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Context. Fast rotating red giants in the upper part of the red giant branch have surface velocities that cannot be explained by single star evolution. Aims. We check whether tides between a star and a planet followed by planet engulfment can indeed accelerate the surface rotation of red giants for a sufficiently long time to produce these fast rotating red giants. Methods. We studied how the surface rotation velocity at the stellar surface evolves using rotating stellar models, accounting for the redistribution of the angular momentum inside the star by different transport mechanisms, the exchanges of angular momentum between the planet orbit and the star before the engulfment, and for the deposition of angular momentum inside the star at the engulfment. We considered different situations with masses of stars in the range between 1.5 and 2.5 M , masses of the planets between 1 and 15 M J (Jupiter mass), and initial semimajor axis between 0.5 and 1.5 au. The metallicity Z for our stellar models is 0.02. Results. We show that the surface velocities reached at the end of the orbital decay due to tidal forces and planet engulfment can be similar to values observed for fast rotating red giants. This surface velocity then decreases when the star evolves along the red giant branch but at a sufficiently slow pace to allowing stars to be detected with such a high velocity. More quantitatively, star-planet interaction can produce a rapid acceleration of the surface of the star, above values equal to 8 km s −1 , for periods lasting up to more than 30% the red giant branch phase. As found already by previous works, the changes of the surface carbon isotopic ratios produced by the dilution of the planetary material into the convective envelope is modest. The increase of the lithium abundance due to this effect might be much more important, however lithium may be affected by many different, still uncertain, processes. Thus any lithium measurement can hardly be taken as a support or argument against any star-planet interaction. Conclusions. The acceleration of the stellar surface to rotation velocities above limits that depend on the surface gravity does appear at the moment to be the clearest signature of a star-planet interaction.

Context. As a star evolves, planet orbits change over time owing to tidal interactions, stellar mass losses, friction and gravitational drag forces, mass accretion, and evaporation on/by the planet. Stellar rotation modifies the structure of the star and therefore the way these different processes occur. Changes in orbits, subsequently, have an impact on the rotation of the star. Aims. Models that account in a consistent way for these interactions between the orbital evolution of the planet and the evolution of the rotation of the star are still missing. The present work is a first attempt to fill this gap. Methods. We compute the evolution of stellar models including a comprehensive treatment of rotational effects, together with the evolution of planetary orbits, so that the exchanges of angular momentum between the star and the planetary orbit are treated in a self-consistent way. The evolution of the rotation of the star accounts for the angular momentum exchange with the planet and also follows the effects of the internal transport of angular momentum and chemicals. These rotating models are computed for initial masses of the host star between 1.5 and 2.5 M , with initial surface angular velocities equal to 10 and 50% of the critical velocity on the zero age main sequence (ZAMS), for a metallicity Z = 0.02, with and without tidal interactions with a planet. We consider planets with masses between 1 and 15 Jupiter masses (M J ), which are beginning their evolution at various distances between 0.35 and 4.5 au. Results. We demonstrate that rotating stellar models without tidal interactions and without any wind magnetic braking during the red giant phase can well reproduce the surface rotations of the bulk of red giants. However, models without any interactions cannot account for fast rotating red giants in the upper part of the red giant branch, where these models, whatever the initial rotation considered on the ZAMS, always predict very low velocities. For these stars, some interaction with a companion is highly probable and the present rotating stellar models with planets confirm that tidal interaction can reproduce their high surface velocities. We also show that the minimum distance between the planet and the star on the ZAMS, which enables the planet to avoid engulfment and survive (i.e. the survival limit) is decreased around faster rotating stars.

Context. The quiet Sun magnetic field probability density function (PDF) remains poorly known. Modeling this field also introduces a magnetic filling factor that is also poorly known. With these two quantities, PDF and filling factor, the statistical description of the quiet Sun magnetic field is complex and needs to be clarified. Aims. In the present paper, we propose a procedure that combines direct determinations and inversion results to derive the magnetic field vector and filling factor, and their PDFs. Methods. We used spectro-polarimetric observations taken with the ZIMPOL polarimeter mounted on the THEMIS telescope. The target was a quiet region at disk center. We analyzed the data by means of the UNNOFIT inversion code, with which we inferred the distribution of the mean magnetic field αB, α being the magnetic filling factor. The distribution of α was derived by an independent method, directly from the spectro-polarimetric data. The magnetic field PDF p(B) could then be inferred. By introducing a joint PDF for the filling factor and the magnetic field strength, we have clarified the definition of the PDF of the quiet Sun magnetic field when the latter is assumed not to be volume-filling. Results. The most frequent local average magnetic field strength is found to be 13 G. We find that the magnetic filling factor is related to the magnetic field strength by the simple law α = B 1 /B with B 1 = 15 G. This result is compatible with the Hanle weak-field determinations, as well as with the stronger field determinations from the Zeeman effect (kGauss field filling 1-2% of space). From linear fits, we obtain the analytical dependence of the magnetic field PDF. Our analysis has also revealed that the magnetic field in the quiet Sun is isotropically distributed in direction. Conclusions. We conclude that the quiet Sun is a complex medium where magnetic fields having different field strengths and filling factors coexist. Further observations with a better polarimetric accuracy are, however, needed to confirm the results obtained in the present work.

Context. The solar surface magnetic field is connected with and even controls most of the solar activity phenomena. Zeeman effect diagnostics allow for measuring only a small fraction of the fractal-like structured magnetic field. The remaining hidden magnetic fields can only be accessed with the Hanle effect. Aims. Molecular lines are very convenient for applying the Hanle effect diagnostics thanks to the broad range of magnetic sensitivities in a narrow spectral region. With the UV version of the Zurich Imaging Polarimeter ZIMPOL II installed at the 45 cm telescope of the Istituto Ricerche Solari Locarno (IRSOL), we simultaneously observed intensity and linear polarization center-to-limb variations in two spectral regions containing the (0, 0) and (1, 1) bandheads of the CN B 2 Σ − X 2 Σ system. Here we present an analysis of these observations. Methods. We have implemented coherent scattering in molecular lines into an NLTE radiative transfer code. A two-step approach was used. First, we separately solved the statistical equilibrium equations and compute opacities and intensity while neglecting polarization. Then we used these quantities as input for calculating scattering polarization and the Hanle effect. Results. We have found that it is impossible to fit the intensity and polarization simultaneously at different limb angles in the framework of standard 1D modeling. The atmosphere models that provide correct intensity center-to-limb variations fail to fit linear polarization center-to-limb variations due to lacking radiation-field anisotropy. We had to increase the anisotropy by means of a specially introduced free parameter. This allows us to successfully interpret our observations. We discuss possible reasons for underestimating the anisotropy in the 1D modeling.