Accurate calculations of starspot spectra are essential for multiple applications in astronomy. The current standard is to represent starspot spectra by spectra of stars that are cooler than the quiet star regions. This implies approximating a starspot as a nonmagnetic 1D structure in radiative-convective equilibrium, parametrizing convective energy transport by mixing-length theory. It is the inhibition of convection by the starspot magnetic field that is emulated by using a lower spot temperature relative to the quiet stellar regions. Here, we take a different approach, avoiding the approximate treatment of convection and instead self-consistently accounting for the interaction between matter, radiation, and the magnetic field. We simulate spots on G2V, K0V, and M0V stars with the 3D radiative magnetohydrodynamics code MURaM and calculate spectra (R approximate to 500 from 250 to 6000 nm) using ray-by-ray radiative transfer with the MPS-ATLAS code. We find that the 1D models fail to return accurate umbral and penumbral spectra on K0V and M0V stars, where convective and radiative transfer of energy is simultaneously important over a broad range of atmospheric heights, rendering mixing-length theory inaccurate. However, 1D models work well for G2V stars, where both radiation and convection significantly contribute to energy transfer only in a narrow region near the stellar surface. Quantitatively, the 1D approximation leads to errors longward of 500 nm of about 50% for both umbral and penumbral flux contrast relative to quiet star regions on M0V stars and less than 2% (for umbrae) and 10% (for penumbrae) for G2V stars.

Context. Three-dimensional (3D) radiative magnetohydrodynamic (MHD) simulations are the only way to model stellar atmospheres without any ad hoc parameterisations. Several 3D radiative MHD codes have achieved good quantitative agreement with observables for our Sun. Aims. We aim to validate the most recent version of the MURaM code by comparing MURaM results to well-established quiet-Sun measurements, in particular spatially averaged measurements that are relevant for stellar studies. This extends the number of solar observables that MURaM can reproduce with high precision. Our validation is an essential condition to ensure that MURaM can be used to accurately calculate the spectra of other cool stars. Methods. We simulated the solar photosphere and upper convection zone, which harbours a small-scale-dynamo. Using time series of 3D snapshots, we calculated the spectral irradiance, limb darkening, and selected spectral lines, which we compared to observations. Results. The computed observables agree well with the observations; in particular, the limb darkening of the quiet Sun is reproduced remarkably well.

Stars appear darker at their limbs than at their disk centres because at the limb we are viewing the higher and cooler layers of stellar photospheres. Yet, 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. Previous models assumed stellar atmospheres devoid of magnetic fields. Here we use stellar atmosphere models computed with the three-dimensional radiative magnetohydrodynamic code MURaM to show that a small-scale concentration of magnetic fields on the stellar surface affects 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 to the infrared. Furthermore, our findings imply that limb darkening allows estimates of the small-scale magnetic field strength on stars with transiting planets. An outstanding discrepancy between observations and models of stellar limb darkening is resolved here by the inclusion of stellar surface magnetism in models. This will enable an improved characterization of transiting exoplanets.

Stellar limb darkening must be properly accounted for to accurately determine the radii of exoplanets at various wavelengths. The standard approach to address limb darkening involves either using laws with coefficients from modeled stellar spectra or determining the coefficients empirically during light-curve fitting of the data. Here, we test how accurately three common laws-quadratic, power, and a three-parameter law-can reproduce stellar limb darkening at different wavelengths and across a broad range of stars. We show that using a quadratic limb-darkening law, which is most frequently employed by the community, leads to wavelength-dependent offsets in retrieved transmission spectra. For planets with high impact parameters (b larger than about 0.5), the amplitude of these offsets can reach 1% of the transit depth, which in some cases is comparable to and can even exceed the expected signals from the planetary atmosphere. Furthermore, the quadratic law causes an offset in the value of the impact parameter when it is determined by fitting the broadband transit light curves. In contrast, using the Kipping-Sing three-parameter law leads to robust retrievals. We advocate the use of this law in retrievals, especially for transits with large impact parameters.

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.

Ultracool dwarf stars are abundant, long-lived and uniquely suited to enable the atmospheric study of transiting terrestrial companions with the JWST. Among them, the most prominent is the M8.5V star TRAPPIST-1 and its seven planets. While JWST Cycle 1 observations have started to yield preliminary insights into the planets, they have also revealed that their atmospheric exploration requires a better understanding of their host star. Here we propose a roadmap to characterize the TRAPPIST-1 system - and others like it - in an efficient and robust manner with JWST. We notably recommend that - although more challenging to schedule - multi-transit windows be prioritized to mitigate the effects of stellar activity and gather up to twice more transits per JWST hour spent. We conclude that, for such systems, planets cannot be studied in isolation by small programmes but rather need large-scale, joint space- and ground-based initiatives to fully exploit the capabilities of JWST for the exploration of terrestrial planets. The JWST has the potential to increase our understanding of terrestrial exoplanets and their atmospheres, but the various signal contaminations need to be isolated and quantified. Using JWST Cycle 1 observations of TRAPPIST-1 as a benchmark, this Perspective proposes a series of steps to use future JWST data efficiently for this purpose.

Stellar spectra contain a large amount of information about the conditions in stellar atmospheres. However, extracting this information is challenging and demands comprehensive numerical modelling. Here, we present stellar spectra synthesized using the recently developed state-of-the-art MPS-ATLAS code on a fine grid of stellar fundamental parameters. These calculations have been extensively validated against solar and stellar observations and can be used for various astrophysical applications. The spectra are available at the Max Planck Digital Library (MPDL, https://edmond.mpdl.mpg.de/dataset.xhtml?persistentId=doi:10.17617/3.NJ56TR) and have been also incorporated into the ExoTiC-LD python package (https://github.com/Exo-TiC/ExoTiC-LD/) which returns stellar limb darkening coefficients used for the software package Exoplanet Timeseries Characterisation (ExoTic).

Study Analysis Group 21 (SAG21) of NASA's Exoplanet Exploration Program Analysis Group (ExoPAG) was organized to study the effect of stellar contamination on space-based transmission spectroscopy, a method for studying exoplanetary atmospheres by measuring the wavelength-dependent radius of a planet as it transits its star. Transmission spectroscopy relies on a precise understanding of the spectrum of the star being occulted. However, stars are not homogeneous, constant light sources but have temporally evolving photospheres and chromospheres with inhomogeneities like spots, faculae, plages, granules, and flares. This SAG brought together an interdisciplinary team of more than 100 scientists, with observers and theorists from the heliophysics, stellar astrophysics, planetary science, and exoplanetary atmosphere research communities, to study the current research needs that can be addressed in this context to make the most of transit studies from current NASA facilities like HST and JWST. The analysis produced 14 findings, which fall into three Science Themes encompassing (1) how the Sun is used as our best laboratory to calibrate our understanding of stellar heterogeneities ("The Sun as the Stellar Benchmark"), (2) how stars other than the Sun extend our knowledge of heterogeneities ("Surface Heterogeneities of Other Stars") and (3) how to incorporate information gathered for the Sun and other stars into transit studies ("Mapping Stellar Knowledge to Transit Studies"). In this invited review, we largely reproduce the final report of SAG21 as a contribution to the peer-reviewed literature.

Atmospheric ozone and oxygen protect the terrestrial biosphere against harmful ultraviolet (UV) radiation. Here, we model atmospheres of Earth-like planets hosted by stars with near-solar effective temperatures (5300 to 6300 K) and a broad range of metallicities covering known exoplanet host stars. We show that paradoxically, although metal-rich stars emit substantially less ultraviolet radiation than metal-poor stars, the surface of their planets is exposed to more intense ultraviolet radiation. For the stellar types considered, metallicity has a larger impact than stellar temperature. During the evolution of the universe, newly formed stars have progressively become more metal-rich, exposing organisms to increasingly intense ultraviolet radiation. Our findings imply that planets hosted by stars with low metallicity are the best targets to search for complex life on land.

The reliable characterization of planetary atmospheres with transmission spectroscopy requires realistic modeling of stellar magnetic features, since features that are attributable to an exoplanet atmosphere could instead stem from the host star's magnetic activity. Current retrieval algorithms for analysing transmission spectra rely on intensity contrasts of magnetic features from 1D radiative-convective models. However, magnetic features, especially faculae, are not fully captured by such simplified models. Here we investigate how well such 1D models can reproduce 3D facular contrasts, taking a G2V star as an example. We employ the well established radiative magnetohydrodynamic code MURaM to obtain three-dimensional simulations of the magneto-convection and photosphere harboring a local small-scale-dynamo. Simulations without additional vertical magnetic fields are taken to describe the quiet solar regions, while simulations with initially 100 G, 200 G and 300 G vertical magnetic fields are used to represent different magnetic activity levels. Subsequently, the spectra emergent from the MURaM cubes are calculated with the MPS-ATLAS radiative transfer code. We find that the wavelength dependence of facular contrast from 1D radiative-convective models cannot reproduce facular contrasts obtained from 3D modeling. This has far reaching consequences for exoplanet characterization using transmission spectroscopy, where accurate knowledge of the host star is essential for unbiased inferences of the planetary atmospheric properties.

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.

We aim to improve the accuracy of radiative energy transport in three-dimensional radiation hydrodynamical simulations in ANTARES (A Numerical Tool for Astrophysical RESearch). We implement in the ANTARES short-characteristics numerical schemes a modification of the Bézier interpolant solver. This method yields a smoother surface structure in simulations of solar convection and reduces the artifacts appearing due to the limited number of rays along which the integration is done. Reducing such artifacts leads to increased stability of the code. We show that our new implementation achieves a better agreement of the temperature structure and its gradient with a semi-empirical model derived from observations, as well as of synthetic spectral-line profiles with the observed solar spectrum.

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 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 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.

Study Analysis Group 21 (SAG21) of the Exoplanet Exploration Program Analysis Group (ExoPAG) was organized to study the effect of stellar contamination on space-based transmission spectroscopy, a method for studying exoplanetary atmospheres by measuring the wavelength-dependent radius of a planet as it transits its star. Transmission spectroscopy relies on a precise understanding of the spectrum of the star being occulted. However, stars are not homogeneous, constant light sources but have temporally evolving photospheres and chromospheres with inhomogeneities like spots, faculae, and plages. This SAG has brought together an interdisciplinary team of more than 100 scientists, with observers and theorists from the heliophysics, stellar astrophysics, planetary science, and exoplanetary atmosphere research communities, to study the current needs that can be addressed in this context to make the most of transit studies from current NASA facilities like HST and JWST. The analysis produced 14 findings, which fall into three Science Themes encompassing (1) how the Sun is used as our best laboratory to calibrate our understanding of stellar heterogeneities ("The Sun as the Stellar Benchmark"), (2) how stars other than the Sun extend our knowledge of heterogeneities ("Surface Heterogeneities of Other Stars") and (3) how to incorporate information gathered for the Sun and other stars into transit studies ("Mapping Stellar Knowledge to Transit Studies").

Context. Helioseismology is the study of the Sun's interior using observations of oscillations at the surface. It suffers from systematic errors, for instance a center-to-limb error in travel-time measurements. Understanding these errors requires an adequate understanding of the nontrivial relationship between wave displacement and helioseismic observables (intensity or velocity). Aims. The wave displacement causes perturbations in the atmospheric thermodynamical quantities which, in turn, perturb the opacity, the optical depth, the source function, and the local ray geometry, thus affecting the emergent intensity. We aim to establish the most complete relationship achieved to date between the wave displacement and the emergent intensity perturbation by solving the radiative transfer problem in the perturbed atmosphere. Methods. We derived an expression for the emergent intensity perturbation caused by acoustic oscillations at any point on the solar disk by applying a first-order perturbation theory. As input perturbations, we considerd adiabatic modes of oscillation of different degrees in a spherically-symmetric solar model. The background and the perturbed intensities are computed by solving the radiative transfer equation considering the main sources of opacity in the continuum (absorption and scattering). Results. We find that for all modes, the perturbations to the thermodynamical quantities are not sufficient to model the intensity perturbations: the geometrical effects due to the wave displacement must always be taken into account as they lead to a difference in amplitude and a phase shift between temperature perturbations at the surface and emergent intensity perturbations. The closer to the limb, the greater the differences. For modes with eigenfrequencies around 3 mHz, we found that the radial and horizontal components of the wave displacement are important, in particular, for high-degree modes. Conclusions. This work presents improvements for the computation of the intensity perturbations, in particular, for high-degree modes. Here, we explain the differences in intensity computations seen in earlier works. The phase shifts and amplitude differences between the temperature and intensity perturbations increase toward the limb. This should prove helpful when interpreting some of the systematic centre-to-limb effects observed in local helioseismology. The computations are fast (3 s for 2000 positions and one frequency for one core) and can be parallelised. This work can be extended to models of the line-of-sight velocity observable.

The correct interpretation of the large amount of complex data from next-generation (in particular, space-based) observational facilities requires a very strong theoretical underpinning. One can thus predict that in the near future the use of atmospheric models obtained through the use of three-dimensional (3-D) radiation magnetohydrodynamics (RMHD) codes, coupled with advanced radiative transfer treatment including non-local thermodynamic equilibrium (non-LTE) effects and polarisation, will become the norm. In particular, stellar brightness variability in cool (i. e., spectral type F, G, K, and M) stars can be induced by several different effects, besides pulsation. We briefly discuss some literature results and mention some of our recent progress. Finally, we attempt to peek into the future of understanding this important aspect of the life of stars.

Context. Theory surrounding the origin of the dust-laden winds from evolved stars remains mired in controversy. Characterizing the formation loci and the dust distribution within approximately the first stellar radius above the surface is crucial for understanding the physics that underlie the mass-loss phenomenon. Aims. By exploiting interferometric polarimetry, we derive the fundamental parameters that govern the dust structure at the wind base of a red supergiant. Methods. We present near-infrared aperture-masking observations of Betelgeuse in polarimetric mode obtained with the NACO/SAMPol instrument. We used both parametric models and radiative transfer simulations to predict polarimetric differential visibility data and compared them to SPHERE/ZIMPOL measurements. Results. Using a thin dust shell model, we report the discovery of a dust halo that is located at only 0.5 R⋆ above the photosphere (i.e. an inner radius of the dust halo of 1.5 R⋆). By fitting the data under the assumption of Mie scattering, we estimate the grain size and density for various dust species. By extrapolating to the visible wavelengths using radiative transfer simulations, we compare our model with SPHERE/ZIMPOL data and find that models based on dust mixtures that are dominated by forsterite are most favored. Such a close dusty atmosphere has profound implications for the dust formation mechanisms around red supergiants.