arXiv subjects

A. I. Shapiro

Publications and source records attributed to A. I. Shapiro.

At least 19 recordsLinked to original sources

arXiv2026

Effect of surface magnetic fields on limb darkening in main-sequence stars

Context.Stellar limb darkening encodes the thermal and radiative structure of stellar photospheres and is a key ingredient in modeling transit light curves and transmission spectra. It was recently shown that stellar surface magnetic fields modify limb darkening in stars with near-solar fundamental parameters, and that only magnetic models can reproduce high-precision transit observations for such stars. However, for stars with non-solar fundamental parameters, the magnitude of the magnetic effect on limb darkening remain unconstrained. Aims.We aim to investigate how surface magnetism affects stellar limb darkening across a range of fundamental parameters and to provide the community with center-to-limb spectra of stars at different magnetization levels. Methods. We use the MPS-ATLAS code to compute synthetic spectra from 3D radiative magnetohydrodynamic box-in-a-star simulations performed with the MURaM code. These simulations self-consistently capture photospheric magneto-convection without relying on ad hoc parameterizations. We perform calculations for main-sequence stars at solar metallicity with effective temperatures in the range Teff = 3200 - 6800 K. For stars with solar effective temperature we also consider metal-poor, M/H = -1.0, and metal-rich, M/H = 0.5, cases. Results. We show that the magnitude of the magnetic effect depends strongly on stellar fundamental parameters, increasing toward hotter and more metal-rich stars. Overall, limb darkening is significantly affected by magnetic fields in K, G, and F dwarfs, while the effect becomes negligible in M-dwarfs. We release a public database of synthetic spectra at 10 disk positions.

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arXiv2026

Sensitivity of spectral lines to granulation: from the Sun to K-type stars

Stellar granulation produces radial-velocity (RV) jitter at the 1 m/s level in Sun-like stars, limiting Earth-analog detection. A route beyond this limit is to weight spectral lines according to their granulation sensitivity. We apply a line-by-line diagnostic from 3D magneto-convection simulations that measures how each line's Doppler shift and strength respond to convective velocity and thermodynamic fluctuations. Extending our solar study, which used spatial line-profile variability across one granulation snapshot as an efficient proxy for temporal variability, we test whether this diagnostic transfers to cooler stars and examine how sensitivity changes with spectral type. We synthesize high-resolution spectra with MPS-ATLAS from 3D time-dependent MURaM simulations of the Sun and late-G and K dwarfs, focusing on FeI and FeII lines spanning broad ranges of excitation potential and strength. With decreasing $T_{\mathrm{eff}}$, weaker convective velocities and changing ionization balance produce a clearer separation between line families: FeI lines show lower velocity sensitivity and smaller fractional strength variability, while FeII lines are more sensitive. Cumulative contribution functions link spectroscopic velocity jitter to characteristic line-formation temperature. The diagnostic robustly separates stable and granulation-sensitive lines in late-G and K dwarfs, enabling spectral-type-aware cross-correlation masks and line-by-line RV weights. Solar-optimized line selections are therefore not generally portable to cooler stars, particularly when based on equivalent-width stability rather than velocity sensitivity.

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arXiv2026

Sensitivity of spectral lines to granulation: The Sun

The intrinsic variability of stars, due to acoustic oscillations, surface granulation, and magnetic activity, introduces radial velocity (RV) jitter in spectral lines, obscuring true planetary signals and hindering the detection of Earth-like planets. Granulation is particularly challenging, as it affects even the most inactive stars introducing substantial signals, with amplitudes up to 1 m/s. Disentangling granulation-induced RV jitter from signal caused by planetary reflex motion requires reliable models of stellar granulation. In this study, we present a new approach for calculating sensitivities of spectral lines to granulation. We simulate near-surface convection with 3D radiative MHD code MURaM and calculate high-resolution emergent spectra with the radiative transfer code MPS-ATLAS. We then introduce a novel methodology that uses spatial variability of spectral lines across the granulation pattern at a single moment in time to compute their temporal variability. This approach significantly reduces computational costs. We apply our approach to analyze the response of lines from neutral and singly ionized elemental species to solar granulation.We find a clear distinction between the two groups of lines: those from neutral elements tend to show stronger variations in line strength, whereas those from singly ionized elements exhibit larger variations in central wavelength. These results enable the development of spectral line masks tailored to granulation sensitivity, offering a promising strategy to reduce granulation-induced RV noise and improve exoplanet detection.

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arXiv2025

The effect of stellar magnetic activity on measurements of morning and evening asymmetry of planetary terminator

Differences in the ingress and egress shapes of transit light curves can indicate morning-evening temperature contrasts on transiting planets. Here, we pinpoint an alternative mechanism that can introduce asymmetries in transit light curves, potentially affecting the accurate determination of morning-evening differences. Small-scale magnetic field concentrations on the surfaces of the host star affect the visibility of stellar limb regions, making them brighter relative to the non-magnetic case. A difference in magnetization between the star's western and eastern limbs can thus create an asymmetry in limb brightness and, consequently, an asymmetry between transit ingress and egress. We model the limb darkening and stellar limb asymmetry in solar-like stars using the 3D radiative MHD code MURaM to simulate magnetized stellar atmospheres and the MPS-ATLAS code to synthesize spectra using ray-by-ray approach. Our results show that ingress-egress depth differences can reach up to 600 ppm for a 10000 ppm transit at 600 nm, depending on the magnetization of the stellar limbs--significantly interfering with planetary signals. Observations of the Sun show that such concentrations are often not accompanied by spots and do not manifest in photometric variability, indicating that even photometrically quiet stars can produce such asymmetries. However, planetary and stellar asymmetries exhibit distinct wavelength dependencies, which we propose to leverage for disentangling them.

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arXiv2025

Modeling HMI observables for the study of solar oscillations

Context: Helioseismology aims to infer the properties of the solar interior by analyzing observations of acoustic oscillations. The interpretation of the helioseismic data is however complicated by the non-trivial relationship between helioseismic observables and the physical perturbations associated with acoustic modes, as well as by various instrumental effects. Aims: We aim to improve our understanding of the signature of acoustic modes measured in the Helioseismic and Magnetic Imager (HMI) continuum intensity and Doppler velocity observables by accounting for radiative transfer, solar background rotation, and spacecraft velocity. Methods: We start with a background model atmosphere that accurately reproduces solar limb darkening and the Fe I 6173Å spectral line profile. We employ first-order perturbation theory to model the effect of acoustic oscillations on inferred intensity and velocity. By solving the radiative transfer equation in the atmosphere, we synthesize the spectral line, convolve it with the six HMI spectral windows, and deduce continuum intensity (hmi.Ic_45s) and Doppler velocity (hmi.V_45s) according to the HMI algorithm. Results: We analytically derive the relationship between mode displacement in the atmosphere and the HMI observables, and show that both intensity and velocity deviate significantly from simple approximations. Specifically, the continuum intensity does not simply reflect the true continuum value, while the line-of-sight velocity does not correspond to a straightforward projection of the velocity at a fixed height in the atmosphere. Our results indicate that these deviations are substantial, with amplitudes of approximately 10% and phase shifts of around 10 degrees across the detector for both observables. Moreover, these effects are highly dependent on the acoustic mode under consideration and the position on the solar disk.

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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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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

Forward modelling of brightness variations in Sun-like stars -- II. Light curves and variability

The amplitude and morphology of light curves of solar-like stars change substantially with increasing rotation rate: brightness variations get amplified and become more regular, which has so far not been explained. We develop a modelling approach for calculating brightness variations of stars with various rotation rates and use it to explain observed trends in stellar photometric variability. We combine numerical simulations of magnetic Flux Emergence And Transport (FEAT) with a model for stellar brightness variability to calculate synthetic light curves of stars as observed by the Kepler telescope. We compute the distribution of magnetic flux on the stellar surface for various rotation rates and degrees of active-region nesting (i.e., the tendency of active regions to emerge in the vicinity of recently emerged ones). Using the resulting maps of the magnetic flux, we compute the rotational variability of our simulated stellar light curves as a function of rotation rate and nesting of magnetic features and compare our calculations to Kepler observations. We show that both rotation rate and degree of nesting have a strong impact on the amplitude and morphology of stellar light curves. In order to explain the variability of the bulk of \K{} targets with known rotation rates, we need to increase the degree of nesting to values much larger than on the Sun. The suggested increase of nesting with the rotation rate can provide clues to the flux emergence process for high levels of stellar activity.

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arXiv2022

Small-scale dynamo in cool main sequence stars. II. The effect of metallicity

All cool main sequence stars including our Sun are thought to have magnetic fields. Observations of the Sun revealed that even in quiet regions small-scale turbulent magnetic fields are present. Simulations further showed that such magnetic fields affect the subsurface and photospheric structure, and thus the radiative transfer and emergent flux. Since small-scale turbulent magnetic fields on other stars cannot be directly observed, it is imperative to study their effects on the near surface layers numerically. Until recently comprehensive three-dimensional simulations capturing the effect of small-scale turbulent magnetic fields only exists for the solar case. A series of investigations extending SSD simulations for other stars has been started. Here we aim to examine small-scale turbulent magnetic fields in stars of solar effective temperature but different metallicity. We investigate the properties of three-dimensional simulations of the magneto-convection in boxes covering the upper convection zone and photosphere carried out with the MURaM code for metallicity values of $ \rm M/H = \{-1.0, 0.0, 0.5\}$ with and without a small-scale-dynamo. We find that small-scale turbulent magnetic fields enhanced by a small-scale turbulent dynamo noticeably affect the subsurface dynamics and significantly change the flow velocities in the photosphere. Moreover, significantly stronger magnetic field strengths are present in the convection zone for low metallicity. Whereas, at the optical surface the averaged vertical magnetic field ranges from 64G for M/H = 0.5 to 85G for M/H = -1.0.

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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

Stellar limb darkening. A new MPS-ATLAS library for Kepler, TESS, CHEOPS, and PLATO passbands

The detection of the first exoplanet paved the way into the era of transit photometry space missions with a revolutionary photometric precision that aim at discovering new exoplanetary systems around different types of stars. With this high precision, it is possible to derive very accurately the radii of exoplanets which is crucial for constraining their type and composition. However, it requires an accurate description of host stars, especially their center-to-limb variation of intensities (so called limb darkening) as it affects the planet-to-star radius ratio determination. We aim at improving the accuracy of limb darkening calculations for stars with a wide range of fundamental parameters. We used the recently developed 1D MPS-ATLAS code to compute model atmosphere structures and to synthesize stellar limb darkening on a very fine grid of stellar parameters. For the computations we utilized the most accurate information on chemical element abundances and mixing length parameters including convective overshoot. The stellar limb darkening was fitted using the two most accurate limb darkening laws: the power-2 and 4-parameters non-linear laws. We present a new extensive library of stellar model atmospheric structures, the synthesized stellar limb darkening curves, and the coefficients of parameterized limb-darkening laws on a very fine grid of stellar parameters in the Kepler, TESS, CHEOPS, and PLATO passbands. The fine grid allows overcoming the sizable errors introduced by the need to interpolate. Our computations of solar limb darkening are in a good agreement with available solar measurements at different view angles and wavelengths. Our computations of stellar limb darkening agree well with available measurements of Kepler stars. A new grid of stellar model structures, limb darkening and their fitted coefficients in different broad filters is provided in CDS.

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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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arXiv2022

Chromospheric Extension of the MURaM Code

Detailed numerical models of chromosphere and corona are required to understand the heating of the solar atmosphere. An accurate treatment of the solar chromosphere is complicated by the effects arising from Non Local Thermodynamic Equilibrium (NLTE) radiative transfer. A small number of strong, highly scattering lines dominate the cooling and heating in the chromosphere. Additionally, the recombination times of ionised hydrogen are longer than the dynamical timescales, requiring a non-equilibrium (NE) treatment of hydrogen ionisation. The MURaM code is extended to include the physical process required for accurate simulation of the solar chromosphere, as implemented in the Bifrost code. This includes a time-dependent treatment of hydrogen ionisation, a scattering multi-group radiation transfer scheme and approximations for NLTE radiative cooling. The inclusion of NE and NLTE physics has a large impact on the structure of the chromosphere; the NE treatment of hydrogen ionisation leads to a higher ionisation fraction and enhanced populations in the first excited state throughout cold inter-shock regions of the chromosphere. Additionally this prevents hydrogen ioniation from buffering energy fluctuations, leading to hotter shocks and cooler inter-shock regions. The hydrogen populations in the ground and first excited state are enhanced by $10^2-10^3$ in the upper chromosphere and up to $10^9$ near the transition region. Including the necessary NLTE physics leads to significant differences in chromospheric structure and dynamics. The thermodynamics and hydrogen populations calculated using the extended version of the MURaM code are consistent with previous non-equilibrium simulations. The electron number and temperature calculated using the non-equilibrium treatment of the chromosphere are required to accurately synthesise chromospheric spectral lines.

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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

MPS-ATLAS: A fast all-in-one code for synthesising stellar spectra

Context. Stellar spectral synthesis is essential for various applications, ranging from determining stellar parameters to comprehensive stellar variability calculations. New observational resources as well as advanced stellar atmosphere modelling, taking three dimensional (3D) effects from radiative magnetohydrodynamics calculations into account, require a more efficient radiative transfer. Aims. For accurate, fast and flexible calculations of opacity distribution functions (ODFs), stellar atmospheres and stellar spectra we developed an efficient code building on the well-established ATLAS9 code. The new code also paves the way for an easy and fast access to different elemental compositions in stellar calculations. Methods. For the generation of ODF tables we further developed the well-established DFSYNTHE code by implementing additional functionality, and a speed-up by employing a parallel computation scheme. In addition, the line lists used can be changed from Kurucz's recent lists. In particular, we implemented the VALD3 line list. Results. A new code, the Merged Parallelised Simplified ATLAS is presented. It combines the efficient generation of ODF, atmosphere modelling and spectral synthesis in local thermodynamic equilibrium, therefore being an all-in-one code. This all-in-one code provides more numerical functionality and is substantially faster compared to other available codes. The fully portable MPS-ATLAS code is validated against previous ATLAS9 calculations, the PHOENIX code calculations, and high quality observations.

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arXiv2021

Radiative transfer with opacity distribution functions: Application to narrow band filters

Modelling of stellar radiative intensities in various spectral pass-bands plays an important role in stellar physics. At the same time the direct calculations of the high-resolution spectrum and then integrating it over the given spectral pass-band is computationally demanding due to the vast number of atomic and molecular lines. This is particularly so when employing three-dimensional (3D) models of stellar atmospheres. To accelerate the calculations, one can employ approximate methods, e.g., the use of Opacity Distribution Functions (ODFs). Generally, ODFs provide a good approximation of traditional spectral synthesis i.e., computation of intensities through filters with strictly rectangular transmission function. However, their performance strongly deteriorates when the filter transmission noticeably changes within its pass-band, which is the case for almost all filters routinely used in stellar physics. In this context, the aims of this paper are a) to generalize the ODFs method for calculating intensities through filters with arbitrary transmission functions; b) to study the performance of the standard and generalized ODFs methods for calculating intensities emergent from 3D models of stellar atmosphere. For this purpose we use the newly-developed MPS-ATLAS radiative transfer code to compute intensities emergent 3D cubes simulated with the radiative magnetohydrodynamics code MURaM. The calculations are performed in the 1.5D regime, i.e., along many parallel rays passing through the simulated cube. We demonstrate that generalized ODFs method allows accurate and fast syntheses of spectral intensities and their centre-to-limb variations.

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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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