The rotation rates and magnetic activity of Sun-like and low-mass (< 1.4 Msun) main-sequence stars are known to decline with time, and there now exist several models for the evolution of rotation and activity. However, the role that chemical composition plays during stellar spin-down has not yet been explored. In this work, we use a structural evolution code to compute the rotational evolution of stars with three different masses (0.7, 1.0, and 1.3Msun and six different metallicities, ranging from [Fe/H]=-1.0 to [Fe/H]=+0.5. We also implement three different wind-braking formulations from the literature (two modern and one classical) and compare their predictions for rotational evolution. The effect that metallicity has on stellar structural properties, and in particular the convective turnover timescale, leads the two modern wind-braking formulations to predict a strong dependence of the torque on metallicity. Consequently, they predict that metal rich stars spin-down more effectively at late ages (> 1 Gyr) than metal poor stars, and the effect is large enough to be detectable with current observing facilities. For example, the formulations predict that a Sun-like (solar-mass and solar-aged) star with [Fe/H]=-0.3 will have a rotation period of less than 20 days. Even though old, metal poor stars are predicted to rotate more rapidly at a given age, they have larger Rossby numbers and are thus expected to have lower magnetic activity levels. Finally, the different wind-braking formulations predict quantitative differences in the metallicity-dependence of stellar rotation, which may be used to test them.
A code used previously to predict O-star mass fluxes as a function of metallicity is used to compute a grid of models with the metallicity of the Small Magellanic Cloud (SMC). These models allow mass-loss rates to be derived by interpolation for all O-type supergiants in the SMC, with the possible exception of extremely massive stars close to the Eddington limit.
The 11-year activity cycle of the Sun is a consequence of a dynamo process occurring beneath its surface. We analyzed photometric data obtained by the CoRoT space mission, showing solar-like oscillations in the star HD49933, for signatures of stellar magnetic activity. Asteroseismic measurements of global changes in the oscillation frequencies and mode amplitudes reveal a modulation of at least 120 days, with the minimum frequency shift corresponding to maximum amplitude as in the Sun. These observations are evidence of a stellar magnetic activity cycle taking place beneath the surface of HD49…
We present a detailed analysis of the possible future Sun's rotational evolution scenario based on the 8 Gyr-old solar twin HIP 102152. Using HARPS high-cadence observations (and TESS light curves), we analyzed the modulation of a variety of activity proxies (Ca II, HI Balmer, and Na I lines), finding a strong rotational signal of 35.7 $\pm$ 1.4 days ($\log B_{\rm factor}\sim70$, in the case of Ca II K line). This value matches with the theoretical expectations regarding the smooth rotational evolution of the Sun towards the end of the main-sequence, validating the use of gyrochronology after …
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 reasoning 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 so…
Understanding how the magnetic activity of low-mass stars depends on their fundamental parameters is an important goal of stellar astrophysics. Previous studies show that activity levels are largely determined by the stellar Rossby number which is defined as the rotation period divided by the convective turnover time. However, we currently have little information on the role that chemical composition plays. In this work, we investigate how metallicity affects magnetic activity using photometric variability as an activity proxy. Similarly to other proxies, we demonstrate that the amplitude of p…
In the past years, a systematic downward revision of the metallicity of the Sun has led to the "solar modeling problem", namely the disagreement between predictions of standard solar models and inferences from helioseismology. Recent solar wind measurements of the metallicity of the Sun, however, provide once more an indication of a high-metallicity Sun. Because of the effects of possible residual fractionation, the derived value of the metallicity $Z_{\odot} = 0.0196 \pm 0.0014$ actually represents a lower limit to the true metallicity of the Sun. However, when compared with helioseismologica…
We search for "solar twins" in the Geneva-Copenhagen Survey (GCS) using high resolution optical spectroscopy. We initially select Sun-like stars from the GCS by absolute magnitude, b-y colour and metallicity close to the solar values. Our aim is to find the stars which are spectroscopically very close to the Sun using line depth ratios and the median equivalent widths and depths of selected lines with a range of excitation potentials. We present the ten best stars fulfilling combined photometric and spectroscopic criteria, of which six are new twins. We use our full sample of Sun-like stars to…
The atmospheric activity of the Sun and Sun-like stars is analyzed involving observations from HK-project at the Mount Wilson Observatory, the California and Carnegie Planet Search Program at the Keck and Lick Observatories and the Magellan Planet Search Program at the Las Campanas Observatory. We show that for stars of F, G and K spectral classes, the cyclic activity, similar to the 11-yr solar cycles, is different: it becomes more prominent in K-stars. Comparative study of Sun-like stars with different levels of the chromospheric and coronal activity confirms that the Sun belongs to stars wi…
We applied the method of continuous wavelet-transform to the time-frequency analysis to the sets of observations of relative sunspot numbers, sunspot areas and to 6 Mount Wilson HK-project stars with well-defined magnetic cycles. Wavelet analysis of these data reveals the following pattern: at the same time there are several activity cycles whose periods vary widely from the quasi-biennial up to the centennial period for the Sun and vary significant during observations time of the HK-project stars. These relatively low-frequency periodic variations of the solar and stellar activity gradually c…
High-energy observations of the Sun provide an opportunity to test the limits of our ability to accurately measure properties of transiting exoplanets in the presence of stellar activity. Here we insert transits of a hot Jupiter into continuous disk integrated data of the Sun in Lyman-alpha (Ly$α$) from NASA's SDO/EVE instrument to assess the impact of stellar activity on the measured planet-to-star radius ratio $(\textrm{R}_\textrm{p}/\textrm{R}_\star)$. In 75% of our simulated light curves we measure the correct radius ratio; however, incorrect values can be measured if there is significant …
Magnetic activity is a global property of the Sun; the complex processes of solar activity are connected with the solar magnetic fields. For solar-type stars and the Sun magnetic activity depends on the physical parameters of the star. In this article we study the relationships between the duration of activity cycle and effective temperature for solar-type stars and the Sun. We've tried to explain these relationships due to the existence of layer of laminar convection near the bottom of the convective zone of the star. In this layer the Rossby waves are formed. They generate the primary poloid…
Stellar activity is a potential important limitation to the detection of low mass extrasolar planets with indirect methods (RV, photometry, astrometry). In previous papers, using the Sun as a proxy, we investigated the impact of stellar activity (spots, plages, convection) on the detectability of an Earth-mass planet in the habitable zone (HZ) of solar-type stars with RV techniques. We extend here the detectability study to the case of astrometry. We used the sunspot and plages properties recorded over one solar cycle to infer the astrometric variations that a Sun-like star seen edge-on, 10 pc…
The atmospheric activity of the Sun and solar-type stars is analysed involving observations from HK-project at the Mount Wilson Observatory, the California and Carnegie Planet Search Program at the Keck and Lick Observatories, and the Magellan Planet Search Program at the Las Campanas Observatory. We show that for stars of F, G and K spectral classes, the cyclic activity, similar to the 11-yr Solar cycles, is different: it becomes more prominent in K-stars. Comparative study of solar-type stars with different levels of the chromospheric and coronal activity confirms that the Sun belongs to sta…
Transits of hot Jupiters in X-rays and the ultraviolet have been shown to be both deeper and more variable than the corresponding optical transits. This variability has been attributed to hot Jupiters having extended atmospheres at these wavelengths. Using resolved images of the Sun from NASA's Solar Dynamics Observatory spanning 3.5 years of Solar Cycle 24 we simulate transit light curves of a hot Jupiter to investigate the impact of Solar like activity on our ability to reliably recover properties of the planet's atmosphere in soft X-rays (94 Å), the UV (131-1700 Å), and the optical (4500 Å)…
Characterising the long-term evolution of magnetic activity on Sun-like stars is important not only for stellar physics but also for understanding the environment in which planets evolve. In the past decades, many photometric surveys of open clusters have produced extensive rotation period measurements on Sun-like stars of different ages. I use these data to infer the long-term evolution of Ca II chromospheric and X-ray coronal emission on solar mass stars combining a best fit parametric model of their rotation evolution with empirical rotation-activity relationships.
While the Earth and Moon are generally similar in composition, a notable difference between the two is the apparent depletion in moderately volatile elements in lunar samples. This is often attributed to the formation process of the Moon and demonstrates the importance of these elements as evolutionary tracers. Here we show that paleo space weather may have driven the loss of a significant portion of moderate volatiles, such as sodium and potassium from the surface of the Moon. The remaining sodium and potassium in the regolith is dependent on the primordial rotation state of the Sun. Notably,…
The analysis of the effect of the hysteresis, which manifests itself in an ambiguous relationship of radiation from the photosphere, chromosphere and corona on the rise and decline phases of the solar and stellar activity cycles have done. Some indices of solar activity: the flux of the hydrogen Lyman-alpha emission, the 10.7 cm flux, the sunspot number SSN, the flux in the coronal green line 530.3 nm, the solar constant TSI and the 280 nm Mg II flux were studied. The stars with the well-determined cycles were examined to detect the effect of hysteresis between the chromosphere's S-index CaII …
The sunspot position from Greenwich Photoheliographic Results (GPR), US Air Force Solar Optical Observing Network and National Oceanic and Atmospheric Administration (USAF/NOAA), and Debrecen Photoheliographic Data (DPD) data bases in the period 1874 to 2016 were used to calculate yearly values of the solar differential-rotation parameters $A$ and $B$. The calculated differential-rotation parameters were compared with the solar-activity level. We found that the Sun rotates more differentially at the minimum than at the maximum of activity during the 1977 - 2016 epoch. An inverse correlation be…
Sunspots are a canonical marker of the Sun's internal magnetic field which flips polarity every ~22-years. The principal variation of sunspots, an ~11-year variation in number, modulates the amount of magnetic field that pierces the solar surface and drives significant variations in our Star's radiative, particulate and eruptive output over that period. This paper presents observations from the Solar and Heliospheric Observatory and Solar Dynamics Observatory indicating that the 11-year sunspot variation is intrinsically tied it to the spatio-temporal overlap of the activity bands belonging to…
We study the variability of solar activity using new photospheric proxies originally developed for the analysis of stellar magnetism with the CoRoT and Kepler photometric observations. These proxies are obtained by tracking the temporal modulations in the observations associated to the spots and magnetic features as the Sun rotates. We analyze here 21 years, spanning solar cycles 23 and 24, of the observations collected by the space-based photometric VIRGO and radial velocity GOLF instruments on board the SoHO satellite. The photospheric activity proxy Sph is then calculated for each of the th…
Stellar radial velocities play a fundamental role in the discovery of extrasolar planets and the measurement of their physical parameters as well as in the study of stellar physical properties. We investigate the impact of the solar activity on the radial velocity of the Sun using the HARPS spectrograph to obtain measurements that can be directly compared with those acquired in the extrasolar planet search programs. We use the Moon, the Galilean satellites, and several asteroids as reflectors to measure the radial velocity of the Sun as a star and correlate it with disc-integrated chromospheri…
The radial velocity of the Sun as a star is affected by its surface convection and magnetic activity. The moments of the cross-correlation function between the solar spectrum and a binary line mask contain information about the stellar radial velocity and line-profile distortions caused by stellar activity. As additional indicators, we consider the disc-averaged magnetic flux and the filling factor of the magnetic regions. Here we show that the activity-induced radial-velocity fluctuations are reduced when we apply a kernel regression to these activity indicators. The disc-averaged magnetic fl…
We present a brief review of observational results contributing to modern ideas on the evolution of stellar activity. Basic laws, derived for both rotation-age and activity-rotation relationships, allow us to trace how the activity of low-mass stars changes with age during their stay on the main sequence. We focus on the evaluation of the activity properties of stars that could be analogs of the young Sun. Our study includes joint consideration of different tracers of activity, rotation and magnetic fields of Sun-like stars of various ages. We identify rotation periods, when the saturated regi…
We applied the method of continuous wavelet-transform to high-quality time-frequency analysis to the sets of observations of relative sunspot numbers. Wavelet analysis of these data reveals the following pattern: at the same time there are several activity cycles whose periods vary widely from the quasi biennial up to the centennial period. These relatively low-frequency periodic variations of the solar activity gradually change the values of periods of different cycles in time. This phenomenon can be observed in every cycle of activity.
Ultra-precise astrometry from the Gaia mission is expected to lead to astrometric detections of more than 20,000 exoplanets in our Galaxy. One of the factors that could hamper such detections is the astrometric jitter caused by the magnetic activity of the planet host stars. In our previous study, we modeled astrometric jitter for the Sun observed equator-on. In this work, we generalize our model and calculate the photocenter jitter as it would be measured by the Gaia and Small-JASMINE missions for stars with solar rotation rate and effective temperature, but with various values of the inclina…
The activity of the Sun as a result of cyclic changes of the global magnetic field is studied. As a consequence of the analysis of magnetic activity of solar-type stars the following power dependencies were found: the dependence between the rotation periods and the effective temperatures, the dependence between the duration of the "11-year" cycles of activity and the effective temperatures, and the dependence between the duration of quasi-biennial cycles and the effective temperatures. It is shown that the physical nature of these dependencies associated with the observed properties of solar-t…
The strong chromospheric absorption lines Ca H & K are tightly connected to stellar surface magnetic fields. Only for the Sun, spectral activity indices can be related to evolving magnetic features on the solar disk. The Solar Disk-Integrated (SDI) telescope feeds the Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) of the Large Binocular Telescope (LBT) at Mt. Graham International Observatory (MGIO), Arizona, U.S.A. We present high-resolution, high-fidelity spectra that were recorded on 184 & 82 days in 2018 & 2019 and derive the Ca H & K emission ratio, i.e., the S-index. In…
The Sun and stars with low magnetic activity levels, become photometrically brighter when their activity increases. Magnetically more active stars display the opposite behaviour and get fainter when their activity increases. We reproduce the observed photometric trends in stellar variations with a model that treats stars as hypothetical Suns with coverage by magnetic features different from that of the Sun. The presented model attributes the variability of stellar spectra to the imbalance between the contributions from different components of the solar atmosphere, such as dark starspots and br…
We analyze the effect of solar features on the variability of the solar irradiance in three different spectral ranges. Our study is based on two solar-cycles' worth of full-disk photometric images from the San Fernando Observatory, obtained with red, blue and Ca II K-line filters. For each image we measure the photometric sum, Sigma, which is the relative contribution of solar features to the disk-integrated intensity of the image. The photometric sums in the red and blue continuum, Sigma_r and Sigma_b, exhibit similar temporal patterns: they are negatively correlated with solar activity, with…
Long-term variations of solar differential rotation and sunspot activity are investigated through re-analyzing the data on parameters of the differential rotation law obtained by Makarov, Tlatov, and Callebaut (1997), Javaraiah, Bertello, and Ulrich (2005a, b), and Javaraiah et al. (2009). Our results indicate that the solar surface rotation rate at the Equator (indicated by the A parameter of the standard solar rotation law) shows a secular decrease since cycle 12 onwards, given by about $1\,-\,1.5\times10^{-3}$($deg\ day^{-1} year^{-1}$). The B parameter of the standard differential rotation…
We present five decades of chromospheric activity measurements in 59 Sun-like stars as time series. These include and extend the 35 yr of stellar chromospheric activity observations by the Mount Wilson Survey (1966--2001), and continued observations at Keck by the California Planet Search (1996--). The Mount Wilson Survey was studied closely in 1995, and revealed periodic activity cycles similar to the Sun's 11 yr cycle. The California Planet Search provides more than five decades of measurements, significantly improving our understanding of these stars' activity behavior. We have curated the …
The inhibition of small-scale convection in the Sun dominates the long-term radial velocity (RV) variability: it therefore has a critical effect on light exoplanet detectability using RV techniques. We here extend our previous analysis of stellar convective blueshift and its dependence on magnetic activity to a larger sample of stars in order to extend the Teff range, to study the impact of other stellar properties, and finally to improve the comparison between observed RV jitter and expected RV variations. We estimate a differential velocity shift for Fe and Ti lines of different depths and d…
A detailed investigation of the magnetic properties of young Sun-like stars can provide valuable information on our Sun's magnetic past and its impact on the early Earth. We determine the properties of the moderately rotating young Sun-like star kappa Ceti's magnetic and activity cycles using 50 years of chromospheric activity data and six epochs of spectropolarimetric observations. The chromospheric activity was determined by measuring the flux in the Ca II H and K lines. A generalised Lomb-Scargle periodogram and a wavelet decomposition were used on the chromospheric activity data to establi…
Observations of Sun-like stars over the last half-century have improved our understanding of how magnetic dynamos, like that responsible for the 11-year solar cycle, change with rotation, mass and age. Here we show for the first time how metallicity can affect a stellar dynamo. Using the most complete set of observations of a stellar cycle ever obtained for a Sun-like star, we show how the solar analog HD 173701 exhibits solar-like differential rotation and a 7.4-year activity cycle. While the duration of the cycle is comparable to that generated by the solar dynamo, the amplitude of the brigh…
The activity levels of the solar-twin candidates HD 101364 and HD 197027 are measured and compared with the Sun, the known solar twin 18 Sco, and the solar-like star 51 Peg. Furthermore, the absolute ages of these five objects are estimated from their positions in the HR diagram and the evolutionary (relative) age compared with their activity levels. To represent the activity level of these stars, the Mount Wilson S-indices were used. To obtain consistent ages and evolutionary advance on the main sequence, we used evolutionary tracks calculated with the Cambridge Stellar Evolution Code. From o…
Despite their importance for determining the evolution of the Earth's atmosphere and surface conditions, the evolutionary histories of the Earth's atmospheric CO$_2$ abundance during the Archean eon and the Sun's activity are poorly constrained. In this study, we apply a state-of-the-art physical model for the upper atmosphere of the Archean Earth to study the effects of different atmospheric CO$_2$/N$_2$ mixing ratios and solar activity levels on the escape of the atmosphere to space. We find that unless CO$_2$ was a major constituent of the atmosphere during the Archean eon, enhanced heating…
The effect of metallicity on the granulation activity in stars is still poorly understood. Available spectroscopic parameters from the updated APOGEE-\textit{Kepler} catalog, coupled with high-precision photometric observations from NASA's \textit{Kepler} mission spanning more than four years of observation, make oscillating red giant stars in open clusters crucial testbeds. We determine the role of metallicity on the stellar granulation activity by discriminating its effect from that of different stellar properties such as surface gravity, mass, and temperature. We analyze 60 known red giant …
Frequency separations used to infer global properties of stars through asteroseismology can change depending on the strength and at what epoch of the stellar cycle the p-mode frequencies are measured. In the Sun these variations have been seen, even though the Sun is a low-activity star. In this paper, we discuss these variations and their impact on the determination of the stellar parameters (radius, mass and age) for the Sun. Using the data from maximum and minimum activity, we fitted an age for the Sun that differs on average by 0.2 Gyr: slightly older during minimum activity. The fitted ra…
We analyze the X-ray emission and chromospheric activity of Sun-like stars of F, G and K spectral classes (late-type stars) studied in the framework of the HK project. More powerful coronas are possessed by stars displaying irregular variations of their chromospheric emission, while stars with regular cyclic activity are characterized by comparatively modest X-ray luminosities and ratios of the X-ray to bolometric luminosity. This indicates that the nature of processes associated with magnetic-field amplification on the convective envelope changes appreciably in the transition from small to la…
After decades of effort, the solar activity cycle is exceptionally well characterized but it remains poorly understood. Pioneering work at the Mount Wilson Observatory demonstrated that other sun-like stars also show regular activity cycles, and suggested two possible relationships between the rotation rate and the length of the cycle. Neither of these relationships correctly describe the properties of the Sun, a peculiarity that demands explanation. Recent discoveries have started to shed light on this issue, suggesting that the Sun's rotation rate and magnetic field are currently in a transi…
Aims. The Sun shows strong variability in its magnetic activity, from Grand minima to Grand maxima, but the nature of the variability is not fully understood, mostly because of the insufficient length of the directly observed solar activity records and of uncertainties related to long-term reconstructions. Here we present a new adjustment-free reconstruction of solar activity over three millennia and study its different modes. Methods. We present a new adjustment-free, physical reconstruction of solar activity over the past three millennia, using the latest verified carbon cycle, 14C productio…
The application of the Wavelet analysis and Fourier analysis to the dataset of variations of radiation fluxes of solar-like stars and the Sun is examined. In case of the Sun the wavelet-analysis helped us to see a set of values of periods of cycles besides "11-year" cycle: the long-duration cycles of 22-year, 40-50 year and 100-120 year and short-duration cycles of 2-3,5 years and 1,3-year. We present a method of the chromospheric flux simulation using the 13 late-type stars, which have well-determined cyclic flux variations similar to the 11-year solar activity cycle. Our flux prediction is b…
The last solar minimum was, by recent standards, unusually deep and long. We are now close to the maximum of the subsequent solar cycle, which is relatively weak. In this article we make comparisons between different global (unresolved) measures of the Sun's magnetic activity, to investigate how they are responding to this weak-activity epoch. We focus on helioseismic data, which are sensitive to conditions, including the characteristics of the magnetic field, in the solar interior. Also considered are measures of the magnetic field in the photosphere (sunspot number and sunspot area), the chr…
This paper develops a planetary model to predict the occurrence of intermediate range periodicity in solar activity, in particular the ~155 day Rieger periodicity in flare activity. It is shown that periodicity at half integer multiples of the period of Mercury occurs consistently in indices of solar activity. For this reason the planetary model is based on the triggering of sunspot emergence when planetary tides peak at times of conjunction of Mercury with Venus, Earth and/or Jupiter. The periodicity of components in the planetary model match reasonably well the observed intermediate periodic…
Recent data on superflares on sun-like stars and radiocarbon data on solar activity in the past are both indicative of transient epochs of unusually high magnetic activity. We propose an explanation for the grand activity maxima in the framework of a solar dynamo model with fluctuating parameters. Solar-type dynamos are oscillatory because of the combination of the solar-type differential rotation with positive (in the Northern hemisphere) alpha-effect. An artificial reversal of the sign in the alpha-effect changes the dynamo to a steady regime with hundreds of times larger magnetic energy com…
How global faculae and network coverage relates to that of sunspots is relevant to the brightness variations of the Sun and Sun-like stars. We extend earlier studies that found the facular-to-sunspot-area ratio diminishes with total sunspot coverage. 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 that takes into account how active regions evolve. This model was inc…
The Kepler mission has been providing high-quality photometric data leading to many breakthroughs in the exoplanet search and in stellar physics. Stellar magnetic activity results from the interaction between rotation, convection, and magnetic field. Constraining these processes is important if we want to better understand stellar magnetic activity. Using the Sun, we want to test a magnetic activity index based on the analysis of the photo- metric response and then apply it to a sample of M dwarfs observed by Kepler. We estimate a global stellar magnetic activity index by measuring the standar…
Multi-wavelength studies of solar analogs (G0-5 V stars) with ages from ~50 Myr to 9 Gyr have been carried out as part of the "Sun in Time" program for nearly 20 yrs. From these studies it is inferred that the young (ZAMS) Sun was rotating more than 10x faster than today. As a consequence, young solar-type stars and the early Sun have vigorous magnetohydrodynamic (MHD) dynamos and correspondingly strong coronal X-ray and transition region / chromospheric FUV-UV emissions. To ensure continuity and homogeneity for this program, we use a restricted sample of G0-5 V stars with masses, radii, T(eff…
The variability of the spectral solar irradiance (SSI) over the course of the 11-year solar cycle is one of the manifestations of solar magnetic activity. There is a strong evidence that the SSI variability has an effect on the Earth's atmosphere. The faster rotation of the Sun in the past lead to a more vigorous action of solar dynamo and thus potentially to larger amplitude of the SSI variability on the timescale of the solar activity cycle. This could led to a stronger response of the Earth's atmosphere as well as other solar system planets' atmospheres to the solar activity cycle. We calcu…
