arXiv subjects

N. A. Krivova

Publications and source records attributed to N. A. Krivova.

At least 19 recordsLinked to original sources

arXiv2026

Reconstruction of annual solar irradiance over the last three millennia

Solar irradiance measurements are limited to the last few decades, requiring reconstructions to assess solar variability on longer timescales and its impact on Earth's climate. We present the first physics-based reconstruction of total solar irradiance (TSI) at annual resolution over the last three millennia. The reconstruction is obtained by extending the SATIRE-T model beyond the telescopic era using recently published, annually resolved sunspot number series derived from cosmogenic isotope records. This yields a continuous, physics-based TSI record extending from the satellite era back over the last three millennia, with annual resolution throughout the pre-telescopic period. Over the full three-millennia interval, the reconstructed TSI exhibits a maximum difference of $1.04_{-0.2}^{+0.14}\,\mathrm{W\,m^{-2}}$, defined as the difference between the maximum and minimum of the 50-yr running mean values.

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arXiv2026

Empirical flare energy limits for the largest historical sunspots

Extreme solar particle events reveal that the Sun can occasionally produce eruptions significantly more energetic than those observed in the modern era. These events are thought to originate from powerful coronal mass ejections, typically associated with large solar flares triggered by magnetic field reconnection in complex active regions. Stellar observations indicate that Sun-like stars can host superflares exceeding 10^34 erg roughly once per century, yet it remains uncertain whether the Sun can reach such flare energies. We empirically estimate the upper limit of solar flare energies using statistical relations between flare - ribbon areas and released energy derived from modern observations. By extrapolating these upper-envelope relations to the largest sunspot group recorded since 1859 - the Great Sunspot of 8 April 1947 - we find that exceptionally large and complex solar active regions could, in principle, produce flares with bolometric energies of a few 10^34 erg.

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arXiv2026

Solar Irradiance Reconstruction over the Telescopic Era Using a Revised Photospheric Magnetic Field Model

The Sun is the primary source of energy for Earth and one of the main external drivers of its climate. Solar irradiance -- the radiative power emitted by the Sun and received at 1-AU -- varies on all observable timescales. It is measured as total solar irradiance (TSI), the spectrally integrated flux, or as spectral solar irradiance (SSI), its wavelength-dependent distribution. However, direct space-based irradiance measurements span only about five decades and are too short to capture long-term trends, making reconstructions crucial for studying solar influence on climate. On climate-relevant timescales, irradiance variations are driven by changes in the solar surface magnetic field, which form the basis of reconstructions guided by physics. Here we present revised reconstructions of TSI and SSI over the past four centuries using the physics-based SATIRE-T (Spectral And Total Irradiance REconstruction, for the Telescopic era) model. SATIRE-T relates irradiance variability to the evolution of the solar surface magnetic field inferred from sunspot number records. In this work, we implement a recently revised description of magnetic field evolution that more realistically links the emergence of small-scale magnetic features to sunspot activity, constrained by modern observations. Using two independent sunspot number series as input, we obtain consistent reconstructions of magnetic flux and solar irradiance. The model reproduces the observed or independently reconstructed total and open magnetic flux, and agrees closely with satellite measurements of TSI and Lyman-$α$ irradiance, with correlation coefficients of 0.81-0.98 for 81-day-smoothed space-based TSI records, 0.69-0.85 for TSI at daily cadence, and 0.92 for daily Lyman-$α$ irradiance. On secular timescales, the reconstructed TSI increases by 0.67-0.75$\,\mathrm{W/m^2}$ between the 50-year means over 1650-1700 and 1967-2017.

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arXiv2025

Solar limb faculae: intensity contrast from two vantage points

Small-scale magnetic flux concentrations contribute significantly to the brightness variations of the Sun, yet observing them - particularly their magnetic field - near the solar limb remains challenging. Solar Orbiter offers an unprecedented second vantage point for observing the Sun. When combined with observations from the perspective of Earth, this enables simultaneous dual-viewpoint measurements of these magnetic structures, thereby helping to mitigate observational limitations. Using such a dual-viewpoint geometry, we characterise the brightness contrast of faculae near the limb as a function of both their associated magnetic field strength and the observation angle. We analyse data from Polarimetric and Helioseismic Imager on board Solar Orbiter (SO/PHI), obtained during an observation program conducted in near-quadrature configuration with Earth, in combination with data from the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory (SDO/HMI). The High Resolution Telescope of SO/PHI observed a facular region located near disc centre as seen from its vantage point, while the same region was simultaneously observed near the solar limb by SDO/HMI. We identify faculae and determine their magnetic field strength from the disc-centre observations, and combine these with continuum intensity measurements at the limb to derive dual-viewpoint contrast curves. We then compare these with contrast curves derived from SDO/HMI alone. Using two viewpoints, we consistently find higher facular contrast near the limb than from a single-viewpoint.

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arXiv2025

Solar variability in the Mg II h and k lines

Solar irradiance and its variations in the ultraviolet (UV) control the photochemistry in Earth's atmosphere and influence Earth's climate. The variability of Mg II h and k core-to-wing ratio, also known as the Mg II index, is highly correlated with the solar UV irradiance variability. Because of this, Mg II index is routinely used as a proxy for solar UV irradiance variability, which can help to get insights into the influence of solar UV irradiance variability on Earth's climate. Measurements of the Mg II index, however, have only been carried out since 1978 and do not cover the climate relevant timescales longer than a few decades. Here we present a model to calculate the Mg II index and its variability based on the well-established SATIRE (Spectral And Total Irradiance REconstruction) model. We demonstrate that our model calculations yield an excellent agreement with the observed Mg II index variations, both on the solar activity cycle and on the solar rotation timescales. Using this model, we synthesize Mg II index timeseries on climate relevant timescales of decades and longer. Here we present the timeseries of the Mg II index spanning nearly three centuries.

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arXiv2024

The variation in the response of solar full-disc magnetographs

We compared magnetograms from the KPVT/SPM, SoHO/MDI, SOLIS/VSM, and SDO/HMI with the aim of probing the effect on measured solar magnetism of the variation in instrument response with time, magnetogram signal level, and position on the solar disc. Taking near-simultaneous observations from the various instruments, we examined the surface coverage by magnetic activity and the effect of cross-calibrating the various instruments under different assumptions. By comparing the surface coverage by magnetic activity in the observations from the various instruments, we traced the effect of the time variation in instrument response on the longitudinal magnetogram signal and disc-integrated unsigned magnetic flux. This yielded evidence of acute changes in the response of MDI and VSM with certain events such as the SoHO vacation in 1998 and the upgrade of the VSM CCD camera in 2009. Excluding these changes, the effect of instrument instability on the magnetogram signal and disc-integrated magnetic flux appears to be rather benign, with an associated uncertainty of less than 2%. We determined the magnetogram signal ratio between each instrument pairing as a function of magnetogram signal level and distance from disc centre and with it cross-calibrated the various instruments. We compared the result with that from repeating the cross-calibration with the overall magnetogram signal ratio. This allowed us to estimate the uncertainty in the magnetogram signal associated with the variation in instrument response with magnetogram signal level and distance from disc centre to be about 8% to 14%. The corresponding uncertainty in the disc-integrated magnetic flux is about 7% to 23 %. The results here will be useful to the interpretation of SPM, MDI, VSM, and HMI magnetograms. As examples, we applied our findings to selected results from earlier studies based on such data.

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arXiv2023

Reconstruction of total solar irradiance variability as simultaneously apparent from Solar Orbiter and Solar Dynamics Observatory

Solar irradiance variability has been monitored almost exclusively from the Earth's perspective. {We present a method to combine the unprecedented observations of the photospheric magnetic field and continuum intensity from outside the Sun-Earth line, which is being recorded by the Polarimetric and Helioseismic Imager on board the Solar Orbiter mission (SO/PHI), with solar observations recorded from the Earth's perspective to examine the solar irradiance variability from both perspectives simultaneously.} Taking SO/PHI magnetograms and continuum intensity images from the cruise phase of the Solar Orbiter mission and concurrent observations from the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) as input into the SATIRE-S model, we successfully reconstructed the total solar irradiance variability as apparent from both perspectives. In later stages of the SO mission, the orbital plane will tilt in such a way as to bring the spacecraft away from the ecliptic to heliographic latitudes of up to $33^{\circ}$. The current study sets the template for the reconstruction of solar irradiance variability as seen from outside the ecliptic from data that SO/PHI is expected to collect from such positions. {Such a reconstruction will be beneficial to factoring inclination into how the brightness variations of the Sun compare to those of other cool stars, whose rotation axes are randomly inclined.

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arXiv2023

Modeling Stellar CaII H & K Emission Variations: Spot Contribution to the S-index

The S-index is a measure of emission in the CaII H & K lines and is a widely used proxy of stellar magnetic activity. It has been assumed until now that the S-index is mainly affected by bright plage regions in the chromosphere. In particular, the effect of starspots on the S-index has been neglected. In this study we revisit this assumption. For this we analyze high-resolution observations of sunspots recorded in the CaII H spectral line at the Swedish 1-m Solar Telescope and determine the contrast of spots with respect to the quiet surroundings. We find that the CaII H line core averaged over whole sunspots (including superpenumbrae) is brighter than in the quiet surroundings and that the spot contrast in the line core is comparable to the facular contrast. This allows us to get a first estimate of the influence of spots on the S-index. We show that spots increase the S-index. While this increase is quite small for the Sun, it becomes significantly larger for more active stars. Further, we show that the inclusion of the contribution of spots to the S-index strongly affects the relationship between the S-index and stellar disk area coverages by spots and faculae, and present the new relations.

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arXiv2023

Intensity contrast of solar network and faculae close to the solar limb, observed from two vantage points

The brightness of faculae and network depends on the angle at which they are observed and the magnetic flux density. Close to the limb, assessment of this relationship has until now been hindered by the increasingly lower signal in magnetograms. This preliminary study aims at highlighting the potential of using simultaneous observations from different vantage points to better determine the properties of faculae close to the limb. We use data from the Solar Orbiter/Polarimetric and Helioseismic Imager (SO/PHI), and the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI), recorded at $\sim60^\circ$ angular separation of their lines of sight at the Sun. We use continuum intensity observed close to the limb by SO/PHI and complement it with the co-observed $B_{\rm LOS}$ from SDO/HMI, originating closer to disc centre (as seen by SDO/HMI), thus avoiding the degradation of the magnetic field signal near the limb. We derived the dependence of facular brightness in the continuum on disc position and magnetic flux density from the combined observations of SO/PHI and SDO/HMI. Compared with a single point of view, we were able to obtain contrast values reaching closer to the limb and to lower field strengths. We find the general dependence of the limb distance at which the contrast is maximum on the flux density to be at large in line with single viewpoint observations, in that the higher the flux density is, the closer the turning point lies to the limb. There is a tendency, however, for the maximum to be reached closer to the limb when determined from two vantage points. We note that due to the preliminary nature of this study, these results must be taken with caution. Our analysis shows that studies involving two viewpoints can significantly improve the detection of faculae near the solar limb and the determination of their brightness contrast relative to the quiet Sun.

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arXiv2022

Faculae cancel out on the surfaces of active Suns

Surfaces of the Sun and other cool stars are filled with magnetic fields, which are either seen as dark compact spots or more diffuse bright structures like faculae. Both hamper detection and characterisation of exoplanets, affecting stellar brightness and spectra, as well as transmission spectra. However, the expected facular and spot signals in stellar data are quite different, for instance they have distinct temporal and spectral profiles. Consequently, corrections of stellar data for magnetic activity can greatly benefit from the insight on whether the stellar signal is dominated by spots or faculae. Here, we utilise a surface flux transport model (SFTM) to show that more effective cancellation of diffuse magnetic flux associated with faculae leads to spot area coverages increasing faster with stellar magnetic activity than that by faculae. Our calculations explain the observed dependence between solar spot and facular area coverages and allow its extension to stars more active than the Sun. This extension enables anticipating the properties of stellar signal and its more reliable mitigation, leading to a more accurate characterisation of exoplanets and their atmospheres.

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arXiv2022

Predictions of Astrometric Jitter for Sun-like Stars. III. Fast Rotators

A breakthrough in exoplanet detections is foreseen with the unprecedented astrometric measurement capabilities offered by instrumentation aboard Gaia space observatory. Besides, astrometric discoveries of exoplanets are expected from the planned space mission, Small-JASMINE. In this setting, the present series of papers focuses on estimating the effect of magnetic activity of G2V-type host stars on the astrometric signal. This effect interferes with the astrometric detections of Earth-mass planets. While the first two papers considered stars rotating at the solar rotation rate, this paper focuses on stars having solar effective temperature and metallicity but rotating faster than the Sun, and consequently more active. By simulating the distribution of active regions on such stars using the Flux Emergence And Transport model, we show that the contribution of magnetic activity to the astrometric measurements becomes increasingly significant with increasing rotation rates. We further show that the jitter for the most variable periodic Kepler stars is high enough to be detected by Gaia. Furthermore, due to a decrease in the facula-to-spot area ratio for more active stars, the magnetic jitter is found to be spot-dominated for rapid rotators. Our simulations of the astrometric jitter has the potential to aid the interpretation of data from Gaia and upcoming space astrometry missions.

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arXiv2021

The relationship between bipolar magnetic regions and their sunspots

The relationship between bipolar magnetic regions (BMRs) and their sunspots is an important property of the solar magnetic field, but it is not well constrained. One consequence is that it is a challenge for surface flux transport models (SFTMs) based on sunspot observations to determine the details of BMR emergence, which they require as input, from such data. We aimed to establish the relationship between the amount of magnetic flux in newly emerged BMRs and the area of the enclosed sunspots. Earlier attempts to constrain BMR magnetic flux were hindered by the fact that there is no proper database of the magnetic and physical properties of newly emerged BMRs currently available. We made use of the empirical model of the relationship between the disc-integrated facular and network magnetic flux and the total surface coverage by sunspots reported in a recent study. The structure of the model is such that it enabled us to establish, from these disc-integrated quantities, an empirical relationship between the magnetic flux and sunspot area of individual newly emerged BMRs, circumventing the lack of any proper BMR database. Applying the constraint on BMR magnetic flux derived here to an established SFTM retained its ability to replicate various independent datasets and the correlation between the model output polar field at the end of each cycle and the observed strength of the following cycle. The SFTM output indicates that facular and network magnetic flux rises with increasing sunspot magnetic flux at a slowing rate such that it appears to gradually saturate, analogous to earlier studies. The activity dependence of the ratio of facular and network flux to sunspot flux is consistent with the findings of recent studies: although the Sun is faculae-dominated, it is only marginally so as facular and network brightening and sunspot darkening appear to be closely balanced.

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arXiv2021

Predictions of Astrometric Jitter for Sun-like Stars. II. Dependence on Inclination, Metallicity, and Active-Region Nesting

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 inclination angle of the stellar rotation axis. In addition, we consider the effect of metallicity and of nesting of active regions (i.e. the tendency of active regions to emerge in the vicinity of each other). We find that, while the jitter of stars observed equator-on does not have any long-term trends and can be easily filtered out, the photocenters of stars observed out of their equatorial planes experience systematic shifts over the course of the activity cycle. Such trends allow the jitter to be detected with continuous measurements, in which case it can interfere with planet detectability. An increase in the metallicity is found to increase the jitter caused by stellar activity. Active-region nesting can further enhance the peak-to-peak amplitude of the photocenter jitter to a level that could be detected by Gaia.

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arXiv2021

Modelling the evolution of the Sun's open and total magnetic flux

Solar activity in all its varied manifestations is driven by the magnetic field. Particularly important for many purposes are two global quantities, the Sun's total and open magnetic flux, which can be computed from sunspot number records using models. Such sunspot-driven models, however, do not take into account the presence of magnetic flux during grand minima, such as the Maunder minimum. Here we present a major update of a widely used simple model, which now takes into account the observation that the distribution of all magnetic features on the Sun follows a single power law. The exponent of the power law changes over the solar cycle. This allows for the emergence of small-scale magnetic flux even when no sunspots are present for multiple decades and leads to non-zero total and open magnetic flux also in the deepest grand minima, such as the Maunder minimum, thus overcoming a major shortcoming of the earlier models. The results of the updated model compare well with the available observations and reconstructions of the solar total and open magnetic flux. This opens up the possibility of improved reconstructions of sunspot number from time series of cosmogenic isotope production rate.

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arXiv2021

Modeling stellar Ca II H & K emission variations. I. Effect of inclination on the S-index

The emission in the near ultraviolet Ca II H & K lines is modulated by stellar magnetic activity. Although this emission, quantified via the S-index, has been serving as a prime proxy of stellar magnetic activity for several decades, many aspects of the complex relation between stellar magnetism and Ca II H & K emission are still unclear. The amount of measured Ca II H & K emission is suspected to be affected not only by the stellar intrinsic properties but also by the inclination angle of the stellar rotation axis. Until now such an inclination effect on S-index has remained largely unexplored. To fill this gap, we develop a physics-based model to calculate S-index, focusing on the Sun. Using the distributions of solar magnetic features derived from observations together with Ca II H & K spectra synthesized in non-local thermodynamic equilibrium, we validate our model by successfully reconstructing the observed variations of solar S-index over four activity cycles. Further, using the distribution of magnetic features over the visible solar disk obtained from surface flux transport simulations, we obtain S-index time series dating back to 1700 and investigate the effect of inclination on S-index variability, both on the magnetic activity cycle and the rotational timescales. We find that when going from an equatorial to a pole-on view, the amplitude of S-index variations decreases weakly on the activity cycle timescale and strongly on the rotational timescale (by about 22% and 81%, respectively, for a cycle of intermediate strength). The absolute value of S-index depends only weakly on the inclination. We provide analytical expressions that model such dependencies.

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arXiv2021

The Dimmest State of the Sun

How the solar electromagnetic energy entering the Earth's atmosphere varied since pre-industrial times is an important consideration in the climate change debate. Detrimental to this debate, estimates of the change in total solar irradiance (TSI) since the Maunder minimum, an extended period of weak solar activity preceding the industrial revolution, differ markedly, ranging from a drop of 0.75 Wm-2 to a rise of 6.3 Wm-2. Consequently, the exact contribution by solar forcing to the rise in global temperatures over the past centuries remains inconclusive. Adopting a novel approach based on state-of-the-art solar imagery and numerical simulations, we establish the TSI level of the Sun when it is in its least-active state to be 2.0 +/- 0.7 Wm-2 below the 2019 level. This means TSI could not have risen since the Maunder minimum by more than this amount, thus restricting the possible role of solar forcing in global warming.

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arXiv2021

Intensity contrast of solar network and faculae -- II. Implications for solar irradiance modelling

We aim to gain insight into the effect of network and faculae on solar irradiance from their apparent intensity. Taking full-disc observations from the Solar Dynamics Observatory, we examined the intensity contrast of network and faculae in the continuum and core of the Fe I 6173 Å line and 1700 Å, including the variation with magnetic flux density, distance from disc centre, nearby magnetic fields, and time. The brightness of network and faculae is believed to be suppressed by nearby magnetic fields from its effect on convection. The difference in intensity contrast between the quiet-Sun network and active region faculae, noted by various studies, arises because active regions are more magnetically crowded and is not due to any fundamental physical differences between network and faculae. These results highlight that solar irradiance models need to include the effect of nearby magnetic fields on network and faculae brightness. We found evidence that suggests that departures from local thermal equilibrium (LTE) might have limited effect on intensity contrast. This could explain why solar irradiance models that are based on the intensity contrast of solar surface magnetic features calculated assuming LTE reproduce the observed spectral variability even where the LTE assumption breaks down. Certain models of solar irradiance employ chromospheric indices as direct indications of the effect of network and faculae on solar irradiance. Based on past studies of the Ca II K line and on the intensity contrast measurements derived here, we show that the fluctuations in chromospheric emission from network and faculae are a reasonable estimate of the emission fluctuations in the middle photosphere, but not of those in the lower photosphere. The data set, which extends from 2010 to 2018, indicates that intensity contrast was stable to about 3% in this period.

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arXiv2020

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

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 incorporated into a total solar irradiance (TSI) model. The model presented here replicates most of the observed variability in the facular indices, 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. 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 as sunspot darkening starts to rise more rapidly with activity than facular brightening. This bolsters the interpretation of this behavior of Sun-like stars as the transition from a faculae-dominated to a spot-dominated regime.

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