaped by tides raised by their host stars. Indeed, the most eccentric planets have relatively large orbital separations and/or high mass ratios, as expected from the equilibrium tide theory. This feature would be the outcome of high-eccentricity migration (HEM). The distribution of $α=a/a_R$, where $a$ and $a_R$ are the semi-major axis and the Roche limit, for well-determined circular orbits peaks at 2.5; this also agrees with expectations from the HEM. The few planets of our sample with circular orbits and $α>5$ values may have migrated through disc-planet interactions instead of HEM. By comparing circularisation times with stellar ages, we found that hot Jupiters with $a < 0.05$ au have modified tidal quality factors $10^{5} < Q'_p < 10^{9}$, and that stellar $Q'_s > 10^{6}-10^{7}$ are required to explain the presence of eccentric planets at the same orbital distance. As a by-product of our analysis, we detected a non-zero eccentricity for HAT-P-29; we determined that five planets that were previously regarded to have hints of non-zero eccentricity have circular orbits or undetermined eccentricities; we unveiled curvatures caused by distant companions in the RV time series of HAT-P-2, HAT-P-22, and HAT-P-29; and we revised the planetary parameters of CoRoT-1b.

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arXiv2017

The GAPS Programme with HARPS-N at TNG XV. A substellar companion around a K giant star identified with quasi-simultaneous HARPS-N and GIANO measurements

Context. Identification of planetary companions of giant stars is made difficult because of the astrophysical noise, that may produce radial velocity (RV) variations similar to those induced by a companion. On the other hand any stellar signal is wavelength dependent, while signals due to a companion are achromatic. Aims. Our goal is to determine the origin of the Doppler periodic variations observed in the thick disk K giant star TYC 4282-605-1 by HARPS-N at the Telescopio Nazionale Galileo (TNG) and verify if they can be due to the presence of a substellar companion. Methods. Several methods have been used to exclude the stellar origin of the observed signal including detailed analysis of activity indicators and bisector and the analysis of the photometric light curve. Finally we have conducted an observational campaign to monitor the near infrared (NIR) RV with GIANO at the TNG in order to verify whether the NIR amplitude variations are comparable with those observed in the visible. Results. Both optical and NIR RVs show consistent variations with a period at 101 days and similar amplitude, pointing to the presence of a companion orbiting the target. The main orbital properties obtained for our giant star with a derived mass of M=0.97+-0.03M_sun are M_Psini=10.78+-0.12MJ;P=101.54+-0.05days;e=0.28+-0.01 and a=0.422+-0.009AU. The chemical analysis shows a significant enrichment in the abundance of Nai, Mgi, Ali and S i while the rest of analyzed elements are consistent with the solar value demonstrating that the chemical composition corresponds with an old K giant (age = 10.1 Gyr) belonging to local thick disk. Conclusions. We conclude that the substellar companion hypothesis for this K giant is the best explanation for the observed periodic RV variation. This study also shows the high potential of multi-wavelength RV observations for the validation of planet candidates.

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arXiv2017

HADES RV Programme with HARPS-N at TNG: V. A super-Earth on the inner edge of the habitable zone of the nearby M-dwarf GJ 625

We report the discovery of a super-Earth orbiting at the inner edge of the habitable zone of the star GJ 625 based on the analysis of the radial-velocity (RV) time series from the HARPS-N spectrograph, consisting in 151 HARPS-N measurements taken over 3.5 yr. GJ 625 b is a planet with a minimum mass M sin $i$ of 2.82 $\pm$ 0.51 M$_{\oplus}$ with an orbital period of 14.628 $\pm$ 0.013 days at a distance of 0.078 AU of its parent star. The host star is the quiet M2 V star GJ 625, located at 6.5 pc from the Sun. We find the presence of a second radial velocity signal in the range 74-85 days that we relate to stellar rotation after analysing the time series of Ca II H\&K and H$α$ spectroscopic indicators, the variations of the FWHM of the CCF and and the APT2 photometric light curves. We find no evidence linking the short period radial velocity signal to any activity proxy.

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arXiv2017

Gaia Data Release 1: The variability processing & analysis and its application to the south ecliptic pole region

The ESA Gaia mission provides a unique time-domain survey for more than one billion sources brighter than G=20.7 mag. Gaia offers the unprecedented opportunity to study variability phenomena in the Universe thanks to multi-epoch G-magnitude photometry in addition to astrometry, blue and red spectro-photometry, and spectroscopy. Within the Gaia Consortium, Coordination Unit 7 has the responsibility to detect variable objects, classify them, derive characteristic parameters for specific variability classes, and provide global descriptions of variable phenomena. We describe the variability processing and analysis that we plan to apply to the successive data releases, and we present its application to the G-band photometry results of the first 14 months of Gaia operations that comprises 28 days of Ecliptic Pole Scanning Law and 13 months of Nominal Scanning Law. Out of the 694 million, all-sky, sources that have calibrated G-band photometry in this first stage of the mission, about 2.3 million sources that have at least 20 observations are located within 38 degrees from the South Ecliptic Pole. We detect about 14% of them as variable candidates, among which the automated classification identified 9347 Cepheid and RR Lyrae candidates. Additional visual inspections and selection criteria led to the publication of 3194 Cepheid and RR Lyrae stars, described in Clementini et al. (2016). Under the restrictive conditions for DR1, the completenesses of Cepheids and RR Lyrae stars are estimated at 67% and 58%, respectively, numbers that will significantly increase with subsequent Gaia data releases. Data processing within the Gaia Consortium is iterative, the quality of the data and the results being improved at each iteration. The results presented in this article show a glimpse of the exceptional harvest that is to be expected from the Gaia mission for variability phenomena. [abridged]

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arXiv2017

The GAPS Programme with HARPS-N at TNG. XIII. The orbital obliquity of three close-in massive planets hosted by dwarf K-type stars: WASP-43, HAT-P-20 and Qatar-2

In the framework of the GAPS project, we are conducting an observational programme aimed at the determination of the orbital obliquity of known transiting exoplanets. The targets are selected to probe the obliquity against a wide range of stellar and planetary physical parameters. We exploit high-precision radial velocity (RV) measurements, delivered by the HARPS-N spectrograph at the 3.6m Telescopio Nazionale Galileo, to measure the Rossiter-McLaughlin (RM) effect in RV time-series bracketing planet transits, and to refine the orbital parameters determinations with out-of-transit RV data. We also analyse new transit light curves obtained with several 1-2m class telescopes to better constrain the physical fundamental parameters of the planets and parent stars. We report here on new transit spectroscopic observations for three very massive close-in giant planets: WASP43b, HATP20b and Qatar2b orbiting dwarf K-type stars with effective temperature well below 5000K. We find lambda = 3.5pm6.8 deg for WASP43b and lambda = -8.0pm6.9 deg for HATP20b, while for Qatar2, our faintest target, the RM effect is only marginally detected, though our best-fit value lambda = 15pm20 deg is in agreement with a previous determination. In combination with stellar rotational periods derived photometrically, we estimate the true spin-orbit angle, finding that WASP43b is aligned while the orbit of HATP20b presents a small but significant obliquity (Psi=36 _{-12}^{+10} deg). By analyzing the CaII H&K chromospheric emission lines for HATP20 and WASP43, we find evidence for an enhanced level of stellar activity which is possibly induced by star-planet interactions.

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arXiv2017

The effect of ISM absorption on stellar activity measurements and its relevance for exoplanet studies

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 absorption. We present the effect of ISM absorption on activity measurements by varying several instrumental, stellar, and ISM parameters. We find that for relative velocities between the stellar and ISM lines smaller than 30-40 km/s and for ISM CaII column densities logN$_{\rm CaII}$>12, the ISM absorption has a significant influence on activity measurements. Direct measurements and three dimensional maps of the Galactic ISM absorption indicate that an ISM CaII column density of logN$_{\rm CaII}$=12 is typically reached by a distance of about 100 pc along most sight lines. In particular, for a Sun-like star lying at a distance greater than 100 pc, we expect a depression (bias) in the logR'$_{\rm HK}$ value larger than 0.05-0.1 dex, about the same size as the typical measurement and calibration uncertainties on this parameter. This work shows that the bias introduced by ISM absorption must always be considered when measuring activity for stars lying beyond 100 pc. We also consider the effect of multiple ISM absorption components. We discuss the relevance of this result for exoplanet studies.

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arXiv2016

The GAPS Programme with HARPS-N@TNG XII: Characterization of the planetary system around HD108874

In order to understand the observed physical and orbital diversity of extrasolar planetary systems, a full investigation of these objects and of their host stars is necessary. Within this field, one of the main purposes of the GAPS observing project with HARPS-N@TNG is to provide a more detailed characterisation of already known systems. In this framework we monitored the star, hosting two giant planets, HD108874, with HARPS-N for three years in order to refine the orbits, to improve the dynamical study and to search for additional low-mass planets in close orbits. We subtracted the radial velocity (RV) signal due to the known outer planets, finding a clear modulation of 40.2 d period. We analysed the correlation between RV residuals and the activity indicators and modelled the magnetic activity with a dedicated code. Our analysis suggests that the 40.2 d periodicity is a signature of the rotation period of the star. A refined orbital solution is provided, revealing that the system is close to a mean motion resonance of about 9:2, in a stable configuration over 1 Gyr. Stable orbits for low-mass planets are limited to regions very close to the star or far from it. Our data exclude super-Earths with Msin i \gtrsim 5 M_Earth within 0.4 AU and objects with Msin i \gtrsim 2 M_Earth with orbital periods of a few days. Finally we put constraints on the habitable zone of the system, assuming the presence of an exomoon orbiting the inner giant planet.

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arXiv2016

The HADES RV Programme with HARPS-N@TNG II. Data treatment and simulations

The distribution of exoplanets around low-mass stars is still not well understood. Such stars, however, present an excellent opportunity of reaching down to the rocky and habitable planet domains. The number of current detections used for statistical purposes is still quite modest and different surveys, using both photometry and precise radial velocities, are searching for planets around M dwarfs. Our HARPS-N red dwarf exoplanet survey is aimed at the detection of new planets around a sample of 78 selected stars, together with the subsequent characterization of their activity properties. Here we investigate the survey performance and strategy. From 2700 observed spectra, we compare the radial velocity determinations of the HARPS-N DRS pipeline and the HARPS-TERRA code, we calculate the mean activity jitter level, we evaluate the planet detection expectations, and we address the general question of how to define the strategy of spectroscopic surveys in order to be most efficient in the detection of planets. We find that the HARPS-TERRA radial velocities show less scatter and we calculate a mean activity jitter of 2.3 m/s for our sample. For a general radial velocity survey with limited observing time, the number of observations per star is key for the detection efficiency. In the case of an early M-type target sample, we conclude that approximately 50 observations per star with exposure times of 900 s and precisions of about 1 m/s maximizes the number of planet detections.

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arXiv2016

The HADES RV Programme with HARPS-N@TNG. III. Flux-flux and activity-rotation relationships of early-M dwarfs

(Abridged) Understanding stellar activity in M dwarfs is crucial for the physics of stellar atmospheres as well as for ongoing radial velocity exoplanet programmes. Despite the increasing interest in M dwarfs, our knowledge of the chromospheres of these stars is far from being complete. We aim to test whether the relations between activity, rotation, and stellar parameters and flux-flux relationships also hold for early-M dwarfs on the main-sequence. We analyse in an homogeneous and coherent way a well defined sample of 71 late-K/early-M dwarfs that are currently being observed in the framework of the HArps-n red Dwarf Exoplanet Survey (HADES). Rotational velocities are derived using the cross-correlation technique while emission flux excesses in the Ca II H & K and Balmer lines from Halpha up to Hepsilon are obtained by using the spectral subtraction technique. The relationships between the emission excesses and the stellar parameters are studied. Relations between pairs of fluxes of different chromospheric lines are also studied. We find that the strength of the chromospheric emission in the Ca II H & K and Balmer lines is roughly constant for stars in the M0-M3 spectral range. Our data suggest that a moderate but significant correlation between activity and rotation might be present as well as a hint of kinematically selected young stars showing higher levels of emission. We find our sample of M dwarfs to be complementary in terms of chromospheric and X-ray fluxes with those of the literature, extending the analysis of the flux-flux relationships to the very low flux domain. Our results agree with previous works suggesting that the activity-rotation-age relationship known to hold for solar-type stars also applies to early-M dwarfs. We also confirm previous findings that the field stars which deviate from the bulk of the empirical flux-flux relationships show evidence of youth.

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arXiv2016

The HADES RV Programme with HARPS-N@TNG IV. Time resolved analysis of the Ca ii H&K and Hα chromospheric emission of low-activity early-type M dwarfs

M dwarfs are prime targets for planet search programs, particularly of those focused on the detection and characterization of rocky planets in the habitable zone. Understanding their magnetic activity is important because it affects our ability to detect small planets, and it plays a key role in the characterization of the stellar environment. We analyze observations of the Ca II H&K and Hα lines as diagnostics of chromospheric activity for low-activity early-type M dwarfs. We analyze the time series of spectra of 71 early-type M dwarfs collected for the HADES project for planet search purposes. The HARPS-N spectra provide simultaneously the H&K doublet and the Hα line. We develop a reduction scheme able to correct the HARPS-N spectra for instrumental and atmospheric effects, and to provide flux-calibrated spectra in units of flux at the stellar surface. The H&K and Hα fluxes are compared with each other, and their variability is analyzed. We find that the H and K flux excesses are strongly correlated with each other, while the Hα flux excess is generally less correlated with the H&K doublet. We also find that Hα emission does not increase monotonically with the H&K line flux, showing some absorption before being filled in by chromospheric emission when H&K activity increases. Analyzing the time variability of the emission fluxes, we derive a tentative estimate of the rotation period (of the order of a few tens of days) for some of the program stars, and the typical lifetime of chromospheric active regions (a few stellar rotations). Our results are in good agreement with previous studies. In particular, we find evidence that the chromospheres of early-type M dwarfs could be characterized by different filaments coverage, affecting the formation mechanism of the Hα line. We also show that chromospheric structure is likely related to spectral type.

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arXiv2016

New Suns in the Cosmos II: Differential rotation in Kepler Sun-like stars

The present study reports the discovery of Sun-like stars, namely main-sequence stars with $T_{\rm eff}$, $\log g$ and rotation periods $P_{rot}$ similar to solar values, presenting evidence of surface differential rotation. An autocorrelation of the time series was used to select stars presenting photometric signal stability from a sample of 881 stars with light curves collected by the $Kepler$ space-borne telescope, in which we have identified 17 stars with stable signals. A simple two-spot model together with a Bayesian information criterion were applied to these stars in the search for indications of differential rotation; in addition, for all 17 stars, it was possible to compute the spot rotation period $P$, the mean values of the individual spot rotation periods and their respective colatitudes, and the relative amplitude of the differential rotation.

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arXiv2016

Disentangling planetary and stellar activity features in the CoRoT-2 light curve

[Abridged] Context. Stellar activity is an important source of systematic errors and uncertainties in the characterization of exoplanets. Most of the techniques used to correct for this activity focus on an ad hoc data reduction. Aims. We have developed a software for the combined fit of transits and stellar activity features in high-precision long-duration photometry. Our aim is to take advantage of the modelling to derive correct stellar and planetary parameters, even in the case of strong stellar activity. Methods. We use an analytic approach to model the light curve. The code KSint, modified by adding the evolution of active regions, is implemented into our Bayesian modelling package PASTIS. The code is then applied to the light curve of CoRoT-2. The light curve is divided in segments to reduce the number of free parameters needed by the fit. We perform a Markov chain Monte Carlo analysis in two ways. In the first, we perform a global and independent modelling of each segment of the light curve, transits are not normalized and are fitted together with the activity features, and occulted features are taken into account during the transit fit. In the second, we normalize the transits with a model of the non-occulted activity features, and then we apply a standard transit fit, which does not take the occulted features into account. Results. Our model recovers the activity features coverage of the stellar surface and different rotation periods for different features. We find variations in the transit parameters of different segments and show that they are likely due to the division applied to the light curve. Neglecting stellar activity or even only bright spots while normalizing the transits yields a $\sim 1.2σ$ larger and $2.3σ$ smaller transit depth, respectively. The stellar density also presents up to $2.5σ$ differences depending on the normalization technique...

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arXiv2016

The HADES RV Programme with HARPS-N@TNG - GJ 3998: An early M-dwarf hosting a system of Super-Earths

Context. M dwarfs are considered ideal targets for Doppler radial velocity searches. Nonetheless, the statistics of frequency of low-mass planets hosted by low mass stars remains poorly constrained. Aims. Our M-dwarf radial velocity monitoring with HARPS-N can provide a major contribution to the widening of the current statistics through the in-depth analysis of accurate radial velocity observations in a narrow range of spectral sub-types (79 stars, between dM0 to dM3). Spectral accuracy will enable us to reach the precision needed to detect small planets with a few earth masses. Our survey will bring a contribute to the surveys devoted to the search for planets around M-dwarfs, mainly focused on the M-dwarf population of the northern emisphere, for which we will provide an estimate of the planet occurence. Methods. We present here a long duration radial velocity monitoring of the M1 dwarf star GJ 3998 with HARPS-N to identify periodic signals in the data. Almost simultaneous photometric observations were carried out within the APACHE and EXORAP programs to characterize the stellar activity and to distinguish from the periodic signals those due to activity and to the presence of planetary companions. Results. The radial velocities have a dispersion in excess of their internal errors due to at least four superimposed signals, with periods of 30.7, 13.7, 42.5 and 2.65 days. The analysis of spectral indices based on Ca II H & K and Halpha lines demonstrates that the periods of 30.7 and 42.5 days are due to chromospheric inhomogeneities modulated by stellar rotation and differential rotation. The shorter periods of 13.74 +/- 0.02 d and 2.6498 +/- 0.0008 d are well explained with the presence of two planets, with minimum masses of 6.26 +/- 0.79 MEarth and 2.47 +/- 0.27 MEarth and distances of 0.089 AU and 0.029 AU from the host, respectively.

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arXiv2016

Tides and angular momentum redistribution inside low-mass stars hosting planets: a first dynamical model

We introduce a general mathematical framework to model the internal transport of angular momentum in a star hosting a close-in planetary/stellar companion. By assuming that the tidal and rotational distortions are small and that the deposit/extraction of angular momentum induced by stellar winds and tidal torques are redistributed solely by an effective eddy-viscosity that depends on the radial coordinate, we can formulate the model in a completely analytic way. It allows us to compute simultaneously the evolution of the orbit of the companion and of the spin and the radial differential rotation of the star. An illustrative application to the case of an F-type main-sequence star hosting a hot Jupiter is presented. The general relevance of our model to test more sophisticated numerical dynamical models and to study the internal rotation profile of exoplanet hosts, submitted to the combined effects of tides and stellar winds, by means of asteroseismology are discussed.

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arXiv2016

Spot modelling of periodic weak-line T Tauri stars observed by CoRoT in NGC 2264

The space telescope CoRoT has provided light curves of T Tauri stars belonging to the star-forming region of NGC 2264 with unprecedented continuity and precision in the framework of a coordinated multi-wavelength observational project. We perform spot modelling of the optical light curves of five weak-line T Tauri stars whose variability is dominated by starspots. We apply two-spot and evolving single spot models in the framework of a Bayesian Monte Carlo Markov Chain approach to derive the a posteriori distribution of the starspot parameters and the inclination of the star rotation axis. We focus on the rotation periods of the spots that can provide evidence for differential rotation in those stars. We find meaningful results in the case of three stars with an inclination higher than 50 deg and a slow variation of the light curve amplitude. The relative difference of the spot rotation periods ranges from 0.02 to 0.05 that is 3-10 times larger than the amplitude of the differential rotation found in similar stars with Doppler imaging techniques. We conclude that the intrinsic starspot evolution, although very slow, has a significant impact on the determination of the differential rotation by means of our spot modelling approach. We estimate typical timescales for the evolution of the starspot pattern between about 20 and 50 rotation periods in our stars.

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