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Natalie A. Krivova

Publications and source records attributed to Natalie A. Krivova.

At least 19 recordsLinked to original sources

Re-evaluating solar irradiance reconstructions: No evidence for large secular trends

Most current irradiance reconstructions suggest only a modest secular increase in TSI between the 1700 and 1986 activity minima ($<1$ Wm$^{-2}$). However, 2 models, the CHRONOS and Penza et al. (2024; PEA24) models, suggest substantially larger changes of 2.1-5.9 Wm$^{-2}$. Although the two models differ in their architecture, both use cosmogenic isotope records combined with neutron monitor data to describe the long-term irradiance variability. However, cross-calibrating modulation potential reconstructions from cosmogenic isotopes against neutron monitor data remains highly uncertain. We reassess the origin and the magnitude of the large secular trends in the CHRONOS and PEA24 models. We update the CHRONOS and PEA24 models using recent heliospheric modulation potential and open solar flux reconstructions based on geomagnetic data and neutron monitor measurements, which provide a more reliable connection between cosmogenic isotope and neutron monitor records. These allow the secular component of the reconstructions to be extended consistently to the satellite era and compare the resulting TSI reconstructions with direct TSI measurements. We find that the original CHRONOS and PEA24 reconstructions substantially overestimated the secular variability in irradiance. When constrained by direct TSI measurements, CHRONOS yields a TSI increase of about 0.1-0.44 Wm$^{-2}$ between the 1700 and 1986 minima, while PEA24 returns about 0.2-0.25 Wm$^{-2}$. Our analysis indicates that the previously inferred large secular trends arose primarily from improper linking cosmogenic isotope and neutron monitor records, together with issues in the adopted smoothing approach. The updated reconstructions presented here point toward a relatively modest secular increase in TSI since the Maunder Minimum, likely below 1 Wm$^{-2}$, consistent with the majority of current irradiance models.

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The rotation-magnetism relationship in solar-type stars. Constraining magnetic flux emergence rates

The rotation-activity relationship of G-type stars results from surface magnetic fields emerging from the interior. How the magnetic flux and its emergence rate scale with rotation rate are not well understood, both observationally and theoretically. We aim to constrain the emerging magnetic flux as a function of the rotation rate in solar-type stars by numerical simulations compared to empirical constraints set by direct measurements of stellar magnetic fields. We used our flux emergence and transport (FEAT) model for stars with a range of power-law slopes for the dependence of the emerging flux on rotation. Complementing this with a heuristic account of the main flux components, we modelled the resulting mean unsigned field strength as a function of the rotation rate. We compared the results with the Zeeman-intensification measurements and spectropolarimetric data of solar-type stars. Deviations of the model from observations of G stars correlate strongly with stellar metallicity (r=0.83) and effective temperature (r=-0.76), with a combined coefficient of 0.90, reflecting the dependence of magnetic activity on these two parameters. Correcting for these effects with multilinear regression, we find that magnetic flux emergence rates must scale steeply with rotation (power-law exponent of ~1.9) to reproduce observed field strengths, significantly exceeding the estimates in the literature. We provide correction factors for metallicity and temperature for measurements of early-G-type stellar magnetic fields. Stellar magnetic flux emergence rates scale steeply with rotation, requiring active-region fields to dominate the total surface flux on rapid rotators, whereas small-scale-dynamo fields dominate for slow rotators such as the Sun. Metallicity significantly influences the rotation-magnetism relationship, necessitating sample-dependent corrections for accurate stellar dynamo modelling.

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Quantifying sunspot group nesting with density-based unsupervised clustering

Sunspot groups often emerge in spatial-temporal clusters, known as nests or complexes of activity. Quantifying how frequently such nesting occurs is important for understanding the organisation and recurrence of solar magnetic fields. We introduce an automated approach based on kernel density estimation and DBSCAN clustering to identify nests in the longitude-time domain and to measure the fraction of sunspot groups that belong to them. The method combines a smooth representation of emergence patterns with a density-based clustering procedure, validated using synthetic solar-like cycles and corrected for variations in data density. We apply this method to 151 years of sunspot-group observations from the Royal Greenwich Observatory Photoheliographic Results (RGO, 1874-1976) and Kislovodsk Mountain Astronomical Station (KMAS, 1955-2025) catalogues. Across all cycles and latitude bands, the mean nesting degree is $\langle D\rangle = 0.61 \pm 0.12$, implying that about 60 percent all sunspot groups emerge within nests. Nesting is strongest at mid-latitudes (10$^\circ$-20$^\circ$), and results from the two independent datasets agree in the period of overlap. The nesting degree significantly correlates with the solar activity level, with the correlation strengthening when small groups are excluded. The characteristic inter-nest spacing contracts from $\sim$200-500~Mm at low activity to $\sim$60-100~Mm at solar maximum, approaching typical sunspot-group dimensions. The identified nests range from compact clusters to long-lived, drifting structures, offering new quantitative constraints on the persistence and organisation of solar magnetic activity.

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Cyclic sunspot activity during the first millennium CE as reconstructed from radiocarbon

Context. Solar activity, dominated by the 11-year cyclic evolution, has been observed directly since 1610. Before that, indirect cosmogenic proxy data are used to reconstruct it over millennia. Recently, the precision of radiocarbon measurements has improved sufficiently to allow reconstructing solar activity over millennia. Aims. The first detailed reconstruction of solar activity, represented by annual sunspot numbers, is presented for 1-969 CE. Methods. The reconstruction of sunspot numbers from D14C was performed using a physics-based method involving several steps: using a carbon-cycle box model, the 14C production rate, corrected for the geomagnetic shielding, was computed from the measured data; The open solar magnetic flux was computed using a model of the heliospheric cosmic-ray modulation; Sunspot numbers were calculated using a model of the evolution of the Sun's magnetic field. The Markov Chain Monte Carlo approach was used to account for different sources of uncertainty. Results. Annual sunspot numbers were reconstructed for the first millennium CE. This period includes one extreme solar event of 774 CE and one Grand solar minimum of 650-730 CE. We could identify 91 solar cycles, of which 26 were well-defined, while 24 and 41 were reasonably and poorly defined, respectively. The mean cycle length was 10.6 years, but the lengths of individual cycles vary between 8 and 15 years. The existence of empirical Waldmeier's relations remains inconclusive. No significant periodicities were found beyond the 11-year cycle. Conclusions. This work fills the gap in the solar cycle statistics between the previously reconstructed first millennium BCE and the second millennium CE, providing vital constraints for the solar dynamo and irradiance models. A consistent 3-millennium-long reconstruction of sunspot numbers, based on a composite multi-proxy cosmogenic record, is pending.

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Structure and Dynamics of the Sun's Interior Revealed by Helioseismic and Magnetic Imager

High-resolution helioseismology observations with the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) provide a unique three-dimensional view of the solar interior structure and dynamics, revealing a tremendous complexity of the physical processes inside the Sun. We present an overview of the results of the HMI helioseismology program and discuss their implications for modern theoretical models and simulations of the solar interior.

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Revisiting the SATIRE-S irradiance reconstruction: Heritage of Mt Wilson magnetograms and Ca II K observations

Accurate information on long-term variations in solar irradiance, important for understanding the solar influence on Earth's climate, cannot be derived from direct irradiance measurements due to the comparatively short lifetimes of space-borne experiments. Models using measurements of the solar photospheric magnetic field as input can provide an independent assessment of the changes. The SATIRE-S model does just that. Unfortunately, the magnetogram archives used by SATIRE-S to recover irradiance variations are also relatively short-lived and have short mutual overlapping periods, making it difficult to evaluate their consistency. We improve SATIRE-S total solar irradiance (TSI) reconstruction by firstly incorporating magnetograms from the Mt Wilson Observatory as well as unsigned magnetograms reconstructed from Meudon, Rome, and San Fernando Ca II K data, and secondly, by re-analysing all periods of overlaps between the various archives. Our combined daily irradiance reconstruction from all eight input archives returns an excellent agreement with direct measurements of irradiance, in particular we find a correlation coefficient of 0.98 when comparing to TSIS1/TIM (Total and Spectral Solar Irradiance Sensor Total Irradiance Monitor) data. The minimum-to-minimum TSI difference between 1976 and 2019 is -0.2$\pm0.17$~Wm$^{-2}$, while the TSI difference between the 1986 and 2019 minima is statistically insignificant (-0.06$\pm0.13$~Wm$^{-2}$). Our analysis also sheds light on the trend shown by the TSI over the so-called ACRIM gap, disfavouring a hypothesised increasing trend in TSI in that period. By including more direct and indirect magnetogram time series, we have made the TSI reconstructed by SATIRE-S more robust and accurate. The new series shows a reduced trend of decreasing TSI over the last half century, which agrees well with most composites of measured TSI.

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Sun-like stars produce superflares roughly once per century

Stellar superflares are energetic outbursts of electromagnetic radiation, similar to solar flares but releasing more energy, up to $10^{36}$ erg on main sequence stars. It is unknown whether the Sun can generate superflares, and if so, how often they might occur. We used photometry from the Kepler space observatory to investigate superflares on other stars with Sun-like fundamental parameters. We identified 2889 superflares on 2527 Sun-like stars, out of 56450 observed. This detection rate indicates that superflares with energies $>10^{34}$ erg occur roughly once per century on stars with Sun-like temperature and variability. The resulting stellar superflare frequency-energy distribution is consistent with an extrapolation of the Sun's flare distribution to higher energies, so we suggest that both are generated by the same physical mechanism.

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Butterfly Diagram and Other Properties of Plage Areas from Kodaikanal Ca II K Photographs Covering 1904-2007

Ca II K observations of the Sun have a great potential for probing the Sun's magnetism and activity, as well as for reconstructing solar irradiance. The Kodaikanal Solar Observatory (KoSO) in India, houses one of the most prominent Ca II K archives, spanning from 1904 to 2007, obtained under the same experimental conditions over a century, a feat very few other sites have achieved. However, the KoSO Ca II K archive suffers from several inconsistencies (e.g., missing/incorrect timestamps of observations and orientation of some images) which have limited the use of the archive. This study is a step towards bringing the KoSO archive to its full potential. We did this by developing an automatic method to orient the images more accurately than in previous studies. Furthermore, we included more data than in earlier studies (considering images that could not previously be analyzed by other techniques as well as 2845 newly digitized images), while also accounting for mistakes in the observational date/time. These images were accurately processed to identify plage regions along with their locations, enabling us to construct the butterfly diagram of plage areas from the entire KoSO Ca II K archive covering 1904-2007. Our butterfly diagram shows significantly fewer data gaps compared to earlier versions due to the larger set of data used in this study. Moreover, our butterfly diagram is consistent with Spörer's law for sunspots, validating our automatic image orientation method. Additionally, we found that the mean latitude of plage areas calculated over the entire period is 20.5%+/-2.0 higher than that of sunspots, irrespective of the phase or the strength of the solar cycle. We also studied the North-South asymmetry showing that the northern hemisphere dominated plage areas during solar cycles 19 and 20, while the southern hemisphere dominated during solar cycles 21--23.

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Stellar Surface Magnetic Fields Impact Limb Darkening

Stars appear darker at their limbs than at their disk centers because at the limb we are viewing the higher and cooler layers of stellar photospheres. Limb darkening derived from state-of-the-art stellar atmosphere models systematically fails to reproduce recent transiting exoplanet light curves from the Kepler, TESS, and JWST telescopes -- stellar brightness obtained from measurements drops less steeply towards the limb than predicted by models. All previous models assumed atmosphere devoid of magnetic fields. Here we use our new stellar atmosphere models computed with the 3D radiative magneto-hydrodynamic code MURaM to show that small-scale concentration of magnetic fields on the stellar surface affect limb darkening at a level that allows us to explain the observations. Our findings provide a way forward to improve the determination of exoplanet radii and especially the transmission spectroscopy analysis for transiting planets, which relies on a very accurate description of stellar limb darkening from the visible through the infrared. Furthermore, our findings imply that limb darkening allows measuring the small-scale magnetic field on stars with transiting planets.

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Analysis of full-disc H alpha observations: Carrington maps and filament properties in 1909-2022

Full disc observations of the Sun in the H$α$ line provide information about the solar chromosphere and in particular about the filaments, which are dark and elongated features that lie along magnetic field polarity inversion lines. This makes them important for studies of solar magnetism. Since full disc H$α$ observations have been performed at various sites since 1800s, with regular photographic data having started in the beginning of the 20th century, they are an invaluable source of information on past solar magnetism. In this work we aimed at deriving accurate information about filaments from historical and modern full disc H$α$ observations. We have consistently processed observations from 15 H$α$ archives spanning 1909-2022. Our data processing includes photometric calibration of the data stored on photographic plates. We have constructed also Carrington maps from the calibrated H$α$ images. We find that filament areas are affected by the bandwidth of the observation. Thus, cross-calibration of the filament areas derived from different archives is needed. We have produced a composite of filament areas from individual archives by scaling all of them to the Meudon series. Our composite butterfly diagram shows very distinctly the common features of filament evolution, that is the poleward migration as well as a decrease in the mean latitude of filaments as the cycle progresses. We also find that during activity maxima, filaments on average cover about 1% of the solar surface. We see only a weak change in the amplitude of cycles in filament areas, in contrast to sunspot and plage areas. Analysis of H$α$ data for archives with contemporaneous Ca II K observations allowed us to identify and verify archive inconsistencies, which will also have implications for reconstructions of past solar magnetism and irradiance from Ca II K data.

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Long-term changes in solar activity and irradiance

The Sun is the main energy source to Earth, and understanding its variability is of direct relevance to climate studies. Measurements of total solar irradiance exist since 1978, but this is too short compared to climate-relevant time scales. Coming from a number of different instruments, these measurements require a cross-calibration, which is not straightforward, and thus several composite records have been created. All of them suggest a marginally decreasing trend since 1996. Most composites also feature a weak decrease over the entire period of observations, which is also seen in observations of the solar surface magnetic field and is further supported by Ca II K data. Some inconsistencies, however, remain and overall the magnitude and even the presence of the long-term trend remain uncertain. Different models have been developed, which are used to understand the irradiance variability over the satellite period and to extend the records of solar irradiance back in time. Differing in their methodologies, all models require proxies of solar magnetic activity as input. The most widely used proxies are sunspot records and cosmogenic isotope data on centennial and millennial time scale, respectively. None of this, however, offers a sufficiently good, independent description of the long-term evolution of faculae and network responsible for solar brightening. This leads to uncertainty in the amplitude of the long-term changes in solar irradiance. Here we review recent efforts to improve irradiance reconstructions on time scales longer than the solar cycle and to reduce the existing uncertainty in the magnitude of the long-term variability. In particular, we highlight the potential of using 3D magnetohydrodynamical simulations of the solar atmosphere as input to more physical irradiance models and of historical full-disc Ca II K observations encrypting direct facular information back to 1892.

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Spectral variability of photospheric radiation due to faculae II: Facular contrasts for cool main-sequence stars

Magnetic features on the surface of stars, such as spots and faculae, cause stellar spectral variability on time-scales of days and longer. For stars other than the Sun, the spectral signatures of faculae are poorly understood, limiting our ability to account for stellar pollution in exoplanet transit observations. Here we present the first facular contrasts derived from magnetoconvection simulations for K0, M0 and M2 main-sequence stars and compare them to previous calculations for G2 main-sequence stars. We simulate photospheres and immediate subsurface layers of main-sequence spectral types between K0 and M2, with different injected vertical magnetic fields (0 G, 100 G, 300 G and 500 G) using MURaM, a 3D radiation-magnetohydrodynamics code. We show synthetic spectra and contrasts from the UV (300 nm) to the IR (10000 nm) calculated using the ATLAS9 radiative transfer code. The calculations are performed for nine viewing angles to characterise the facular radiation across the disc. The brightness contrasts of magnetic regions are found to change significantly across spectral type, wavelength and magnetic field strength, leading to the conclusion that accurate contrasts cannot be found by scaling solar values. This is due to features of different size, apparent structure and spectral brightness emerging in the presence of a given magnetic field for different spectral types.

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Full-disc Ca II K observations -- a window to past solar magnetism

First such observations were made in 1892 and since then various sites around the world have carried out regular observations, with Kodaikanal, Meudon, Mt Wilson, and Coimbra being some of the most prominent ones. By now, Ca II K observations from over 40 different sites allow an almost complete daily coverage of the last century. Ca II K images provide direct information on plage and network regions on the Sun and, through their connection to solar surface magnetic field, offer an excellent opportunity to study solar magnetism over more than a century. This makes them also extremely important, among others, for solar irradiance reconstructions and studies of the solar influence on Earth's climate. However, these data also suffer from numerous issues, which for a long time have hampered their analysis. Without properly addressing these issues, Ca II K data cannot be used to their full potential. Here, we first provide an overview of the currently known Ca II K data archives and sources of the inhomogeneities in the data, before discussing existing processing techniques, followed by a recap of the main results derived with such data so far.

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Superflares on solar-like stars: A new method for identifying the true flare sources in photometric surveys

Over the past years, thousands of stellar flares have been detected by harvesting data from large photometric surveys. These detections, however, do not account for potential sources of contamination such as background stars appearing in the same aperture as the primary target. We present a new method for identifying the true flare sources in large photometric surveys using data from the Kepler mission. Potential flares are identified in two steps: first, we search the light curves for at least two subsequent data points exceeding a 5σ threshold above the running mean. For these two cadences, we subtract the "quiet" stellar flux from the Kepler pixel data to obtain new images where the potential flare is the main light source. In the second step, we use a Bayesian approach to fit the point spread function of the instrument to determine the most likely location of the flux excess on the detector. We applied our method to 5862 main-sequence stars with near-solar effective temperatures. We found 2274 events exceeding the 5-sigma in at least two consecutive points in the light curves. Applying the second step reduced this number to 342 superflares. Of these, 283 flares happened on 178 target stars, 47 events are associated with fainter background stars, and in 10 cases, the flare location cannot be distinguished between the target and a background star. We also present cases where flares have been reported previously but our technique could not attribute them to the target star. We conclude that 1) identifying outliers in the light curves alone is insufficient to attribute them to stellar flares and 2) flares can only be uniquely attributed to a certain star when the instrument pixel-level data together with the point spread function are taken into account. As a consequence, previous flare statistics are likely contaminated by instrumental effects and unresolved astrophysical sources.

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Scrutinizing the relationship between plage areas and sunspot areas and numbers

Studies and reconstructions of past solar activity require data on sunspots as well as faculae/plage and network. Such data are also important for understanding the magnetic activity and variability of the Sun and Sun-like stars. The longest available direct faculae/plage datasets are white-light facular and Ca II K observations going back to 1874 and 1892, respectively. Prior to that time, the only direct data available are for sunspots. We reassess the relationship between plage areas and sunspot records (areas and numbers) since 1892, to allow reconstructions of facular/plage areas which can be employed for studies going further back in time, i.e. over the period when solely sunspot observations are available. We use the plage areas derived from 38 consistently processed Ca II K archives as well as the plage area composite based on these archives. We find the relationship between plage and sunspot areas and numbers to be well represented by a power law function. We further find that the relationships depend on the bandwidth and the solar cycle strength. The reconstructions with a power law relationship are in good agreement with the original plage area series, whereas employment of a cycle-strength-dependent relationship improves the reconstructions only marginally. Performing the same analysis on other previously published plage area series, usually derived from a single archive with diverse processing techniques, returns different results when using different time series. This highlights the importance of applying a consistent processing to the various archives and demonstrates the uncertainties introduced by using previously published series. Our results have implications for past solar activity and irradiance reconstructions as well as for stellar activity studies, which sometimes assume a linear dependence between plage and sunspot areas.

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Reconstructing solar irradiance from historical Ca II K observations. I. Method and its validation

Knowledge of solar irradiance variability is critical to Earth's climate models and understanding the solar influence on Earth's climate. Direct solar irradiance measurements are only available since 1978. Reconstructions of past variability typically rely on sunspot data. These provide only indirect information on the facular and network regions, which are decisive contributors to irradiance variability on timescales of the solar cycle and longer. Our ultimate goal is to reconstruct past solar irradiance variations using historical full-disc Ca II K observations to describe the facular contribution independently of sunspot observations. Here, we develop the method and test it extensively by using modern CCD-based Ca II K observations and carry out initial tests on two photographic archives. We employ carefully reduced and calibrated Ca II K images from 13 datasets, such as those from the Meudon, Mt Wilson, and Rome observatories. We convert them to unsigned magnetograms and then use them as input to the adapted SATIRE model to reconstruct TSI variations over the period 1978-2019, for which direct irradiance measurements are available. The reconstructed TSI from the analysed Ca II K archives agrees well with direct TSI measurements and existing reconstructions. The model also returns good results on data taken with different bandpasses and images with low spatial resolution. Historical Ca II K archives suffer from numerous inconsistencies, but we show that these archives can still be used to reconstruct TSI with reasonable accuracy provided the observations are accurately processed. By using the unsigned magnetograms of the Sun reconstructed from high-quality Ca II K observations as input into the SATIRE model, we can reconstruct solar irradiance variations nearly as accurately as from directly recorded magnetograms.

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On the size distribution of spots within sunspot groups

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 solar cycles 17 to 24. We find that at the time when the group area reaches its maximum, the single biggest spot in a group typically occupies about 60% of the group area. For half of all groups, $\rm R$ lies in the range between roughly 50% and 70%. We also find R to change with the group area, $\rm{A_{group}}$, such that $\rm{R}$ reaches a maximum of about 0.65 for groups with $\rm{A_{group}}\approx 200μ$Hem and then remains at about 0.6 for lager groups. Our findings imply a scale invariant emergence pattern, providing an observational constraint on the emergence process. Furthermore, extrapolation of our results to larger sunspot groups may have a bearing on the giant unresolved starspot features found in Doppler images of highly active sun-like stars. Our results suggest that such giant features are composed of multiple spots, with the largest spot occupying roughly 55--75% of the total group area (i.e. of the area of the giant starspots seen in Doppler images).

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Predictions of astrometric jitter for Sun-like stars. I. The model and its application to the Sun as seen from the ecliptic

The advent of Gaia, capable of measuring stellar wobbles caused by orbiting planets, raised an interest to the astrometric detection of exoplanets. Another source of such wobbles (often also called jitter) is stellar magnetic activity. A quantitative assessment of the stellar astrometric jitter is important for a more reliable astrometric detection and characterisation of exoplanets. We calculate the displacement of the solar photocentre due to the magnetic activity for an almost 16-year period (February 2, 1999 - August 1, 2014). We also investigate how the displacement depends on the spectral passband chosen for observations, including the wavelength range to be covered by the upcoming Small-JASMINE mission of JAXA. This is done by extending the SATIRE-S model for solar irradiance variability to calculating the displacement of the solar photocentre caused by the magnetic features on the surface of the Sun. We found that the peak to peak amplitude of the solar photocentre displacement would reach 0.5 mas if the Sun were located 10 pc away from the observer and observed in the Gaia G filter. This is by far too small to be detected by the Gaia mission. However, the Sun is a relatively inactive star so that one can expect significantly larger signals for younger, and, consequently, more active stars. The model developed in this study can be combined with the simulations of emergence and surface transport of magnetic flux which have recently became available to model the astrometric jitter over the broad range of magnetic activities.

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