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In recent years it has become common practice to divide observed transit absorption spectra by synthetic absorption spectra computed for the transit of an atmosphere-less planet. This action supposedly corrects the observed absorption spectrum, leaving the sole atmospheric absorption signature free from the biases induced by stellar rotation and centre-to-limb variations. We aim to show that while this practice is beneficial, it does not completely correct the absorption spectrum from the stellar distortions and that some residual biases remain, leaving a possibly altered atmospheric signature. By reducing the problem to its most basic form, we show that dividing the observed absorption spectrum by a synthetic absorption spectrum of the planet does not isolate the pure atmospheric absorption signature. We also used simulated synthetic transit observations to assess the magnitude of these residual biases in typical transit observations. We show that dividing the observed absorption spectrum by the planetary absorption spectrum results in an atmospheric signature modulated by the ratio of the flux behind the atmosphere and the flux behind the planet. Depending on the non-homogeneity of the stellar spectrum, this leads to distorted atmospheric signatures. Eventually, directly analysing these biased signatures will lead to wrong estimates of planetary atmosphere properties.

Aims: Our aim is to build upon the analysis presented in our previous work by attempting to match the observational data obtained with VLTI GRAVITY for RU Lup in 2021 with an expanded radiative transfer model of Br$\gamma$ emission. Specifically, we will determine if the inclusion of an additional disk wind as a Br$\gamma$ emitter in the inner disk will be able to reproduce the trend of increasing sizes at higher velocities, as well as the observed photocenter shifts. Methods: We make use of the MCFOST radiative transfer code to solve for Br$\gamma$ line formation in the innermost disk of an RU Lupl-like system. From the resulting images we compute synthetic interferometric observables. We first investigate how individual parameter variations in a pure magnetospheric accretion model and a pure parameteric disk wind model translate to changes in these derived quantities. Then we attempt to reproduce the RU Lup GRAVITY data with different parameter variants of magnetospheric accretion models, disk wind models, and combined hybrid models. Results: We demonstrate that magnetospheric accretion models and disk wind models on their own can emulate certain individual characteristics from the observational results, but individually fail to comprehensively reproduce the observational trends. Disk wind plus accretion hybrid models are in principle capable of explaining the variation in characteristic radii across the line and the corresponding flux ratios. While the model parameters of the hybrid models are mostly in good agreement with the known attributes of RU Lup, we find that our best-fitting models deviate in terms of rotational period and the size of the magnetosphere. The best-fitting hybrid model does not respect the co-rotation criterion, as the magnetospheric truncation radius is about 50% larger than the co-rotation radius.

Methods. We use the code MCFOST to solve the non-LTE problem of line formation in non-axisymmetric accreting magnetospheres. We compute the Br{\gamma} line profile originating from accretion columns for models with different magnetic obliquities. We also derive monochromatic synthetic images of the Br{\gamma} line emitting region across the line profile. This spectral line is a prime diagnostics of magnetospheric accretion in young stars and is accessible with the long baseline near-infrared interferometer GRAVITY installed at the ESO Very Large Telescope Interferometer. Results. We derive Br{\gamma} line profiles as a function of rotational phase and compute interferometric observables, visibilities and phases, from synthetic images. The line profile shape is modulated along the rotational cycle, exhibiting inverse P Cygni profiles at the time the accretion shock faces the observer. The size of the line's emission region decreases as the magnetic obliquity increases, which is reflected in a lower line flux. We apply interferometric models to the synthetic visibilities in order to derive the size of the line-emitting region. We find the derived interferometric size to be more compact than the actual size of the magnetosphere, ranging from 50 to 90\% of the truncation radius. Additionally, we show that the rotation of the non-axisymmetric magnetosphere is recovered from the rotational modulation of the Br{\gamma}-to-continuum photo-centre shifts, as measured by the differential phase of interferometric visibilities.

Aims. We seek to understand convection in red supergiants and the mechanisms that trigger the mass loss from cool evolved stars. Methods. Linear spectropolarimetry of the atomic lines of the spectrum of $\mu$ Cep reveals information well outside the wavelength range expected from previous models. This is interpreted as structures in expansion that are visible in the front hemisphere and sometimes also in the back hemisphere. We model the plasma distribution together with its associated velocities through an inversion algorithm to fit the observed linear polarization. Results. We find that supposing the existence of plasma beyond the limb rising high enough to be visible above it can explain the observed linear polarization signatures as well as their evolution in time. From this we are able to infer the geometric heights of the convective plumes and establish that this hot plasma rises to at least 1.1 R*. Conclusions. $\mu$ Cep appears to be in an active phase in which plasma rises often above 1.1 R* . We generalize this result to all red supergiants in a similarly evolved stage, which at certain epochs may easily send plasma to greater heights, as $\mu$ Cep appears to be doing at present. Plasma rising to such heights can easily escape the stellar gravity., Comment: Accepted for publication in A&A

Aims: We aim to spatially and spectrally resolve the Br-gamma hydrogen emission line with the methods of interferometry in order to examine the kinematics of the hydrogen gas emission region in the inner accretion disk of a sample of solar-like young stellar objects. The goal is to identify trends and categories among the sources of our sample and to discuss whether or not they can be tied to different origin mechanisms associated with Br-gamma emission in T Tauri stars, chiefly and most prominently magnetospheric accretion. Methods: We observed a sample of seven T Tauri stars for the first time with VLTI GRAVITY, recording spectra and spectrally dispersed interferometric quantities across the Br-gamma line in the NIR K-band. We use them to extract the size of the Br-gamma emission region and the photocenter shifts. To assist in the interpretation, we also make use of radiative transfer models of magnetospheric accretion to establish a baseline of expected interferometric signatures if accretion is the primary driver of Br-gamma emission. Results: From among our sample, we find that five of the seven T~Tauri stars show an emission region with a half-flux radius in the range broadly expected for magnetospheric truncation. Two of the five objects also show Br-gamma emission primarily originating from within the corotation radius, while two other objects exhibit extended emission on a scale beyond 10 R$_*$, one of them even beyond the K~band continuum half-flux radius of 11.3 R$_*$. Conclusions: We find strong evidence to suggest that for the two weakest accretors in the sample, magnetospheric accretion is the primary driver of Br-gamma radiation. The results for the remaining sources imply either partial or strong contributions coming from spatially extended emission components in the form of outflows, such as stellar or disk winds., Comment: Version corresponds to the one in A&A production. The author list has been amended with "GRAVITY Collaboration" as first entry in keeping with the convention established for papers published by the GRAVITY consortium in recent years

Aims. We present MCFOST-art, a new non-local thermodynamic equilibrium radiative transfer solver for multilevel atomic systems. The code is embedded in the 3D radiative transfer code MCFOST and is compatible with most of the MCFOST modules. The code is versatile and designed to model the close environment of stars in 3D. Methods. The code solves for the statistical equilibrium and radiative transfer equations using the Multilevel Accelerated Lambda Iteration (MALI) method. We tested MCFOST-art on spherically symmetric models of stellar photospheres as well as on a standard model of the solar atmosphere. We computed atomic level populations and outgoing fluxes and compared these values with the results of the TURBOspectrum and RH codes. Calculations including expansion and rotation of the atmosphere were also performed. We tested both the pure local thermodynamic equilibrium and the out-of-equilibrium problems. Results. In all cases, the results from all codes agree within a few percent at all wavelengths and reach the sub-percent level between RH and MCFOST-art. We still note a few marginal discrepancies between MCFOST-art and TURBOspectrum as a result of different treatments of background opacities at some critical wavelength ranges.

Aims: From a coherent interpretation of the linear polarisation detected in the spectral lines of the Mira star $\chi$ Cyg, we derive information about the dynamics of the stellar photosphere, including pulsation. Methods: From spectropolarimetric observations of $\chi$ Cyg, we perform careful analysis of the polarisation signals observed in atomic and molecular lines, both in absorption and emission, using the radiative transfer in the polarisation context, through two mechanisms: intrinsic polarisation and continuum depolarisation. We also explain the observed line doubling phenomenon in terms of an expanding shell in spherical geometry, which allows us to pinpoint the coordinates over the stellar disk with enhanced polarisation. Results: We find that the polarised spectrum of $\chi$ Cyg is dominated by intrinsic polarisation, with a negligible continuum depolarisation. The observed polarised signals can only be explained by assuming that this polarisation is locally enhanced by velocity fields. During the pulsation, radial velocities are not homogeneous over the disk. We map these regions of enhanced velocities. Conclusions: We have set an algorithm to distinguish in any stellar spectra of linear polarisation the origin of this polarisation and the way to increase signal by coherently adding many lines with an appropriated weight. Applied to the Mira star $\chi$ Cyg, we reached the unexpected result that during the pulsation, velocities are radial but not homogeneous over the disk. The reason for these local velocity enhancements are probably related to the interplay between the atmospheric pulsation dynamics and the underlying stellar convection., Comment: Accepted for publication in A&A

We assess the ability to image the photosphere of red supergiants and, in particular Betelgeuse, through the modelling of the observed linear polarization in atomic spectral lines. We also aim to analyse the resulting images over time, to measure the size and dynamics of the convective structures in these stars. Rayleigh scattering polarizes the continuum and spectral lines depolarize it.This depolarization is seen as a linear polarization signal parallel to the radial direction on the stellar disk. Integrated over the disk, it would result in a null signal, except if brightness asymmetries/inhomogeneities are present. This is the basic concept behind our imaging technique. The several tests and comparisons performed prove that our technique reliably retrieves the salient brightness structures in the photosphere of Betelgeuse, and should be relevant to other red supergiants. We demonstrate that these structures are convective cells, with a characteristic size of more than 60% of the stellar radius. We also derive the characteristic upflow and downflow speeds, 22 and 10 km/s respectively. We find weak magnetic fields concentrated in the downflow lanes in between granules. We follow those convective structures in time. Changes happen on timescales of one week, but individual structures can be tracked over four years of observations., Comment: Accepted for publication in A&A

Betelgeuse is an M-type supergiant that presents a circularly polarized (Stokes V) signal in its line profiles, interpreted in terms of a surface magnetic field. The weak circular polarization signal has been monitored over 7.5 years in order to follow its evolution on different timescales, and eventually to determine its physical origin. Linear polarization measurements have also been obtained regularly in the last few years. We used both the ESPaDOnS and Narval spectropolarimeters to obtain high signal-to-noise ratio (S/N) spectra, which were processed by means of the least-squares deconvolution (LSD) method. In order to ensure the reality of the very weak circular polarization, special care has been taken to limit instrumental effects. In addition, several tests were performed on the Stokes V signal to establish its stellar and Zeeman origin. We confirm the magnetic nature of the circular polarization, pointing to a surface magnetic field of the order of 1G. The Stokes V profiles present variations over different timescales, the most prominent one being close to the long secondary period (LSP; around 2000d for Betelgeuse) often invoked in red evolved stars. This long period is also dominant for all the other Stokes parameters. The circular polarization is tentatively modeled by means of magnetic field concentrations mimicking spots, showing in particular that the velocity associated with each "spot" also follows the long timescale, and that this signal is nearly always slightly redshifted. From the coupled variations of both linear and circular polarization signatures in amplitude, velocity and timescale, we favour giant convection cells as the main engine at the origin of polarization signatures and variations in all the Stokes parameters. This strengthens support for the hypothesis that large convective cells are at the origin of the LSP.

Context. Red supergiant stars are one of the latest stages in the evolution of massive stars. Their photospheric convection may play an important role in the launching mechanism of their mass loss; however, its characteristics and dynamics are still poorly constrained. Aims. By observing red supergiant stars with near infrared interferometry at different epochs, we expect to reveal the evolution of bright convective features on their stellar surface. Methods. We observed the M2Iab-Ib red supergiant star CE Tau with the VLTI/PIONIER instrument in the H band at two different epochs separated by one month. Results. We derive the angular diameter of the star and basic stellar parameters, and reconstruct two reliable images of its H-band photosphere. The contrast of the convective pattern of the reconstructed images is $5 \pm 1 \%$ and $6 \pm 1 \%$ for our two epochs of observation. Conclusions. The stellar photosphere shows few changes between the two epochs. The contrast of the convective pattern is below the average contrast variations obtained on 30 randomly chosen snapshots of the best matching 3D radiative hydrodynamics simulation: $23 \pm 1~\%$ for the original simulation images and $16 \pm 1~\%$ for the maps degraded to the reconstruction resolution. We offer two hypotheses to explain this observation. CE Tau may be experiencing a quiet convective activity episode or it could be a consequence of its warmer effective temperature (hence its smaller radius) compared to the simulation., Comment: 12 pages, 8 figures. Accepted for publication in Astronomy & Astrophysics

Betelgeuse is an M supergiant that harbors spots and giant granules at its surface and presents linear polarization of its continuum. We have previously discovered linear polarization signatures associated with individual lines in the spectra of cool and evolved stars. Here, we investigate whether a similar linearly polarized spectrum exists for Betelgeuse. We used the spectropolarimeter Narval, combining multiple polarimetric sequences to obtain high signal-to-noise ratio spectra of individual lines, as well as the least-squares deconvolution (LSD) approach. We have discovered the existence of a linearly polarized spectrum for Betelgeuse, detecting a rather strong signal (at a few times 10$^{-4}$ of the continuum intensity level), both in individual lines and in the LSD profiles. Studying its properties and the signal observed for the resonant \ion{Na}{i}\,D lines, we conclude that we are mainly observing depolarization of the continuum by the absorption lines. The linear polarization of the Betelgeuse continuum is due to the anisotropy of the radiation field induced by brightness spots at the surface and Rayleigh scattering in the atmosphere. We have developed a geometrical model to interpret the observed polarization, from which we infer the presence of two brightness spots and their positions on the surface of Betelgeuse. We show that applying the model to each velocity bin along the Stokes Q and U profiles allows the derivation of a map of the bright spots. We use the Narval linear polarization observations of Betelgeuse obtained over a period of 1.4 years to study the evolution of the spots. Our study of the linearly polarized spectrum of Betelgeuse provides a novel method for studying the evolution of brightness spots at its surface and complements quasi-simultaneous observations obtained with PIONIER at the VLTI., Comment: 13 pages, 10 figures, accepted for publication in Astronomy and Astrophysics