Stellar Brightness Variations Research Articles

How faculae and network relate to sunspots, and the implications for solar and stellar brightness variations(Corrigendum)

How faculae and network relate to sunspots, and the implications for solar and stellar brightness variations(<i>Corrigendum</i>)

Inflection point in the power spectrum of stellar brightness variations

Context. Stellar rotation periods can be determined by observing brightness variations caused by active magnetic regions transiting visible stellar disk as the star rotates. Successful stellar photometric surveys stemming from the Kepler and TESS observations have led to the determination of rotation periods in tens of thousands of young and active stars. However, there is still a lack of information on the rotation periods of older and less active stars like the Sun. The irregular temporal profiles of light curves caused by the decay times of active regions, which are comparable to, or even shorter than, stellar rotation periods, in combination with the random emergence of active regions make period determination for such stars very difficult. Aims. We tested the performance of a new method for the determination of stellar rotation periods against stars with previously determined rotation periods. The method is based on calculating the gradient of the power spectrum (GPS) and identifying the position of the inflection point (i.e. point with the highest gradient). The GPS method is specifically aimed at determining rotation periods of low-activity stars like the Sun. Methods. We applied the GPS method to 1047 Sun-like stars observed by the Kepler telescope. We considered two stellar samples individually: one with near-solar rotation periods (24–27.4 d) and a broad range of effective temperatures (5000–6000 K) and the other with near-solar effective temperatures (5700–5900 K) and a broad range of rotation periods (15–40 d). Results. We show that the GPS method returns precise values for stellar rotation periods. Furthermore, it allows us to constrain the ratio between facular and spot areas of active regions at the moment of their emergence. We also show that the relative facular area decreases with the stellar rotation rate. Conclusions. Our results suggest that the GPS method can be successfully applied to retrieve the periods of stars with both regular and non-regular light curves.

How faculae and network relate to sunspots, and the implications for solar and stellar brightness variations

Context. How global faculae and network coverage relates to that of sunspots is relevant to the brightness variations of the Sun and Sun-like stars. Aims. We aim to extend and improve on earlier studies that established that the facular-to-sunspot-area ratio diminishes with total sunspot coverage. Methods. Chromospheric indices and the total magnetic flux enclosed in network and faculae, referred to here as “facular indices”, are modulated by the amount of facular and network present. We probed the relationship between various facular and sunspot indices through an empirical model, taking into account how active regions evolve and the possible non-linear relationship between plage emission, facular magnetic flux, and sunspot area. This model was incorporated into a model of total solar irradiance (TSI) to elucidate the implications for solar and stellar brightness variations. Results. The reconstruction of the facular indices from the sunspot indices with the model presented here replicates most of the observed variability, and is better at doing so than earlier models. Contrary to recent studies, we found the relationship between the facular and sunspot indices to be stable over the past four decades. The model indicates that, like the facular-to-sunspot-area ratio, the ratio of the variation in chromospheric emission and total network and facular magnetic flux to sunspot area decreases with the latter. The TSI model indicates the ratio of the TSI excess from faculae and network to the deficit from sunspots also declines with sunspot area, with the consequence being that TSI rises with sunspot area more slowly than if the two quantities were linearly proportional to one another. This explains why even though solar cycle 23 is significantly weaker than cycle 22, TSI rose to comparable levels over both cycles. The extrapolation of the TSI model to higher activity levels indicates that in the activity range where Sun-like stars are observed to switch from growing brighter with increasing activity to becoming dimmer instead, the activity-dependence of TSI exhibits a similar transition. This happens as sunspot darkening starts to rise more rapidly with activity than facular and network brightening. This bolsters the interpretation of this behaviour of Sun-like stars as the transition from a faculae-dominated to a spot-dominated regime.

Connecting measurements of solar and stellar brightness variations

Context. A comparison of solar and stellar brightness variations is hampered by the difference in spectral passbands that are used in observations, and also by the possible difference in the inclination of the solar and stellar rotation axes from the line of sight. Aims. We calculate the rotational variability of the Sun as it would be measured in passbands used for stellar observations. In particular, we consider the filter systems used by the CoRoT, Kepler, TESS, and Gaia space missions. We also quantify the effect of the inclination of the rotation axis on the solar rotational variability. Methods. We employed the spectral and total irradiance reconstruction (SATIRE) model to calculate solar brightness variations in different filter systems as observed from the ecliptic plane. We then combined the simulations of the surface distribution of the magnetic features at different inclinations using a surface flux transport model with the SATIRE calculations to compute the dependence of the variability on the inclination. Results. For an ecliptic-bound observer, the amplitude of the solar rotational variability, as observed in the total solar irradiance (TSI), is 0.68 mmag (averaged over solar cycles 21–24). We obtained corresponding amplitudes in the Kepler (0.74 mmag), CoRoT (0.73 mmag), TESS (0.62 mmag), Gaia G (0.74 mmag), Gaia GRP (0.62 mmag), and Gaia GBP (0.86 mmag) passbands. Decreasing the inclination of the rotation axis decreases the rotational variability. For a sample of randomly inclined stars, the variability is on average 15% lower in all filter systems we considered. This almost compensates for the difference in amplitudes of the variability in TSI and Kepler passbands, making the amplitudes derived from the TSI records an ideal representation of the solar rotational variability for comparison to Kepler stars with unknown inclinations. Conclusions. The TSI appears to be a relatively good measure of solar variability for comparisons with stellar measurements in the CoRoT, Kepler, TESS Gaia G, and Gaia GRP filters. Whereas the correction factors can be used to convert the variability amplitude from solar measurements into the values expected for stellar missions, the inclination affects the shapes of the light curves so that a much more sophisticated correction than simple scaling is needed to obtain light curves out of the ecliptic for the Sun.

Inflection point in the power spectrum of stellar brightness variations

Context. Young and active stars generally have regular, almost sinusoidal, patterns of variability attributed to their rotation, while the majority of older and less active stars, including the Sun, have more complex and non-regular light curves, which do not have clear rotational-modulation signals. Consequently, the rotation periods have been successfully determined only for a small fraction of the Sun-like stars (mainly the active ones) observed by transit-based planet-hunting missions, such as CoRoT, Kepler, and TESS. This suggests that only a small fraction of such systems have been properly identified as solar-like analogues. Aims. We aim to apply a new method of determining rotation periods of low-activity stars, such as the Sun. The method is based on calculating the gradient of the power spectrum (GPS) of stellar brightness variations and identifying a tell-tale inflection point in the spectrum. The rotation frequency is then proportional to the frequency of that inflection point. In this paper, we compare this GPS method to already-available photometric records of the Sun. Methods. We applied GPS, auto-correlation functions, Lomb-Scargle periodograms, and wavelet analyses to the total solar irradiance (TSI) time series obtained from the Total Irradiance Monitor on the Solar Radiation and Climate Experiment and the Variability of solar IRradiance and Gravity Oscillations experiment on the SOlar and Heliospheric Observatory missions. We analysed the performance of all methods at various levels of solar activity. Results. We show that the GPS method returns accurate values of solar rotation independently of the level of solar activity. In particular, it performs well during periods of high solar activity, when TSI variability displays an irregular pattern, and other methods fail. Furthermore, we show that the GPS and light curve skewness can give constraints on facular and spot contributions to brightness variability. Conclusions. Our results suggest that the GPS method can successfully determine the rotational periods of stars with both regular and non-regular light curves.

Inflection point in the power spectrum of stellar brightness variations

Context. Considerable effort has gone into using light curves observed by such space telescopes as CoRoT, Kepler, and TESS for determining stellar rotation periods. While rotation periods of active stars can be reliably determined, the light curves of many older and less active stars, such as stars that are similar to the Sun, are quite irregular. This hampers the determination of their rotation periods. Aims. We aim to examine the factors causing these irregularities in stellar brightness variations and to develop a method for determining rotation periods for low-activity stars with irregular light curves. Methods. We extended the Spectral And Total Irradiance Reconstruction approach for modeling solar brightness variations to Sun-like stars. We calculated the power spectra of stellar brightness variations for various combinations of parameters that define the surface configuration and evolution of stellar magnetic features. Results. The short lifetime of spots in comparison to the stellar rotation period, as well as the interplay between spot and facular contributions to brightness variations of stars with near solar activity, cause irregularities in their light curves. The power spectra of such stars often lack a peak associated with the rotation period. Nevertheless, the rotation period can still be determined by measuring the period where the concavity of the power spectrum plotted in the log–log scale changes its sign, that is, by identifying the position of the inflection point. Conclusions. The inflection point of the (log–log) power spectrum is found to be a new diagnostic for stellar rotation periods which is shown to work even in cases where the power spectrum shows no peak at the rotation rate.

Autoregressive Planet Search: Application to the Kepler Mission

Abstract The 4 yr light curves of 156,717 stars observed with NASA’s Kepler mission are analyzed using the autoregressive planet search (ARPS) methodology described by Caceres et al. The three stages of processing are maximum-likelihood ARIMA modeling of the light curves to reduce stellar brightness variations, constructing the transit comb filter periodogram to identify transit-like periodic dips in the ARIMA residuals, and Random Forest classification trained on Kepler team confirmed planets using several dozen features from the analysis. Orbital periods between 0.2 and 100 days are examined. The result is a recovery of 76% of confirmed planets, 97% when period and transit depth constraints are added. The classifier is then applied to the full Kepler data set; 1004 previously noticed and 97 new stars have light-curve criteria consistent with the confirmed planets, after subjective vetting removes clear false alarms and false positive cases. The 97 Kepler ARPS candidate transits mostly have periods of P &lt; 10 days; many are ultrashort period hot planets with radii &lt;1% of the host star. Extensive tabular and graphical output from the ARPS time series analysis is provided to assist in other research relating to the Kepler sample.

The CARMENES search for exoplanets around M dwarfs

Context. Teegarden’s Star is the brightest and one of the nearest ultra-cool dwarfs in the solar neighbourhood. For its late spectral type (M7.0 V), the star shows relatively little activity and is a prime target for near-infrared radial velocity surveys such as CARMENES. Aims. As part of the CARMENES search for exoplanets around M dwarfs, we obtained more than 200 radial-velocity measurements of Teegarden’s Star and analysed them for planetary signals. Methods. We find periodic variability in the radial velocities of Teegarden’s Star. We also studied photometric measurements to rule out stellar brightness variations mimicking planetary signals. Results. We find evidence for two planet candidates, each with 1.1 M⊕ minimum mass, orbiting at periods of 4.91 and 11.4 d, respectively. No evidence for planetary transits could be found in archival and follow-up photometry. Small photometric variability is suggestive of slow rotation and old age. Conclusions. The two planets are among the lowest-mass planets discovered so far, and they are the first Earth-mass planets around an ultra-cool dwarf for which the masses have been determined using radial velocities.

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.

From solar to stellar brightness variations

Context. Comparison studies of Sun-like stars with the Sun suggest an anomalously low photometric variability of the Sun compared to Sun-like stars with similar magnetic activity. Comprehensive understanding of stellar variability is needed to find a physical reason for this observation. Aims. We investigate the effect of metallicity and effective temperature on the photometric brightness change of Sun-like stars seen at different inclinations. The considered range of fundamental stellar parameters is sufficiently small so the stars investigated here still count as Sun-like or even as solar twins. Methods. To model the brightness change of stars with solar magnetic activity, we extended a well-established model of solar brightness variations based on solar spectra, Spectral And Total Irradiance REconstruction (SATIRE), to stars with different fundamental parameters. For this we calculated stellar spectra for different metallicities and effective temperature using the radiative transfer code ATLAS9. Results. We show that even a small change (e.g. within the observational error range) of metallicity or effective temperature significantly affects the photometric brightness change compared to the Sun. We find that for Sun-like stars, the amplitude of the brightness variations obtained for Strömgren (b + y)/2 reaches a local minimum for fundamental stellar parameters close to the solar metallicity and effective temperature. Moreover, our results show that the effect of inclination decreases for metallicity values greater than the solar metallicity. Overall, we find that an exact determination of fundamental stellar parameters is crucially important for understanding stellar brightness changes.

Wind dynamics and circumstellar extinction variations in the T Tauri star RY Tau

The wind interaction with the dusty environment of the classical T Tauri star RY Tau has been investigated. During two seasons of 2013-2015 we carried out a spectroscopic and photometric (BVR) monitoring of the star. A correlation between the stellar brightness and the radial velocity of the wind determined from the H-alpha and Na D line profiles has been found for the first time. The irregular stellar brightness variations are shown to be caused by extinction in a dusty disk wind at a distance of about 0.2 AU from the star. We suppose, that variations of the circumstellar extinction results from cyclic rearrangements of the stellar magnetosphere and coronal mass ejections, which affect the dusty disk wind near the inner boundary of the circumstellar disk.

Activity and cold spots on the surface of G-type superflare stars

Based on the high precision photometric observations of the Kepler space telescope, we have investigated the properties of the active regions (cold spots) on the surface of 279 stars of the spectral class G, for which 1547 superflares with energies in the range of 1033–1036 erg have been revealed. The main conclusion of our study is the quantitative estimation of the increased surface spottedness of superflare stars, which indicates enhancedmagnetic activity of these objects. The increased spottedness on the surfaces of the studied stars was confirmed based on two independent estimations of stellar brightness variations. In addition, it was concluded that superflare stars do not stand out in the common dataset of differential rotation parameters. Based on the data considered, no correlation was found of the spottedness parameters or the differential rotation parameters with the characteristics of these objects—their Rossby numbers and superflare energy. Additionally, the correlation between the superflare energy and the inverse Rossby number was considered. None of these comparisons gave an indication for the presence of any obvious correlation. The results of the analysis of five stars with a few dozen flares registered indicate that for the same star whereas spottedness S variations are small, significant changes in the superflare energy can be achieved. On the example of KIC 10422252, we show that at sixfold S variations, the flare energy varies by orders of magnitude at any given S value.

An observational correlation between stellar brightness variations and surface gravity

Surface gravity is a basic stellar property, but it is difficult to measure accurately, with typical uncertainties of 25 to 50 per cent if measured spectroscopically and 90 to 150 per cent if measured photometrically. Asteroseismology measures gravity with an uncertainty of about 2 per cent but is restricted to relatively small samples of bright stars, most of which are giants. The availability of high-precision measurements of brightness variations for more than 150,000 stars provides an opportunity to investigate whether the variations can be used to determine surface gravities. The Fourier power of granulation on a star's surface correlates physically with surface gravity: if brightness variations on timescales of hours arise from granulation, then such variations should correlate with surface gravity. Here we report an analysis of archival data that reveals an observational correlation between surface gravity and root mean squared brightness variations on timescales of less than eight hours for stars with temperatures of 4,500 to 6,750 kelvin, log surface gravities of 2.5 to 4.5 (cgs units) and overall brightness variations of less than three parts per thousand. A straightforward observation of optical brightness variations therefore allows a determination of the surface gravity with a precision of better than 25 per cent for inactive Sun-like stars at main-sequence to giant stages of evolution.

Twinkling stars

A correlation between stellar brightness variations and the gravitational acceleration at a star's surface has been observed that allows this acceleration to be measured with a precision of better than 25%. See Letter p.427

Molecular Masers in Variable Stars

AbstractWhen a star with a mass of one to a few solar masses enters the red giant stage of its evolution, the radius of its atmosphere reaches several astronomical units. Pulsational instability is typical for this stage. Most stars become Mira-type or semiregular variables with light cycles of a few hundred days. Red giants lose mass at a rate M = 10−7−10−5M⊙ yr−1. Extensive gas–dust circumstellar envelopes form. These envelopes contain various molecular species. Some of these molecules (OH, H2O, SiO, HCN) manifest themselves in maser radio emission. Data on the H2O maser variability and its connection with the stellar brightness variations are discussed. In the H2O line circumstellar masers can be divided into ‘stable’ (showing persistent emission — R Aql, U Her, S CrB, X Hya) and ‘transient’ (appearing in the H2O line once per 10–15 stellar light cycles — R Leo, R Cas, U Aur). Physical mechanisms of the maser variability are discussed. The most probable process explaining the observed visual–H2O correlation is the influence of shock waves on the masing region. Usually it is assumed that shocks in Mira atmospheres are driven by stellar pulsations. Here an alternative explanation is proposed. If a star during its main sequence life possessed a planetary system, similar to the solar system, the planets will be embedded in a rather dense and hot medium. Effects of a planet revolving around a red giant at a short distance (inside its circumstellar envelope) are discussed. A shock produced by the supersonic motion of a planet can account for the correlated variability of the Hα line emission and H2O maser. If the planetary orbit is highly eccentric, then the connected Hα–H2O flare episodes may be explained by the periastron passage of the planet. New tasks for the upgraded ATCA are discussed.

Stellar Activity and Brightness Variations: A Glimpse at the Sun's History

Radiometric measurements during the past decade from the Solar Maximum Mission and Nimbus 7 satellites have shown that the total solar irradiance varies in step with the sun's 11-year magnetic activity cycle. Stellar observations from the Lowell and Mount Wilson observatories now confirm and elaborate this discovery. These measurements show that older stars similar to the sun tend to become brighter as their magnetic activity level increases, just as the sun does during its 11-year activity cycle. Younger stars, however, tend to become fainter as their magnetic activity level increases. This contrasting behavior suggests that the balance between the competing phenomena that influence solar brightness variability has shifted during the sun's lifetime.