The Sun is the most studied of all stars, and thus constitutes a benchmark for stellar models. However, our vision of the Sun is still incomplete, as illustrated by the current debate on its chemical composition. The problem reaches far beyond chemical abundances and is intimately linked to microscopic and macroscopic physical ingredients of solar models such as radiative opacity, for which experimental results have been recently measured that still await theoretical explanations. We present opacity profiles derived from helioseismic inferences and compare them with detailed theoretical computations of individual element contributions using three different opacity computation codes, in a complementary way to experimental results. We find that our seismic opacity is about 10% higher than theoretical values used in current solar models around 2 million degrees, but lower by 35% than some recent available theoretical values. Using the Sun as a laboratory of fundamental physics, we show that quantitative comparisons between various opacity tables are required to understand the origin of the discrepancies between reported helioseismic, theoretical and experimental opacity values.

The European Space Agency has selected PLATO (PLAnetary Transits and Oscillations of stars) for its M3 launch which is scheduled for 2026. With its extremely large field of view, PLATO is designed to obtain photometric measurements over an extended period for bright stars in order to detect and characterise (primarily) rocky planets in the habitable zones of solar type stars. The PLATO measurements will have sufficient sensitivity to determine the mass, radius and age of the host stars with unprecedented accuracy. The PLATO planet database will provide the first large-scale catalogue of accurately and homogeneously characterised small planets at intermediate orbital periods, which will can be used to severely constraint planet formation theories. This would facilitate large scale comparative exo-planetology. In addition the bright PLATO host stars will be ideal targets for atmospheric study with next generation facilities such as the ELT. The PLATO sensitivity will be sufficient to detect pulsations from stars across the HR diagram allowing a deep understanding of stellar structure and evolution to be developed using parameters determined from asteroseismology.

AbstractWe present a new method to measure the rotational height gradient in the solar photosphere. The method is inspired from differential interferometric techniques, we applied it to spectroscopic observations in the FeI 630.15 nm obtained at the solar telescope THEMIS which is equipped with an efficient adaptive optics system. The spectroscopic data was used to obtain images of the granulation at different line cords formed at different heights in the photosphere. Cross-correlation allows us to measure small systematic shifts between similar images. When observations are performed out of the center of the solar disk, the perspective effect gives rise to a radial shift between images formed at different heights. The measurement of this shift provides us with their formation-height difference. At the center of the disk the perspective effect vanishes but we measured a systematic retrograde shift along the east/west direction of the images formed at higher heights. The measured shifts are proportional to the formation height of the images. We interpret these findings as the evidence of a decrease of the rotational velocity with height in the low photosphere of the Sun and we give an estimate of this gradient.

Observations of the chromosphere with Deslandres's spectroheliograph started at Paris Observatory in 1893 and were followed by systematic observations at Meudon since 1908. The solar collection of Hα and CaII K images is probably the longest available worldwide, with associated products such as synoptic maps and tables. Since 2018, Meudon spectroheliograph is the only instrument producing data-cubes of full line profiles of CaII H, CaII K and Hα, for each pixel of the solar disk. Slices of the cubes provide monochromatic images. We summarize in this paper the capabilities of the successive generations of the instrument, and explore the potential of the collection and products for analysis of rare events, investigations of past solar activity and studies of long term variability.

Context.Radial differential rotation is an important physical ingredient in stellar dynamo theory. In the case of the Sun, heliosismology techniques have revealed the existence of a near-surface shear layer covering 15–20% of the upper convection zone. It was recently shown that the rotation velocity gradient is not uniform in this layer and that it displays a steep increase in a shallow layer near the surface.Aims.We report the detection of a rotation velocity depth-gradient in the low photosphere that is not accessible to heliosismology techniques.Methods.We applied differential interferometric methods to spectroscopic data obtained with the solar telescope THEMIS, which is equipped with an efficient adaptative optics system. The detection was based on the measurement of a systematic east-west shift between images of the solar granulation at different depths in the FeI 630.15 nm at the center of the solar disk. The same technique was applied to obtain the depth-difference between the images from their perspective shift when they are observed away from the disk center. Both THEMIS and HINODE/SOT data were used for the height-difference measurement, giving similar results.Results.At the center of the solar disk, we measured a systematic retrograde shift of the photospheric granular structures on the east-west axis and with no shift in the north-south direction. The retrograde shift increases linearly with height. We interpret these findings as a signature of a steep decrease in the angular velocity in the low photosphere.Conclusions.The rotational radial shear in the low solar photosphere is likely related to the dynamics of the subsurface shear layer. Its measurement yields a valuable constraint on the numerical simulations of the solar upper convection zone.

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We present in this reference paper an instrumental project dedicated to the monitoring of solar activity during solar cycle 25. It concerns the survey of fast evolving chromospheric events implied in Space Weather, such as flares, coronal mass ejections, filament instabilities and Moreton waves. Coronal waves are produced by large flares around the solar maximum and propagate with chromospheric counterparts; they are rare, faint, difficult to observe, and for that reason, challenging. They require systematic observations with automatic, fast and multi-channel optical instruments. MeteoSpace is a high cadence telescope assembly specially designed for that purpose. The large amount of data will be freely available to the solar community. We describe in details the optical design, the qualification tests and capabilities of the telescopes, and show how waves can be detected. MeteoSpace will be installed at Calern observatory (Côte d’Azur, 1270 m) and will be in full operation in 2023.

A mission to view the solar poles from high helio-latitudes (above 60°) will build on the experience of Solar Orbiter as well as a long heritage of successful solar missions and instrumentation (e.g. SOHO Domingo et al. (Solar Phys. 162 (1-2), 1–37 1995 ), STEREO Howard et al. (Space Sci. Rev. 136 (1-4), 67–115 2008 ), Hinode Kosugi et al. (Solar Phys. 243 (1), 3–17 2007 ), Pesnell et al. Solar Phys. 275 (1–2), 3–15 2012 ), but will focus for the first time on the solar poles, enabling scientific investigations that cannot be done by any other mission. One of the major mysteries of the Sun is the solar cycle. The activity cycle of the Sun drives the structure and behaviour of the heliosphere and of course, the driver of space weather. In addition, solar activity and variability provides fluctuating input into the Earth climate models, and these same physical processes are applicable to stellar systems hosting exoplanets. One of the main obstructions to understanding the solar cycle, and hence all solar activity, is our current lack of understanding of the polar regions. In this White Paper, submitted to the European Space Agency in response to the Voyage 2050 call, we describe a mission concept that aims to address this fundamental issue. In parallel, we recognise that viewing the Sun from above the polar regions enables further scientific advantages, beyond those related to the solar cycle, such as unique and powerful studies of coronal mass ejection processes, from a global perspective, and studies of coronal structure and activity in polar regions. Not only will these provide important scientific advances for fundamental stellar physics research, they will feed into our understanding of impacts on the Earth and other planets’ space environment.

We present the observing program proposed by Paris and Côte d’Azur Observatories for monitoring solar activity during the upcoming cycle 25 and providing near real time images and movies of the chromosphere for space-weather research and applications. Two optical instruments are fully dedicated to this task and we summarize their capabilities. Short-term and fast-cadence observations of the chromosphere will be performed automatically at Calern observatory (Côte d’Azur), where dynamic events, as flare development, Moreton waves, filament instabilities and Coronal Mass Ejections onset, will be tracked. This new set of telescopes will operate in 2021 with narrow bandpass filters selecting Hα and CaII K lines. We present the instrumental design and a simulation of future images. At Meudon, the Spectroheliograph is well adapted to the long-term and low-cadence survey of chromospheric activity by recently improved and optimized spectroscopic means. Surface scans deliver daily (x, y, λ) datacubes of Hα, CaII K and CaII H line profiles. We describe the nature of available data and emphasize the new calibration method of spectra.

Context. The Sun constitutes an excellent laboratory of fundamental physics. With the advent of helioseismology, we were able to probe its internal layers with unprecendented precision and thoroughness. However, the current state of solar modelling is still stained by tedious issues. One of these central problems is related to the disagreement between models computed with recent photospheric abundances and helioseismic constraints. The observed discrepancies raise questions on some fundamental ingredients entering the computation of solar and stellar evolution models. Aims. We used solar evolutionary models as initial conditions for reintegrating their structure using Ledoux discriminant inversions. The resulting models are defined as seismic solar models, satisfying the equations of hydrostatic equilibrium. These seismic models will allow us to better constrain the internal structure of the Sun and provide complementary information to that of calibrated standard and non-standard models. Methods. We used inversions of the Ledoux discriminant to reintegrate seismic solar models satisfying the equations of hydrostatic equilibrium. These seismic models were computed using various reference models with different equations of state, abundances, and opacity tables. We checked the robustness of our approach by confirming the good agreement of our seismic models in terms of sound speed, density, and entropy proxy inversions, as well as frequency-separation ratios of low-degree pressure modes. Results. Our method allows us to determine the Ledoux discriminant profile of the Sun with an excellent accuracy and compute full profiles of this quantity. Our seismic models show an agreement with seismic data of ≈0.1% in sound speed, density, and entropy proxy after seven iterations in addition to an excellent agreement with the observed frequency-separation ratios. They surpass all standard and non-standard evolutionary models including ad hoc modifications of their physical ingredients that aim to reproduce helioseismic constraints. Conclusions. The obtained seismic Ledoux discriminant profile, as well as the full consistent structure obtained from our reconstruction procedure paves the way for renewed attempts at constraining the solar modelling problem and the missing physical processes acting in the solar interior by breaking free from the hypotheses of evolutionary models.

In this work we study in details the influence of pure astronomical refraction on solar metrological measurements made from ground-based full disc imagery and provide the tools for correcting the measurements and estimating the associated uncertainties. For a given standard atmospheric model, we first use both analytical and numerical methods in order to test the validity of the commonly or historically used approximations of the differential effect of refraction as a function of zenith distance. For a given refraction model, we provide the exact formulae for correcting solar radius measurements at any heliographic angle and for any zenith distance. Then, using solar images recorded in the near-infrared between 2011 and 2016, we show that these corrections can be applied up to 70° using the usual approximate formulae and can be extended up to 80° of zenith distance provided that a standard atmospheric model and a full numerical integration of the refraction integral are used. We also provide estimates of the absolute uncertainties associated with the differential refraction corrections and show that approximate formulae can be used up to 80° of zenith distance for computing these uncertainties. For a given instrumental setup and the knowledge of the uncertainties associated with local weather records, this can be used to fix the maximum zenith distance one can observe depending on the required astrometric accuracy.

High cadence observations of solar activity (active regions, flares, filaments) in the H$\alpha$ line were performed at Meudon and Haute Provence Observatories from 1956 to 2004. More than 7 million images were recorded, mainly on 35 mm films. After a review of the scientific interest of solar surveys at high temporal resolution and the historical background, we describe the new instrument which will operate automatically in 2020 at the Calern station of the C\^{o}te d'Azur observatory (1270 m). It will replace the former heliographs with improved cadence, seeing and time coverage. We summarize the capabilities of the optical design and present new scientific perspectives in terms of flare onset and Moreton wave detection.

Context. The recent claims of g-mode detection have restarted the search for these potentially extremely important modes. The claimed detection of g modes was obtained from the analysis of the power spectrum of the time series of round-trip travel time of p modes. Aims. The goal of this paper is to reproduce these results on which the claims are based for confirming or invalidating the detection of g modes with the method used to make the claims. Methods. We computed the time series of round-trip travel time using the procedure given in Fossat et al. (2017, A&A, 604, A40), and used different variations of the times series for comparison. We used the recently calibrated GOLF data (published in Paper I) with different sampling, different photomultipliers, different length of data for reproducing the analysis. We also correlated the power spectrum with an asymptotic model of g-mode frequencies in a similar manner to Fossat and Schmider (2018, A&A, 612, L1). We devised a scheme for optimising the correlation both for pure noise and for the GOLF data. Results. We confirm the analysis performed in Fossat et al. (2017) but draw different conclusions. Their claims of detection of g modes cannot be confirmed when changing parameters such as sampling interval, length of time series, or photomultipliers. Other instrument such as GONG and BiSON do not confirm their detection. We also confirm the analysis performed in Fossat and Schmider (2018), but again draw different conclusions. For GOLF, the correlation of the power spectrum with the asymptotic model of g-mode frequencies for l = 1 and l = 2 show a high correlation at lag=0 and at lag corresponding to the rotational splitting νl, but the same occurs for pure noise due to the large number of peaks present in the model. In addition, other very different parameters defining the asymptotic model also provide a high correlation at these lags. We conclude that the detection performed in Fossat and Schmider (2018) is an artefact of the methodology.

PICARD is a mission devoted to solar variability observation, which aims at perpetuating valuable historical time-series of the solar radius. PICARD contains a double program with in-space and on-ground measurements using Ritchey-Chrétien telescopes. The PICARD spacecraft was launched on June 15, 2010, commissioned in-flight in October of the same year, and was retired in April 2014. PICARD ground-based observatory is functional since May 2011 in the Plateau de Calern (France), and is still operational today. We shall give an overview of the PICARD instrumentation and the performances of the existing ground-based telescope. We will also present our current results about solar radius variations after eight years of solar observations.

Context. In 2015, the International Astronomical Union (IAU) passed Resolution B3, which defined a set of nominal conversion constants for stellar and planetary astronomy. Resolution B3 defined a new value of the nominal solar radius (R⊙N = 695 700 km km) that is different from the canonical value used until now (695 990 km). The nominal solar radius is consistent with helioseismic estimates. Recent results obtained from ground-based instruments, balloon flights, or space-based instruments highlight solar radius values that are significantly different. These results are related to the direct measurements of the photospheric solar radius, which are mainly based on the inflection point position methods. The discrepancy between the seismic radius and the photospheric solar radius can be explained by the difference between the height at disk center and the inflection point of the intensity profile on the solar limb. At 535.7 nm (photosphere), there may be a difference of ∼330 km between the two definitions of the solar radius. Aims. The main objective of this work is to present new results of the solar radius in the near-ultraviolet, the visible, and the near-infrared from PICARD space-based and ground-based observations. Simulations show the strong influence of atmosphere effects (refraction and turbulence) on ground-based solar radius determinations and highlight the interest of space-based solar radius determinations, particularly during planet transits (Venus or Mercury), in order to obtain more realistic and accurate measurements. Methods. Solar radius observations during the 2012 Venus transit have been made with the SOlar Diameter Imager and Surface Mapper (SODISM) telescope on board the PICARD spacecraft. We used the transit of Venus as an absolute calibration to determine the solar radius accurately at several wavelengths. Our results are based on the determination of the inflection point position of the solar limb-darkening function (the most common solar radius definition). A realistic uncertainty budget is provided for each solar radius obtained with the PICARD space-based telescope during the 2012 Venus transit. The uncertainty budget considers several sources of error (detection of the centers of Venus and Sun in PICARD images, positions of Sun and Venus from ephemeris (planetary theory), PICARD on-board timing, PICARD spacecraft position, and optical distortion correction from PICARD images). Results. We obtain new values of the solar radius from the PICARD mission at several wavelengths and in different solar atmosphere regions. The PICARD spacecraft with its SODISM telescope was used to measure the radius of the Sun during the Venus transit in 2012. At 535.7 nm, the solar radius is equal to 696 134 ± 261 km (combined standard uncertainty based (ξ) on the uncertainty budget). At 607.1 nm, the solar radius is equal to 696 156 ± 145 km (ξ), and the standard deviation of the solar radius mean value is ±22 km. At 782.2 nm, the solar radius is equal to 696 192 ± 247 km (ξ). The PICARD space-based results as well as PICARD ground-based results show that the solar radius wavelength dependence in the visible and the near-infrared is extremely weak. The differences in inflection point position of the solar radius at 607.1 nm, 782.2 nm, and 1025.0 nm from a reference at 535.7 nm are less than 60 km for the different PICARD measurements.

Context. The recent claims of g-mode detection have restarted the search for these potentially extremely important modes. These claims can be reassessed in view of the different data sets available from the SoHO instruments and ground-based instruments. Aims. We produce a new calibration of the GOLF data with a more consistent p-mode amplitude and a more consistent time shift correction compared to the time series used in the past. Methods. The calibration of 22 yr of GOLF data is done with a simpler approach that uses only the predictive radial velocity of the SoHO spacecraft as a reference. Using p-modes, we measure and correct the time shift between ground- and space-based instruments and the GOLF instrument. Results. The p-mode velocity calibration is now consistent to within a few percent with other instruments. The remaining time shifts are within +/- 5 s for 99.8% of the time series.

Context. Over the past 40 years, helioseismology has been enormously successful in the study of the solar interior. A shortcoming has been the lack of a convincing detection of the solar g modes, which are oscillations driven by gravity and are hidden in the deepest part of the solar body-its hydrogen-burning core. The detection of g modes is expected to dramatically improve our ability to model this core, the rotational characteristics of which have, until now, remained unknown.Aims. We present the identification of very low frequency g modes in the asymptotic regime and two important parameters that have long been waited for: the core rotation rate, and the asymptotic equidistant period spacing of these g modes.Methods. The GOLF instrument on board the SOHO space observatory has provided two decades of full-disk helioseismic data. The search for g modes in GOLF measurements has been extremely difficult because of solar and instrumental noise. In the present study, the p modes of the GOLF signal are analyzed differently: we search for possible collective frequency modulations that are produced by periodic changes in the deep solar structure. Such modulations provide access to only very low frequency g modes, thus allowing statistical methods to take advantage of their asymptotic properties.Results. For oscillatory periods in the range between 9 and nearly 48 h, almost 100 g modes of spherical harmonic degree 1 and more than 100 g modes of degree 2 are predicted. They are not observed individually, but when combined, they unambiguously provide their asymptotic period equidistance and rotational splittings, in excellent agreement with the requirements of the asymptotic approximations. When the period equidistance has been measured, all of the individual frequencies of each mode can be determined. Previously, p-mode helioseismology allowed the g-mode period equidistance parameter P-0 to be bracketed inside a narrow range, between approximately 34 and 35 min. Here, P-0 is measured to be 34 min 01 s, with a 1 s uncertainty. The previously unknown g-mode splittings have now been measured from a non-synodic reference with very high accuracy, and they imply a mean weighted rotation of 1277 +/- 10 nHz ( 9-day period) of their kernels, resulting in a rapid rotation frequency of 1644 +/- 23 nHz ( period of one week) of the solar core itself, which is a factor 3.8 +/- 0.1 faster than the rotation of the radiative envelope.Conclusions. The g modes are known to be the keys to a better understanding of the structure and dynamics of the solar core. Their detection with these precise parameters will certainly stimulate a new era of research in this field.

We present the identification of very low frequency g modes, in the asymptotic regime, and two important parameters: the core rotation rate and the asymptotic equidistant period spacing of these g modes. The GOLF instrument on the SOHO space observatory has provided two decades of full disk helioseismic data. The search for g modes in GOLF measurements has been extremely difficult, due to solar and instrumental noise. In the present study, the p modes of the GOLF signal are analyzed differently, searching for possible collective frequency modulations produced by periodic changes in the deep solar structure. Such modulations provide access to only very low frequency g modes, thus allowing statistical methods to take advantage of their asymptotic properties. For oscillatory periods in the range between 9 and nearly 48 hours, almost 100 g modes of spherical harmonic degree 1 and more than 100 g modes of degree 2 are predicted. They are not observed individually, but when combined, they unambiguously provide their asymptotic period equidistance and rotational splittings, in excellent agreement with the requirements of the asymptotic approximations. P0, the g-mode period equidistance parameter, is measured to be 34 min 01 s, with a 1 s uncertainty. The previously unknown g-mode splittings have now been measured from a non synodic reference with a very high accuracy, and they imply a mean weighted rotation of 1277 ± 10 nHz (9-day period) of their kernels, resulting in a rapid rotation frequency of 1644 ± 23 nHz (period of one week) of the solar core itself, which is a factor 3:8 ± 0:1 faster than the rotation of the radiative envelope.