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Emerging active regions are associated with convective flows on the spatial scale and lifetimes of supergranules. To understand how these flows are involved in the formation of active regions, we aim to identify where active regions emerge in the supergranulation flow pattern. We computed supergranulation scale flow maps at the surface for all active regions in the Solar Dynamics Observatory Helioseismic Emerging Active Region Survey. We classified each of the active regions into four bins, based on the amplitude of their average surface flow divergence at emergence. We then averaged the flow divergence over the active regions in each bin as a function of time. We also considered a corresponding set of control regions. We found that, on average, the flow divergence increases during the day prior to emergence at a rate independent of the amount of flux that emerges. By subtracting the averaged flow divergence of the control regions, we found that active region emergence is associated with a remaining converging flow at 0.5-1 days prior to emergence. This remnant flow, $\Delta \, \mathrm{div} \, \mathbf{v_h} = (-4.9 \pm 1.7) \times 10^{-6}$ 1/s, corresponds to a flow speed of 10-20 m/s (an order of magnitude less than supergranulation flows) out to a radius of about 10 Mm. We show that these observational results are qualitatively supported by simulations of a small bipole emerging through the near-surface convective layers of the Sun. The question remains whether these flows are driving the emergence, or are caused by the emergence., Comment: 22 pages, 27 figures, accepted to be published in MNRAS

Solar pores are intense concentrations of magnetic flux that emerge through the Sun's photosphere. When compared to sunspots, they are much smaller in diameter and hence can be impacted and buffeted by neighbouring granular activity to generate significant magnetohydrodynamic (MHD) wave energy flux within their confines. However, observations of solar pores from ground-based telescope facilities may struggle to capture subtle motions synonymous with higher-order MHD wave signatures due to seeing effects produced in the Earth's atmosphere. Hence, we have exploited timely seeing-free and high-quality observations of four small magnetic pores from the Polarimetric and Helioseismic Imager (PHI) on board the Solar Orbiter spacecraft. Through acquisition of data under stable observing conditions, we have been able to measure the area fluctuations and horizontal displacements of the solar pores. Cross correlations between perturbations in intensity, area, line-of-sight velocity, and magnetic fields, coupled with the first-time application of novel Proper Orthogonal Decomposition (POD) techniques on the boundary oscillations, provide a comprehensive diagnosis of the embedded MHD waves as sausage and kink modes. Additionally, the previously elusive m = 2 fluting mode is identified in the most magnetically isolated of the four pores. An important consideration lies in how the identified wave modes contribute towards the transfer of energy into the upper solar atmosphere. We find that the four pores examined have approximately 56%, 72%, 52%, and 34% of their total wave energy associated with the identified sausage modes, and around 23%, 17%, 39%, and 49% to their kink modes, respectively, while the first pore also has around an 11% contribution linked to the fluting mode. This study marks the first-time identification of concurrent sausage, kink, and fluting MHD wave modes in solar magnetic pores., Comment: Accepted for publication in Astronomy & Astrophysics

The modeling of convection is a long standing problem in stellar physics. Up-to-now, all ad hoc models rely on a free parameter alpha (among others) which has no real physical justification and is therefore poorly constrained. However, a link exists between this free parameter and the entropy of the stellar adiabat. Prescriptions, derived from 3D stellar atmospheric models, are available that provide entropy as a function of stellar atmospheric parameters (effective temperature, surface gravity, chemical composition). This can provide constraints on alpha through the development of entropy-calibrated models. Several questions arise as these models are increasingly used. Which prescription should be used? How do uncertainties impact entropy-calibrated models? We aim to study the three existing prescriptions and determine which one should be used, and how. We implemented the entropy-calibration method into the stellar evolution code Cesam2k20 and performed comparisons with the Sun and the alpha Cen system. In addition, we used data from the CIFIST grid of 3D atmosphere models to evaluate the accuracy of the prescriptions. Of the three entropy prescriptions available, we determine which one best reproduces the entropies of the 3D models. We also demonstrate that the entropy obtained from this prescription should be corrected for the evolving chemical composition and for an entropy offset different between various EoS tables, following a precise procedure, otherwise classical parameters obtained from the models will be strongly biased. Finally, we also provide table with entropy of the adiabat of the CIFIST grid, as well as fits of these entropies. We performed a precise examination of entropy-calibrated modelling, and gave recommendations on which adiabatic entropy prescription to use, how to correct it and to implement the method into a stellar evolution code., Comment: 18 pages, 11 figures. Submitted to Astronomy and Astrophysics, recommended for publication with minor revisions

We investigate whether the Babcock-Leighton flux-transport dynamo model remains in agreement with observations if the meridional flow profile is taken from helioseismic inversions. Additionally, we investigate the effect of the loss of toroidal flux through the solar surface. We employ the 2D flux-transport BL dynamo framework. We use the helioseismically-inferred meridional flow profile, and include toroidal flux loss in a way that is consistent with the amount of poloidal flux generated by Joy's law. Our model does not impose a preference for emergences at low latitudes, but we do require that the model produces such a preference. We can find solutions in general agreement with observations, including the equatorward drift of the butterfly wings and the cycle's 11 year period. The most important free parameters in the model are the depth to which the radial turbulent pumping extends and the turbulent diffusivity in the lower half of the convection zone. We find that the pumping needs to extend to depths of about $0.80R_{\odot}$ and the bulk turbulent diffusivity needs to be around 10 km$^2$/s or less. We find that the emergences are restricted to low latitudes without the need to impose such a preference. The flux-transport BL model, incorporating the helioseismically inferred meridional flow and toroidal field loss term, is compatible with the properties of the observed butterfly diagram and with the observed toroidal loss rate. Reasonably tight constraints are placed on the remaining free parameters. The pumping needs to be to just below the depth corresponding to the location where the meridional flow changes direction. Our linear model does not however reproduce the observed "rush to the poles" of the diffuse surface radial field resulting from the decay of sunspots -- reproducing this might require the imposition of a preference for flux to emerge near the equator., Comment: 10 pages, 8 figures, accepted by A&A

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.

Extreme ultraviolet (EUV) observations of the quiet solar atmosphere reveal extended regions of weak emission compared to the ambient quiescent corona. The magnetic nature of these coronal features is not well understood. We study the magnetic properties of the weakly emitting extended regions, which we name coronal voids. In particular, we aim to understand whether these voids result from a reduced heat input into the corona or if they are associated with mainly unipolar and possibly open magnetic fields, similar to coronal holes. We defined the coronal voids via an intensity threshold of 75% of the mean quiet-Sun (QS) EUV intensity observed by the high-resolution EUV channel (HRIEUV) of the Extreme Ultraviolet Imager on Solar Orbiter. The line-of-sight magnetograms of the same solar region recorded by the High Resolution Telescope of the Polarimetric and Helioseismic Imager allowed us to compare the photospheric magnetic field beneath the coronal voids with that in other parts of the QS. The coronal voids studied here range in size from a few granules to a few supergranules and on average exhibit a reduced intensity of 67% of the mean value of the entire field of view. The magnetic flux density in the photosphere below the voids is 76% (or more) lower than in the surrounding QS. Specifically, the coronal voids show much weaker or no network structures. The detected flux imbalances fall in the range of imbalances found in QS areas of the same size. Conclusions. We conclude that coronal voids form because of locally reduced heating of the corona due to reduced magnetic flux density in the photosphere. This makes them a distinct class of (dark) structure, different from coronal holes., Comment: 10 pages, 11 figures

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.

Spectropolarimetric reconstructions of the photospheric vector magnetic field are intrinsically limited by the 180$^\circ$-ambiguity in the orientation of the transverse component. So far, the removal of such an ambiguity has required assumptions about the properties of the photospheric field, which makes disambiguation methods model-dependent. The basic idea is that the unambiguous line-of-sight component of the field measured from one vantage point will generally have a non-zero projection on the ambiguous transverse component measured by the second telescope, thereby determining the ``true'' orientation of the transverse field. Such an idea was developed and implemented in the Stereoscopic Disambiguation Method (SDM), which was recently tested using numerical simulations. In this work we present a first application of the SDM to data obtained by the High Resolution Telescope (HRT) onboard Solar Orbiter during the March 2022 campaign, when the angle with Earth was 27 degrees. The method is successfully applied to remove the ambiguity in the transverse component of the vector magnetogram solely using observations (from HRT and from the Helioseismic and Magnetic Imager), for the first time. The SDM is proven to provide observation-only disambiguated vector magnetograms that are spatially homogeneous and consistent. A discussion about the sources of error that may limit the accuracy of the method, and of the strategies to remove them in future applications, is also presented., Comment: 32 pages, 12 figures, accepted in A&A on 09/07/2023

We use wavefront sensing to characterise the image quality of the the High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (SO/PHI) data products during the second remote sensing window of the Solar Orbiter (SO) nominal mission phase. Our ultimate aims are to reconstruct the HRT data by deconvolving with the HRT point spread function (PSF) and to correct for the effects of optical aberrations on the data. We use a pair of focused--defocused images to compute the wavefront error and derive the PSF of HRT by means of a phase diversity (PD) analysis. The wavefront error of HRT depends on the orbital distance of SO to the Sun. At distances $>0.5$\,au, the wavefront error is small, and stems dominantly from the inherent optical properties of HRT. At distances $<0.5$\,au, the thermo-optical effect of the Heat Rejection Entrance Window (HREW) becomes noticeable. We develop an interpolation scheme for the wavefront error that depends on the thermal variation of the HREW with the distance of SO to the Sun. We also introduce a new level of image reconstruction, termed `aberration correction', which is designed to reduce the noise caused by image deconvolution while removing the aberrations caused by the HREW. The computed PSF via phase diversity significantly reduces the degradation caused by the HREW in the near-perihelion HRT data. In addition, the aberration correction increases the noise by a factor of only $1.45$ compared to the factor of $3$ increase that results from the usual PD reconstructions.

Earth-side observations of solar p modes can be used to image and monitor magnetic activity on the Sun's far side. Here we use magnetograms of the far side obtained by the Polarimetric and Helioseismic Imager (PHI) onboard Solar Orbiter (SO) to directly assess -- for the first time -- the validity of far-side helioseismic holography. We wish to co-locate the positions of active regions in helioseismic images and magnetograms, and to calibrate the helioseismic measurements in terms of magnetic field strength. We identify three magnetograms on 18 November 2020, 3 October 2021, and 3 February 2022 displaying a total of six active regions on the far side. The first two dates are from SO's cruise phase, the third from the beginning of the nominal operation phase. We compute contemporaneous seismic phase maps for these three dates using helioseismic holography applied to time series of Dopplergrams from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO). Among the six active regions seen in SO/PHI magnetograms, five active regions are identified on the seismic maps at almost the same positions as on the magnetograms. One region is too weak to be detected above the seismic noise. To calibrate the seismic maps, we fit a linear relationship between the seismic phase shifts and the unsigned line-of-sight magnetic field averaged over the active region areas extracted from the SO/PHI magnetograms. SO/PHI provides the strongest evidence so far that helioseismic imaging provides reliable information about active regions on the far side, including their positions, areas, and mean unsigned magnetic field., Comment: 10 pages, 9 figures

In November 2021, Solar Orbiter started its nominal mission phase. The remote-sensing instruments on board the spacecraft acquired scientific data during three observing windows surrounding the perihelion of the first orbit of this phase. The aim of the analysis is the detection of magnetohydrodynamic (MHD) wave modes in an active region by exploiting the capabilities of spectropolarimetric measurements. The High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (SO/PHI) on board the Solar Orbiter acquired a high-cadence data set of an active region. This is studied in the paper. B-$\omega$ and phase-difference analyses are applied on line-of-sight velocity and circular polarization maps and other averaged quantities. We find that several MHD modes at different frequencies are excited in all analysed structures. The leading sunspot shows a linear dependence of the phase lag on the angle between the magnetic field and the line of sight of the observer in its penumbra. The magnetic pore exhibits global resonances at several frequencies, which are also excited by different wave modes. The SO/PHI measurements clearly confirm the presence of magnetic and velocity oscillations that are compatible with one or more MHD wave modes in pores and a sunspot. Improvements in modelling are still necessary to interpret the relation between the fluctuations of different diagnostics.

Inertial modes have been observed on the Sun at low longitudinal wavenumbers. These modes probe the dynamics and structure of the solar convection zone down to the tachocline. While linear analysis allows the complex eigenfrequencies and eigenfunctions of these modes to be computed, it gives no information about their excitation nor about their amplitudes. We tested the hypothesis that solar inertial modes are stochastically excited by the turbulent motions entailed by convection. We have developed a theoretical formalism where the turbulent velocity fluctuations provide the mechanical work necessary to excite the modes. The modes are described by means of a 2D linear wave equation, relevant for the quasi-toroidal modes observed on the Sun, with a source term, under the beta plane approximation. Latitudinal differential rotation is included in the form of a parabolic profile that approximates the solar differential rotation at low and mid latitudes. We obtain synthetic power spectra for the wave's latitudinal velocity, longitudinal velocity, and radial vorticity, with azimuthal orders between 1 and 20. The synthetic power spectra contain the classical equatorial Rossby modes, as well as a rich spectrum of additional modes. The mode amplitudes are found to be of the same order of magnitude as observed on the Sun (~ 1 m/s). There is a qualitative transition between low and high azimuthal orders: the power spectra for m < 5 show modes that are clearly resolved in frequency space, while the power spectra for m > 5 display regions of excess power that consist of many overlapping modes. The general agreement between the predicted and observed inertial mode amplitudes supports the assumption of stochastic excitation by turbulent convection. Our work shows that the power spectra are not easily separable into individual modes, thus complicated the interpretation of the observations., Comment: 19 pages, accepted for publication in Astronomy & Astrophysics

In order to make accurate inferences about the solar interior using helioseismology, it is essential to understand all the relevant physical effects on the observations. One effect to understand is the (complex-valued) ratio of the horizontal to vertical displacement of the p- and f-modes at the height at which they are observed. Unfortunately, it is impossible to measure this ratio directly from a single vantage point, and it has been difficult to disentangle observationally from other effects. In this paper we attempt to measure the ratio directly using 7.5 hours of simultaneous observations from the Polarimetric and Helioseismic Imager on board Solar Orbiter and the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory. While image geometry problems make it difficult to determine the exact ratio, it appears to agree well with that expected from adiabatic oscillations in a standard solar model. On the other hand it does not agree with a commonly used approximation, indicating that this approximation should not be used in helioseismic analyses. In addition, the ratio appears to be real-valued., Comment: Accepted for publication in Astronomy & Astrophysics. 8 pages, 8 figures

The High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager on board the Solar Orbiter spacecraft (SO/PHI) and the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) both infer the photospheric magnetic field from polarised light images. SO/PHI is the first magnetograph to move out of the Sun--Earth line and will provide unprecedented access to the Sun's poles. This provides excellent opportunities for new research wherein the magnetic field maps from both instruments are used simultaneously. We aim to compare the magnetic field maps from these two instruments and discuss any possible differences between them. We used data from both instruments obtained during Solar Orbiter's inferior conjunction on 7 March 2022. The HRT data were additionally treated for geometric distortion and degraded to the same resolution as HMI. The HMI data were re-projected to correct for the $3^{\circ}$ separation between the two observatories. SO/PHI-HRT and HMI produce remarkably similar line-of-sight magnetograms, with a slope coefficient of $0.97$, an offset below $1$ G, and a Pearson correlation coefficient of $0.97$. However, SO/PHI-HRT infers weaker line-of-sight fields for the strongest fields. As for the vector magnetic field, SO/PHI-HRT was compared to both the $720$-second and $90$-second HMI vector magnetic field: SO/PHI-HRT has a closer alignment with the $90$-second HMI vector. In the weak signal regime ($< 600$ G), SO/PHI-HRT measures stronger and more horizontal fields than HMI, very likely due to the greater noise in the SO/PHI-HRT data. In the strong field regime ($\gtrsim 600$ G), HRT infers lower field strengths but with similar inclinations (a slope of $0.92$) and azimuths (a slope of $1.02$). The slope values are from the comparison with the HMI $90$-second vector., Comment: 10 pages, 5 figures, accepted for publication in A&A; manuscript is a part of Astronomy & Astrophysics special issue: Solar Orbiter First Results (Nominal Mission Phase)

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)., Comment: 3 pages

KIC 6951642 has been reported as a candidate hybrid pulsator of type-$\gamma$ Doradus-$\delta$ Scuti from observations of the first quarters of the Kepler mission. We aim to investigate the pulsating nature of KIC 6951642 and to search for the signature of rotation and/or activity in the light curves. We performed an iterative frequency search of both Fourier spectra, and searched for regular patterns in them. We applied spectrum synthesis to determine the atmospheric stellar parameters. Since KIC 6951642 was reported to belong to a spectroscopic binary system, we fitted the time delays derived from the light curves with the radial velocities obtained from published as well as new spectra in an attempt to improve the quality of the first orbit. Follow-up spectroscopy showed that KIC 6951642 is a fast-rotating F0-type star in a possible single-lined binary with a period of $\sim$4.8 yr. In the low-frequency regime, we identified the frequencies of 0.721 d$^{-1}$ as well as of 0.0087 d$^{-1}$. We attribute the first frequency to stellar rotation and the second one to stellar activity with a cycle. We also detected $g$ modes, with the strongest mode located at 2.238 d$^{-1}$, as well as three asymmetric multiplets (with a mean spacing of 0.675$\pm$0.044 d$^{-1}$). In the high-frequency regime, we detected frequencies of type-$\delta$ Scuti, with the strongest mode located at 13.96 d$^{-1}$, as well as seven asymmetric multiplets (with a mean spacing of 0.665$\pm$0.084 d$^{-1}$). We subsequently identified a few more frequencies that appear to be combinations of a $g$ or $p$ mode and one of the higher cited frequencies not due to pulsations. We propose that KIC 6951642 accommodates for a fast-rotating $\gamma$ Dor-$\delta$ Sct hybrid star with various rotationally split multiplets of $g$ and $p$ modes and that it also displays a cycle lasting years of (possible) stellar activity.

The ESA/NASA Solar Orbiter space mission has been successfully launched in February 2020. Onboard is the Polarimetric and Helioseismic Imager (SO/PHI), which has two telescopes, a High Resolution Telescope (HRT) and the Full Disc Telescope (FDT). The instrument is designed to infer the photospheric magnetic field and line-of-sight velocity through differential imaging of the polarised light emitted by the Sun. It calculates the full Stokes vector at 6 wavelength positions at the Fe I 617.3 nm absorption line. Due to telemetry constraints, the instrument nominally processes these Stokes profiles onboard, however when telemetry is available, the raw images are downlinked and reduced on ground. Here the architecture of the on-ground pipeline for HRT is presented, which also offers additional corrections not currently available on board the instrument. The pipeline can reduce raw images to the full Stokes vector with a polarimetric sensitivity of $10^{-3}\cdot I_{c}$ or better.

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., Comment: 10 pages, 6 Figures, accepted for publication in ApJL

The twist of the magnetic field above a sunspot is an important quantity in solar physics. For example, magnetic twist plays a role in the initiation of flares and coronal mass ejections (CMEs). Various proxies for the twist above the photosphere have been found using models of uniformly twisted flux tubes, and are routinely computed from single photospheric vector magnetograms. One class of proxies is based on $\alpha_z$, the ratio of the vertical current to the vertical magnetic field. Another class of proxies is based on the so-called twist density, $q$, which depends on the ratio of the azimuthal field to the vertical field. However, the sensitivity of these proxies to temporal fluctuations of the magnetic field has not yet been well characterized. We aim to determine the sensitivity of twist proxies to temporal fluctuations in the magnetic field as estimated from time-series of SDO/HMI vector magnetic field maps. To this end, we introduce a model of a sunspot with a peak vertical field of 2370 Gauss at the photosphere and a uniform twist density $q= -0.024$ Mm$^{-1}$. We add realizations of the temporal fluctuations of the magnetic field that are consistent with SDO/HMI observations, including the spatial correlations. Using a Monte-Carlo approach, we determine the robustness of the different proxies to the temporal fluctuations. The temporal fluctuations of the three components of the magnetic field are correlated for spatial separations up to 1.4 Mm (more than expected from the point spread function alone). The Monte-Carlo approach enables us to demonstrate that several proxies for the twist of the magnetic field are not biased in each of the individual magnetograms. The associated random errors on the proxies have standard deviations in the range between $0.002$ and $0.006$ Mm$^{-1}$, which is smaller by approximately one order of magnitude than the mean value of $q$., Comment: accepted in A&A

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., Comment: 19 pages, 17 figures, accepted to Astronomy and Astrophysics. All tables are available in CDS

The Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter (SO) spacecraft observed small extreme ultraviolet (EUV) bursts, termed campfires, that have been proposed to be brightenings near the apexes of low-lying loops in the quiet-Sun atmosphere. The underlying magnetic processes driving these campfires are not understood. During the cruise phase of SO and at a distance of 0.523\,AU from the Sun, the Polarimetric and Helioseismic Imager on Solar Orbiter (SO/PHI) observed a quiet-Sun region jointly with SO/EUI, offering the possibility to investigate the surface magnetic field dynamics underlying campfires at a spatial resolution of about 380~km. In 71\% of the 38 isolated events, campfires are confined between bipolar magnetic features, which seem to exhibit signatures of magnetic flux cancellation. The flux cancellation occurs either between the two main footpoints, or between one of the footpoints of the loop housing the campfire and a nearby opposite polarity patch. In one particularly clear-cut case, we detected the emergence of a small-scale magnetic loop in the internetwork followed soon afterwards by a campfire brightening adjacent to the location of the linear polarisation signal in the photosphere, that is to say near where the apex of the emerging loop lays. The rest of the events were observed over small scattered magnetic features, which could not be identified as magnetic footpoints of the campfire hosting loops. The majority of campfires could be driven by magnetic reconnection triggered at the footpoints, similar to the physical processes occurring in the burst-like EUV events discussed in the literature. About a quarter of all analysed campfires, however, are not associated to such magnetic activity in the photosphere, which implies that other heating mechanisms are energising these small-scale EUV brightenings.

PLATO (PLAnetary Transits and Oscillations of stars) is an ESA M-class satellite planned for launch by end 2026 and dedicated to the wide-field search of transiting planets around bright and nearby stars, with a strong focus on discovering habitable rocky planets hosted by solar-like stars. The choice of the fields to be pointed at is a crucial task since it has a direct impact on the scientific return of the mission. In this paper we describe and discuss the formal requirements and the key scientific prioritization criteria that have to be taken into account in the Long-duration Observation Phase (LOP) field selection, and apply a quantitative metric to guide us in this complex optimization process. We identify two provisional LOP fields, one for each hemisphere (LOPS1, LOPN1), and discuss their properties and stellar content. While additional fine-tuning shall be applied to LOP selection before the definitive choice (to be made two years before launch), we expect their position will not move by more than a few degrees with respect to what is proposed in this paper., Comment: 17 pages, 10 figures, 3 tables, A&A in press (accepted: October 26, 2021). Some typos corrected. Author list corrected

Context. The ESA PLAnetary Transits and Oscillations of stars (PLATO) mission will search for terrestrial planets in the habitable zone of solar-type stars. Because of telemetry limitations, PLATO targets need to be pre-selected. Aims. In this paper, we present an all sky catalogue that will be fundamental to selecting the best PLATO fields and the most promising target stars, deriving their basic parameters, analysing the instrumental performances, and then planing and optimising follow-up observations. This catalogue also represents a valuable resource for the general definition of stellar samples optimised for the search of transiting planets. Methods. We used Gaia Data Release 2 (DR2) astrometry and photometry and 3D maps of the local interstellar medium to isolate FGK (V$\leq$13) and M (V$\leq$16) dwarfs and subgiant stars. Results. We present the first public release of the all-sky PLATO Input Catalogue (asPIC1.1) containing a total of 2 675 539 stars including 2 378 177 FGK dwarfs and subgiants and 297 362 M dwarfs. The median distance in our sample is 428 pc for FGK stars and 146 pc for M dwarfs, respectively. We derived the reddening of our targets and developed an algorithm to estimate stellar fundamental parameters (Teff, radius, mass) from astrometric and photometric measurements. Conclusions. We show that the overall (internal+external) uncertainties on the stellar parameter determined in the present study are $\sim$230 K (4%) for the effective temperatures, $\sim$0.1 R$_{\odot}$ (9%) for the stellar radii, and $\sim$0.1 M$_{\odot}$ (11%) for the stellar mass. We release a special target list containing all known planet hosts cross-matched with our catalogue., Comment: Accepted for publication in Astronomy & Astrophysics

Helioseismology is the study of the solar interior using observations of oscillations at the surface. It suffers from systematic errors, such as a center-to-limb error in travel-time measurements. Understanding these errors requires a good understanding of the nontrivial relationship between wave displacement and helioseismic observables. The wave displacement causes perturbations in the atmospheric thermodynamical quantities which 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 up to now between the displacement and the intensity perturbation by solving the radiative transfer problem in the atmosphere. We derive an expression for the intensity perturbation caused by acoustic oscillations at any point on the solar disk by applying the first-order perturbation theory. As input, we consider adiabatic modes of oscillation of different degrees. The background and the perturbed intensities are computed considering the main sources of opacity in the continuum. We find that, for all modes, the perturbations to the thermodynamical quantities are not sufficient to model the intensity. In addition, the geometrical effects due to the displacement must be taken into account as they lead to a difference in amplitude and a phase shift between the temperature at the surface and intensity perturbations. The closer to the limb, the larger the differences. This work presents improvements for the computation of the intensity perturbations, in particular for high-degree modes, and explains differences in intensity computations in earlier works. The phase shifts and amplitude differences between the temperature and intensity perturbations increase towards the limb. This should help to interpret some of the systematic center-to-limb effects observed in local helioseismology., Comment: 11 pages, 7 figures, Accepted to A&A

Retrograde Rossby waves, measured to have significant amplitudes in the Sun, likely have notable implications for various solar phenomena. Rossby waves create small-amplitude, very-low frequency motions (on the order of the rotation rate and lower), which in turn shift the resonant frequencies and eigenfunctions of the acoustic modes of the Sun. The detection of even azimuthal orders Rossby modes using mode coupling presents additional challenges and prior work therefore only focused on odd orders. Here, we successfully extend the methodology to measure even azimuthal orders as well. We analyze 4 and 8 years of Helioseismic and Magnetic Imager (HMI) data and consider coupling between different-degree acoustic modes (of separations 1 and 3 in harmonic degree). The technique uses couplings between different frequency bins to capture the temporal variability of the Rossby modes. We observe significant power close to the theoretical dispersion relation for sectoral Rossby modes (where the azimuthal order is same as harmonic degree, s = |t|). Our results are consistent with prior measurements of Rossby modes with azimuthal orders over the range t = 4 to 16 with maximum power occurring at mode t = 8. The amplitudes of these modes vary from 1 to 2 m/s. We place an upper bound of 0.2 m/s on the sectoral t = 2 mode, which we do not detect in our measurements. This effort adds credence to the mode-coupling methodology in helioseismology, Comment: Accepted for publication in Astronomy & Astrophysics. 9 pages, 5 figures

Solar active regions are associated with Evershed outflows in sunspot penumbrae, moat outflows surrounding sunspots, and extended inflows surrounding active regions. The latter have been identified on established active regions by various methods. The evolution of these inflows and their dependence on active region properties as well as their impact on the global magnetic field are not yet understood. We aim to understand the evolution of the average inflows around emerging active regions and to derive an empirical model for these inflows. We analyze horizontal flows at the surface of the Sun using local correlation tracking of solar granules observed in continuum images of SDO/HMI. We measure average flows of a sample of 182 isolated active regions up to seven days before and after their emergence onto the solar surface with a cadence of 12 hours. We investigate the average inflow properties with respect to active region characteristics of total flux and latitude. We fit a model to these observed inflows for a quantitative analysis. We find that converging flows of around $20$ to $30$ m/s are first visible one day prior to emergence, in agreement with recent results. These converging flows are present independently of active region properties of latitude or flux. We confirm a recently found prograde flow of about $40$ m/s at the leading polarity during emergence. We find that the time after emergence when the latitudinal inflows increase in amplitude depends on the flux of the active region, ranging from one to four days after emergence and increasing with flux. The largest extent of the inflows is up to about $7 \pm 1^\circ$ away from the center of the active region within the first six days after emergence. The inflow velocities have amplitudes of about $50$ m/s., Comment: Accepted for publication in Astronomy & Astrophysics. 16 pages, 17 figures

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., Comment: 28 pages, 11 figures, accepted for publication in ApJS

The solar photosphere provides us with a laboratory for understanding turbulence in a layer where the fundamental processes of transport vary rapidly and a strongly superadiabatic region lies very closely to a subadiabatic layer. Our tools for probing the turbulence are high-resolution spectropolarimetric observations such as have recently been obtained with the two sunrise missions, and numerical simulations. Our aim is to study photospheric turbulence with the help of Fourier power spectra that we compute from observations and simulations. We also attempt to explain some properties of the photospheric overshooting flow with the help of its governing equations and simulations. We find that quiet-Sun observations and smeared simulations exhibit a power-law behavior in the subgranular range of their Doppler velocity power spectra with an index of$~\approx -2$. The unsmeared simulations exhibit a power-law index of$~\approx -2.25$. The smearing considerably reduces the extent of the power-law-like portion of the spectra. Therefore, the limited spatial resolution in some observations might eventually result in larger uncertainties in the estimation of the power-law indices. The simulated vertical velocity power spectra as a function of height show a rapid change in the power-law index from the solar surface to $300$~km above it. A scale-dependent transport of the vertical momentum occurs. At smaller scales, the vertical momentum is more efficiently transported sideways than at larger scales. This results in less vertical velocity power transported upward at small scales than at larger scales and produces a progressively steeper vertical velocity power law below $180$ km. Above this height, the gravity work progressively gains importance at all scales, making the atmosphere progressively more hydrostatic and resulting in a gradually less steep power law., Comment: 10 pages, 7 figures, Accepted in A and A

Context. The frequencies, lifetimes, and eigenfunctions of solar acoustic waves are affected by turbulent convection, which is random in space and in time. Since the correlation time of solar granulation and the periods of acoustic waves ($\sim$5 min) are similar, the medium in which the waves propagate cannot a priori be assumed to be time independent. Aims. We compare various effective-medium solutions with numerical solutions in order to identify the approximations that can be used in helioseismology. For the sake of simplicity, the medium is one dimensional. Methods. We consider the Keller approximation, the second-order Born approximation, and spatial homogenization to obtain theoretical values for the effective wave speed and attenuation (averaged over the realizations of the medium). Numerically, we computed the first and second statistical moments of the wave field over many thousands of realizations of the medium (finite-amplitude sound-speed perturbations are limited to a 30 Mm band and have a zero mean). Results. The effective wave speed is reduced for both the theories and the simulations. The attenuation of the coherent wave field and the wave speed are best described by the Keller theory. The numerical simulations reveal the presence of coda waves, trailing the coherent wave packet. These late arrival waves are due to multiple scattering and are easily seen in the second moment of the wave field. Conclusions. We find that the effective wave speed can be calculated, numerically and theoretically, using a single snapshot of the random medium (frozen medium); however, the attenuation is underestimated in the frozen medium compared to the time-dependent medium. Multiple scattering cannot be ignored when modeling acoustic wave propagation through solar granulation., Comment: 13 pages, 16 figures, to be published in A&A

Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate? (2) How do solar transients drive heliospheric variability? (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere? (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission's science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit's science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans (SOOPs), resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime., Comment: 20 pages, 1 figure, accepted by Astronomy & Astrophysics

Retrograde-propagating waves of vertical vorticity with longitudinal wavenumbers between 3 and 15 have been observed on the Sun with a dispersion relation close to that of classical sectoral Rossby waves. The observed vorticity eigenfunctions are symmetric in latitude, peak at the equator, switch sign near $20^\circ$-$30^\circ$, and decrease at higher latitudes. We search for an explanation that takes into account solar latitudinal differential rotation. In the equatorial $\beta$ plane, we study the propagation of linear Rossby waves (phase speed $c <0$) in a parabolic zonal shear flow, $U = - \overline{U}\ \xi^2<0$, where $\overline{U} = 244$ m/s and $\xi$ is the sine of latitude. In the inviscid case, the eigenvalue spectrum is real and continuous and the velocity stream functions are singular at the critical latitudes where $U = c$. We add eddy viscosity in the problem to account for wave attenuation. In the viscous case, the stream functions are solution of a fourth-order modified Orr-Sommerfeld equation. Eigenvalues are complex and discrete. For reasonable values of the eddy viscosity corresponding to supergranular scales and above (Reynolds number $100 \le Re \le 700$), all modes are stable. At fixed longitudinal wavenumber, the least damped mode is a symmetric mode with a real frequency close to that of the classical Rossby mode, which we call the R mode. For $Re \approx 300$, the attenuation and the real part of the eigenfunction is in qualitative agreement with the observations (unlike the imaginary part of the eigenfunction, which has a larger amplitude in the model. Conclusion: Each longitudinal wavenumber is associated with a latitudinally symmetric R mode trapped at low latitudes by solar differential rotation. In the viscous model, R modes transport significant angular momentum from the dissipation layers towards the equator., Comment: Submitted to Astron. Astrophys. on 29 May 2020

Context. Large-scale equatorial Rossby modes have been observed on the Sun over the last two solar cycles. Aims. We investigate the impact of the time-varying zonal flows on the frequencies of Rossby modes. Methods. A first-order perturbation theory approach is used to obtain an expression for the expected shift in the mode frequencies due to perturbations in the internal rotation rate. Results. Using the time-varying rotation from helioseismic inversions we predict the changes in Rossby mode frequencies with azimuthal orders from m = 1 to m = 15 over the last two solar cycles. The peak-to-peak frequency change is less than 1 nHz for the m = 1 mode, grows with m, and reaches 25 nHz for m = 15. Conclusions. Given the observational uncertainties on mode frequencies due to the finite mode lifetimes, we find that the predicted frequency shifts are near the limit of detectability.

Large-scale Rossby waves have recently been discovered from measurements of horizontal surface and near-surface solar flows (L\"optien at al. 2018). We are interested in understanding why only the sectoral modes are seen in the observations and also in modelling the radial structure of the observed modes. To do so, we characterise here the radial eigenfunctions of r modes for slowly-rotating polytropes in uniform rotation. We find that for free-surface boundary conditions on a spheroid of non-vanishing surface density, r modes can only exist for $\ell=m$ spherical harmonics in the inviscid case, and we compute their depth dependence and frequencies to leading order. For quasi-adiabatic stratification the sectoral modes with no radial nodes are the only modes which are almost toroidal and the depth dependence of the corresponding horizontal motion scales as $r^m$. For all r modes except the zero radial order sectoral ones, non-adiabatic stratification plays a crucial role in the radial force balance. The lack of quasi-toroidal solutions when stratification is close to neutral, except for the sectoral modes without nodes in radius, follows from the statement that the system needs to be in both horizontal and radial force balance. In the absence of super- or subadiabatic stratification and viscosity, both the horizontal and radial force balances independently determine the pressure perturbation. The only quasi-toroidal cases in which the two determinations of the pressure perturbation are consistent are the special cases where $\ell=m$, and the horizontal displacement scales with $r^m$., Comment: 10 pages, 8 figures, accepted in A&A

Global-scale Rossby waves have recently been unambiguously identified on the Sun. Here we study the latitude and depth dependence of the Rossby wave eigenfunctions. By applying helioseismic ring-diagram analysis and granulation tracking to SDO/HMI observations, we compute maps of the radial vorticity of flows in the upper solar convection zone (down to depths of more than $16$ Mm). We use a Fourier transform in longitude to separate the different azimuthal orders m in the range $3 \le m \le 15$. At each $m$ we obtain the phase and amplitude of the Rossby waves as a function of depth using the helioseismic data. At each $m$ we also measure the latitude dependence of the eigenfunctions by calculating the covariance between the equator and other latitudes. We then study the horizontal and radial dependences of the radial vorticity eigenfunctions. The horizontal eigenfunctions are complex. As observed previously, the real part peaks at the equator and switches sign near $\pm 30^\circ$, thus the eigenfunctions show significant non-sectoral contributions. The imaginary part is smaller than the real part. The phase of the radial eigenfunctions varies by only roughly $\pm 5^\circ$ over the top $15$ Mm. The amplitude of the radial eigenfunctions decreases by about $10\%$ from the surface down to $8$ Mm (the region where ring-diagram analysis is most reliable, as seen by comparing with the rotation rate measured by global-mode seismology). The radial dependence of the radial vorticity eigenfunctions deduced from ring-diagram analysis is consistent with a power-law down to $8$ Mm and is unreliable at larger depths. However, the observations provide only weak constraints on the power-law exponents. For the real part, the latitude dependence of the eigenfunctions is consistent with previous work (using granulation tracking). The imaginary part is smaller than the real part but significantly nonzero., Comment: Submitted to and accepted by Astronomy and Astrophysics; includes minor changes from language editing report

This paper describes the Polarimetric and Helioseismic Imager on the Solar Orbiter mission (SO/PHI), the first magnetograph and helioseismology instrument to observe the Sun from outside the Sun-Earth line. It is the key instrument meant to address the top-level science question: How does the solar dynamo work and drive connections between the Sun and the heliosphere? SO/PHI will also play an important role in answering the other top-level science questions of Solar Orbiter, as well as hosting the potential of a rich return in further science. SO/PHI measures the Zeeman effect and the Doppler shift in the FeI 617.3nm spectral line. To this end, the instrument carries out narrow-band imaging spectro-polarimetry using a tunable LiNbO_3 Fabry-Perot etalon, while the polarisation modulation is done with liquid crystal variable retarders (LCVRs). The line and the nearby continuum are sampled at six wavelength points and the data are recorded by a 2kx2k CMOS detector. To save valuable telemetry, the raw data are reduced on board, including being inverted under the assumption of a Milne-Eddington atmosphere, although simpler reduction methods are also available on board. SO/PHI is composed of two telescopes; one, the Full Disc Telescope (FDT), covers the full solar disc at all phases of the orbit, while the other, the High Resolution Telescope (HRT), can resolve structures as small as 200km on the Sun at closest perihelion. The high heat load generated through proximity to the Sun is greatly reduced by the multilayer-coated entrance windows to the two telescopes that allow less than 4% of the total sunlight to enter the instrument, most of it in a narrow wavelength band around the chosen spectral line., Comment: 36 pages, 41 figures

Asteroseismology has undergone a profound transformation as a scientific field following the CoRoT and Kepler space missions. The latter is now yielding the first measurements of latitudinal differential rotation obtained directly from oscillation frequencies. Differential rotation is a fundamental mechanism of the stellar dynamo effect. Our goal is to measure the amount of differential rotation in the solar analogues 16 Cyg A and B, which are the components of a binary system. These stars are the brightest observed by Kepler and have therefore been extensively observed, with exquisite precision on their oscillation frequencies. We modelled the acoustic power spectrum of 16 Cyg A and B using a model that takes into account the contribution of differential rotation to the rotational frequency splitting. The estimation was carried out in a Bayesian setting. We then inverted these results to obtain the rotation profile of both stars under the assumption of a solar-like functional form. We observe that the magnitude of latitudinal differential rotation has a strong chance of being solar-like for both stars, their rotation rates being higher at the equator than at the pole. The measured latitudinal differential rotation, defined as the difference of rotation rate between the equator and the pole, is $320\pm269$ nHz and $440^{+363}_{-383}$ nHz for 16 Cyg A and B, respectively, confirming that the rotation rates of these stars are almost solar-like. Their equatorial rotation rates are $535\pm75$ nHz and $565_{-129}^{+150}$ nHz. Our results are in good agreement with measurements obtained from spectropolarimetry, spectroscopy, and photometry. We present the first conclusive measurement of latitudinal differential rotation for solar analogues. Their rotational profiles are very close to those of the Sun. These results depend weakly on the uncertainties of the stellar parameters., Comment: Accepted in A&A

Radial velocity (RV) measurements are used to search for planets orbiting late-type main-sequence stars and confirm the transiting planets. The most advanced spectrometers are approaching a precision of $\sim 10$ cm/s that implies the need to identify and correct for all possible sources of RV oscillations intrinsic to the star down to this level and possibly beyond. The recent discovery of global-scale equatorial Rossby waves in the Sun, also called r modes, prompted us to investigate their possible signature in stellar RV measurements. R modes are toroidal modes of oscillation whose restoring force is the Coriolis force and propagate in the retrograde direction in a frame that corotates with the star. The solar r modes with azimuthal orders $3 \leq m \lesssim 15$ were identified unambiguously because of their dispersion relation and their long e-folding lifetimes of hundreds of days. Here we simulate the RV oscillations produced by sectoral r modes with $2 \leq m \leq 5$ assuming a stellar rotation period of 25.54 days and a maximum amplitude of the surface velocity of each mode of 2 m/s. This amplitude is representative of the solar measurements, except for the $m=2$ mode which has not yet been observed. Sectoral r modes with azimuthal orders $m=2$ and $3$ would produce RV oscillations with amplitudes of 76.4 and 19.6 cm/s and periods of 19.16 and 10.22 days, respectively, for a star with an inclination of the rotation axis $i=60^{\circ}$. Therefore, they may produce rather sharp peaks in the Fourier spectrum of the radial velocity time series that could lead to spurious planetary detections. Sectoral r~modes may represent a source of confusion in the case of slowly rotating inactive stars that are preferential targets for RV planet search. The main limitation of the present investigation is the lack of observational constraint on the amplitude of the $m=2$ mode on the Sun., Comment: 7 pages; 4 figures; 1 table; accepted to Astronomy & Astrophysics

During the solar magnetic activity cycle the emergence latitudes of sunspots change, leading to the well-known butterfly diagram. This phenomenon is poorly understood for other stars as starspot latitudes are generally unknown. The related changes in starspot rotation rates caused by latitudinal differential rotation can however be measured. Using the set of 3093 Kepler stars with activity cycles identified by Reinhold et al. (2017), we aim to study the temporal change in starspot rotation rates over magnetic activity cycles, and how this relates to the activity level, mean rotation rate, and effective temperature of the star. We measure the photometric variability as a proxy for the magnetic activity and the spot rotation rate in each quarter over the duration of the Kepler mission. We phase-fold these measurements with the cycle period. We perform averages over stars with comparable mean rotation rates and effective temperature at fixed activity-cycle phases. We detect a clear correlation between the variation of activity level and the variation of the starspot rotation rate. The sign and amplitude of this correlation depends on the mean stellar rotation and, to a lesser extent, on the effective temperature. For slowly rotating stars (with periods between 15-28 days) the starspot rotation rates are clearly anti-correlated with the level of activity during the activity cycles. A transition is seen at periods of 10-15 days, where stars with effective temperature above 4200K instead show positive correlation. Our results can be interpreted in terms of a stellar "butterfly diagram", but these appear different from the Sun's as the starspot rotation rates are either in phase or anti-phase with the activity level. Alternatively, the activity cycles seen by Kepler are short (around 2.5 years) and may therefore be secondary cycles, perhaps analogous to the solar quasi-biennial oscillations., Comment: Accepted for publication in Astronomy & Astrophysics. 11 pages, 8 figures

Stellar magnetic fields are poorly understood but are known to be important for stellar evolution and exoplanet habitability. They drive stellar activity, which is the main observational constraint on theoretical models for magnetic field generation and evolution. Starspots are the main manifestation of the magnetic fields at the stellar surface. In this study we measure the variation of their latitude with time, called a butterfly diagram in the solar case, for the solar analogue HD 173701 (KIC 8006161). To that effect, we use Kepler data, to combine starspot rotation rates at different epochs and the asteroseismically determined latitudinal variation of the stellar rotation rates. We observe a clear variation of the latitude of the starspots. It is the first time such a diagram is constructed using asteroseismic data., Comment: 8 pages, 4 figures, accepted in A&A Letters

The differentially rotating outer layers of stars are thought to play a role in driving their magnetic activity, but the underlying mechanisms that generate and sustain differential rotation are poorly understood. We report the measurement of latitudinal differential rotation in the convection zones of 40 Sun-like stars using asteroseismology. For the most significant detections, the stars' equators rotate approximately twice as fast as their mid-latitudes. The latitudinal shear inferred from asteroseismology is much larger than predictions from numerical simulations., Comment: 45 pages, 11 figures, 4 tables, published in Science

Previous helioseismology of sunspots has been sensitive to both the structural and magnetic aspects of sunspot structure. We aim to develop a technique that is insensitive to the magnetic component so the two aspects can be more readily separated. We study waves reflected almost vertically from the underside of a sunspot. Time-distance helioseismology was used to measure travel times for the waves. Ray theory and a detailed sunspot model were used to calculate travel times for comparison. It is shown that these large distance waves are insensitive to the magnetic field in the sunspot. The largest travel time differences for any solar phenomena are observed. With sufficient modeling effort, these should lead to better understanding of sunspot structure.

Solar supergranulation presents us with many mysteries. For example, previous studies in spectral space found that supergranulation has wave-like properties. Here we study, in real space, the wave-like evolution of the average supergranule over a range of spatial scales (from 10 to 80 Mm). We complement this by characterizing the evolution of the associated network magnetic field. We use one year of data from the Helioseismic and Magnetic Imager (HMI) to measure horizontal near-surface flows near the solar equator by applying time-distance helioseismology on Dopplergrams and granulation tracking on intensity images. The average supergranule outflow (or inflow) is constructed by averaging over 10000 individual outflows (or inflows). The contemporaneous evolution of the magnetic field is studied with HMI line-of-sight observations. We confirm and extend previous measurements of the supergranular wave dispersion relation to angular wavenumbers in the range 50120. In real space, larger supergranules undergo oscillations with longer periods and lifetimes than smaller cells. We find excellent agreement between TD and LCT and obtain wave properties that are independent of the tracking rate. The observed network magnetic field follows the oscillations of the supergranular flows with a six-hour time lag. This behavior can be explained by computing the motions of corks carried by the supergranular flows. Signatures of supergranular waves in surface horizontal flows near the solar equator can be observed in real space. These oscillatory flows control the evolution of the network magnetic field, in particular they explain the recently discovered east-west anisotropy of the magnetic field around the average supergranule. Background flow measurements that we obtain from Doppler frequency shifts do not favor shallow models of supergranulation., Comment: 13 pages, 14 figures (plus appendix), accepted for publication in A&A

Oscillation properties are usually measured by fitting symmetric Lorentzian profiles to the power spectra of Sun-like stars. However the line profiles of solar oscillations have been observed to be asymmetrical for the Sun. The physical origin of this line asymmetry is not fully understood, although it should depend on the depth dependence of the source of wave excitation (convective turbulence) and details of the observable (velocity or intensity). For oscillations of the Sun, it has been shown that neglecting the asymmetry leads to systematic errors in the frequency determination. This could subsequently affects the results of seismic inferences of the solar internal structure. Using light curves from the {\it Kepler} spacecraft we have measured mode asymmetries in 43 stars. We confirm that neglecting the asymmetry leads to systematic errors that can exceed the $1\sigma$ confidence intervals for seismic observations longer than one year. Therefore, the application of an asymmetric Lorentzian profile is to be favoured to improve the accuracy of the internal stellar structure and stellar fundamental parameters. We also show that the asymmetry changes sign between cool Sun-like stars and hotter stars. This provides the best constraints to date on the location of the excitation sources across the Hertzsprung-Russel diagram., Comment: 8 pages, 7 Figures, 1 Table, Accepted to ApJ

The observed magnetic field on the solar surface is characterized by a very complex spatial and temporal behavior. Although feature-tracking algorithms have allowed us to deepen our understanding of this behavior, subjectivity plays an important role in the identification and tracking of such features. In this paper, we continue studies Gorobets, A. Y., Borrero, J. M., & Berdyugina, S. 2016, ApJL, 825, L18 of the temporal stochasticity of the magnetic field on the solar surface without relying either on the concept of magnetic features or on subjective assumptions about their identification and interaction. We propose a data analysis method to quantify fluctuations of the line-of-sight magnetic field by means of reducing the temporal field's evolution to the regular Markov process. We build a representative model of fluctuations converging to the unique stationary (equilibrium) distribution in the long time limit with maximum entropy. We obtained different rates of convergence to the equilibrium at fixed noise cutoff for two sets of data. This indicates a strong influence of the data spatial resolution and mixing-polarity fluctuations on the relaxation process. The analysis is applied to observations of magnetic fields of the relatively quiet areas around an active region carried out during the second flight of the Sunrise/IMaX and quiet Sun areas at the disk center from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory satellite., Comment: 11 pages, 5 figures, The Astrophysical Journal Supplement Series (accepted)

Deciphering the assembly history of the Milky Way is a formidable task, which becomes possible only if one can produce high-resolution chrono-chemo-kinematical maps of the Galaxy. Data from large-scale astrometric and spectroscopic surveys will soon provide us with a well-defined view of the current chemo-kinematical structure of the Milky Way, but will only enable a blurred view on the temporal sequence that led to the present-day Galaxy. As demonstrated by the (ongoing) exploitation of data from the pioneering photometric missions CoRoT, Kepler, and K2, asteroseismology provides the way forward: solar-like oscillating giants are excellent evolutionary clocks thanks to the availability of seismic constraints on their mass and to the tight age-initial-mass relation they adhere to. In this paper we identify five key outstanding questions relating to the formation and evolution of the Milky Way that will need precise and accurate ages for large samples of stars to be addressed, and we identify the requirements in terms of number of targets and the precision on the stellar properties that are needed to tackle such questions. By quantifying the asteroseismic yields expected from PLATO for red-giant stars, we demonstrate that these requirements are within the capabilities of the current instrument design, provided that observations are sufficiently long to identify the evolutionary state and allow robust and precise determination of acoustic-mode frequencies. This will allow us to harvest data of sufficient quality to reach a 10% precision in age. This is a fundamental pre-requisite to then reach the more ambitious goal of a similar level of accuracy, which will only be possible if we have to hand a careful appraisal of systematic uncertainties on age deriving from our limited understanding of stellar physics, a goal which conveniently falls within the main aims of PLATO's core science., Comment: 17 pages, 9 figures, accepted for publication in Astronomical Notes

Rotational shear in Sun-like stars is thought to be an important ingredient in models of stellar dynamos. Thanks to helioseismology, rotation in the Sun is characterized well, but the interior rotation profiles of other Sun-like stars are not so well constrained. Until recently, measurements of rotation in Sun-like stars have focused on the mean rotation, but little progress has been made on measuring or even placing limits on differential rotation. Using asteroseismic measurements of rotation we aim to constrain the radial shear in five Sun-like stars observed by the NASA Kepler mission: KIC004914923, KIC005184732, KIC006116048, KIC006933899, and KIC010963065. We used stellar structure models for these five stars from previous works. These models provide the mass density, mode eigenfunctions, and the convection zone depth, which we used to compute the sensitivity kernels for the rotational frequency splitting of the modes. We used these kernels as weights in a parametric model of the stellar rotation profile of each star, where we allowed different rotation rates for the radiative interior and the convective envelope. This parametric model was incorporated into a fit to the oscillation power spectrum of each of the five Kepler stars. This fit included a prior on the rotation of the envelope, estimated from the rotation of surface magnetic activity measured from the photometric variability. The asteroseismic measurements without the application of priors are unable to place meaningful limits on the radial shear. Using a prior on the envelope rotation enables us to constrain the interior rotation rate and thus the radial shear. In the five cases that we studied, the interior rotation rate does not differ from the envelope by more than approximately +/-30%. Uncertainties in the rotational splittings are too large to unambiguously determine the sign of the radial shear., Comment: Accepted for publication in Astronomy & Astrophysics. 8 pages, 4 figures, 1 table

Context. Local helioseismology has detected spatially extended converging surface flows into solar active regions. These play an important role in flux-transport models of the solar dynamo. Aims. We aim to validate the existence of the inflows by deriving horizontal flow velocities around active regions with local correlation tracking of granulation. Methods. We generate a six-year long-time series of full-disk maps of the horizontal velocity at the solar surface by tracking granules in continuum intensity images provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Results. On average, active regions are surrounded by inflows extending up to 10 deg from the center of the active region of magnitudes of 20-30 m/s, reaching locally up to 40 m/s, which is in agreement with results from local helioseismology. By computing an ensemble average consisting of 243 individual active regions, we show that the inflows are not azimuthally symmetric but converge predominantly towards the trailing polarity of the active region with respect to the longitudinally and temporally averaged flow field., Comment: 10 pages, 9 figures. Submitted to Astronomy & Astrophysics

Accurate modelling of solar-like oscillators requires that modelled mode frequencies are corrected for the systematic shift caused by improper modelling of the near-surface layers, known as the surface effect. ... We investigate how much additional uncertainty is introduced to stellar model parameters by our uncertainty about the functional form of the surface effect. At the same time, we test whether any of the parametrizations is significantly better or worse at modelling observed subgiants and low-luminosity red giants. We model six stars observed by Kepler that show clear mixed modes. We fix the input physics of the stellar models and vary the choice of surface correction ... Models using a solar-calibrated power law correction consistently fit the observations more poorly than the other four corrections. Models with the remaining four corrections generally fit ... about equally well, with the combined surface correction by Ball & Gizon perhaps being marginally superior. The fits broadly agree on the model parameters within about the $2\sigma$ uncertainties, with discrepancies between the modified Lorentzian and free power law corrections occasionally exceeding the $3\sigma$ level. Relative to the best-fitting values, the total uncertainties on the masses, radii and ages of the stars are all less than 2, 1 and 6 per cent, respectively. A solar-calibrated power law ... appears unsuitable for use with more evolved solar-like oscillators. Among the remaining surface corrections, the uncertainty in the model parameters introduced by the surface effects is about twice as large as the uncertainty in the individual fits for these six stars. Though the fits are thus somewhat less certain because of our uncertainty of how to manage the surface effect, these results also demonstrate that it is feasible to model the individual mode frequencies of subgiants and low-luminosity red giants. ..., Comment: Accepted for publication in Astronomy & Astrophysics. 13 pages, 6 figures, 5 tables. Abstract slightly abridged to meet arXiv's 1920 character limit