Starspot Distributions Research Articles

Localizing Stellar Activity on Low-mass Stars with the Transiting Exoplanet Survey Satellite

Magnetic reconnection is the underlying cause of stellar flares which are linked to regions of high magnetic activity, like star spots. To understand trends in stellar activity, we need to study how it is heightened by rapid rotation and deep convection in young low-mass stars. We analyze light curves of such stars observed by the Transiting Exoplanet Survey Satellite to investigate trends in flare timing with starspot modulation signals. Trends in flare properties and spot modulation can provide a means to “localize” which face of a star flares more frequently and better understand their association with active regions. We present an analysis of light curves from M and K dwarfs with no companions from five nearby and young moving groups spanning ages ∼20–150 Myr. We discuss a technique to analyze the distribution of flares and star spots and describe our results, which reveal a tentative correlation.

Distribution of Cool Starspots on the Surface of the Red Dwarf V647 Her

An analysis of photometric observations of the star V647 Her (M3.5V) obtained at the 1.25-m telescope of the Crimean Astrophysical Observatory in 2022 is presented. The presence of a low-amplitude variability in brightness of the star with a period of 20.69 d, found from observations in 2019 was confirmed. It is shown that as the brightness decreases, the star becomes redder. The observed kind of photometric variability is due to the presence of cool spots on the surface of the star and rotational modulation of brightness with a full amplitude of no more than 0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{{\ ext{m}}}_{.}$$\\end{document}05. We perform a comparison of the photometric results obtained in 2019, 2022, and 2004. The locations of starspots at different epochs were determined from the analysis of phase curves. The distribution of starspots has been maintained for 40–100 days. Starspot parameters were estimated in the framework of the zonal model. The temperature of starspots is 2700–2800 K. The area they occupied in 2004 is 15% of the total surface area of the star. According to the 2019 and 2022 data, it increases up to 30%. The seasonal redistribution of starspots leads to the difference between the spottedness of hemispheres, which is less than 2%.

G 68-34: A Double-lined M-dwarf Eclipsing Binary in a Hierarchical Triple System

Using high-resolution spectra from the Tillinghast Reflector Echelle Spectrograph and photometry from sector 56 of the Transiting Exoplanet Survey Satellite, we report that the nearby M dwarf G 68-34 is a double-lined eclipsing binary. The pair is spin–orbit synchronized with a period of 0.655 days. The light curve shows significant spot modulation with a larger photometric amplitude than that of the grazing eclipses. We perform a joint fit to the spectroscopic and photometric data, obtaining masses of 0.3280 ± 0.0034M ⊙ and 0.3207 ± 0.0036M ⊙ and radii of 0.345 ± 0.014R ⊙ and 0.342 ± 0.014R ⊙ after marginalizing over unknowns in the starspot distribution. This system adds to the small but growing population of fully convective M dwarfs with precisely measured masses and radii that can be used to test models of stellar structure. The pair also has a white-dwarf primary at 9″ separation, with the system known to be older than 5 Gyr from the white-dwarf cooling age. The binarity of G 68–34 confirms our hypothesis from Pass et al.: in that work, we noted that G 68-34 was both rapidly rotating and old, highly unusual given our understanding of the spin-down of M dwarfs, and that a close binary companion may be responsible.

An investigation of the magnetic activity of HD 134319 based on TESS photometry and ground-based spectroscopy

ABSTRACT We present an analysis of the starspot properties and chromospheric activity on HD 134319 using high-precision photometry by Transiting Exoplanet Survey Satellite (TESS) in sectors 14–16 (T1) and 21–23 (T2) and high-resolution spectroscopy by the ELODIE spectrograph on 1.93-m telescope of Observatoire de Haute-Provence (OHP/ELODIE) and the High Resolution Echelle Spectrometer on Keck 10-m telescope of W. M. Keck Observatory (Keck/HIRES) during the years 1995–2013. We applied a two-spot model with generalized Lomb–Scargle (GLS) periodogram determined period of P = 4.436391 ± 0.00137 d to model chunks sliding over TESS light curve. We also measured the relative equivalent widths of Ca ii H and K, Hβ and Hα emissions by subtracting the overall spectrum from individual spectra. It was found that a two-spot configuration, namely a primary, slowly evolving and long-lasting spot (P) plus a secondary, rapidly evolving spot (S), was capable of explaining the data, although the actual starspot distribution cannot be derived from the collected data. Despite the spot radius–latitude degeneracy revealed in the best-fitting solutions, a sudden alternation between P and S radii followed by a gradual decrease of S in T1 and a decrease of both P and S from T1 to T2 were significant, corresponding to the evolution of magnetic activity. In addition, S revealed rotation and an oscillatory longitude migration synchronized to P in T1, but had a much larger migration than P in T2. This might indicate the evolution of the internal magnetic configuration. Chromospheric activity indicators were found to be tightly correlated with each other and revealed rotational modulation as well as a long-term decrease of emissions, implying the existence and evolution of magnetic activity on HD 134319.

Mapping Stellar Surfaces. I. Degeneracies in the Rotational Light-curve Problem

Abstract Thanks to missions like Kepler and TESS, we now have access to tens of thousands of high-precision, fast-cadence, and long-baseline stellar photometric observations. In principle, these light curves encode a vast amount of information about stellar variability and, in particular, the distribution of starspots and other features on their surfaces. Unfortunately, the problem of inferring stellar surface properties from a rotational light curve is famously ill-posed, as it often does not admit a unique solution. Inferences about the number, size, contrast, and location of spots can therefore depend very strongly on the assumptions of the model, the regularization scheme, or the prior. The goal of this paper is twofold: (1) to explore the various degeneracies affecting the stellar light-curve “inversion” problem and their effect on what can and cannot be learned from a stellar surface, given unresolved photometric measurements, and (2) to motivate ensemble analyses of the light curves of many stars at once as a powerful data-driven alternative to common priors adopted in the literature. We further derive novel results on the dependence of the null space on stellar inclination and limb darkening and show that single-band photometric measurements cannot uniquely constrain quantities like the total spot coverage without the use of strong priors. This is the first in a series of papers devoted to the development of novel algorithms and tools for the analysis of stellar light curves and spectral time series, with the explicit goal of enabling statistically robust inferences about their surface properties.

Simulations of starspot anomalies within TESS exoplanetary transit light curves

Aims. We determine the starspot detection rate in exoplanetary transit light curves for M and K dwarf stars observed by the Transiting Exoplanet Survey Satellite (TESS) using various starspot filling factors and starspot distributions. Methods. We used 3.6 × 109 simulations of planetary transits around spotted stars using the transit-starspot model PRISM. The simulations cover a range of starspot filling factors using one of three distributions: uniform, polar-biased, and mid-latitude. After construction of the stellar disc and starspots, we checked the transit cord for starspots and examined the change in flux of each starspot to determine whether or not a starspot anomaly would be detected. The results were then compared to predicted planetary detections for TESS. Results. The results show that for the case of a uniform starspot distribution, 64 ± 9 M dwarf and 23 ± 4 K dwarf transit light curves observed by TESS will contain a starspot anomaly. This reduces to 37 ± 6 M dwarf and 12 ± 2 K dwarf light curves for a polar-biased distribution and 47 ± 7 M dwarf and 21 ± 4 K dwarf light curves for a mid-latitude distribution. Conclusions. Currently there are only 17 M dwarf and 10 K dwarf confirmed planetary systems from TESS, none of which are confirmed as showing starspot anomalies. All three starspot distributions can explain the current trend. However, with such a small sample, a firm conclusion cannot be made at present. In the coming years when more TESS M and K dwarf exoplanetary systems have been detected and characterised, it will be possible to determine the dominant starspot distribution.

Observing and modelling the young solar analogue EK Draconis: starspot distribution, elemental abundances, and evolutionary status

ABSTRACT Observations and modelling of stars with near-solar masses in their early phases of evolution are critical for a better understanding of how dynamos of solar-type stars evolve. We examine the chemical composition and the spot distribution of the pre-main-sequence solar analogue EK Dra. Using spectra from the HERMES Spectrograph (La Palma), we obtain the abundances of 23 elements with respect to the solar ones, which lead to a [Fe/H] = 0.03, with significant overabundance of Li and Ba. The s-process elements Sr, Y, and Ce are marginally overabundant, while Co, Ni, Cu, Zn are marginally deficient compared to solar abundances. The overabundance of Ba is most likely due to the assumption of depth-independent microturbulent velocity. Li abundance is consistent with the age and the other abundances may indicate distinct initial conditions of the pre-stellar nebula. We estimate a mass of 1.04 M⊙ and an age of $27^{+11}_{-8}$ Myr using various spectroscopic and photometric indicators. We study the surface distribution of dark spots, using 17 spectra collected during 15 nights using the CAFE Spectrograph (Calar Alto). We also conduct flux emergence and transport (FEAT) simulations for EK Dra’s parameters and produce 15-d-averaged synoptic maps of the likely starspot distributions. Using Doppler imaging, we reconstruct the surface brightness distributions for the observed spectra and FEAT simulations, which show overall agreement for polar and mid-latitude spots, while in the simulations there is a lack of low-latitude spots compared to the observed image. We find indications that cross-equatorial extensions of mid-latitude spots can be artefacts of the less visible southern-hemisphere activity.

The Information Content in Analytic Spot Models of Broadband Precision Light Curves. II. Spot Distributions and Lifetimes and Global and Differential Rotation

Abstract With the advent of space-based precision photometry missions, the quantity and quality of starspot light curves has greatly increased. This paper presents a large number of starspot models and their resulting light curves to (1) better determine light-curve metrics and methods that convey useful physical information and (2) understand how the underlying degeneracies of the translation from physical starspot distributions to the resulting light curves obscure that information. We explore models of relatively active stars at several inclinations while varying the number of (dark) spots, random spot distributions in position and time, timescales of growth and decay, and differential rotation. We examine the behavior of absolute and differential variations of individual intensity dips and overall light curves and demonstrate how complex spot distributions and behaviors result in light curves that typically exhibit only one or two dips per rotation. Unfortunately, simplistic “one- or two-spot” or “active longitude” descriptions or modeling of light curves can often be highly misleading. We also show that short “activity cycles” can easily be simply due to random processes. It turns out to be quite difficult to disentangle the competing effects of spot lifetime and differential rotation, but under most circumstances, spot lifetime is the more influential of the two. Many of the techniques tried to date only work when spots live for many rotations. These include autocorrelation degradation for spot lifetimes and periodograms for both global and differential rotation. Differential rotation may be nearly impossible to accurately infer from light curves alone unless spots live for many rotations. The Sun and solar-type stars its age or older are unfortunately the most difficult type of case. Further work is needed to have increased confidence in light-curve inferences.

Hunt for Starspots in HARPS Spectra of G and K Stars

Abstract We present a method for detecting starspots on cool stars using the cross-correlation function (CCF) of high-resolution molecular spectral templates applied to archival high-resolution spectra of G and K stars observed with the High Accuracy Radial Velocity Planet Searcher (HARPS)/HARPS-N. We report nondetections of starspots on the Sun even when the Sun was spotted, the solar twin 18 Scorpii, and the very spotted Sun-like star HAT-P-11, suggesting that Sun-like starspot distributions will be invisible to the CCF technique, and should not produce molecular absorption signals that might be confused for signatures of exoplanet atmospheres. We detect strong TiO absorption in the T Tauri K-dwarfs LkCa 4 and AA Tau, consistent with significant coverage by cool regions. We show that despite the nondetections, the technique is sensitive to relatively small spot coverages on M dwarfs and large starspot areas on Sun-like stars.

A Relationship between Stellar Age and Spot Coverage

Abstract We investigate starspot distributions consistent with space-based photometry of F, G, and K stars in six stellar associations ranging in age from 10 Myr to 4 Gyr. We show that a simple light-curve statistic called the “smoothed amplitude” is proportional to stellar age as t −1/2, following a Skumanich-like spin-down relation. We marginalize over the unknown stellar inclinations by forward modeling the ensemble of light curves for direct comparison with the Kepler, K2, and TESS photometry. We sample the posterior distributions for spot coverage with approximate Bayesian computation. We find typical spot coverages in the range 1%–10%, which decrease with increasing stellar age. The spot coverage is proportional to t n where n = −0.37 ± 0.16, also statistically consistent with a Skumanich-like t −1/2 decay of starspot coverage with age. We apply two techniques to estimate the spot coverage of young exoplanet-hosting stars likely to be targeted for transmission spectroscopy with the James Webb Space Telescope, and estimate the bias in exoplanet radius measurements due to varying starspot coverage.

Forward modelling of brightness variations in Sun-like stars

Context. The latitudinal distribution of starspots deviates from the solar pattern with increasing rotation rate. Numerical simulations of magnetic flux emergence and transport can help model the observed stellar activity patterns and the associated brightness variations. Aims. We set up a composite model for the processes of flux emergence and transport on Sun-like stars to simulate stellar brightness variations for various levels of magnetic activity and rotation rates. Methods. Assuming that the distribution of magnetic flux at the base of the convection zone follows solar scaling relations, we calculate the emergence latitudes and tilt angles of bipolar regions at the surface for various rotation rates, using thin-flux-tube simulations. Taking these two quantities as input to a surface flux transport (SFT) model, we simulate the diffusive-advective evolution of the radial field at the stellar surface, including effects of active region nesting. Results. As the rotation rate increases, (1) magnetic flux emerges at higher latitudes and an inactive gap opens around the equator, reaching a half-width of 20° for 8 Ω⊙; and (2) the tilt angles of freshly emerged bipolar regions show stronger variations with latitude. Polar spots can form at 8 Ω⊙ by accumulation of follower-polarity flux from decaying bipolar regions. From 4 Ω⊙ to 8 Ω⊙, the maximum spot coverage changes from 3 to 20%, respectively, compared to 0.4% in the solar model. Nesting of activity can lead to strongly non-axisymmetric spot distributions. Conclusions. On Sun-like stars rotating at 8 Ω⊙ (Prot ≃ 3 days), polar spots can form, owing to higher levels of flux emergence rate and tilt angles. Defining spots by a threshold field strength yields global spot coverages that are roughly consistent with stellar observations.

Statistical properties of starspots on solar-type stars and their correlation with flare activity

AbstractWe analyzed the statistical properties of starspots on solar-type stars and the correlation between properties of starspots and flare activity using observations from the Kepler mission. We found the size distribution of starspots on solar-type stars shows the power-law distribution and both size distributions of starspots on slowly-rotating solar-type stars and of relatively large sunspots are roughly lie on the same power-law line. We also found that the frequency-energy distributions for superflares and solar flares from spots with different sizes are the same for solar-type stars and the Sun. These results suggest that the magnetic activity on solar-type stars and that on the Sun are caused by the same physical processes

Star-spot distributions and chromospheric activity on the RS CVn type eclipsing binary SV Cam

Using a time series of high-resolution spectra and high-quality multi-colour photometry, we reconstruct surface maps of the primary component of the RS CVn type rapidly rotating eclipsing binary, SV Cam (F9V + K4V). We measure a mass ratio, q, of 0.641(2) using our highest quality spectra and obtain surface brightness maps of the primary component, which exhibit predominantly high-latitude spots located between 60-70-degree latitudes with a mean filling factor of about 35%. This is also indicated by the R-band light curve inversion, subjected to rigourous numerical tests. The spectral subtraction of the H-alpha line reveals strong activity of the secondary component. The excess H-alpha absorption detected near the secondary minimum hints to the presence of cool material partially obscuring the primary star. The flux ratios of Ca II IRT excess emission indicate that the contribution of chromospheric plage regions associated with star-spots is dominant, even during the passage of the filament-like absorption feature.

Surprisingly different star-spot distributions on the near equal-mass equal-rotation-rate stars in the M dwarf binary GJ 65 AB

We aim to understand how stellar parameters such as mass and rotation impact the distribution of starspots on the stellar surface. To this purpose, we have used Doppler imaging to reconstruct the surface brightness distributions of three fully convective M dwarfs with similar rotation rates. We secured high cadence spectral time series observations of the 5.5 AU separation binary GJ 65, comprising GJ 65A (M5.5V, Prot = 0.24 d) and GJ 65B (M6V, Prot = 0.23 d). We also present new observations of GJ 791.2A (M4.5V, Prot = 0.31 d). Observations of each star were made on two nights with UVES, covering a wavelength range from 0.64 - 1.03 microns. The time series spectra reveal multiple line distortions, which we interpret as cool starspots and which are persistent on both nights suggesting stability on the timescale of 3 days. Spots are recovered with resolutions down to 8.3 degs at the equator. The global spot distributions for GJ 791.2A are similar to observations made a year earlier. Similar high latitude and circumpolar spot structure is seen on GJ791.2A and GJ 65A. However, they are surprisingly absent on GJ 65B, which instead reveals more extensive, larger, spots concentrated at intermediate latitudes. All three stars show small amplitude latitude-dependent rotation that is consistent with solid body rotation. We compare our measurements of differential rotation with previous Doppler imaging studies and discuss the results in the wider context of other observational estimates and recent theoretical predictions.

Starspot activity and superflares on solar-type stars

Abstract We analyze the correlation between starspots and superflares on solar-type stars using observations from the Kepler mission. The analysis shows that the observed fraction of stars with superflares decreases as the rotation period increases and as the amplitude of photometric variability associated with rotation decreases. We found that the fraction of stars with superflares among the stars showing large-amplitude rotational variations, which are thought to be the signature of the large starspots, also decreases as the rotation period increases. The small fraction of superflare stars among the stars with large starspots in the longer-period regime suggests that some of the stars with large starspots show a much lower flare activity than the superflare stars with the same spot area. Assuming simple relations between spot area and lifetime and between spot temperature and photospheric temperature, we compared the size distribution of large starspot groups on slowly rotating solar-type stars with that of sunspot groups. The size distribution of starspots shows the power-law distribution and the size distribution of larger sunspots lies on this power-law line. We also found that frequency–energy distributions for flares originating from spots with different sizes are the same for solar-type stars with superflares and the Sun. These results suggest that the magnetic activity we observe on solar-type stars with superflares and on the Sun is caused by the same physical processes.

General Model for Light Curves of Chromospherically Active Binary Stars∗

Abstract The starspots on the surface of many chromospherically active binary stars concentrate on long-lived active longitudes separated by 180°. Shifts in activity between these two longitudes, the “flip-flop” events, have been observed in single stars like FK Comae and binary stars like σ Geminorum. Recently, interferometry has revealed that ellipticity may at least partly explain the flip-flop events in σ Geminorum. This idea was supported by the double-peaked shape of the long-term mean light curve of this star. Here we show that the long-term mean light curves of 14 chromospherically active binaries follow a general model that explains the connection between orbital motion, changes in starspot distribution, ellipticity, and flip-flop events. Surface differential rotation is probably weak in these stars, because the interference of two constant period waves may explain the observed light curve changes. These two constant periods are the active longitude period and the orbital period . We also show how to apply the same model to single stars, where only the value of P act is known. Finally, we present a tentative interference hypothesis about the origin of magnetic fields in all spectral types of stars.

Learning about the latitudinal distribution of starspots through the periodogram analysis of photometric data

Starspots are cooler and darker than the stellar surface. Therefore, the emitted flux of a star changes when spots are visible on its surface. The presence of spots together with the stellar rotation leads to a periodic modulation on the light curve. By studying that modulation one can then learn about the stellar rotation and also magnetic activity. Recently, Reinhold & Arlt (2015) proposed a method based on the analysis of the Lomb Scargle periodogram of the light curve to identify the sign of the differential rotation, i.e. whether the equator rotates faster than the poles or the opposite. We have been studying in detail the spots' impact on the light curve and on the resulting periodogram. We find that, under some conditions, the periodogram can actually provide an estimate of the true spot latitudes and/or the stellar inclination angle. Moreover, we find that the impact of the spot on the ratio between the heights of the second and first harmonics of the main peaks in the periodogram can be described by a single parameter, the visibility time of the spot. Finally, we also identify possible sources of false positives/negatives for the sign of the differential rotation.

Recovering planet radial velocity signals in the presence of starspot activity in fully convective stars

Accounting for stellar activity is a crucial component of the search for ever-smaller planets orbiting stars of all spectral types. We use Doppler imaging methods to demonstrate that starspot induced radial velocity variability can be effectively reduced for moderately rotating, fully convective stars. Using starspot distributions extrapolated from sunspot observations, we adopt typical M dwarf starspot distributions with low contrast spots to synthesise line profile distortions. The distortions are recovered using maximum entropy regularised fitting and the corresponding stellar radial velocities are measured. The procedure is demonstrated for a late-M star harbouring an orbiting planet in the habitable zone. The technique is effective for stars with vsini = 1-10 km/s, reducing the stellar noise contribution by factors of nearly an order of magnitude. With a carefully chosen observing strategy, the technique can be used to determine the stellar rotation period and is robust to uncertainties such as unknown stellar inclination. While demonstrated for late-type M stars, the procedure is applicable to all spectral types.

Anti-solar differential rotation on the active sub-giant HU Virginis,

Measuring surface differential rotation (DR) on different types of stars is important when characterizing the underlying stellar dynamo. It has been suggested that anti-solar DR laws can occur when strong meridional flows exist. We aim to investigate the differential surface rotation on the primary star of the RS CVn binary HU Vir by tracking its starspot distribution as a function of time. We also aim to recompute and update the values for several system parameters of the triple system HU Vir (close and wide orbits). Time-series high-resolution spectroscopy for four continuous months was obtained with the 1.2-m robotic STELLA telescope. Nine consecutive Doppler images were reconstructed from these data, using our line-profile inversion code iMap. An image cross-correlation method was applied to derive the surface differential-rotation law for HU Vir. New orbital elements for the close and the wide orbits were computed using our new STELLA radial velocities (RVs) combined with the RV data available in the literature. Photometric observations were performed with the Amadeus Automatic Photoelectric Telescope (APT), providing contemporaneous Johnson-Cousins $V$ and $I$ data for approximately 20 years. This data was used to determine the stellar rotation period and the active longitudes. We confirm anti-solar DR with a surface shear parameter $\alpha$ of -0.029 $\pm$ 0.005 and -0.026 $\pm$ 0.009, using single-term and double-term differential rotation laws, respectively. The best fit is achieved assuming a solar-like double-term law with a lap time of $\approx$ 400 d. Our orbital solutions result in a period of 10.387678 $\pm$ 0.000003 days for the close orbit and 2726 $\pm$ 7 d ($\approx$ 7.5 yr) for the wide orbit. A Lomb-Scarge (L-S) periodogram of the pre-whitened $V$-band data reveals a strong single peak providing a rotation period of 10.391 $\pm$ 0.008 d.

WHY ARE RAPIDLY ROTATING M DWARFS IN THE PLEIADES SO (INFRA)RED? NEW PERIOD MEASUREMENTS CONFIRM ROTATION-DEPENDENT COLOR OFFSETS FROM THE CLUSTER SEQUENCE

ABSTRACT Stellar rotation periods (P rot) measured in open clusters have proved to be extremely useful for studying stars’ angular momentum content and rotationally driven magnetic activity, which are both age- and mass-dependent processes. While P rot measurements have been obtained for hundreds of solar-mass members of the Pleiades, measurements exist for only a few low-mass (<0.5 M ⊙) members of this key laboratory for stellar evolution theory. To fill this gap, we report P rot for 132 low-mass Pleiades members (including nearly 100 with M ≤ 0.45 M ⊙), measured from photometric monitoring of the cluster conducted by the Palomar Transient Factory in late 2011 and early 2012. These periods extend the portrait of stellar rotation at 125 Myr to the lowest-mass stars and re-establish the Pleiades as a key benchmark for models of the transport and evolution of stellar angular momentum. Combining our new P rot with precise BVIJHK photometry reported by Stauffer et al. and Kamai et al., we investigate known anomalies in the photometric properties of K and M Pleiades members. We confirm the correlation detected by Kamai et al. between a star's P rot and position relative to the main sequence in the cluster's color–magnitude diagram. We find that rapid rotators have redder (V − K) colors than slower rotators at the same V, indicating that rapid and slow rotators have different binary frequencies and/or photospheric properties. We find no difference in the photometric amplitudes of rapid and slow rotators, indicating that asymmetries in the longitudinal distribution of starspots do not scale grossly with rotation rate.