We consider the lifetimes of spots on the Sun and other stars from the standpoint of magnetic diffusion. While normal magnetic diffusivity predicts lifetimes of sunspots that are too large by at least two orders of magnitude, turbulent magnetic diffusivity accounts for both the functional form of the solar empirical spot-lifetime relation and for the observed sunspot lifetimes, provided that the relevant diffusion length is the supergranule size. Applying this relation to other stars, the value of turbulent diffusivity depends almost entirely on supergranule size, with very weak dependence on other variables such as magnetic field strength and density. Overall, the best observational data for other stars is consistent with the extension of the solar relation provided that stellar supergranule sizes for some stars are significantly larger than they are on the Sun.
Disintegration of sunspots (and starspots) by fluxtube erosion, originally proposed by Simon and Leighton, is considered. A moving boundary problem is formulated for a nonlinear diffusion equation that describes the sunspot magnetic field profile. Explicit expressions for the sunspot decay rate and lifetime by turbulent erosion are derived analytically and verified numerically. A parabolic decay law for the sunspot area is obtained. For moderate sunspot magnetic field strengths, the predicted decay rate agrees with the results obtained by Petrovay and Moreno-Insertis. The new analytical and nu…
Quantitative models of sunspot and starspot decay predict the timescale of magnetic diffusion and may yield important constraints in stellar dynamo models. Motivated by recent measurements of starspot lifetimes, we investigate the disintegration of a magnetic flux tube by nonlinear diffusion. Previous theoretical studies are extended by considering two physically motivated functional forms for the nonlinear diffusion coefficient $D$: an inverse power-law dependence $D \propto B^{-ν}$ and a step-function dependence of $D$ on the magnetic field magnitude $B$. Analytical self-similar solutions ar…
Observations of cool stars reveal dark spot-like features on their surfaces. Compared to sunspots, starspots can be bigger or cover a larger fraction of the stellar surface. While sunspots appear only at low latitudes, starspots are also found in polar regions, in particular on rapidly rotating stars. Sunspots are believed to result from the eruption of magnetic flux-tubes rising from the deep interior of the Sun. The strong magnetic field locally reduces convective heat transport to the solar surface. Such flux-tube models have also been invoked to explain starspot properties. However, these …
We measure the starspot radii and latitude distribution on the K4 dwarf HAT-P-11 from Kepler short-cadence photometry. We take advantage of starspot occultations by its highly-misaligned planet to compare the spot size and latitude distributions to those of sunspots. We find that the spots of HAT-P-11 are distributed in latitude much like sunspots near solar activity maximum, with mean spot latitude of $16 \pm 1$ degrees. The majority of starspots of HAT-P-11 have physical sizes that closely resemble the sizes of sunspots at solar maximum. We estimate the mean spotted area coverage on HAT-P-11…
We present a method that utilizes autocorrelation functions from long-term precision broadband differential light curves to estimate the average lifetimes of starspot groups for two large sample of Kepler stars: stars with and without previously known rotation periods. Our method is calibrated by comparing the strengths of the first few normalized autocorrelation peaks using ensembles of models that have various starspot lifetimes. We find that we must mix models of short and long lifetimes together (in heuristically determined ratios) to align the models with the Kepler data. Our fundamental …
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 …
The spotted detached eclipsing binary (DEB) offers insights into starspots on the binary. Three spotted DEBs, KIC 8097825, KIC 6859813, and KIC 5527172, which were observed by the Kepler photometry and LAMOST spectroscopy, are studied in this work. The physical parameters of binaries are determined by binary modeling. The sizes, lifetimes, and single/double-dip ratio (SDR) of starspots are derived by starspot analysis. KIC 8097825 has large starspots. KIC 6859813 has a spot rotation period shorter than its orbital period but the system should be synchronized inferred from timescale estimation.…
Size distribution of sunspots provides key information about the generation and emergence processes of the solar magnetic field. Previous studies on the size distribution have primarily focused on either the whole group or individual spot areas. In this paper, we investigate the organization of spot areas within sunspot groups. In particular, we analyze the ratio, $\rm{R}$, of the area of the biggest spot ($\rm{A_{big\_spot}}$) inside a group, to the total area of that group ($\rm{A_{group}}$). We use sunspot observations from Kislovodsk, Pulkovo and Debrecen observatories, together covering s…
Temperature contrasts and magnetic field strengths of sunspot umbrae broadly follow the thermal-magnetic relationship obtained from magnetohydrostatic equilibrium. Using a compilation of recent observations, especially in molecular bands, of temperature contrasts of starspots in cool stars, and a grid of Kurucz stellar model atmospheres constructed to cover layers of sub-surface convection zone, we examine how the above relationship scales with effective temperature T_{eff}, surface gravity g and the associated changes in opacity of stellar photospheric gas. We calculate expected field strengt…
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 veloci…
Long-lived (>20 days) sunspot groups extracted from the Greenwich Photo- heliographic Results (GPR) are examined for evidence of decadal change. The problem of identifying sunspot groups which are observed on consecutive solar rotations (recurrent sunspot groups) is tackled by first constructing manually an example dataset of recurrent sunspot groups and then using machine learning to generalise this subset to the whole GPR. The resulting dataset of recurrent sunspot groups is verified against previous work by A. Maunder and other Royal Greenwich Observatory (RGO) compilers. Recurrent groups a…
We studied the weak-lined T Tauri star Hubble 4, a known long-period binary, and its starspot phenomena. We used optical radial velocity (RV) data taken over a span of 14 years (2004-2010, 2017-2019) at the McDonald Observatory 2.7m Harlan J. Smith telescope and single epoch imaging from the HST/WFC3 instrument. The observed and apparent RV variations show contributions, respectively, from the binary motion as well as from a large spot group on one of the stars, presumed to be the primary. Fitting and removing the orbital signal from the RVs, we found the lower bound on the lifetime of a previ…
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…
There are no direct spatially resolved observations of spots on stars other than the Sun and starspot properties are inferred indirectly through lightcurves and spectropolarimetric data. We present the first self-consistent 3D radiative MHD computations of starspots on G2V, K0V and M0V stars, which will help to better understand observations of activity, variability and magnetic fields in late-type main-sequence stars. We used the MURaM code, which has been extensively used to compute "realistic" sunspots, for our simulations. We aim to study how fundamental starspot properties such as intensi…
We present a model that predicts the light curve amplitude distribution for an ensemble of low-mass magnetically active stars, under the assumptions that stellar spin axes are randomly orientated and that cool starspots have a characteristic scale length and are randomly distributed across the stellar surfaces. The model is compared with observational data for highly magnetically active M-dwarfs in the young cluster NGC 2516. We find that the best fitting starspot scale length is not constrained by these data alone, but requires assumptions about the overall starspot filling factor and starspo…
Aims. In this paper, we aim to study the time dependence of sunspot group areas in a large sample composed of various databases spanning over 130 years, used state-of-the-art statistical methods. Methods. For a carefully selected but unbiased sample, we use Bayesian modelling to fit the temporal evolution of the combined umbral and penumbral area of spot groups with a skew-normal function to determine the existence of any asymmetry in spot growth or decay. Our primary selection criteria guaranteed that only spot groups with a well-defined maximum area were taken into account. We also analysed …
Wide-field high precision photometric surveys such as Kepler have produced reams of data suitable for investigating stellar magnetic activity of cooler stars. Starspot activity produces quasi-sinusoidal light curves whose phase and amplitude vary as active regions grow and decay over time. Here we investigate, firstly, whether there is a correlation between the size of starspots - assumed to be related to the amplitude of the sinusoid - and their decay timescale and, secondly, whether any such correlation depends on the stellar effective temperature. To determine this, we computed the autocorr…
Sunspots are cool areas caused by strong surface magnetic fields inhibiting convection. Moreover, strong magnetic fields can alter the average atmospheric structure, degrading our ability to measure stellar masses and ages. Stars more active than the Sun have more and stronger dark spots than in the solar case, including on the rotational pole itself. Doppler imaging, which has so far produced the most detailed images of surface structures on other stars than the Sun, cannot always distinguish the hemisphere in which the starspots are located, especially in the equatorial region and if the dat…
During the solar magnetic activity cycle the emergence latitudes of sunspots change, leading to the well-known butterfly diagram. This phenomenon is poorly understood for other stars as starspot latitudes are generally unknown. The related changes in starspot rotation rates caused by latitudinal differential rotation can however be measured. Using the set of 3093 Kepler stars with activity cycles identified by Reinhold et al. (2017), we aim to study the temporal change in starspot rotation rates over magnetic activity cycles, and how this relates to the activity level, mean rotation rate, and …
Back Reaction of the Untwisting Solar Corona Scars Sunspots
Sorbonne Université, Observatoire de Paris-PSL, École Polytechnique, IP Paris, CNRS（索邦大学，巴黎天文台-PSL，巴黎综合理工学院，巴黎理工学院，法国国家科学研究中心）；School of Astronomy and Space Science, Nanjing University, Nanjing, China（南京大学天文与空间科学学院）；Laboratoire de Physique des Plasmas, Paris, France（等离子体物理实验室）
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, 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 d…
Major solar flares are prone to occur in active region atmospheres associated with large, complex, dynamically-evolving sunspots. This points to the importance of monitoring the evolution of starspots, not only in visible but also in ultra violet (UV) and X-rays, in understanding the origin and occurrence of stellar flares. To this end, we perform spectral irradiance analysis on different types of transiting solar active regions by using a variety of full-disk synoptic observations. The target events are an isolated sunspot, spotless plage, and emerging flux in prolonged quiet-Sun conditions s…
Photometry from Kepler has revealed the presence of cool starspots on the surfaces of thousands of stars, presenting a wide range of spot morphologies and lifetimes. Understanding the lifetime and evolution of starspots across the main sequence reveals critical information about the strength and nature of stellar dynamos. We probe the dynamo by modeling the starspot properties over time using Kepler light curves. In particular, we use planetary systems like Kepler 17 that show in-transit starspot crossing features. Spot-occulting transits probe smaller-scale starspot features on the stellar su…
Stellar magnetic activity, just like that of the Sun, manifests itself in the form of flares and spots on the surface of the star. In the solar case, the largest flares originate from large active regions. In this work, we present a study of the activity of the star Kepler-411, including spot modeling from planetary transits. Our goal was to search for a connection between the area of starspots with the energy of superflares produced by this star. Kepler-411 is a K2V-type star with an average rotation period of 10.52 days, radius of 0.79 $R_{\odot}$ and a mass of 0.83 $M_{\odot} $, which was o…
Active solar-type stars show large quasi-periodic brightness variations caused by stellar rotations with star spots, and the amplitude changes as the spots emerge and decay. The Kepler data are suitable for investigations on the emergence and decay processes of star spots, which are important to understand underlying stellar dynamo and stellar flares. In this study, we measured temporal evolutions of star spot area with Kepler data by tracing local minima of the light curves. In this analysis, we extracted temporal evolutions of star spots showing clear emergence and decay without being distur…
We report observations of bright dots (BDs) in a sunspot penumbra using High Resolution Coronal Imager (Hi-C) data in 193 Å and examine their sizes, lifetimes, speeds, and intensities. The sizes of the BDs are on the order of 1\arcsec\ and are therefore hard to identify in the Atmospheric Imaging Assembly (AIA) 193 Å images, which have 1.2\arcsec\ spatial resolution, but become readily apparent with Hi-C's five times better spatial resolution. We supplement Hi-C data with data from AIA's 193 Å passband to see the complete lifetime of the BDs that appeared before and/or lasted longer than Hi-C'…
The flare-prolific active region NOAA 10930 offered both a developing delta-spot and a decaying satellite sunspot of opposite polarity. The objective of this study is to characterize the photometric decay of the satellite sunspot and the evolution of photospheric and chromospheric horizontal proper motions in its surroundings. We apply the local correlation tracking technique to a 16-hour time-series of Hinode G-band and CaIIH images and study the horizontal proper motions in the vicinity of the satellite sunspot on 2006 December 7. Decorrelation times were computed to measure the lifetime of …
We report the discovery of a new relationship between a simple morphological characteristic of light curves produced by starspots and stellar rotation periods. The characteristic we examine is whether the light curve exhibits one dip or two during a single rotation. We analyze thousands of Kepler light curves of main sequence stars from 3200-6200K. Almost all the stars exhibit segments of their light curve that contain either single or double dip segments (very few have more than two significant dips per rotation). We define a variable, the "single/double ratio" (SDR) that expresses the ratio …
Magnetohydrodynamic interactions between plasma flows and magnetic fields is fundamental to the origin and sustenance of the 11-year sunspot cycle. These processes are intrinsically three-dimensional (3D) in nature. Our goal is to construct a 3D solar dynamo model that on the one hand captures the buoyant emergence of tilted bipolar sunspot pairs, and on the other hand produces cyclic large-scale field reversals mediated via surface flux-transport processes -- that is, the Babcock-Leighton mechanism. We perform kinematic dynamo simulations where the prescribed velocity field is a combination o…
We observed an elongated filamentary bright structure inside the umbra of the big sunspot in active region NOAA 12529, which differs from the light bridges usually observed in sunspots for its morphology, magnetic configuration, and velocity field. We used observations taken with the Solar Dynamic Observatory satellite to characterize this feature. Its lifetime is 5 days, during which it reaches a maximum length of about 30". In the maps of the vertical component of the photospheric magnetic field, a portion of the feature has a polarity opposite to that of the hosting sunspot. At the same tim…
Umbral dots (UDs) were observed in a stable sunspot in NOAA 10944 by the Hinode Solar Optical Telescope on 2007 March 1. The observation program consisted of blue continuum images and spectropolarimetric profiles of Fe I 630 nm line. An automatic detection algorithm for UDs was applied to the 2-hour continuous blue continuum images, and using the obtained data, the lifetime, size, and proper motion of UDs were calculated. The magnetic structure of the sunspot was derived through the inversion of the spectropolarimetric profiles. We calculated the correlations between UD's parameters (size, lif…
We conducted high dispersion spectroscopic observations of 50 superflare stars with Subaru/HDS. These 50 stars were selected from the solar-type superflare stars that we had discovered from the Kepler data. More than half (34 stars) of these 50 target superflare stars show no evidence of binarity, and we estimated stellar parameters of these 34 stars in our previous study (Notsu et al. 2015, hereafter called Paper I). According to our previous studies using Kepler data, superflare stars show quasi-periodic brightness variations whose amplitude (0.1-10\%) is much larger than that of the solar b…
We have investigated the probability distributions of sunspot area and magnetic flux by using the data from Royal Greenwich Observatory and USAF/NOAA. We have constructed a sample of 2995 regions with maximum-development areas $\ge$ 500 MSH (millionths of solar hemisphere), covering 146.7 years (1874--2020). The data were fitted by a power-law distribution and four two-parameter distributions (tapered power-law, gamma, lognormal, and Weibull distributions). The power-law model was unfavorable compared to the four models in terms of AIC, and was not acceptable by the classical Kolmogorov-Smirno…
Umbral dots (UDs) are small isolated brightenings observed in sunspot umbrae. They are convective phenomena existing inside umbrae. UDs are usually divided into central UDs (CUDs) and peripheral UDs (PUDs) according to their positions inside an umbra. Our purpose is to investigate UD properties and analyze their relationships, and further to find whether or not the properties depend on umbral magnetic field strengths. Thus, we selected high-resolution TiO images of four active regions (ARs) taken under the best seeing conditions with the \textit{New Vacuum Solar Telescope} in the Fuxian Solar …
Context : Penumbrae are an important characteristic of sunspots, whose formation is intricately related to the nature of sub-photospheric magnetic fields. Aims : We study the formation of a penumbra in a decaying sunspot and compare its properties with those seen during the development of a proto-spot. Methods : High-resolution spectropolarimetric observations of active region NOAA 11283 were obtained from the spectro-polarimeter on board Hinode. These were complemented with full-disk filtergrams of continuum intensity, line-of-sight magnetograms, and dopplergrams from the Helioseismic and Mag…
In G dwarfs, the surface distribution, coverage and lifetimes of starspots deviate from solar-like patterns as the rotation rate increases. We set up a numerical platform which includes the large-scale rotational and surface flow effects, aiming to simulate evolving surface patterns over an activity cycle for up to 8 times the solar rotation and flux emergence rates. At the base of the convection zone, we assume a solar projected butterfly diagram. We then follow the rotationally distorted trajectories of rising thin flux tubes to obtain latitudes and tilt angles. Using them as source distribu…
We study the velocity field of umbral dots at a resolution of 0.14". Our analysis is based on full Stokes spectropolarimetric measurements of a pore taken with the CRISP instrument at the Swedish 1-m Solar Telescope. We determine the flow velocity at different heights in the photosphere from a bisector analysis of the Fe I 630 nm lines. In addtion, we use the observed Stokes Q, U, and V profiles to characterize the magnetic properties of these structures. We find that most umbral dots are associated with strong upflows in deep photospheric layers. Some of them also show concentrated patches of…
Penumbral microjets (PJs) are transient narrow bright features in the chromosphere of sunspot penumbrae, first characterized by Katsukawa et al (2007) using the \CaII\ H-line filter on {\it Hinode}'s Solar Optical Telescope (SOT). It was proposed that the PJs form as a result of reconnection between two magnetic components of penumbra (spines and interspines), and that they could contribute to the transition region (TR) and coronal heating above sunspot penumbrae. We propose a modified picture of formation of PJs based on recent results on internal structure of sunspot penumbral filaments. Usi…
Recent high-resolution observations reveal that subarcsecond bright dots (BDs) with sub-minute lifetimes appears ubiquitously in the transition region (TR) above sunspot penumbra. The presence of penumbral micro-jets (PMJs) in the chromosphere have also been reported earlier. It was proposed that both the PMJs and BDs are formed due to magnetic reconnection process and may play an important role in heating of the penumbra. Using simultaneous observation of the chromosphere from the Solar Optical Telescope (SOT) aboard Hinode and the TR from the Interface Region Imaging Spectrograph (IRIS), we …
The study of young Sun-like stars is of fundamental importance to understand the magnetic activity and rotational evolution of the Sun. Space-borne photometry by the Kepler telescope provides unprecedented datasets to investigate these phenomena in Sun-like stars. We present a new analysis of the entire Kepler photometric time series of the moderately young Sun-like star Kepler-17 that is accompanied by a transiting hot Jupiter. We applied a maximum-entropy spot model to the long-cadence out-of-transit photometry of the target to derive maps of the starspot filling factor versus the longitude …
The solar cycle and its associated magnetic activity are the main drivers behind changes in the interplanetary environment and the Earth's upper atmosphere (commonly referred to as space weather). These changes have a direct impact on the lifetime of space-based assets and can create hazards to astronauts in space. In recent years there has been an effort to develop accurate solar cycle predictions (with aims at predicting the long-term evolution of space weather), leading to nearly a hundred widely spread predictions for the amplitude of solar cycle 24. A major contributor to the disagreement…
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 rotational evolution of cool stars is governed by magnetised stellar winds which slow the stellar rotation during their main sequence lifetimes. Magnetic variability is commonly observed in Sun-like stars, and the changing strength and topology of the global field is expected to affect the torque exerted by the stellar wind. We present three different methods for computing the angular momentum loss in the solar wind. Two are based on MHD simulations from Finley & Matt (2018), with one using the open flux measured in the solar wind, and the other using remotely-observed surface magnetograms…
Umbral flashes (UFs) are most common phenomenon of wave processes in sunspots. Studying the relationship between wave time dynamics and the origin of UFs requires further investigation of their fine spatial and height structure. We investigated the association between a short time increase in the variations of three-minute extreme ultraviolet (EUV) emission at footpoints of coronal magnetic loops and the UF emergence in sunspot umbra. We applied the pixelized wavelet filtering (PWF) technique to analyse a cube of the images obtained by SDO/AIA at 1600A, 304A, and 171A to study the spatio-tempo…
Accounting for the effects of stellar magnetic phenomena is indispensable to fully exploit radial velocities (RVs). Correlated time variations are often mitigated by Gaussian processes (GP). They rely on fitting kernel functions that are motivated on mathematical grounds, and whose physical interpretation is often elusive. We aim to establish a connection between stellar activity affecting RVs and their correlations with physical parameters, and compare this connection with kernels used in the literature. We use simple activity models to investigate the relationship between the physical proces…
Understanding magnetic activity on the surface of stars other than the Sun is important for exoplanet analyses to properly characterize an exoplanet's atmosphere and to further characterize stellar activity on a wide range of stars. Modeling stellar surface features of a variety of spectral types and rotation rates are key to understanding of the magnetic activity of these stars. Using data from Kepler, we use the starspot modeling program STarSPot (STSP) to measure the position and size of spots for KOI-340 which is an eclipsing binary consisting of a subgiant star ($\rm T_{\rm eff} = 5593 \p…
As many as 10\% of OB-type stars have global magnetic fields, which is surprising given their internal structure is radiative near the surface. A direct probe of internal structure is pulsations, and some OB-type stars exhibit pressure modes ($β$ Cep pulsators) or gravity modes (slowly pulsating B-type stars; SPBs); a few rare cases of hybrid $β$ Cep/SPBs occupy a narrow instability strip in the H-R diagram. The most precise fundamental properties of stars are obtained from eclipsing binaries (EBs), and those in clusters with known ages and metallicities provide the most stringent constraints …
We show that non-magnetic models for the evolution of pre-main-sequence (PMS) stars *cannot* simultaneously describe the colour-magnitude diagram (CMD) and the pattern of lithium depletion seen in the cluster of young, low-mass stars surrounding $γ^2$ Velorum. The age of 7.5+/-1 Myr inferred from the CMD is much younger than that implied by the strong Li depletion seen in the cluster M-dwarfs and the Li depletion occurs at much redder colours than predicted. The epoch at which a star of a given mass depletes its Li and the surface temperature of that star are both dependent on its radius. We d…
