Author name code: rieutord ADS astronomy entries on 2022-09-14 author:"Rieutord, Michel" ------------------------------------------------------------------------ Title: Predictions for Gravity-mode Periods and Surface Abundances in Intermediate-mass Dwarfs from Shear Mixing and Radiative Levitation Authors: Mombarg, Joey S. G.; Dotter, Aaron; Rieutord, Michel; Michielsen, Mathias; Van Reeth, Timothy; Aerts, Conny Bibcode: 2022ApJ...925..154M Altcode: 2021arXiv211114853M The treatment of chemical mixing in the radiative envelopes of intermediate-mass stars has hardly been calibrated so far. Recent asteroseismic studies demonstrated that a constant diffusion coefficient in the radiative envelope is not able to explain the periods of trapped gravity modes in the oscillation spectra of γ Doradus pulsators. We present a new generation of MESA stellar models with two major improvements. First, we present a new implementation for computing radiative accelerations and Rosseland mean opacities that requires significantly less CPU time. Second, the inclusion of shear mixing based on rotation profiles computed with the 2D stellar structure code ESTER is considered. We show predictions for the mode periods of these models covering stellar masses from 1.4 to 3.0 M ⊙ across the main sequence, computed for different metallicities. The morphology of the chemical mixing profile resulting from shear mixing in combination with atomic diffusion and radiative levitation does allow for mode trapping, while the diffusion coefficient in the outer envelope is large (>106 cm2 s-1). Furthermore, we make predictions for the evolution of surface abundances for which radiative accelerations can be computed. We find that the N/C and C/O abundance ratios correlate with stellar age. We predict that these correlations are observable with precisions ≲ 0.1 dex on these ratios, given that a precise age estimate can be made. Title: Seismology of Altair with MOST Authors: Le Dizès, Cécile; Rieutord, Michel; Charpinet, Stéphane Bibcode: 2021A&A...653A..26L Altcode: 2021arXiv210710515L Context. Altair is the fastest rotating star at less than 10 parsecs from the Sun. Its precise modelling is a landmark for our understanding of stellar evolution with fast rotation, and all observational constraints are most welcome to better determine the fundamental parameters of this star.
Aims: We wish to improve the seismic spectrum of Altair and confirm the δ-Scuti nature of this star.
Methods: We used the photometric data collected by the Microvariability and Oscillations of STars (MOST) satellite in the form of a series of Fabry images to derive Altair light curves at four epochs, namely in 2007, 2011, 2012, and 2013.
Results: We first confirm the presence of δ-Scuti oscillations in the light curves of Altair. We extend the precision of some eigenfrequencies and add new ones to the spectrum of Altair, which now has 15 detected eigenmodes. The rotation period, which is expected at ∼7h46min from models reproducing interferometric data, seems to appear in the 2012 data set, but it still needs confirmation. Finally, Altair modal oscillations show noticeable amplitude variations on a timescale of 10-15 days, which may be the signature of a coupling between oscillations and thermal convection in the layer where the kappa-mechanism is operating.
Conclusions: The Altair oscillation spectrum does not contain a large number of excited eigenmodes, which is similar to the fast rotating star HD220811. This supports the idea that fast rotation hinders the excitation of eigenmodes as already pointed out by theoretical investigations.

This work is based on data from the MOST satellite, a Canadian Space Agency mission, jointly operated by Dynacon Inc., the University of Toronto Institute for Aerospace Studies and the University of British Columbia, with the assistance of the University of Vienna. Title: Oscillations of 2D ESTER models. I. The adiabatic case Authors: Reese, D. R.; Mirouh, G. M.; Espinosa Lara, F.; Rieutord, M.; Putigny, B. Bibcode: 2021A&A...645A..46R Altcode: 2020arXiv201011312R Context. Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula. In parallel, recent studies have revealed the presence of regular pulsation frequency patterns in rapidly rotating δ Scuti stars that seem to match theoretical expectations.
Aims: In this context, a key question is whether strong gradients or discontinuities can adversely affect the asymptotic frequency pattern to the point of hindering its identification. Other important questions are how rotational splittings are affected by the 2D rotation profiles expected from baroclinic effects and whether it is possible to probe the rotation profile using these splittings.
Methods: In order to address these questions, we numerically calculate stellar pulsation modes in continuous and discontinuous rapidly rotating models produced by the 2D Evolution STEllaire en Rotation (ESTER) code. This code self-consistently calculates the rotation profile based on baroclinic effects and uses a spectral multi-domain approach, thus making it possible to introduce discontinuities at the domain interfaces without loss of numerical accuracy. The pulsation calculations are carried out using an adiabatic version of the Two-dimensional Oscillation Program (TOP) code. The variational principle is then used to confirm the high numerical accuracy of the pulsation frequencies and to derive an integral formula for the generalised rotational splittings. Acoustic glitch theory, combined with ray dynamics, is applied to the discontinuous models in order to interpret their pulsation spectra.
Results: Our results show that the generalised rotational splittings are very well approximated by the integral formula, except for modes involved in avoided crossings. This potentially allows the application of inverse theory for probing the rotation profile. We also show that glitch theory applied along the island mode orbit can correctly predict the periodicity of the glitch frequency pattern produced by the discontinuity or Γ1 dip related to the He II ionisation zone in some of the models. Furthermore, the asymptotic frequency pattern remains sufficiently well preserved to potentially allow its detection in observed stars. Title: Stress-driven spin-down of a viscous fluid within a spherical shell Authors: Gagnier, D.; Rieutord, M. Bibcode: 2020JFM...904A..35G Altcode: 2020arXiv200310403G We investigate the linear properties of the steady and axisymmetric stress-driven spin-down flow of a viscous fluid inside a spherical shell, both within the incompressible and anelastic approximations, and in the asymptotic limit of small viscosities. From boundary layer analysis, we derive an analytical geostrophic solution for the 3D incompressible steady flow, inside and outside the cylinder $\mathcal{C}$ that is tangent to the inner shell. The Stewartson layer that lies on $\mathcal{C}$ is composed of two nested shear layers of thickness $O(E^{2/7})$ and $O(E^{1/3})$. We derive the lowest order solution for the $E^{2/7}$-layer. A simple analysis of the $E^{1/3}$-layer laying along the tangent cylinder, reveals it to be the site of an upwelling flow of amplitude $O(E^{1/3})$. Despite its narrowness, this shear layer concentrates most of the global meridional kinetic energy of the spin-down flow. Furthermore, a stable stratification does not perturb the spin-down flow provided the Prandtl number is small enough. If this is not the case, the Stewartson layer disappears and meridional circulation is confined within the thermal layers. The scalings for the amplitude of the anelastic secondary flow have been found to be the same as for the incompressible flow in all three regions, at the lowest order. However, because the velocity no longer conforms the Taylor-Proudman theorem, its shape differs outside the tangent cylinder $\mathcal{C}$, that is, where differential rotation takes place. Finally, we find the settling of the steady-state to be reached on a viscous time for the weakly, strongly and thermally unstratified incompressible flows. Large density variations relevant to astro- and geophysical systems, tend to slightly shorten the transient. Title: A realistic two-dimensional model of Altair Authors: Bouchaud, K.; Domiciano de Souza, A.; Rieutord, M.; Reese, D. R.; Kervella, P. Bibcode: 2020A&A...633A..78B Altcode: 2019arXiv191203138B Context. Fast rotation is responsible for important changes in the structure and evolution of stars and the way we see them. Optical long baseline interferometry now allows for the study of its effects on the stellar surface, mainly gravity darkening and flattening.
Aims: We aim to determine the fundamental parameters of the fast-rotating star Altair, in particular its evolutionary stage (represented here by the core hydrogen mass fraction Xc), mass, and differential rotation, using state-of-the-art stellar interior and atmosphere models together with interferometric (ESO-VLTI), spectroscopic, and asteroseismic observations.
Methods: We use ESTER two-dimensional stellar models to produce the relevant surface parameters needed to create intensity maps from atmosphere models. Interferometric and spectroscopic observables are computed from these intensity maps and several stellar parameters are then adjusted using the publicly available MCMC algorithm Emcee.
Results: We determined Altair's equatorial radius to be Req = 2.008 ± 0.006 R⊙, the position angle PA = 301.1 ± 0.3°, the inclination i = 50.7 ± 1.2°, and the equatorial angular velocity Ω = 0.74 ± 0.01 times the Keplerian angular velocity at equator. This angular velocity leads to a flattening of ɛ = 0.220 ± 0.003. We also deduce from the spectroscopically derived v sin i ≃ 243 km s-1, a true equatorial velocity of ∼314 km s-1 corresponding to a rotation period of 7h46m (∼3 cycles/day). The data also impose a strong correlation between mass, metallicity, hydrogen abundance, and core evolution. Thanks to asteroseismic data, and provided our frequencies identification is correct, we constrain the mass of Altair to 1.86 ± 0.03 M⊙ and further deduce its metallicity Z = 0.019 and its core hydrogen mass fraction Xc = 0.71, assuming an initial solar hydrogen mass fraction X = 0.739. These values suggest that Altair is a young star ∼100 Myr old. Finally, the 2D ESTER model also gives the internal differential rotation of Altair, showing that its core rotates approximately 50% faster than the envelope, while the surface differential rotation does not exceed 6%.

Based on VLTI observations performed at ESO, Chile under programme IDs 60.A-9164(A), 87.D-0150(A), and 094.C-0232(A). Title: Multi-Dimensional Processes In Stellar Physics Authors: Rieutord, Michel; Baraffe, Isabelle; Lebreton, Yveline Bibcode: 2020mdps.conf.....R Altcode: When one has to deal with fluid flows, magnetic fields or heat transfer in stars, one faces the partial differential equations that govern these processes. These phenomena are naturally multi-dimensional and their study requires new and sophisticated models. This volume gathers the lecture notes which summarize the essence of the lectures and conferences given by world experts in the field of multi-dimensional modelling of stars, during the 2018 Evry Schatzman School held in Roscoff, France. It gives the present status of our understanding of several processes that occur in stars, like thermal convection, double-diffusive convection, dynamo effect or baroclinic flows. Every subject is discussed under the light of the most recent results of nowadays research and is made accessible to all newcomers, either students or researchers who wish to join the field. HRA provides a unique way to study regions of stellar formation, proto-planetary discs as well as the surfaces of stars and their environments. This volume offers lectures given by world experts in the field during the Evry Schatzman School on Stellar Physics (EES 2017) held in Roscoff, France. The addressed topics include a course of introduction to optical/IR interferometry covering the history and basic principles, a course on diffraction-dominated observational astronomy, and a course presenting the principles and instrumentation of optical long baseline interferometry. This book will be a valuable reference for researchers and students in the coming years. Title: The first view of δ Scuti and γ Doradus stars with the TESS mission Authors: Antoci, V.; Cunha, M. S.; Bowman, D. M.; Murphy, S. J.; Kurtz, D. W.; Bedding, T. R.; Borre, C. C.; Christophe, S.; Daszyńska-Daszkiewicz, J.; Fox-Machado, L.; García Hernández, A.; Ghasemi, H.; Handberg, R.; Hansen, H.; Hasanzadeh, A.; Houdek, G.; Johnston, C.; Justesen, A. B.; Kahraman Alicavus, F.; Kotysz, K.; Latham, D.; Matthews, J. M.; Mønster, J.; Niemczura, E.; Paunzen, E.; Sánchez Arias, J. P.; Pigulski, A.; Pepper, J.; Richey-Yowell, T.; Safari, H.; Seager, S.; Smalley, B.; Shutt, T.; Sódor, A.; Suárez, J. -C.; Tkachenko, A.; Wu, T.; Zwintz, K.; Barceló Forteza, S.; Brunsden, E.; Bognár, Z.; Buzasi, D. L.; Chowdhury, S.; De Cat, P.; Evans, J. A.; Guo, Z.; Guzik, J. A.; Jevtic, N.; Lampens, P.; Lares Martiz, M.; Lovekin, C.; Li, G.; Mirouh, G. M.; Mkrtichian, D.; Monteiro, M. J. P. F. G.; Nemec, J. M.; Ouazzani, R. -M.; Pascual-Granado, J.; Reese, D. R.; Rieutord, M.; Rodon, J. R.; Skarka, M.; Sowicka, P.; Stateva, I.; Szabó, R.; Weiss, W. W. Bibcode: 2019MNRAS.490.4040A Altcode: 2019MNRAS.tmp.2389A; 2019arXiv190912018A We present the first asteroseismic results for δ Scuti and γ Doradus stars observed in Sectors 1 and 2 of the TESS mission. We utilize the 2-min cadence TESS data for a sample of 117 stars to classify their behaviour regarding variability and place them in the Hertzsprung-Russell diagram using Gaia DR2 data. Included within our sample are the eponymous members of two pulsator classes, γ Doradus and SX Phoenicis. Our sample of pulsating intermediate-mass stars observed by TESS also allows us to confront theoretical models of pulsation driving in the classical instability strip for the first time and show that mixing processes in the outer envelope play an important role. We derive an empirical estimate of 74 per cent for the relative amplitude suppression factor as a result of the redder TESS passband compared to the Kepler mission using a pulsating eclipsing binary system. Furthermore, our sample contains many high-frequency pulsators, allowing us to probe the frequency variability of hot young δ Scuti stars, which were lacking in the Kepler mission data set, and identify promising targets for future asteroseismic modelling. The TESS data also allow us to refine the stellar parameters of SX Phoenicis, which is believed to be a blue straggler. Title: Classical and general relativistic post-Keplerian effects in binary pulsars hosting fast rotating main sequence stars Authors: Iorio, Lorenzo; Rieutord, Michel; Rozelot, Jean-Pierre; Domiciano de Souza, Armando Bibcode: 2019EPJC...79..690I Altcode: 2019arXiv190505514I We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star of mass M, spin angular momentum S , dimensionless mass quadrupole moment J_2, equatorial and polar radii R_ {e}, R_ {p}, flattening ν \doteq (R_ {e}-R_ {p})/R_ {e}, and ellipticity ɛ \doteq √{1-R_ {p}^2/R_ {e}^2} as a potential scenario to dynamically put to the test certain post-Keplerian effects of both Newtonian and post-Newtonian nature. We numerically produce time series of the perturbations Δ ( δ τ ) of the Rømer-like, orbital component of the pulsar's time delay δ τ induced over 10 years by the pN gravitoelectric mass monopole ( {Schwarzschild}, GMc^{-2}) , quadrupole ( GMR^2_ {e}J_2 c^{-2}) , gravitomagnetic spin dipole ( {Lense}{-} {Thirring}, GSc^{-2}) and octupole ( GSR^2_ {e}ɛ ^2 c^{-2}) accelerations along with the Newtonian quadrupolar ( GMR^2_ {e}J_2) one. We do not deal with the various propagation time delays due to the travelling electromagnetic waves. It turns out that, for a Be-type star with M = 15 {M}_⊙ , R_ {e} = 5.96 {R}_⊙ , ν = 0.203, S = 3.41× 10^{45} {J} {s}, J_2 = 1.92× 10^{-3} orbited by a pulsar with an orbital period P_b∼ 40-70 days, the classical oblateness-driven effects are at the ≲ 4-150 {s} level, while the pN shifts are of the order of ≲ 1.5-20 {s} ( GMc^{-2}) , ≲ 10-40 {ms} ( GMR^2_ {e} J_2 c^{-2}) , ≲ 0.5-6 {ms} ( GSc^{-2}) , ≲ 5-20 μ {s} ( GSR^2_ {e}ɛ ^2 c^{-2}) , depending on their orbital configuration. The root-mean-square (rms) timing residuals σ_{τ } of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are ≲ {ms}. Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian (GMc^{-2}, GMJ_2c^{-2}, and, perhaps, GSc^{-2} as well) key features of the distorted gravitational fields of the fast rotating stars hosted by them. Title: Core overshooting under the light of fluid dynamics Authors: Rieutord, M. Bibcode: 2019EAS....82..153R Altcode: We discuss the possible contraints that are brought about by a fluid mechanical analysis of the overshooting phenomenon at the interface of convective cores and radiative envelopes of early-type stars. We investigate an improvement of Roxburgh's criterion by taking into account the viscous dissipation but show that this criterion remains not stringent enough to be predictive. We then discuss the thickness of the overshooting layer and show that all estimates, including the one of Zahn (<xref ref-type="bibr" rid="R21">1991</xref>), lead to a very thin mixing layer typically less than a percent of the pressure scale height. Title: Evolution of rotation in rapidly rotating early-type stars during the main sequence with 2D models Authors: Gagnier, D.; Rieutord, M.; Charbonnel, C.; Putigny, B.; Espinosa Lara, F. Bibcode: 2019A&A...625A..89G Altcode: 2019arXiv190405219G The understanding of the rotational evolution of early-type stars is deeply related to that of anisotropic mass and angular momentum loss. In this paper, we aim to clarify the rotational evolution of rapidly rotating early-type stars along the main sequence (MS). We have used the 2D ESTER code to compute and evolve isolated rapidly rotating early-type stellar models along the MS, with and without anisotropic mass loss. We show that stars with Z = 0.02 and masses between 5 and 7 M⊙ reach criticality during the main sequence provided their initial angular velocity is larger than 50% of the Keplerian one. More massive stars are subject to radiation-driven winds and to an associated loss of mass and angular momentum. We find that this angular momentum extraction from the outer layers can prevent massive stars from reaching critical rotation and greatly reduce the degree of criticality at the end of the MS. Our model includes the so-called bi-stability jump of the Ṁ - Teff relation of 1D-models. This discontinuity now shows up in the latitude variations of the mass-flux surface density, endowing rotating massive stars with either a single-wind regime (no discontinuity) or a two-wind regime (a discontinuity). In the two-wind regime, mass loss and angular momentum loss are strongly increased at low latitudes inducing a faster slow-down of the rotation. However, predicting the rotational fate of a massive star is difficult, mainly because of the non-linearity of the phenomena involved and their strong dependence on uncertain prescriptions. Moreover, the very existence of the bi-stability jump in mass-loss rate remains to be substantiated by observations. Title: Critical angular velocity and anisotropic mass loss of rotating stars with radiation-driven winds Authors: Gagnier, D.; Rieutord, M.; Charbonnel, C.; Putigny, B.; Espinosa Lara, F. Bibcode: 2019A&A...625A..88G Altcode: 2019arXiv190405089G Context. The understanding of the evolution of early-type stars is tightly related to that of the effects of rapid rotation. For massive stars, rapid rotation combines with their strong radiation-driven wind.
Aims: The aim of this paper is to investigate two questions that are prerequisite to the study of the evolution of massive rapidly rotating stars: (i) What is the critical angular velocity of a star when radiative acceleration is significant in its atmosphere? (ii) How do mass and angular momentum loss depend on the rotation rate?
Methods: To investigate fast rotation, which makes stars oblate, we used the 2D ESTER models and a simplified approach, the ω-model, which gives the latitudinal dependence of the radiative flux in a centrifugally flattened radiative envelope.
Results: We find that radiative acceleration only mildly influences the critical angular velocity, at least for stars with masses lower than 40 M⊙. For instance, a 15 M⊙ star on the zero-age main sequence would reach criticality at a rotation rate equal to 0.997 the Keplerian equatorial rotation rate. We explain this mild reduction of the critical angular velocity compared to the classical Keplerian angular velocity by the combined effects of gravity darkening and a reduced equatorial opacity that is due to the centrifugal acceleration. To answer the second question, we first devised a model of the local surface mass flux, which we calibrated with previously developed 1D models. The discontinuity (the so-called bi-stability jump) included in the Ṁ - Teff relation of 1D models means that the mass flux of a fast-rotating star is controlled by either a single wind or a two-wind regime. Mass and angular momentum losses are strong around the equator if the star is in the two-wind regime. We also show that the difficulty of selecting massive stars that are viewed pole-on makes detecting the discontinuity in the relation between mass loss and effective temperature also quite challenging. Title: Neural Network to Emulate Numerical Simulations of the Sun and Infer Synthetic Observations for Data Assimilation Authors: Tremblay, Benoit; Roudier, Thierry; Cossette, Jean-François; Attié, Raphaël; Rieutord, Michel; Vincent, Alain Bibcode: 2019shin.confE..30T Altcode: Satellites and ground-based observatories probe the Sun's photosphere and atmosphere and are key in studying solar activity. Meanwhile, numerical models have attempted to bridge the gap between the physics of the solar interior and such observations. However, there are physical quantities relevant to solar activity that can be modeled but that cannot be directly measured and must be inferred. For example, direct measurements of plasma motions at the photosphere are limited to the line-of-sight component. Recently, neural network computing has been used in conjunction with numerical models of the Sun to be able to recover the full velocity vector in photospheric plasma of the Quiet Sun. We used satellite observations as input in a fully convolutional neural network to generate instantaneous synthetic plasma motions, i.e. plasma motions that reflect the physics of a model but are made to look as if they were observed by a specific instrument. A parallel technique could then be invoked to eventually be able to derive the plasma velocity vector maps of the Active Sun and, by extension, other physical quantities of interest that can not yet be measured directly at the photosphere or anywhere else in the solar atmosphere. Title: Do tidally-generated inertial waves heat the subsurface oceans of Europa and Enceladus? Authors: Rovira-Navarro, Marc; Rieutord, Michel; Gerkema, Theo; Maas, Leo R. M.; van der Wal, Wouter; Vermeersen, Bert Bibcode: 2019Icar..321..126R Altcode: Some of the moons of the outer solar system harbour subsurface liquid oceans. Tidal dissipation plays an important role in preventing these oceans from freezing. In the past, most studies considered only tidal dissipation in the solid layers of these bodies (rock and ice). Recently, new studies considering tidal dissipation in the oceans of these moons have appeared. All of them make use of the shallow water approximation. However, the use of this approximation might not be adequate. Here we consider the linear non-hydrostatic three dimensional response of these oceans to tidal forcing with the full Coriolis force. To do so we consider an ocean of homogeneous density contained within a perfectly spherical shell and neglect the effect of the ice shell. We force the ocean with a time changing tidal potential and observe patterns of periodic inertial waves that take energy from the global tidal forcing and focus it along thin shear layers that propagate in the fluid. We focus on Europa and Enceladus, showing that inertial waves result in fluid flows of significant amplitude (a few cm/s). Nevertheless, we find that under the previously mentioned assumptions tidal dissipation due to inertial waves is several orders of magnitude smaller than Europa's radiogenic heating and Enceladus' observed heat flux. Finally, we propose additional dissipation mechanisms that might play a relevant role in Europa and Enceladus and could be further investigated. Title: Gravity darkening in late-type stars Authors: Raynaud, R.; Rieutord, M.; Petitdemange, L.; Gastine, T.; Putigny, B. Bibcode: 2018sf2a.conf...91R Altcode: Recent interferometric data have been able to constrain the brightness distribution at the surface of nearby stars, in particular the gravity darkening that makes fast rotating stars brighter at their poles than at their equator. However, good models of gravity darkening are missing when the stars own a convective envelope. In order to better understand how rotation affects the heat transfer in stellar convective envelopes, we studied the heat flux distribution in latitude at the outer surface of numerical models of anelastic convection in rotating sphericall shells. We found that the variations of the surface brightness are mainly controlled by the surface value of the local Rossby number: when the Coriolis force dominates the dynamics, the heat flux is weakened in the equatorial region by the zonal wind and enhanced at the poles by convective motions inside the tangent cylinder. However, in presence of a strong background density stratification, as expected in real stars, the increase of the local Rossby number in the outer layers leads to the uniformisation of the surface heat flux distribution. Title: Tidally-induced inertial waves in the subsurface ocean of Enceladus Authors: Rovira-Navarro, M.; Rieutord, M.; Gerkema, T.; Maas, L. R.; van der Wal, W.; Vermeersen, B. L. A. Bibcode: 2018AGUFM.P33A..03R Altcode: Recently, studies on tidally-induced ocean currents in Enceladus have appeared [e.g., Tyler, Nature, 456 (7223), 770-772, 2008; Matsuyama et al., Icarus, 312, 208-230, 2018]. All of these studies make use of the shallow water approximation, which consists on assuming that currents are predominantly horizontal. This approximation might not be adequate to capture Enceladus' ocean dynamics. We study for the first time the fully non-hydrostatic three dimensional response of Enceladus' ocean to tidal forcing. To do so we consider an ocean of constant density inside a perfectly spherical shell and force it with the tidal potential. We observe patterns of internal inertial waves that take energy from the global forcing and focus it along internal shear layers. We observe that these waves are of significant amplitude and speculate that they might be the origin of the characteristic "tiger stripes". We also compute tidal dissipation due to inertial waves and show that for an ocean of constant depth their contribution to Enceladus tidal budget is not significant. We argue , however, that this estimation represents a lower bound for tidal dissipation. Further study is required to assess the importance of inertial waves in an ocean basin with variable depth. Title: The evolved fast rotator Sargas. Stellar parameters and evolutionary status from VLTI/PIONIER and VLT/UVES Authors: Domiciano de Souza, A.; Bouchaud, K.; Rieutord, M.; Espinosa Lara, F.; Putigny, B. Bibcode: 2018A&A...619A.167D Altcode: 2018arXiv181009903D Context. Gravity darkening (GD) and flattening are important consequences of stellar rotation. The precise characterization of these effects across the Hertzsprung-Russell (H-R) diagram is crucial to a deeper understanding of stellar structure and evolution.
Aims: We seek to characterize such important effects on Sargas (θ Scorpii), an evolved, fast-rotating, intermediate-mass (∼5 M⊙) star, located in a region of the H-R diagram where they have never been directly measured as far as we know.
Methods: We use our numerical model CHARRON to analyze interferometric (VLTI/PIONIER) and spectroscopic (VLT/UVES) observations through a MCMC model-fitting procedure. The visibilities and closure phases from the PIONIER data are particularly sensitive to rotational flattening and GD. Adopting the Roche approximation, we investigate two GD models: (1) the β-model (Teff ∝ geff β<!--inline-formula id="FI1"> <alternatives> g eff β <![CDATA[ g{{eff}}^β ]]> <inline-graphic id="img_eq1" mime-subtype="gif" mimetype="image" xlink:href="aa33450-18-eq1.gif" xmlns:xlink="http://www.w3.org/1999/xlink"/> </alternatives> ), which includes the classical von Zeipel's GD law, and (2) the ω-model, where the flux is assumed to be anti-parallel to geff.
Results: Using this approach we measure several physical parameters of Sargas, namely, equatorial radius, mass, equatorial rotation velocity, mean Teff, inclination and position angle of the rotation axis, and β. In particular, we show that the measured β leads to a surface flux distribution equivalent to the one given by the ω-model. Thanks to our results, we also show that Sargas is most probably located in a rare and interesting region of the H-R diagram: within the Hertzsprung gap and over the hot edge of the instability strip (equatorial regions inside it and polar regions outside it because of GD).
Conclusions: These results show once more the power of optical/infrared long-baseline interferometry, combined with high-resolution spectroscopy, to directly measure fast-rotation effects and stellar parameters, in particular GD. As was the case for a few fast rotators previously studied by interferometry, the ω-model provides a physically more profound description of Sargas' GD, without the need of a β exponent. It will also be interesting to further investigate the implications of the singular location of such a fast rotator as Sargas in the H-R diagram.

Based on observations performed at ESO, Chile under program IDs 097.D-0230(ABC) and 266.D-5655(A).

The OIFits files with the VLTI/PIONIER data that we used are publicly available at the JMMC OIDB website service: http://oidb.jmmc.fr/index.html Title: The Sun's supergranulation Authors: Rincon, François; Rieutord, Michel Bibcode: 2018LRSP...15....6R Altcode: Supergranulation is a fluid-dynamical phenomenon taking place in the solar photosphere, primarily detected in the form of a vigorous cellular flow pattern with a typical horizontal scale of approximately 30-35 Mm, a dynamical evolution time of 24-48 h, a strong 300-400 m/s (rms) horizontal flow component and a much weaker 20-30 m/s vertical component. Supergranulation was discovered more than 60 years ago, however, explaining its physical origin and most important observational characteristics has proven extremely challenging ever since, as a result of the intrinsic multiscale, nonlinear dynamical complexity of the problem concurring with strong observational and computational limitations. Key progress on this problem is now taking place with the advent of twenty-first-century supercomputing resources and the availability of global observations of the dynamics of the solar surface with high spatial and temporal resolutions. This article provides an exhaustive review of observational, numerical and theoretical research on supergranulation, and discusses the current status of our understanding of its origin and dynamics, most importantly in terms of large-scale nonlinear thermal convection, in the light of a selection of recent findings. Title: Mode Identification in Rapidly Rotating Stars from BRITE Data Authors: Reese, Daniel R.; Dupret, Marc-Antoine; Rieutord, Michel Bibcode: 2018pas8.conf...80R Altcode: 2018arXiv180307442R Apart from recent progress in Gamma Dor stars, identifying modes in rapidly rotating stars is a formidable challenge due to the lack of simple, easily identifiable frequency patterns. As a result, it is necessary to look to observational methods for identifying modes. Two popular techniques are spectroscopic mode identification based on line profile variations (LPVs) and photometric mode identification based on amplitude ratios and phase differences between multiple photometric bands. In this respect, the BRITE constellation is particularly interesting as it provides space-based multi-colour photometry. The present contribution describes the latest developments in obtaining theoretical predictions for amplitude ratios and phase differences for pulsation modes in rapidly rotating stars. These developments are based on full 2D non-adiabatic pulsation calculations, using models from the ESTER code, the only code to treat in a self-consistent way the thermal equilibrium of rapidly rotating stars. These predictions are then specifically applied to the BRITE photometric bands to explore the prospects of identifying modes based on BRITE observations. Title: Axisymmetric inertial modes in a spherical shell at low Ekman numbers Authors: Rieutord, M.; Valdettaro, L. Bibcode: 2018JFM...844..597R Altcode: 2018arXiv180207582R We investigate the asymptotic properties of axisymmetric inertial modes propagating in a spherical shell when viscosity tends to zero. We identify three kinds of eigenmodes whose eigenvalues follow very different laws as the Ekman number$E$becomes very small. First are modes associated with attractors of characteristics that are made of thin shear layers closely following the periodic orbit traced by the characteristic attractor. Second are modes made of shear layers that connect the critical latitude singularities of the two hemispheres of the inner boundary of the spherical shell. Third are quasi-regular modes associated with the frequency of neutral periodic orbits of characteristics. We thoroughly analyse a subset of attractor modes for which numerical solutions point to an asymptotic law governing the eigenvalues. We show that three length scales proportional to$E^{1/6}$,$E^{1/4}$and$E^{1/3}$control the shape of the shear layers that are associated with these modes. These scales point out the key role of the small parameter$E^{1/12}$in these oscillatory flows. With a simplified model of the viscous Poincaré equation, we can give an approximate analytical formula that reproduces the velocity field in such shear layers. Finally, we also present an analysis of the quasi-regular modes whose frequencies are close to$\sin (\unicode[STIX]{x03C0}/4)$and explain why a fluid inside a spherical shell cannot respond to any periodic forcing at this frequency when viscosity vanishes. Title: Reconstruction of Horizontal Plasma Motions at the Photosphere from Intensitygrams: A Comparison Between DeepVel, LCT, FLCT, and CST Authors: Tremblay, Benoit; Roudier, Thierry; Rieutord, Michel; Vincent, Alain Bibcode: 2018SoPh..293...57T Altcode: Direct measurements of plasma motions in the photosphere are limited to the line-of-sight component of the velocity. Several algorithms have therefore been developed to reconstruct the transverse components from observed continuum images or magnetograms. We compare the space and time averages of horizontal velocity fields in the photosphere inferred from pairs of consecutive intensitygrams by the LCT, FLCT, and CST methods and the DeepVel neural network in order to identify the method that is best suited for generating synthetic observations to be used for data assimilation. The Stein and Nordlund (Astrophys. J. Lett.753, L13, 2012) magnetoconvection simulation is used to generate synthetic SDO/HMI intensitygrams and reference flows to train DeepVel. Inferred velocity fields show that DeepVel performs best at subgranular and granular scales and is second only to FLCT at mesogranular and supergranular scales. Title: Large-scale photospheric motions determined from granule tracking and helioseismology from SDO/HMI data Authors: Roudier, Th.; Švanda, M.; Ballot, J.; Malherbe, J. M.; Rieutord, M. Bibcode: 2018A&A...611A..92R Altcode: 2017arXiv171205255R Context. Large-scale flows in the Sun play an important role in the dynamo process linked to the solar cycle. The important large-scale flows are the differential rotation and the meridional circulation with an amplitude of km s-1 and few m s-1, respectively. These flows also have a cycle-related components, namely the torsional oscillations. Aim. Our attempt is to determine large-scale plasma flows on the solar surface by deriving horizontal flow velocities using the techniques of solar granule tracking, dopplergrams, and time-distance helioseismology.
Methods: Coherent structure tracking (CST) and time-distance helioseismology were used to investigate the solar differential rotation and meridional circulation at the solar surface on a 30-day HMI/SDO sequence. The influence of a large sunspot on these large-scale flows with a specific 7-day HMI/SDO sequence has been also studied.
Results: The large-scale flows measured by the CST on the solar surface and the same flow determined from the same data with the helioseismology in the first 1 Mm below the surface are in good agreement in amplitude and direction. The torsional waves are also located at the same latitudes with amplitude of the same order. We are able to measure the meridional circulation correctly using the CST method with only 3 days of data and after averaging between ± 15° in longitude.
Conclusions: We conclude that the combination of CST and Doppler velocities allows us to detect properly the differential solar rotation and also smaller amplitude flows such as the meridional circulation and torsional waves. The results of our methods are in good agreement with helioseismic measurements. Title: Gravity darkening in late-type stars. I. The Coriolis effect Authors: Raynaud, R.; Rieutord, M.; Petitdemange, L.; Gastine, T.; Putigny, B. Bibcode: 2018A&A...609A.124R Altcode: 2017arXiv171203130R Context. Recent interferometric data have been used to constrain the brightness distribution at the surface of nearby stars, in particular the so-called gravity darkening that makes fast rotating stars brighter at their poles than at their equator. However, good models of gravity darkening are missing for stars that posses a convective envelope. Aim. In order to better understand how rotation affects the heat transfer in stellar convective envelopes, we focus on the heat flux distribution in latitude at the outer surface of numerical models.
Methods: We carry out a systematic parameter study of three-dimensional, direct numerical simulations of anelastic convection in rotating spherical shells. As a first step, we neglect the centrifugal acceleration and retain only the Coriolis force. The fluid instability is driven by a fixed entropy drop between the inner and outer boundaries where stress-free boundary conditions are applied for the velocity field. Restricting our investigations to hydrodynamical models with a thermal Prandtl number fixed to unity, we consider both thick and thin (solar-like) shells, and vary the stratification over three orders of magnitude. We measure the heat transfer efficiency in terms of the Nusselt number, defined as the output luminosity normalised by the conductive state luminosity.
Results: We report diverse Nusselt number profiles in latitude, ranging from brighter (usually at the onset of convection) to darker equator and uniform profiles. We find that the variations of the surface brightness are mainly controlled by the surface value of the local Rossby number: when the Coriolis force dominates the dynamics, the heat flux is weakened in the equatorial region by the zonal wind and enhanced at the poles by convective motions inside the tangent cylinder. In the presence of a strong background density stratification however, as expected in real stars, the increase of the local Rossby number in the outer layers leads to uniformisation of the surface heat flux distribution. Title: The 2D dynamics of radiative zones of low-mass stars Authors: Hypolite, D.; Mathis, S.; Rieutord, M. Bibcode: 2018A&A...610A..35H Altcode: 2017arXiv171108544H Context. Helioseismology and asteroseismology allow us to probe the differential rotation deep within low-mass stars. In the solar convective envelope, the rotation varies with latitude with an equator rotating faster than the pole, which results in a shear applied on the radiative zone below. However, a polar acceleration of the convective envelope can be obtained through 3D numerical simulations in other low-mass stars and the dynamical interaction of the surface convective envelope with the radiative core needs to be investigated in the general case. Aim. In the context of secular evolution, we aim to describe the dynamics of the radiative core of low-mass stars to get a deeper understanding of the internal transport of angular momentum in such stars, which results in a solid rotation in the Sun from 0.7R⊙ to 0.2R⊙ and a weak radial core-envelope differential rotation in solar-type stars. This study requires at least a 2D description to capture the latitudinal variations of the differential rotation.
Methods: We build 2D numerical models of a radiative core on the top of which we impose a latitudinal shear so as to reproduce a conical or cylindrical differential rotation in a convective envelope. We perform a systematic study over the Rossby number ℛo = ΔΩ/2Ω0 measuring the latitudinal differential rotation at the radiative-convective interface. We provide a 2D description of the differential rotation and the associated meridional circulation in the incompressible and stably stratified cases using the Boussinesq approximation.
Results: The imposed shear generates a geostrophic flow implying a cylindrical differential rotation in the case of an isotropic viscosity. When compared to the baroclinic flow that arises from the stable stratification, we find that the geostrophic flow is dominant when the Rossby number is high enough (ℛo ≥ 1) with a cylindrical rotation profile. For low Rossby numbers (ℛo < 1), the baroclinic solution dominates with a quasi-shellular rotation profile. Using scaling laws from 3D simulations, we show that slow rotators (Ω0 < 30Ω⊙) are expected to have a cylindrical rotation profile. Fast rotators (Ω0 > 30Ω⊙) may have a shellular profile at the beginning of the main sequence in stellar radiative zones.
Conclusions: This study enables us to predict different types of differential rotation and emphasizes the need for a new generation of 2D rotating stellar models developed in synergy with 3D numerical simulations. The shear induced by a surface convective zone has a strong impact on the dynamics of the underlying radiative zone in low-mass stars. However, it cannot produce a flat internal rotation profile in a solar configuration calling for additional processes for the transport of angular momentum in both radial and latitudinal directions. Title: Non-adiabatic oscillations of fast-rotating stars: the example of Rasalhague Authors: Mirouh, G. M.; Reese, D. R.; Rieutord, M.; Ballot, J. Bibcode: 2017sf2a.conf..103M Altcode: 2017arXiv171106053M Early-type stars generally tend to be fast rotators. In these stars, mode identification is very challenging as the effects of rotation are not well known. We consider here the example of α Ophiuchi, for which dozens of oscillation frequencies have been measured. We model the star using the two-dimensional structure code ESTER, and we compute both adiabatic and non-adiabatic oscillations using the TOP code. Both calculations yield very complex spectra, and we used various diagnostic tools to try and identify the observed pulsations. While we have not reached a satisfactory mode-to-mode identification, this paper presents promising early results. Title: The 2D dynamics of the differentially rotating envelope of massive stars Authors: Hypolite, Delphine; Mathis, Stéphane; Rieutord, Michel Bibcode: 2017IAUS..329..409H Altcode: We build a 2D model of the radiative envelope of main sequence massive stars. We set a dynamical boundary condition at the bottom of the radiative envelope at η = r C /R (where r C is the core size and R the radius of the star) to account for the differential rotation of the convective core as computed in 3D simulations (e.g. Browning et al. (2004, IAUS, 224, 149). We seek the differential rotation and associated meridional circulation induced by such a shear competing with the baroclinic flow of the stably stratified radiative envelope using the Boussinesq approximation. Title: Gravity darkening in stars with surface differential rotation Authors: Zorec, J.; Rieutord, M.; Espinosa Lara, F.; Frémat, Y.; Domiciano de Souza, A.; Royer, F. Bibcode: 2017A&A...606A..32Z Altcode: 2017arXiv170506485Z Context. The interpretation of stellar apparent fundamental parameters (viewing-angle dependent) requires that they be treated consistently with the characteristics of their surface rotation law.
Aims: We aim to develop a model to determine the distribution of the effective temperature and gravity, which explicitly depend on the surface differential rotation law and on the concomitant stellar external geometry.
Methods: The basic assumptions in this model are: a) the external stellar layers are in radiative equilibrium; b) the emergent bolometric flux is anti-parallel with the effective gravity; c) the angular velocity in the surface obeys relations like Ω(θ) = Ωo [ 1 + αΥ(θ,k) ] where Υ(θ,k) = coskθ or sinkθ, and where (α,k) are free parameters.
Results: The effective temperature varies with co-latitude θ, with amplitudes that depend on the differential-rotation law through the surface effective gravity and the gravity-darkening function (GDF). Although the derived expressions can be treated numerically, for some low integer values of k, analytical forms of the integral of characteristic curves, on which the determination of the GDF relies, are obtained. The effects of the quantities (η,α,k) (η = ratio between centrifugal and gravitational accelerations at the equator) on the determination of the Vsini parameter and on the gravity-darkening exponent are studied. Depending on the values of (η,α,k) the velocity V in the derived Vsini may strongly deviate from the equatorial rotational velocity. It is shown that the von Zeipel's-like gravity-darkening exponent β1 depends on all parameters (η,α,k) and that its value also depends on the viewing-angle i. Hence, there no unique interpretation of this exponent determined empirically in terms of (i,α).
Conclusions: We stress that the data on rotating stars should be analyzed by taking into account the rotational effects through the GDF, by assuming k = 2 as a first approximation. Instead of the classic pair (η,β1), it would be more useful to determine the quantities (η,α,i) to characterize stellar rotation. Title: On the oscillation spectrum of a magnetized core in a giant star Authors: Rieutord, Michel Bibcode: 2017EPJWC.16002011R Altcode: The spectrum of gravito-acoustic modes is depleted in dipolar modes for a significant fraction of the giant stars observed by the Kepler mission, a feature that has been explained by the presence of magnetic fields in the core of these stars (Fuller et al. 2015, Cantiello et al. 2016). We further investigate this possible scenario by considering first the oscillation spectrum of the core of a giant star modeled by a stably stratified, self-gravitating fluid of uniform density in a sphere pervaded by a uniform magnetic field. Our results show that the first effect of a magnetic field on the g-modes is to reduce their wavenumber and therefore reduce their damping. The magnetic effect, on this model, is therefore opposite Fuller's et al scenario. Moreover, the model shows that it is not possible to change the damping rate without changing the frequency of the modes and this latter change is not observed. Because of the simplicity of our model, the magnetized core scenario cannot be dismissed but further investigations are needed, and other ways of explaining the presence of depressed modes should also be considered. Title: Non-adiabatic pulsations in ESTER models Authors: Reese, Daniel Roy; Dupret, Marc-Antoine; Rieutord, Michel Bibcode: 2017EPJWC.16002007R Altcode: 2017arXiv171007451R One of the greatest challenges in interpreting the pulsations of rapidly rotating stars is mode identification, i.e. correctly matching theoretical modes to observed pulsation frequencies. Indeed, the latest observations as well as current theoretical results show the complexity of pulsation spectra in such stars, and the lack of easily recognisable patterns. In the present contribution, the latest results on non-adiabatic effects in such pulsations are described, and we show how these come into play when identifying modes. These calculations fully take into account the effects of rapid rotation, including centrifugal distortion, and are based on models from the ESTER project, currently the only rapidly rotating models in which the energy conservation equation is satisfied, a prerequisite for calculating non-adiabatic effects. Non-adiabatic effects determine which modes are excited and play a key role in the near-surface pulsation-induced temperature variations which intervene in multi-colour amplitude ratios and phase differences, as well as line profile variations. Title: 2D dynamics of the radiative core of low mass stars Authors: Hypolite, Delphine; Mathis, Stéphane; Rieutord, Michel Bibcode: 2017EPJWC.16002006H Altcode: 2016arXiv161008798H Understanding the internal rotation of low mass stars all along their evolution is of primary interest when studying their rotational dynamics, internal mixing and magnetic field generation. In this context, helio- and asteroseismology probe angular velocity gradients deep within solar type stars at different evolutionary stages. Still the rotation close to the center of such stars on the main sequence is hardly detectable and the dynamical interaction of the radiative core with the surface convective envelope is not well understood. For instance, the influence of the differential rotation profile sustained by convection and applied as a boundary condition to the radiation zone is very important in the formation of tachoclines. In this work, we study a 2D hydrodynamical model of a radiative core when an imposed, solar or anti-solar, differential rotation is applied at the upper boundary. This model uses the Boussinesq approximation and we find that the shear induces a cylindrical differential rotation associated with a unique cell of meridional circulation in each hemisphere (counterclockwise when the shear is solar-like and clockwise when it is anti-solar). The results are discussed in the framework of seismic observables (internal rotation rate, core-to-surface rotation ratio) while perspectives to improve our modeling by including magnetic field or transport by internal gravity waves will be discussed. Title: Completeness of inertial modes of an incompressible inviscid fluid in a corotating ellipsoid Authors: Backus, George; Rieutord, Michel Bibcode: 2017PhRvE..95e3116B Altcode: 2016arXiv160602114B Inertial modes are the eigenmodes of contained rotating fluids restored by the Coriolis force. When the fluid is incompressible, inviscid, and contained in a rigid container, these modes satisfy Poincaré's equation that has the peculiarity of being hyperbolic with boundary conditions. Inertial modes are, therefore, solutions of an ill-posed boundary-value problem. In this paper, we investigate the mathematical side of this problem. We first show that the Poincaré problem can be formulated in the Hilbert space of square-integrable functions, with no hypothesis on the continuity or the differentiability of velocity fields. We observe that with this formulation, the Poincaré operator is bounded and self-adjoint, and as such, its spectrum is the union of the point spectrum (the set of eigenvalues) and the continuous spectrum only. When the fluid volume is an ellipsoid, we show that the inertial modes form a complete base of polynomial velocity fields for the square-integrable velocity fields defined over the ellipsoid and meeting the boundary conditions. If the ellipsoid is axisymmetric, then the base can be identified with the set of Poincaré modes, first obtained by Bryan [Philos. Trans. R. Soc. London 180, 187 (1889), 10.1098/rsta.1889.0006], and completed with the geostrophic modes. Title: Supergranulation and multiscale flows in the solar photosphere. Global observations vs. a theory of anisotropic turbulent convection Authors: Rincon, F.; Roudier, T.; Schekochihin, A. A.; Rieutord, M. Bibcode: 2017A&A...599A..69R Altcode: 2016arXiv160905785R The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric flows and subsequently formulate an anisotropic extension of the Bolgiano-Obukhov theory of hydrodynamic stratified turbulence that may explain several of their distinctive dynamical properties. Our combined analysis suggests that photospheric flows in the horizontal range of scales between supergranulation and granulation have a typical vertical correlation scale of 2.5 to 4 Megameters and operate in a strongly anisotropic, self-similar, nonlinear, buoyant dynamical regime. While the theory remains speculative at this stage, it lends itself to quantitative comparisons with future high-resolution acoustic tomography of subsurface layers and advanced numerical models. Such a validation exercise may also lead to new insights into the asymptotic dynamical regimes in which other, unresolved turbulent anisotropic astrophysical fluid systems supporting waves or instabilities operate. Title: Tidal dissipation by inertial waves in differentially rotating convective envelopes of low-mass stars Authors: Guenel, Mathieu; Mathis, Stéphane; Baruteau, Clément; Rieutord, Michel Bibcode: 2016arXiv161205071G Altcode: Tidal interactions in close star-planet or binary star systems may excite inertial waves (their restoring force is the Coriolis force) in the convective region of the stars. The dissipation of these waves plays a prominent role in the long-term orbital and rotational evolution of the bodies involved. If the primary star rotates as a solid body, inertial waves have a Doppler-shifted frequency restricted to the range $[-2\Omega, 2\Omega]$ ($\Omega$ being the angular velocity of the star), and they can propagate in the entire convective region. However, turbulent convection can sustain differential rotation with an equatorial acceleration (as in the Sun) or deceleration that modifies the frequency range and propagation domain of inertial waves and allows corotation resonances for non-axisymmetric oscillations. In this work, we perform numerical simulations of tidally excited inertial waves in a differentially rotating convective envelope with a conical (or latitudinal) rotation profile. The tidal forcing that we adopt contains spherical harmonics that correspond to the case of a circular and coplanar orbit. We study the viscous dissipation of the waves as a function of tidal frequency for various stellar masses and differential rotation parameters, as well as its dependence on the turbulent viscosity coefficient. We compare our results with previous studies assuming solid-body rotation and point out the potential key role of corotation resonances in the dynamical evolution of close-in star-planet or binary systems. Title: 2D dynamics of the radiation zone of low mass stars Authors: Hypolite, Delphine; Mathis, Stéphane; Rieutord, Michel Bibcode: 2016arXiv160900592H Altcode: The internal rotation of low mass stars all along their evolution is of primary interest when studying their rotational dynamics, internal mixing and magnetic fields generation. In this context, helio- and asteroseismology probe angular velocity gradients deep within solar type stars. Still the rotation of the close center of such stars on the main sequence is hardly detectable and the dynamical interactions of the radiative core with the surface convective envelope is not well understood. Among them, the influence of the differential rotation profile sustained by convection and applied as a boundary condition to the radiation zone may be very important leading to the formation of tachoclines. In the solar convective region, the equator is rotating faster than the pole while numerical simulations predict either a solar or an anti-solar rotation in other low mass stars envelopes depending on their convective Rossby number. In this work, we therefore build for the first time 2D steady hydrodynamical models of low mass stars radiation zone providing a full 2D description of their dynamics and studying the influence of a general shear boundary condition accounting for a solar or an anti-solar differential rotation in the convective envelope. We compute coherently differential rotation and the associated meridional circulation using the Boussinesq approximation. Title: Gravito-inertial waves in a differentially rotating spherical shell Authors: Mirouh, G. M.; Baruteau, C.; Rieutord, M.; Ballot, J. Bibcode: 2016JFM...800..213M Altcode: 2015arXiv151105832M The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show a weak dependence with respect to viscosity and heat diffusion just like truly regular modes. Some axisymmetric modes are found unstable and likely destabilized by baroclinic instabilities. Similarly, some non-axisymmetric modes that meet a critical layer (or corotation resonance) can turn unstable at sufficiently low diffusivities. In all cases, the instability is driven by the differential rotation. For many modes of the spectrum, neat power laws are found for the dependence of the damping rates with diffusion coefficients, but the theoretical explanation for the exponent values remains elusive in general. The eigenvalue spectrum turns out to be very rich and complex, which lets us suppose an even richer and more complex spectrum for rotating stars or planets that own a differential rotation driven by baroclinicity. Title: An algorithm for computing the 2D structure of fast rotating stars Authors: Rieutord, Michel; Espinosa Lara, Francisco; Putigny, Bertrand Bibcode: 2016JCoPh.318..277R Altcode: 2016arXiv160502359R Stars may be understood as self-gravitating masses of a compressible fluid whose radiative cooling is compensated by nuclear reactions or gravitational contraction. The understanding of their time evolution requires the use of detailed models that account for a complex microphysics including that of opacities, equation of state and nuclear reactions. The present stellar models are essentially one-dimensional, namely spherically symmetric. However, the interpretation of recent data like the surface abundances of elements or the distribution of internal rotation have reached the limits of validity of one-dimensional models because of their very simplified representation of large-scale fluid flows. In this article, we describe the ESTER code, which is the first code able to compute in a consistent way a two-dimensional model of a fast rotating star including its large-scale flows. Compared to classical 1D stellar evolution codes, many numerical innovations have been introduced to deal with this complex problem. First, the spectral discretization based on spherical harmonics and Chebyshev polynomials is used to represent the 2D axisymmetric fields. A nonlinear mapping maps the spheroidal star and allows a smooth spectral representation of the fields. The properties of Picard and Newton iterations for solving the nonlinear partial differential equations of the problem are discussed. It turns out that the Picard scheme is efficient on the computation of the simple polytropic stars, but Newton algorithm is unsurpassed when stellar models include complex microphysics. Finally, we discuss the numerical efficiency of our solver of Newton iterations. This linear solver combines the iterative Conjugate Gradient Squared algorithm together with an LU-factorization serving as a preconditioner of the Jacobian matrix. Title: Tidal inertial waves in differentially rotating convective envelopes of low-mass stars. I. Free oscillation modes Authors: Guenel, M.; Baruteau, C.; Mathis, S.; Rieutord, M. Bibcode: 2016A&A...589A..22G Altcode: 2016arXiv160104617G Context. Star-planet tidal interactions may result in the excitation of inertial waves in the convective region of stars. In low-mass stars, their dissipation plays a prominent role in the long-term orbital evolution of short-period planets. Turbulent convection can sustain differential rotation in their envelopes with an equatorial acceleration (as in the Sun) or deceleration, which can modify the propagation properties of the waves.
Aims: We explore in this first paper the general propagation properties of free linear inertial waves in a differentially rotating homogeneous fluid inside a spherical shell. We assume that the angular velocity background flow depends on the latitudinal coordinate alone, close to what is expected in the external convective envelope of low-mass stars.
Methods: We use an analytical approach in the inviscid case to get the dispersion relation, from which we compute the characteristic trajectories along which energy propagates. This allows us to study the existence of attractor cycles and infer the different families of inertial modes. We also use high-resolution numerical calculations based on a spectral method for the viscous problem.
Results: We find that modes that propagate in the whole shell (D modes) behave the same way as with solid-body rotation. However, another family of inertial modes exists (DT modes), which can only propagate in a restricted part of the convective zone. Our study shows that they are less common than D modes and that the characteristic rays and shear layers often focus towards a wedge - or point-like attractor. More importantly, we find that for non-axisymmetric oscillation modes, shear layers may cross a corotation resonance with a local accumulation of kinetic energy. Their damping rate scales very differently from the value we obtain for standard D modes, and we show an example where it is independent of viscosity (Ekman number) in the astrophysical regime in which it is small. Title: Relation between trees of fragmenting granules and supergranulation evolution Authors: Roudier, Th.; Malherbe, J. M.; Rieutord, M.; Frank, Z. Bibcode: 2016A&A...590A.121R Altcode: 2016arXiv160404118R Context. The determination of the underlying mechanisms of the magnetic elements diffusion over the solar surface is still a challenge. Understanding the formation and evolution of the solar network (NE) is a challenge, because it provides a magnetic flux over the solar surface comparable to the flux of active regions at solar maximum.
Aims: We investigate the structure and evolution of interior cells of solar supergranulation. From Hinode observations, we explore the motions on solar surface at high spatial and temporal resolution. We derive the main organization of the flows inside supergranules and their effect on the magnetic elements.
Methods: To probe the superganule interior cell, we used the trees of fragmenting granules (TFG) evolution and their relations to horizontal flows.
Results: Evolution of TFG and their mutual interactions result in cumulative effects able to build horizontal coherent flows with longer lifetime than granulation (1 to 2 h) over a scale up to 12''. These flows clearly act on the diffusion of the intranetwork (IN) magnetic elements and also on the location and shape of the network.
Conclusions: From our analysis during 24 h, TFG appear as one of the major elements of the supergranules which diffuse and advect the magnetic field on the Sun's surface. The strongest supergranules contribute the most to magnetic flux diffusion in the solar photosphere.

Movies are available in electronic form at http://www.aanda.org Title: Physical Processes Leading to Surface Inhomogeneities: The Case of Rotation Authors: Rieutord, Michel Bibcode: 2016LNP...914..101R Altcode: 2015arXiv150503997R In this lecture I discuss the bulk surface heterogeneity of rotating stars, namely gravity darkening. I especially detail the derivation of the ω-model of Espinosa Lara and Rieutord (Astron Astrophys 533:A43, 2011), which gives the gravity darkening in early-type stars. I also discuss the problem of deriving gravity darkening<IndexTerm> <Secondary>darkening</Secondary> in stars owning a convective envelope and in those that are members of a binary system. Title: Two-dimensional models of early-type fast rotating stars: the ESTER project Authors: Rieutord, Michel Bibcode: 2016IAUFM..29B.147R Altcode: 2015arXiv150908609R In this talk I present the latest results of the ESTER project that has taken up the challenge of building two dimensional (axisymmetric) models of stars rotating at any rotation rate. In particular, I focus on main sequence massive and intermediate mass stars. I show what should be expected in such stars as far as the differential rotation and the associated meridional circulation are concerned, notably the emergence of a Stewartson layer along the tangent cylinder of the core. I also indicate what may be inferred about the evolution of an intermediate-mass star at constant angular momentum and how Be stars may form. I finally give some comparisons between models and observations of the gravity darkening on some nearby fast rotators as it has been derived from interferometric observations. In passing, I also discuss how 2D models can help to recover the fundamental parameters of a star. Title: Free inertial modes in differentially rotating convective envelopes of low-mass stars : numerical exploration Authors: Guenel, M.; Baruteau, C.; Mathis, S.; Rieutord, M. Bibcode: 2015sf2a.conf..371G Altcode: 2015arXiv151005825G Tidally-excited inertial waves in stellar convective regions are a key mechanism for tidal dissipation in stars and therefore the evolution of close-in binary or planetary systems. As a first step, we explore here the impact of latitudinal differential rotation on the properties of free inertial modes and identify the different families of modes. We show that they differ from the case of solid-body rotation. Using an analytical approach as well as numerical calculations, we conclude that critical layers --- where the Doppler-shifted frequency vanishes --- could play a very important role for tidal dissipation. Title: Using the Sun to estimate Earth-like planet detection capabilities. VI. Simulation of granulation and supergranulation radial velocity and photometric time series Authors: Meunier, N.; Lagrange, A. -M.; Borgniet, S.; Rieutord, M. Bibcode: 2015A&A...583A.118M Altcode: Context. Stellar variability, at a variety of timescales, can strongly affect the ability to detect exoplanets, in particular when using radial velocity (RV) techniques. Accurately characterized solar variations are precious in this context to study the impact of stellar variations on planet detectability. Here we focus on the impact of small timescale variability.
Aims: The objective of this paper is to model realistic RV time series due to granulation and supergranulation and to study in greater detail the impact of granulation and supergranulation on RV times series in the solar case.
Methods: We have simulated a collection of granules and supergranules evolving in time to reproduce solar photometric and RV time series. Synthetic time series are built over the full hemisphere over one solar cycle.
Results: We obtain intensity and RV rms due to solar granulation of respectively 0.8 m/s and 67 ppm, with a strong variability at timescales up to more than 1 h. The rms RV due to supergranulation is between 0.28 and 1.12 m/s.
Conclusions: To minimize the effect of granulation, the best strategy is to split the observing time during the night into several periods instead of observing over a consecutive duration. However, the best strategy depends on the precise nature of the signal. The granulation RV remains large after even an hour of smoothing (about 0.4 m/s) while the supergranulation signal cannot be significantly reduced on such timescales: a reduction of a factor 2 in rms RV can for example be obtained over 7 nights (with 26 min/night). The activity RV variability dominates at larger timescales. Detection limits can easily be as high as 1 MEarth or above for periods of tens or hundreds of days. The impact on detection limits is therefore important and may prevent the detection of 1 MEarth planets for long orbital periods, while the impact is much smaller at small orbital periods. These results do not take the presence of pulsations into account. Title: Gravito-inertial modes in a differentially rotating spherical shell Authors: Mirouh, Giovanni M.; Baruteau, Clément; Rieutord, Michel; Ballot, Jérôme Bibcode: 2015EPJWC.10106046M Altcode: While many intermediate- and high-mass main sequence stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study of axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. We consider a simplified model where the radiative zone of the star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral computations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire shell and those that are restricted to a sub-domain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We describe various geometries for the propagation domains, conditioning the surface visibility of the corresponding modes. Title: Two-dimensional models of fast rotating early-type stars Authors: Rieutord, Michel Bibcode: 2015IAUGA..2252835R Altcode: Rotation has now become an unavoidable parameter of stellar models, but for most massive or intermediate-mass stars rotation is fast, at least of a significant fraction of the critical angular velocity. Current spherically symmetric models try to cope with this feature of the stars using various approximations, like for instance the so-called shellular rotation usually accompanied with a diffusion that is meant to represent the mixing induced by rotationally generated flows. Such approximations may be justified in the limit of slow rotation where anisotropies and associated flows are weak. However, when rotation is fast, say larger than 50% of the critical velocities the use of a spherically symmetric 1D-model is doubtful. This is not only because of the centrifugal flattening of the star, but also because of the flows that are induced by the baroclinic torque that naturally appears in the radiative envelope of an early-type (rotating) star. These flows face the cylindrical symmetry of the Coriolis force and the spheroidal symmetry of the effective gravity.In this talk I shall present the latest results of the ESTER project that has taken up the challenge of making two-dimensional (axisymmetric) models of stars rotating at any rotation rate. In particular, I will focus on main sequence massive and intermediate-mass stars. I'll show what should be expected in such stars as far as the differential rotation and the associated meridional circulation are concerned, notably the emergence of a Stewartson layer along the tangential cylinder of the core. I'll also indicate what may be inferred about the evolution of an intermediate-mass star at constant angular momentum and how Be stars may form. I shall finally give some comparisons between models and observations of the gravity darkening on some nearby fast rotators as it has been derived from interferometric observations. In passing, I'll also discuss how 2D models can help to recover the fundamental parameters of a star. Title: Families of Granules, Flows, and Acoustic Events in the Solar Atmosphere from Hinode Observations Authors: Malherbe, J. -M.; Roudier, T.; Frank, Z.; Rieutord, M. Bibcode: 2015SoPh..290..321M Altcode: 2014SoPh..tmp..189M We investigate the relationship between trees of fragmenting granules (TFG), horizontal and vertical flows, and acoustic events (AE) in the photospheric network. AE are spatially concentrated and short-duration locations of acoustic energy flux. We performed observations at disk center of a 2D field of view (FOV) with high spatial and temporal resolutions provided by the Solar Optical Telescope onboard Hinode. Line profiles of Fe I 557.6 nm were recorded by the Narrow-band Filter Imager on an 80″×36″ FOV during five hours with a cadence of 22 seconds and 0.08″ pixel size. Vertical velocities were derived at two atmospheric levels allowing the determination of the energy flux at the acoustic frequency of 3.3 mHz. Families of granules and horizontal velocities were obtained from local correlation tracking (LCT) after segmentation and labeling of either continuum intensities or granular Doppler shifts. AE exhibit durations in the range 0.25 to 1 hour compatible with the lifetime of families (80 % do not last more than two hours). High-energy AE have the shortest lifetimes. We found that most AE occur in intergranular lanes located in or close to the boundaries between different families (called inter families) in regions with predominantly downward vertical motions and horizontal converging flows. In contrast, diverging flows are observed inside families, with a few AE in the intergranules. At the beginning of the sequence, when families are not yet detected, the distribution of AE is not uniform and is already organized at spatial lengths related to the mesogranular scale, with maximum contribution in the range 5″ to 10″, fully compatible with the scale of the maximum contribution of families in the TFG space. Although all sizes and durations seem to exist for families, their number decreases with increasing size and lifetime. Title: Fluid Dynamics: An Introduction Authors: Rieutord, M. Bibcode: 2015fldy.book.....R Altcode: No abstract at ADS Title: Dynamics of the envelope of a rapidly rotating star or giant planet in gravitational contraction Authors: Hypolite, D.; Rieutord, M. Bibcode: 2014A&A...572A..15H Altcode: 2014arXiv1409.6129H
Aims: We wish to understand the processes that control the fluid flows of a gravitationally contracting and rotating star or giant planet.
Methods: We consider a spherical shell containing an incompressible fluid that is slowly absorbed by the core so as to mimic gravitational contraction. We also consider the effects of a stable stratification that may modify the dynamics of a pre-main-sequence star of intermediate mass.
Results: This simple model reveals the importance of both the Stewartson layer attached to the core and the boundary conditions met by the fluid at the surface of the object. In the case of a pre-main-sequence star of intermediate mass where the envelope is stably stratified, shortly after the birth line, the spin-up flow driven by contraction overwhelms the baroclinic flow that would take place otherwise. This model also shows that for a contracting envelope, a self-similar flow of growing amplitude controls the dynamics. It suggests that initial conditions on the birth line are most probably forgotten. Finally, the model shows that the shear (Stewartson) layer that lies on the tangent cylinder of the core is likely a key feature of the dynamics that is missing in 1D models. This layer can explain the core and envelope rotational coupling that is required to explain the slow rotation of cores in giant and subgiant stars. Title: Gravito-inertial modes in a differentially rotating spherical shell Authors: Mirouh, G. M.; Baruteau, C.; Rieutord, M.; Ballot, J. Bibcode: 2014sf2a.conf..493M Altcode: 2014arXiv1411.3559M Oscillations have been detected in a variety of stars, including intermediate- and high-mass main sequence stars. While many of these stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study on axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. These modes probe the deep layers of the star around its convective core. We consider a simplified model where the radiative zone of a star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral simulations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire shell and those that are restricted to a subdomain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We characterise these attractors by the dependence of their Lyapunov exponent with the BV frequency of the background and the oscillation frequency of the mode. Finally, we note that, as modes associated with short-period attractors form dissipative structures, they could play an important role for tidal interactions but should be dismissed in the interpretation of observed oscillation frequencies. Title: Magnetohydrodynamics and Solar Physics Authors: Rieutord, M. Bibcode: 2014sf2a.conf...45R Altcode: 2014arXiv1410.3725R In this short review, I present some of the recent progresses on the pending questions of solar physics. These questions let us revisit the solar wind, the solar dynamo problem, the dynamics of the photosphere and finally have a glimpse at other solar type stars. Discussing the use of direct numerical simulations in solar physics, I show that the full numerical calculation of the flow in a single supergranule would require more electric power than the luminosity of the sun itself with present computer technology. Title: Inertial waves in differentially rotating low-mass starsand tides Authors: Guenel, M.; Baruteau, C.; Mathis, S.; Rieutord, M. Bibcode: 2014sf2a.conf..233G Altcode: 2014arXiv1410.3295G Star-planet tidal interactions may result in the excitation of inertial waves in the convective region of stars. Their dissipation plays a prominent role in the long-term orbital evolution of short-period planets. If the star is assumed to be rotating as a solid-body, the waves' Doppler-shifted frequency is restricted to [-2 Ω, 2 Ω] (Ω being the angular velocity of the star) and they can propagate in the entire convective region. However, turbulent convection can sustain differential rotation with an equatorial acceleration (as in the Sun) or deceleration that may modify waves propagation. We thus explore the properties of inertial modes of oscillation in a conically differentially rotating background flow whose angular velocity depends on the latitudinal coordinate only, close to what is expected in the external convective envelope of low-mass stars. We find that their frequency range is broadened by differential rotation, and that they may propagate only in a restricted part of the envelope. In some cases, inertial waves form shear layers around short-period attractor cycles. In others, they exhibit a remarkable behavior when a turning surface or a corotation layer exists in the star. We discuss how all these cases can impact tidal dissipation in stars. Title: Gravito-inertial modes in a differentially rotating spherical shell Authors: Mirouh, Giovanni M.; Baruteau, Clément; Rieutord, Michel; Ballot, Jérôme Bibcode: 2014arXiv1410.3655M Altcode: Oscillations have been detected in a variety of stars, including intermediate- and high-mass main sequence stars. While many of these stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study on axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. These modes probe the deep layers of the star around its convective core. We consider a simplified model where the radiative zone of a star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral simulations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire shell and those that are restricted to a subdomain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We characterise these attractors by the dependence of their Lyapunov exponent with the \BV frequency of the background and the oscillation frequency of the mode. Finally, we note that, as modes associated with short-period attractors form dissipative structures, they could play an important role for tidal interactions but should be dismissed in the interpretation of observed oscillation frequencies. Title: Dynamics of the radiative envelope of rapidly rotating stars: Effects of spin-down driven by mass loss Authors: Rieutord, M.; Beth, A. Bibcode: 2014A&A...570A..42R Altcode: 2014arXiv1407.0946R
Aims: This paper aims at deciphering the dynamics of the envelope of a rotating star when some angular momentum loss due to mass loss is present. We especially wish to know when the spin-down flow forced by the mass loss supersedes the baroclinic flows that pervade the radiative envelope of rotating stars.
Methods: We consider a Boussinesq fluid enclosed in a rigid sphere whose flows are forced both by the baroclinic torque, the spin-down of an outer layer, and an outward mass flux. The spin-down forcing is idealized in two ways: either by a rigid layer that imposes its spinning down velocity at some interface or by a turbulent layer that imposes a stress at this same interface to the interior of the star.
Results: In the case where the layer is rigid and imposes its velocity, we find that, as the mass-loss rate increases, the flow inside the star shows two transitions: the meridional circulation associated with baroclinic flows is first replaced by its spin-down counterpart, while at much stronger mass-loss rates the baroclinic differential rotation is superseded by the spin-down differential rotation. When boundary conditions specify the stress instead of the velocity, we find just one transition as the mass-loss rate increases. Besides the two foregoing transitions, we find a third transition that separates an angular momentum flux dominated by stresses from an angular momentum flux dominated by advection. Thus, with this very simplified two-dimensional stellar model, we find three wind regimes: weak (or no wind), moderate, and strong. In the weak wind case, the flow in the radiative envelope is of baroclinic origin. In the moderate case, the circulation results from the spin-down while the differential rotation may either be of baroclinic or of spin-down origin, depending on the boundary conditions or more generally on the coupling between mass and angular momentum losses. For fast rotating stars, our model says that the moderate wind regime starts when mass loss is higher than ~ 10-11 M⊙/yr. In the strong wind case, the flow in the radiative envelope is mainly driven by angular momentum advection. This latter transition mass-loss rate depends on the mass and the rotation rate of the star, being around 10-8 M⊙/yr for a 3 M⊙ ZAMS star rotating at 200 km s-1 according to our model. Title: The environment of the fast rotating star Achernar. III. Photospheric parameters revealed by the VLTI Authors: Domiciano de Souza, A.; Kervella, P.; Moser Faes, D.; Dalla Vedova, G.; Mérand, A.; Le Bouquin, J. -B.; Espinosa Lara, F.; Rieutord, M.; Bendjoya, P.; Carciofi, A. C.; Hadjara, M.; Millour, F.; Vakili, F. Bibcode: 2014A&A...569A..10D Altcode: Context. Rotation significantly impacts on the structure and life of stars. In phases of high rotation velocity (close to critical), the photospheric structure can be highly modified, and present in particular geometrical deformation (rotation flattening) and latitudinal-dependent flux (gravity darkening). The fastest known rotators among the nondegenerate stars close to the main sequence, Be stars, are key targets for studying the effects of fast rotation on stellar photospheres.
Aims: We seek to determine the purely photospheric parameters of Achernar based on observations recorded during an emission-free phase (normal B phase).
Methods: Several recent works proved that optical/IR long-baseline interferometry is the only technique able to sufficiently spatially resolve and measure photospheric parameters of fast rotating stars. We thus analyzed ESO-VLTI (PIONIER and AMBER) interferometric observations of Achernar to measure its photospheric parameters by fitting our physical model CHARRON using a Markov chain Monte Carlo method. This analysis was also complemented by spectroscopic, polarimetric, and photometric observations to investigate the status of the circumstellar environment of Achernar during the VLTI observations and to cross-check our model-fitting results.
Results: Based on VLTI observations that partially resolve Achernar, we simultaneously measured five photospheric parameters of a Be star for the first time: equatorial radius (equatorial angular diameter), equatorial rotation velocity, polar inclination, position angle of the rotation axis projected on the sky, and the gravity darkening β coefficient (effective temperature distribution). The close circumstellar environment of Achernar was also investigated based on contemporaneous polarimetry, spectroscopy, and interferometry, including image reconstruction. This analysis did not reveal any important circumstellar contribution, so that Achernar was essentially in a normal B phase at least from mid-2009 to end-2012, and the model parameters derived in this work provide a fair description of its photosphere. Finally, because Achernar is the flattest interferometrically resolved fast rotator to-date, the measured β and flattening, combined with values from previous works, provide a crucial test for a recently proposed gravity darkening model. This model offers a promising explanation to the fact that the measured β parameter decreases with flattening and shows significantly lower values than the classical prediction of von Zeipel.

Based on observations performed at ESO, Chile under VLTI PIONIER and AMBER programme IDs 087.D-0150 and 084.D-0456. Title: Pulsations of rapidly rotating stars with compositional discontinuities Authors: Reese, Daniel R.; Lara, Francisco Espinosa; Rieutord, Michel Bibcode: 2014IAUS..301..169R Altcode: 2013arXiv1310.3058R Recent observations of rapidly rotating stars have revealed the presence of regular patterns in their pulsation spectra. This has raised the question as to their physical origin, and, in particular, whether they can be explained by an asymptotic frequency formula for low-degree acoustic modes, as recently discovered through numerical calculations and theoretical considerations. In this context, a key question is whether compositional/density gradients can adversely affect such patterns to the point of hindering their identification. To answer this question, we calculate frequency spectra using two-dimensional ESTER stellar models. These models use a multi-domain spectral approach, allowing us to easily insert a compositional discontinuity while retaining a high numerical accuracy. We analyse the effects of such discontinuities on both the frequencies and eigenfunctions of pulsation modes in the asymptotic regime. We find that although there is more scatter around the asymptotic frequency formula, the semi-large frequency separation can still be clearly identified in a spectrum of low-degree acoustic modes. Title: Asteroseismology of fast-rotating stars: the example of α Ophiuchi Authors: Mirouh, Giovanni M.; Reese, Daniel R.; Lara, Francisco Espinosa; Ballot, Jérôme; Rieutord, Michel Bibcode: 2014IAUS..301..455M Altcode: 2013arXiv1309.3887M Many early-type stars have been measured with high angular velocities. In such stars, mode identification is difficult as the effects of fast and differential rotation are not well known. Using fundamental parameters measured by interferometry, the ESTER structure code and the TOP oscillation code, we investigate the oscillation spectrum of α Ophiuchi, for which observations by the MOST satellite found 57 oscillations frequencies. Results do not show a clear identification of the modes and highlight the difficulties of asteroseismology for such stars with a very complex oscillation spectrum. Title: Two-dimensional models of early-type fast rotating stars: new challenges in stellar physics Authors: Rieutord, M.; Espinosa Lara, F. Bibcode: 2013EAS....63..385R Altcode: 2013arXiv1310.1017R Two-dimensional models of rapidly rotating stars are already unavoidable for the interpretation of interferometric or asteroseismic data of this kind of stars. When combined with time evolution, they will allow the including of a more accurate physics for the computation of element transport and the determination of surface abundances. In addition, modeling the evolution of rotation will improve gyrochronology. Presently, two-dimensional ESTER models predict the structure and the large-scale flows (differential rotation and meridional circulation) of stars with mass larger than 1.7 M⊙ at any rotation rate. Main sequence evolution can be mimicked by varying the hydrogen content of the convective core. Models have been successfully tested on half a dozen of nearby fast rotating stars observed with optical or infra-red interferometers. They are now the right tool to investigate the oscillation spectrum of early-type fast rotators. Title: Present status of two-dimensional ESTER models: Application to Be stars Authors: Rieutord, M.; Espinosa, Lara F. Bibcode: 2013sf2a.conf..101R Altcode: 2013arXiv1310.0908R ESTER two-dimensional models solve the steady state structure of fast rotating early-type stars including the large scale flows associated with the baroclinicity of the radiative zones. Models are compared successfully to the fundamental parameters of the two main components of the triple system δ Velorum that have been derived from interferometric and orbit measurements. Testing the models on the Be star Achernar (α Eri), we cannot reproduce the data and conclude that this star has left the main sequence and is likely crossing the Herzsprung gap. Computing main sequence evolution of fast rotating stars at constant angular momentum shows that their criticality increases with time suggesting that the Be phenomenon and the ensuing mass ejections is the result of evolution. Title: Modeling rotating stars in two dimensions Authors: Rieutord, M. Bibcode: 2013EAS....62..307R Altcode: 2013arXiv1305.0496R In this lecture I present the way stars can be modeled in two dimensions and especially the fluid flows that are driven by rotation. I discuss some of the various ways of taking into account turbulence and conclude this contribution by a short presentation of some of the first results obtained with the ESTER code on the modeling of interferometrically observed fast rotating early-type stars. Title: Comparison of Solar Surface Flows Inferred from Time-Distance Helioseismology and Coherent Structure Tracking Using HMI/SDO Observations Authors: Švanda, Michal; Roudier, Thierry; Rieutord, Michel; Burston, Raymond; Gizon, Laurent Bibcode: 2013ApJ...771...32S Altcode: 2013arXiv1305.0875S We compare measurements of horizontal flows on the surface of the Sun using helioseismic time-distance inversions and coherent structure tracking of solar granules. Tracking provides two-dimensional horizontal flows on the solar surface, whereas the time-distance inversions estimate the full three-dimensional velocity flows in the shallow near-surface layers. Both techniques use Helioseismic and Magnetic Imager observations as input. We find good correlations between the various measurements resulting from the two techniques. Further, we find a good agreement between these measurements and the time-averaged Doppler line-of-sight velocity, and also perform sanity checks on the vertical flow that resulted from the three-dimensional time-distance inversion. Title: ESTER: Evolution STEllaire en Rotation Authors: Rieutord, Michel Bibcode: 2013ascl.soft05001R Altcode: The ESTER code computes the steady state of an isolated star of mass larger than two solar masses. The only convective region computed as such is the core where isentropy is assumed. ESTER provides solutions of the partial differential equations, for the pressure, density, temperature, angular velocity and meridional velocity for the whole volume. The angular velocity (differential rotation) and meridional circulation are computed consistently with the structure and are driven by the baroclinic torque. The code uses spectral methods, both radially and horizontally, with spherical harmonics and Chebyshev polynomials. The iterations follow Newton's algorithm. The code is object-oriented and is written in C++; a python suite allows an easy visualization of the results. While running, PGPLOT graphs are displayed to show evolution of the iterations. Title: Comparison of solar horizontal velocity fields from SDO/HMI and Hinode data Authors: Roudier, Th.; Rieutord, M.; Prat, V.; Malherbe, J. M.; Renon, N.; Frank, Z.; Švanda, M.; Berger, T.; Burston, R.; Gizon, L. Bibcode: 2013A&A...552A.113R Altcode: 2013arXiv1303.4271R Context. The measurement of the Sun's surface motions with a high spatial and temporal resolution is still a challenge.
Aims: We wish to validate horizontal velocity measurements all over the visible disk of the Sun from Solar Dynamics Observatory/ Helioseismic and Magnetic Imager (SDO/HMI) data.
Methods: Horizontal velocity fields are measured by following the proper motions of solar granules using a newly developed version of the coherent structure tracking (CST) code. The comparison of the surface flows measured at high spatial resolution (Hinode, 0.1 arcsec) and low resolution (SDO/HMI, 0.5 arcsec) allows us to determine corrections to be applied to the horizontal velocity measured from HMI white light data.
Results: We derive horizontal velocity maps with spatial and temporal resolutions of respectively 2.5 Mm and 30 min. From the two components of the horizontal velocity vx and vy measured in the sky plane and the simultaneous line of sight component from SDO/HMI dopplergrams vD, we derive the spherical velocity components (vr, vθ, vϕ). The azimuthal component vϕ gives the solar differential rotation with a high precision (± 0.037 km s-1) from a temporal sequence of only three hours.
Conclusions: By following the proper motions of the solar granules, we can revisit the dynamics of the solar surface at high spatial and temporal resolutions from hours to months and years with the SDO data. Title: Self-consistent 2D models of fast-rotating early-type stars Authors: Espinosa Lara, F.; Rieutord, M. Bibcode: 2013A&A...552A..35E Altcode: 2012arXiv1212.0778E
Aims: This work aims at presenting the first two-dimensional models of an isolated rapidly rotating star that include the derivation of the differential rotation and meridional circulation in a self-consistent way.
Methods: We use spectral methods in multidomains, together with a Newton algorithm to determine the steady state solutions including differential rotation and meridional circulation for an isolated non-magnetic, rapidly rotating early-type star. In particular we devise an asymptotic method for small Ekman numbers (small viscosities) that removes the Ekman boundary layer and lifts the degeneracy of the inviscid baroclinic solutions.
Results: For the first time, realistic two-dimensional models of fast-rotating stars are computed with the actual baroclinic flows that predict the differential rotation and the meridional circulation for intermediate-mass and massive stars. These models nicely compare with available data of some nearby fast-rotating early-type stars like Ras Alhague (α Oph), Regulus (α Leo), and Vega (α Lyr). It is shown that baroclinicity drives a differential rotation with a slow pole, a fast equator, a fast core, and a slow envelope. The differential rotation is found to increase with mass, with evolution (here measured by the hydrogen mass fraction in the core), and with metallicity. The core-envelope interface is found to be a place of strong shear where mixing will be efficient.
Conclusions: Two-dimensional models offer a new view of fast-rotating stars, especially of their differential rotation, which turns out to be strong at the core-envelope interface. They also offer more accurate models for interpreting the interferometric and spectroscopic data of early-type stars. Title: Inertial waves in a differentially rotating spherical shell Authors: Baruteau, C.; Rieutord, M. Bibcode: 2013JFM...719...47B Altcode: 2012arXiv1203.4347B We investigate the properties of small-amplitude inertial waves propagating in a differentially rotating incompressible fluid contained in a spherical shell. For cylindrical and shellular rotation profiles and in the inviscid limit, inertial waves obey a second-order partial differential equation of mixed type. Two kinds of inertial modes therefore exist, depending on whether the hyperbolic domain where characteristics propagate covers the whole shell or not. The occurrence of these two kinds of inertial modes is examined, and we show that the range of frequencies at which inertial waves may propagate is broader than with solid-body rotation. Using high-resolution calculations based on a spectral method, we show that, as with solid-body rotation, singular modes with thin shear layers following short-period attractors still exist with differential rotation. They exist even in the case of a full sphere. In the limit of vanishing viscosities, the width of the shear layers seems to weakly depend on the global background shear, showing a scaling in E^{1/3} with the Ekman number E, as in the solid-body rotation case. There also exist modes with thin detached layers of width scaling with E^{1/2} as Ekman boundary layers. The behavior of inertial waves with a corotation resonance within the shell is also considered. For cylindrical rotation, waves get dramatically absorbed at corotation. In contrast, for shellular rotation, waves may cross a critical layer without visible absorption, and such modes can be unstable for small enough Ekman numbers. Title: Ab Initio Modelling of Steady Rotating Stars Authors: Rieutord, Michel; Espinosa Lara, Francisco Bibcode: 2013LNP...865...49R Altcode: 2012arXiv1208.4926R Modelling isolated rotating stars at any rotation rate is a challenge for the next generation of stellar models. These models will couple dynamical aspects of rotating stars, like angular momentum and chemicals transport, with classical chemical evolution, gravitational contraction or mass-loss. Such modelling needs to be achieved in two dimensions, combining the calculation of the structure of the star, its mean flows and the time-evolution of the whole. We present here a first step in this challenging programme. It leads to the first self-consistent two-dimensional models of rotating stars in a steady state generated by the ESTER code. In these models the structure (pressure, density and temperature) and the flow fields are computed in a self-consistent way allowing the prediction of the differential rotation and the associated meridian circulation of the stars. After a presentation of the physical properties of such models and the numerical methods at work, we give the first grid of such models describing massive and intermediate-mass stars for a selection of rotation rates up to 90 % of the breakup angular velocity. Title: Rotation Effects as Possible Responsible for the Surface Effects on the Sun and Solar-Type Stars Authors: Suárez, J. C.; Goupil, M. J.; Reese, D. R.; Samadi, R.; Lignières, F.; Rieutord, M.; Lochard, J. Bibcode: 2013ASSP...31..197S Altcode: One of the main sources of uncertainty in the asteroseismic models of the Sun and solar-like stars is the poor match between predicted oscillation frequencies and observed ones in the very high frequency domain. Today, effects of turbulence, diffusion, etc., i.e., the so-called "surface effects" are signaled as possible responsible for such a discrepancy. We show that the effect of the stellar deformation due to rotation is of the same order or even larger than these effects. We show that rotation effects, are important for the asteroseismic analysis of the Sun and solar-like stars and they cannot be neglected when modeling such stars. Title: Gravity darkening in binary stars Authors: Espinosa Lara, F.; Rieutord, M. Bibcode: 2012A&A...547A..32E Altcode: 2012arXiv1210.4004E Context. Interpretation of light curves of many types of binary stars requires the inclusion of the (cor)relation between surface brightness and local effective gravity. Until recently, this correlation has always been modeled by a power law relating the flux or the effective temperature and the effective gravity, namely Teff ∝ geffβ .
Aims: We look for a simple model that can describe the variations of the flux at the surface of stars belonging to a binary system.
Methods: This model assumes that the energy flux is a divergence-free vector anti-parallel to the effective gravity. The effective gravity is computed from the Roche model.
Results: After explaining in a simple manner the old result of Lucy (1967, Z. Astrophys., 65, 89), which says that β ~ 0.08 for solar type stars, we first argue that one-dimensional models should no longer be used to evaluate gravity darkening laws. We compute the correlation between log Teff and log geff using a new approach that is valid for synchronous, weakly magnetized, weakly irradiated binaries. We show that this correlation is approximately linear, validating the use of a power law relation between effective temperature and effective gravity as a first approximation. We further show that the exponent β of this power law is a slowly varying function, which we tabulate, of the mass ratio of the binary star and the Roche lobe filling factor of the stars of the system. The exponent β remains mostly in the interval [0.20,0.25] if extreme mass ratios are eliminated.
Conclusions: For binary stars that are synchronous, weakly magnetized and weakly irradiated, the gravity darkening exponent is well constrained and may be removed from the free parameters of the models. Title: Solar Astronomy and its Wealth of Data Authors: Rieutord, M. Bibcode: 2012ASPC..461..457R Altcode: 2012adass..21..457R The only part of the Sun of which we have a detailed view is its surface. But this surface is also that of its convection zone which evolves on shorter and shorter time scales as smaller and smaller length scales are detected. Monitoring the Sun at a given (visible) wavelength thus generates a data flow which increases as the cube of the spatial resolution. A series of images covering the whole visible hemisphere of the Sun at the resolution of a 50 cm aperture would generate a data flow rate of 0.8Tb per day. However, knowing its physical state reduces to the knowledge of eight physical quantities: vx, vy, vz, Bx, By, Bz, ρ, T (velocity, magnetic, density and temperature fields respectively). In this work, I give the orders of magnitude of the data flow rates that should be expected for an ideal monitoring of the Sun. I also discuss the effects of seeing or the physical constraints that affect the measurement of quantities like the horizontal component of the velocity field. Finally, I present the various numerical simulations data sets that have emerged while investigating the dynamics of the Sun. Title: 2D Computations of g-modes in Fast Rotating Stars Authors: Ballot, J.; Lignières, F.; Prat, V.; Reese, D. R.; Rieutord, M. Bibcode: 2012ASPC..462..389B Altcode: 2011arXiv1109.6856B We present complete 2D computations of g-modes in distorted polytropic models of stars performed with the Two-dimensional Oscillation Program (TOP). We computed low-degree modes (ℓ =1 modes with radial order n = -1,…,-14, and ℓ = 2, 3 modes with n = -1,…,-5 and -16,…,-20) of a non-rotating model and followed them by slowly increasing the rotation rate up to 70 % of the Keplerian break-up velocity. We use these computations to determine the domain of validity of perturbative methods up to the 3rd order. We study the evolution of the regularities of the spectrum and show quantitative agreement with the traditional approximation for not too large values of the ratio of the rotation rate to the pulsation frequency. We also show the appearance of new types of modes, called “rosette” modes due to their spatial structure. Thanks to the ray theory for gravito-inertial waves that we developed, we can associate these modes with stable periodic rays. Title: Excitation of inertial modes in an experimental spherical Couette flow Authors: Rieutord, Michel; Triana, Santiago Andrés; Zimmerman, Daniel S.; Lathrop, Daniel P. Bibcode: 2012PhRvE..86b6304R Altcode: 2012arXiv1208.4937R Spherical Couette flow (flow between concentric rotating spheres) is one of flows under consideration for the laboratory magnetic dynamos. Recent experiments have shown that such flows may excite Coriolis restored inertial modes. The present work aims to better understand the properties of the observed modes and the nature of their excitation. Using numerical solutions describing forced inertial modes of a uniformly rotating fluid inside a spherical shell, we first identify the observed oscillations of the Couette flow with nonaxisymmetric, retrograde, equatorially antisymmetric inertial modes, confirming first attempts using a full sphere model. Although the model has no differential rotation, identification is possible because a large fraction of the fluid in a spherical Couette flow rotates rigidly. From the observed sequence of the excited modes appearing when the inner sphere is slowed down by step, we identify a critical Rossby number associated with a given mode, below which it is excited. The matching between this critical number and the one derived from the phase velocity of the numerically computed modes shows that these modes are excited by an instability likely driven by the critical layer that develops in the shear layer, staying along the tangent cylinder of the inner sphere. Title: The Power Spectrum of the Solar Surface Flows from Hinode Data and First Observations with MOF/CALAS Pic-du-Midi Authors: Roudier, T.; Rieutord, M.; Rincon, F.; Malherbe, J. -M.; Brito, D.; Berger, T.; Frank, Z.; Parés, L.; Bourrec, E.; Beigbeder, F. Bibcode: 2012ASPC..454...47R Altcode: Many features of solar surface turbulence, like the supergranulation, are still poorly understood.We use long time series of images taken by the Solar Optical Telescope on board the Hinode satellite to determine the velocity fields. The dynamics in the subgranulation range can be investigated with unprecedented precision thanks to the absence of seeing effects and the use of the MTF of SOT for correcting the spectra. The first MOF/CALAS/Pic-du-Midi results are also shown. Title: Acoustic Events in the Solar Atmosphere from Hinode/SOT NFI Observations Authors: Malherbe, J. -M.; Roudier, T.; Rieutord, M.; Berger, T.; Franck, Z. Bibcode: 2012SoPh..278..241M Altcode: 2012arXiv1207.1170M We investigate the properties of acoustic events (AEs), defined as spatially concentrated and short duration energy flux, in the quiet Sun, using observations of a 2D field of view (FOV) with high spatial and temporal resolution provided by the Solar Optical Telescope (SOT) onboard Hinode. Line profiles of Fe I 557.6 nm were recorded by the Narrow-band Filter Imager (NFI) on a 82″×82″ FOV during 75 min with a time step of 28.75 s and 0.08″ pixel size. Vertical velocities were computed at three atmospheric levels (80, 130, and 180 km) using the bisector technique, allowing the determination of energy flux to be made in the range 3 - 10 mHz using two complementary methods (Hilbert transform and Fourier power spectrum). Horizontal velocities were computed using local correlation tracking (LCT) of continuum intensities providing divergences. We found that the net energy flux is upward. In the range 3 - 10 mHz, a full FOV space and time averaged flux of 2700 W m−2 (lower layer 80 - 130 km) and 2000 W m−2 (upper layer 130 - 180 km) is concentrated in less than 1 % of the solar surface in the form of narrow (0.3″) AE. Their total duration (including rise and decay) is of the order of 103 s. Inside each AE, the mean flux is 1.6×105 W m−2 (lower layer) and 1.2×105 W m−2 (upper). Each event carries an average energy (flux integrated over space and time) of 2.5×1019 J (lower layer) to 1.9×1019 J (upper). More than 106 events could exist permanently on the Sun, with a birth and decay rate of 3500 s−1. Most events occur in intergranular lanes, downward velocity regions, and areas of converging motions. Title: MHD simulations of the solar photosphere Authors: Rieutord, M.; Rincon, F.; Roudier, T. Bibcode: 2012EAS....55....5R Altcode: 2012arXiv1206.6630R We briefly review the observations of the solar photosphere and pinpoint some open questions related to the magnetohydrodynamics of this layer of the Sun. We then discuss the current modelling efforts, addressing among other problems, that of the origin of supergranulation. Title: Some Dynamic Analysis of the Photosphere from Hinode/SOT and SDO/HMI Observations Authors: Roudier, T.; Malherbe, J.; Rieutord, M.; Berger, T.; Frank, Z.; Prat, V.; Renon, N.; Gizon, L.; Svanda, M. Bibcode: 2012ASPC..456...65R Altcode: We first present the important role played by the families of granule (or Tree of Fragmenting granules) in the formation of the photospheric network. Then, we describe the occurence and characteristics of acoustic events (AE), defined as spatially concentrated energy flux, in the quiet Sun. Finally, we present how horizontal velocities obtained from SDO/HMI data are calibrated by using Hinode/SOT observations. Title: Quasi full-disk maps of solar horizontal velocities using SDO/HMI data Authors: Roudier, Th.; Rieutord, M.; Malherbe, J. M.; Renon, N.; Berger, T.; Frank, Z.; Prat, V.; Gizon, L.; Švanda, M. Bibcode: 2012A&A...540A..88R Altcode: 2012arXiv1203.0514R
Aims: For the first time, the motion of granules (solar plasma on the surface on scales larger than 2.5 Mm) has been followed over the entire visible surface of the Sun, using SDO/HMI white-light data.
Methods: Horizontal velocity fields are derived from image correlation tracking using a new version of the coherent structure tracking algorithm. The spatial and temporal resolutions of the horizontal velocity map are 2.5 Mm and 30 min, respectively.
Results: From this reconstruction, using the multi-resolution analysis, one can obtain to the velocity field at different scales with its derivatives such as the horizontal divergence or the vertical component of the vorticity. The intrinsic error on the velocity is ~0.25 km s-1 for a time sequence of 30 min and a mesh size of 2.5 Mm. This is acceptable compared to the granule velocities, which range between 0.3 km s-1 and 1.8 km s-1. A high correlation between velocities computed from Hinode and SDO/HMI has been found (85%). From the data we derive the power spectrum of the supergranulation horizontal velocity field, the solar differential rotation, and the meridional velocity. Title: An r-mode in a magnetic rotating spherical layer: application to neutron stars Authors: Abbassi, S.; Rieutord, M.; Rezania, V. Bibcode: 2012MNRAS.419.2893A Altcode: 2011MNRAS.tmp.1917A; 2011arXiv1110.0277A The combined impact of rotation and magnetic fields on oscillations of stellar fluids is still not well known theoretically. It mixes Alfvén and inertial waves. Neutron stars are a place where both effects may be at work. We aim to solve this problem in the context of the r-mode instability in neutron stars, as it appears when these modes are coupled to gravitational radiation.

We consider a rotating spherical shell filled with a viscous fluid of infinite electrical conductivity and analyse propagation of model perturbations when a dipolar magnetic field is bathing the fluid layer. We perform an extensive numerical analysis and find that the m= 2 r-mode oscillation is influenced by the magnetic field when the Lehnert number (the ratio of Alfvén speed to rotation speed) exceeds a value proportional to the one-fourth power of the Ekman number (a non-dimensional measure of viscosity). This scaling is interpreted as the coincidence of the width of internal shear layers of inertial modes and the wavelength of the Alfvén waves. Applied to the case of rotating magnetic neutron stars, we find that dipolar magnetic fields above 1014 G are necessary to perturb the r-mode instability. Title: Rotation on the oscillation spectrum of solar-like stars Authors: Suárez, J. C.; Goupil, M. -J.; Reese, D. R.; Samadi, R.; Lignières, F.; Rieutord, M.; Lochard, J. Bibcode: 2011sf2a.conf..249S Altcode: One of the main sources of uncertainty in the asteroseismic models of solar-like stars is the poor match between predicted oscillation frequencies and observed ones in the very high frequency domain. Today, such deviation is usually corrected by fitting the affected frequencies with polynomials which are then physically explained by possible effects of turbulence, diffusion, etc., i.e., the so-called ``surface effects". In this work, we show that the effect of the stellar deformation due to rotation is of the same order or even larger than the aforementioned surface effects. Moreover, we show that rotation effects, even for the low velocities generally observed in solar-like stars, becomes important for the asteroseismic analysis and cannot be neglected when modeling such stars. Title: Gravity darkening in rotating stars Authors: Espinosa Lara, F.; Rieutord, M. Bibcode: 2011A&A...533A..43E Altcode: 2011arXiv1109.3038E Context. Interpretation of interferometric observations of rapidly rotating stars requires a good model of their surface effective temperature. Until now, laws of the form T_eff∝ g_eff^β have been used, but they are only valid for slowly rotating stars.
Aims: We propose a simple model that can describe the latitudinal variations in the flux of rotating stars at any rotation rate.
Methods: This model assumes that the energy flux is a divergence-free vector that is antiparallel to the effective gravity.
Results: When mass distribution can be described by a Roche model, the latitudinal variations in the effective temperature only depend on a single parameter, namely the ratio of the equatorial velocity to the Keplerian velocity. We validate this model by comparing its predictions to those of the most realistic two-dimensional models of rotating stars issued from the ESTER code. The agreement is very good, as it is with the observations of two rapidly rotating stars, α Aql and α Leo.
Conclusions: We suggest that as long as a gray atmosphere can be accepted, the inversion of data on flux distribution coming from interferometric observations of rotating stars uses such a model, which has just one free parameter. Title: The effects of μ gradients on pulsations of rapidly rotating stars Authors: Reese, Daniel R.; Espinosa Lara, Francisco; Rieutord, Michel Bibcode: 2011IAUS..272..535R Altcode: Recently, Reese et al. (2008), Lignières & Georgeot (2008) and Lignières & Georgeot (2009) showed that the frequencies of low-degree acoustic modes in rapidly rotating stars, also known as ``island modes'', follow an asymptotic formula, the coefficients of which can be deduced from ray dynamics. We investigate how this asymptotic behaviour is affected by μ gradients by comparing pulsation spectra from models with and without such a discontinuity. Title: The Sun's Supergranulation Authors: Rieutord, Michel; Rincon, François Bibcode: 2010LRSP....7....2R Altcode: 2010arXiv1005.5376R The Sun's supergranulation refers to a physical pattern covering the surface of the quiet Sun with a typical horizontal scale of approximately 30,000 km and a lifetime of around 1.8 d. Its most noticeable observable signature is as a fluctuating velocity field of 360 m st-1 rms whose components are mostly horizontal. Supergranulation was discovered more than fifty years ago, however explaining why and how it originates still represents one of the main challenges of modern solar physics. Title: On the Interpretation of Echelle Diagrams for Solar-like Oscillations Effect of Centrifugal Distortion Authors: Suárez, J. C.; Goupil, M. J.; Reese, D. R.; Samadi, R.; Lignières, F.; Rieutord, M.; Lochard, J. Bibcode: 2010ApJ...721..537S Altcode: 2010arXiv1009.0123S This work aims at determining the impact of slow to moderate rotation on the regular patterns often present in solar-like oscillation spectra, i.e., the frequency spacings. We focus on the well-known asteroseismic diagnostic echelle diagrams, examining how rotation may modify the estimates of the large and small spacings, as well as the identification of modes. We illustrate the work with a real case: the solar-like star ηBootis. We study a main-sequence 1.3 M sun star as a typical case. The modeling takes into account rotation effects on the equilibrium models through an effective gravity and on the oscillation frequencies through both perturbative and non-perturbative calculations. We compare the results of both type of calculations in the context of the regular spacings (like the small spacings and the scaled small spacings) and echelle diagrams. We show that for echelle diagrams the perturbative approach remains valid for rotational velocities up to 40-50 km s-1. We show that for the rotational velocities measured in solar-like stars, i.e., vsin i up to 20-30 km s-1, rotation effects must be taken into account in the modeling for a correct interpretation of the observed oscillations. In particular, theoretical oscillation frequencies must be corrected up to the second order in terms of rotation rate, including near degeneracy effects. For rotational velocities of about 16 km s-1 and higher, diagnostics on large spacings and on modal identification through echelle diagrams can be significantly altered by the presence of the m ≠ 0 components of the rotationally split modes. We found these effects to be detectable in the observed frequency range. Analysis of the effects of rotation on small spacings and scaled small spacings reveals that these can be of the order of or even larger than surface effects, typically turbulence, microscopic diffusion, etc. Furthermore, we show that scaled spacings are significantly affected by stellar distortion even for small stellar rotational velocities (from 10 to 15 km s-1) and therefore some care must be taken when using them as indicators for probing deep stellar interiors. Title: Gravity modes in rapidly rotating stars. Limits of perturbative methods Authors: Ballot, J.; Lignières, F.; Reese, D. R.; Rieutord, M. Bibcode: 2010A&A...518A..30B Altcode: 2010arXiv1005.0275B Context. CoRoT and Kepler missions are now providing high-quality asteroseismic data for a large number of stars. Among intermediate-mass and massive stars, fast rotators are common objects. Taking the rotation effects into account is needed to correctly understand, identify, and interpret the observed oscillation frequencies of these stars. A classical approach is to consider the rotation as a perturbation.
Aims: In this paper, we focus on gravity modes, such as those occurring in γ Doradus, slowly pulsating B (SPB), or Be stars. We aim to define the suitability of perturbative methods.
Methods: With the two-dimensional oscillation program (TOP), we performed complete computations of gravity modes - including the Coriolis force, the centrifugal distortion, and compressible effects - in 2D distorted polytropic models of stars. We started with the modes ℓ = 1, n = 1-14, and ℓ = 2-3, n = 1-5, 16-20 of a nonrotating star, and followed these modes by increasing the rotation rate up to 70% of the break-up rotation rate. We then derived perturbative coefficients and determined the domains of validity of the perturbative methods.
Results: Second-order perturbative methods are suited to computing low-order, low-degree mode frequencies up to rotation speeds ~100 km s-1 for typical γ Dor stars or ~150 km s-1 for B stars. The domains of validity can be extended by a few tens of km s-1 thanks to the third-order terms. For higher order modes, the domains of validity are noticeably reduced. Moreover, perturbative methods are inefficient for modes with frequencies lower than the Coriolis frequency 2Ω. We interpret this failure as a consequence of a modification in the shape of the resonant cavity that is not taken into account in the perturbative approach. Title: On the power spectrum of solar surface flows Authors: Rieutord, M.; Roudier, T.; Rincon, F.; Malherbe, J. -M.; Meunier, N.; Berger, T.; Frank, Z. Bibcode: 2010A&A...512A...4R Altcode: 2009arXiv0911.3319R Context. The surface of the Sun provides us with a unique and very detailed view of turbulent stellar convection. Studying its dynamics can therefore help us make significant progress in stellar convection modelling. Many features of solar surface turbulence like the supergranulation are still poorly understood.
Aims: The aim of this work is to give new observational constraints on these flows by determining the horizontal scale dependence of the velocity and intensity fields, as represented by their power spectra, and to offer some theoretical guidelines to interpret these spectra.
Methods: We use long time-series of images taken by the Solar Optical Telescope (SOT) on board the Hinode satellite; we reconstruct both horizontal (by granule tracking) and vertical (by Doppler effect) velocity fields in a field-of-view of ~ 75 × 75 Mm2. The dynamics in the subgranulation range can be investigated with unprecedented precision thanks to the absence of seeing effects and the use of the modulation transfer function of SOT for correcting the spectra.
Results: At small subgranulation scales down to 0.4 Mm the spectral density of kinetic energy associated with vertical motions exhibits a k-10/3-like power law, while the intensity fluctuation spectrum follows either a k-17/3 or a k-3-like power law at the two continuum levels investigated (525 and 450 nm respectively). We discuss the possible physical origin of these scalings and interpret the combined presence of k-17/3 and k-10/3 power laws for the intensity and vertical velocity as a signature of buoyancy-driven turbulent dynamics in a strongly thermally diffusive regime. In the mesogranulation range and up to a scale of 25 Mm, we find that the amplitude of the vertical velocity field decreases like λ-3/2 with the horizontal scale λ. This behaviour corresponds to a k2 spectral power law. Still in the 2.5-10 Mm mesoscale range, we find that intensity fluctuations in the blue continuum also follow a k2 power law. In passing we show that granule tracking cannot sample scales below 2.5 Mm. We finally further confirm the presence of a significant supergranulation energy peak at 30 Mm in the horizontal velocity power spectrum and show that the emergence of a pore erases this spectral peak. We tentatively estimate the scale height of the vertical velocity field in the supergranulation range and find 1 Mm; this value suggests that supergranulation flows are shallow. Title: Viscous dissipation by tidally forced inertial modes in a rotating spherical shell Authors: Rieutord, M.; Valdettaro, L. Bibcode: 2010JFM...643..363R Altcode: 2009arXiv0909.3922R We investigate the properties of forced inertial modes of a rotating fluid inside a spherical shell. Our forcing is tidal like, but its main property is that it is on the large scales. Our solutions first confirm some analytical results obtained on a two-dimensional model by Ogilvie (2005). We also note that as the frequency of the forcing varies, the dissipation varies drastically if the Ekman number E is low (as is usually the case). We then investigate the three-dimensional case and compare the results to the foregoing model. These solutions show, like their 2D counterpart, a spiky dissipation curve when the frequency of the forcing is varied; they also display small frequency intervals where the viscous dissipation is independent of viscosity. However, we show that the response of the fluid in these frequency intervals is crucially dominated by the shear layer that is emitted at the critical latitude on the inner sphere. The asymptotic regime is reached when an attractor has been excited by this shear layer. This property is not shared by the two-dimensional model. Finally, resonances of the three-dimensional model correspond to some selected least-damped eigenmodes. Unlike their two-dimensional counter parts these modes are not associated with simple attractors; instead, they show up in frequency intervals with a weakly contracting web of characteristics. Besides, we show that the inner core is negligible when its relative radius is less than the critical value 0.4E^{1/5}. For these spherical shells, the full sphere solutions give a good approximation of the flows (abridged abstract). Title: Tidal instability in stellar and planetary binary systems Authors: Le Bars, M.; Lacaze, L.; Le Dizès, S.; Le Gal, P.; Rieutord, M. Bibcode: 2010PEPI..178...48L Altcode: In this paper, we combine theoretical and experimental approaches to study the tidal instability in planetary liquid cores and stars. We demonstrate that numerous complex modes can be excited depending on the relative values of the orbital angular velocity Ωorbit and of the spinning angular velocity Ωspin, except in a stable range characterized by Ωspin/ Ωorbit ∈ [-1;1/3]. Even if the tidal deformation is small, its subsequent instability - coming from a resonance process - may induce motions with large amplitude, which play a fundamental role at the planetary scale. This general conclusion is illustrated in the case of Jupiter's moon Io by a coupled model of synchronization, demonstrating the importance of energy dissipation by elliptical instability. Title: Supergranulation, Network Formation, and TFGs Evolution from Hinode Observations Authors: Roudier, T.; Rincon, F.; Rieutord, M.; Brito, D.; Beigbeder, F.; Parès, L.; Malherbe, J. -M.; Meunier, N.; Berger, T.; Frank, Z. Bibcode: 2009ASPC..415..203R Altcode: In this paper, we analyse a a 48h high-resolution time sequence of the quiet Sun photosphere obtained with the Solar Optical Telescope onboard Hinode. Using floating corks advected by velocity fields inferred from photometry measurements, we show that long-living Trees of Fragmenting Granules play a crucial role in the advection of small-scale magnetic fields and in the build-up of the magnetic network. Title: Gravity modes in rapidly rotating polytropic stars Authors: Ballot, J.; Lignières, F.; Reese, D. R.; Rieutord, M. Bibcode: 2009arXiv0912.1679B Altcode: Using the Two-dimensional Oscillation Program (TOP), we have explored the effects of rapid rotation on gravity modes in polytropic stars. Coriolis force, centrifugal distortion as well as compressible effects have been taken into account. Thanks to our complete calculation, we have first studied the validity domain of perturbative methods and started to explore properties of these modes. We focus on l=1 in this analysis. Title: On the dynamics of a radiative rapidly rotating star Authors: Rieutord, M.; Espinosa Lara, F. Bibcode: 2009CoAst.158...99R Altcode: The envelope of massive rapidly rotating stars is pervaded by baroclinic fluid flows, namely a differential rotation with a meridional circulation and likely a small-scale turbulence. We present here some of the first results of the ESTER project (Evolution STEllaire en Rotation). More specifically, using for the first time the spheroidal geometry, we give the shape of the differential rotation and show that the baroclinic torque imposes a fast rotating core and a slow envelope, together with a slow pole and a fast equator. The angular velocity of the core is 50% larger than that of the envelope. Title: Mesoscale dynamics on the Sun's surface from HINODE observations Authors: Roudier, Th.; Rieutord, M.; Brito, D.; Rincon, F.; Malherbe, J. M.; Meunier, N.; Berger, T.; Frank, Z. Bibcode: 2009A&A...495..945R Altcode: 2009arXiv0902.2299R Context:
Aims: The interactions of velocity scales on the Sun's surface, from granulation to supergranulation are still not understood, nor are their interaction with magnetic fields. We thus aim at giving a better description of dynamics in the mesoscale range which lies between the two scales mentioned above.
Methods: We analyse a 48 h high-resolution time sequence of the quiet Sun photosphere at the disk center obtained with the Solar Optical Telescope onboard Hinode. The observations, which have a field of view of 100´´ × 100´´, typically contain four supergranules. We monitor in detail the motion and evolution of granules as well as those of the radial magnetic field.
Results: This analysis allows us to better characterize Trees of Fragmenting Granules issued from repeated fragmentation of granules, especially their lifetime statistics. Using floating corks advected by measured velocity fields, we show their crucial role in the advection of the magnetic field and in the build up of the network. Finally, thanks to the long duration of the time series, we estimate that the turbulent diffusion coefficient induced by horizontal motion is approximately 430 km2 s-1.
Conclusions: These results demonstrate that the long living families contribute to the formation of the magnetic network and suggest that supergranulation could be an emergent length scale building up as small magnetic elements are advected and concentrated by TFG flows. Our estimate for the magnetic diffusion associated with this horizontal motion might provide a useful input for mean-field dynamo models. Title: Development of large and fast cmos aps cameras at latt Authors: Beigbeder, F.; Bourrec, E.; Dupieux, M.; Delaigue, G.; Rondi, S.; Rieutord, M.; Meunier, N.; Roudier, T. Bibcode: 2009EAS....37..301B Altcode: Since 2004, at the Laboratoire d'Astrophysique de Toulouse Tarbes (LATT), we work with CMOS APS detectors, firstly to develop a large-field,high-resolution camera for the observation of the solar supergranulation, secondly to develop a fast camera for an adaptive optics test bench. In these two projects, we use detectors from FillFactory, now continued by Cypress Semiconductor Corporation: IBIS4-14000, IBIS-16000, LUPA-4000, 14 Mpixels, 16 Mpixels, 4 Mpixels respectively. The last one just reads in a 240 × 240 pixels window to obtain readout rate of 1000 Image/s. For these purposes we developed dedicated controllers to follow the high pixel rate and multi-output readout of this type of detectors. We also studied the characterization methods and measured the main parameters of these CMOS detectors to know their behaviour. Using these kinds of APS detectors in these two particular projects proves that we can already find niches to use CMOS detectors in astronomy taking advantage of their present specificities. Recent improvements like back illumination, noise reduction, should rapidly open news possibilities. Title: Approaching the Low-Frequency Spectrum of Rotating Stars Authors: Rieutord, M. Bibcode: 2009LNP...765..101R Altcode: In this lecture I present the basic knowledge needed to understand the properties of the low-frequency spectrum of rotating stars. This spectrum is a mixture of inertial and gravity modes. These modes both have singularities in the limit of vanishing diffusion for a generic container. I explain the nature and the role of these singularities; I also discuss the way these modes can be computed and the actual difficulties that need to be circumvented to get sensible results. Title: Solar Convection Dynamics Derived from Long Time Series Observations Authors: Hanslmeier, A.; Roudier, Th.; Rieutord, M.; Muller, R. Bibcode: 2009CEAB...33...39H Altcode: Long time series of solar granulation are extremely difficult to be obtained from ground based observations because of the unstable Earth's atmosphere. The Hinode-SOT instrument provided long term stable time series of solar granulation at different wavelengths in the visible. After appropriate calibration, these data can be used for studies of long time series of several hours. In this study we concentrate on the question of whether granulation can be considered as an ergodic phenomenon. The answer to such question is very important when comparing observational results with theoretical models since these models are limited either in time or in the extension of the spatial grid. We have analysed a series of 8 h of Hinode-SOT blue continuum images, the average separation between the successive images was at maximum about 50 sec. The images were aligned in order to minimize tracking problems. A quiet region located near the solar disc centre at the beginning of the observations was selected. The analysis shows that it seems to be that solar granulation is at least near the behaviour of ergodicity. That means, that the behaviour along the time axis and along a spatial coordinate become similar on a long interval. From sufficient spatial sampling the time behaviour could be derived. Title: Photospheric flows around a quiescent filament at Large and small scale and their ffects on filament destabilization Authors: Roudier, Th.; Malherbe, J. M.; Švanda, M.; Molodij, G.; Keil, S.; Sütterlin, P.; Schmieder, B.; Bommier, V.; Aulanier, G.; Meunier, N.; Rieutord, M.; Rondi, S. Bibcode: 2008sf2a.conf..569R Altcode: We study the influence of large and small scales photospheric motions on the destabilization of an eruptive filament, observed on October 6, 7, and 8, 2004 as part of an international observing campaign (JOP 178). Large-scale horizontal flows are invetigated from a series of MDI/SOHO full-disc Dopplergrams and magnetograms from THEMIS. Small-scale horizontal flows were derived using local correlation tracking on TRACE satellite, Dutch Open Telescope (DOT) and The Dunn Solar telescope (DST) data. The topology of the flow field changed significantly during the filament eruptive phase, suggesting a possible coupling between the surface flow field and the coronal magnetic field. We measured an increase of the shear below the point where the eruption starts and a decrease in shear after the eruption. We conclude that there is probably a link between changes in surface flow and the disappearance of the eruptive filament. Title: CoRoT Measures Solar-Like Oscillations and Granulation in Stars Hotter Than the Sun Authors: Michel, Eric; Baglin, Annie; Auvergne, Michel; Catala, Claude; Samadi, Reza; Baudin, Frédéric; Appourchaux, Thierry; Barban, Caroline; Weiss, Werner W.; Berthomieu, Gabrielle; Boumier, Patrick; Dupret, Marc-Antoine; Garcia, Rafael A.; Fridlund, Malcolm; Garrido, Rafael; Goupil, Marie-Jo; Kjeldsen, Hans; Lebreton, Yveline; Mosser, Benoît; Grotsch-Noels, Arlette; Janot-Pacheco, Eduardo; Provost, Janine; Roxburgh, Ian W.; Thoul, Anne; Toutain, Thierry; Tiphène, Didier; Turck-Chieze, Sylvaine; Vauclair, Sylvie D.; Vauclair, Gérard P.; Aerts, Conny; Alecian, Georges; Ballot, Jérôme; Charpinet, Stéphane; Hubert, Anne-Marie; Lignières, François; Mathias, Philippe; Monteiro, Mario J. P. F. G.; Neiner, Coralie; Poretti, Ennio; Renan de Medeiros, José; Ribas, Ignasi; Rieutord, Michel L.; Roca Cortés, Teodoro; Zwintz, Konstanze Bibcode: 2008Sci...322..558M Altcode: 2008arXiv0812.1267M Oscillations of the Sun have been used to understand its interior structure. The extension of similar studies to more distant stars has raised many difficulties despite the strong efforts of the international community over the past decades. The CoRoT (Convection Rotation and Planetary Transits) satellite, launched in December 2006, has now measured oscillations and the stellar granulation signature in three main sequence stars that are noticeably hotter than the sun. The oscillation amplitudes are about 1.5 times as large as those in the Sun; the stellar granulation is up to three times as high. The stellar amplitudes are about 25% below the theoretic values, providing a measurement of the nonadiabaticity of the process ruling the oscillations in the outer layers of the stars. Title: Supergranules over the solar cycle Authors: Meunier, N.; Roudier, T.; Rieutord, M. Bibcode: 2008A&A...488.1109M Altcode: Context: The origin of supergranulation has not been understood yet. Contradictory results have been obtained in the past concerning the relation between supergranule properties (mostly cell size) and the solar cycle.
Aims: We propose to study the variation in supergranule cell sizes and velocity fields over the solar cycle, as well as the intensity variation inside supergranules.
Methods: We define supergranule cells from maps of horizontal velocity field divergences. The flow fields are derived from MDI/SOHO intensity maps. The intensity variation in supergranules are compared to the variation inside granules resulting from a numerical simulation. The variation in these profiles with the cell size and over the solar cycle is also analysed.
Results: We find that cell sizes are smaller on average at cycle maximum. We also find that the slope between Log (V_rms) and Log (R) is weakly correlated with the spot number (i.e. the global activity level) but anti-correlated with the local magnetic field. We also confirm the decrease in the intensity variation from cell centre to the boundary, which puts a lower limit on the temperature variation of 0.57 ± 0.06 K. This temperature difference is of 1.03 ± 0.05 K when considering the areas of strongest divergence and strongest convergence. We observe a strong similarity in the intensity variation inside supergranules and granules. A significant variation with the cell size is observed, also similar to that in granules, but the variation over the solar cycle is not significant.
Conclusions: The sign of the variation in supergranule cell sizes over the solar cycle is in agreement with what can be expected from the influence of the magnetic field. The observed intensity variations show that a common process could be the origin of both granules and supergranules. Title: Dynamics of the Solar Surface Reavealed by Granule Tracking Authors: Rieutord, M.; Roudier, T. Bibcode: 2008ESPM...12..2.9R Altcode: We present the recent results obtained by the Toulouse-Tarbes group on the dynamics of the solar surface at meso and supergranular scale, and their interactions with the magnetic field.

First, using the 14-Mpixel CALAS camera at the Pic-du-Midi observatory, we obtained a 7.5h-long sequence of high resolution images with unprecedented field size (524"x350"). Tracking granules, we have determined the velocity field at the Sun's surface in great detail from a scale of 2.5 Mm up to 250 Mm. The kinetic energy density spectrum shows that supergranulation peaks at 36Mm and spans on scales ranging between 20Mm and 75Mm. The decrease of supergranular flows in the small scales is close to a 1/k^2-power law, steeper than the equipartition Kolmogorov one. The probability distribution function of the divergence field shows the signature of intermittency of the supergranulation and thus its turbulent nature.

Second, using a 48hours-long sequence of white light images from the HINODE satellite, we determined the evolution of granule families, which give birth to correlated motion at mesogranular scale. Using passive cork and magnetic field observations, we show that the surface velocity field via family organization is sufficient to explain the magnetic field concentrations at the Sun's surface, namely the magnetic network. We also find robust scaling laws for the life time of granule families. Title: Regular patterns in the acoustic spectrum of rapidly rotating stars Authors: Reese, D.; Lignières, F.; Rieutord, M. Bibcode: 2008A&A...481..449R Altcode: 2008arXiv0801.4630R Context: Rapid rotation modifies the structure of the frequency spectrum of pulsating stars, thus making mode identification difficult.
Aims: We look for new forms of organisation for the frequency spectrum that can provide a basis for mode identification at high rotation rates.
Methods: Acoustic modes in uniformly rotating polytropic models of stars are computed using a numerical code that fully takes the effects of rotation (centrifugal distortion and Coriolis acceleration) into account. All low-degree modes, ℓ = 0 to 3, with radial orders n = 1-10 and 21-25 for N = 3 polytropic models and n = 1-10 for N = 1.5 polytropic models are followed from a zero rotation rate up to 59% of the break-up velocity.
Results: We find an empirical formula that gives a good description of the high-frequency range of the computed acoustic spectrum for high rotation rates. Differences between this formula and complete eigenmode calculations are shown to be substantially smaller than those obtained with a 3rd order perturbative method valid at low rotation rates. Title: Large-scale horizontal flows in the solar photosphere. III. Effects on filament destabilization Authors: Roudier, T.; Švanda, M.; Meunier, N.; Keil, S.; Rieutord, M.; Malherbe, J. M.; Rondi, S.; Molodij, G.; Bommier, V.; Schmieder, B. Bibcode: 2008A&A...480..255R Altcode: 2007arXiv0711.3112R Aims:We study the influence of large-scale photospheric motions on the destabilization of an eruptive filament, observed on October 6, 7, and 8, 2004, as part of an international observing campaign (JOP 178).
Methods: Large-scale horizontal flows were investigated from a series of MDI full-disc Dopplergrams and magnetograms. From the Dopplergrams, we tracked supergranular flow patterns using the local correlation tracking (LCT) technique. We used both LCT and manual tracking of isolated magnetic elements to obtain horizontal velocities from magnetograms.
Results: We find that the measured flow fields obtained by the different methods are well-correlated on large scales. The topology of the flow field changed significantly during the filament eruptive phase, suggesting a possible coupling between the surface flow field and the coronal magnetic field. We measured an increase in the shear below the point where the eruption starts and a decrease in shear after the eruption. We find a pattern in the large-scale horizontal flows at the solar surface that interact with differential rotation.
Conclusions: We conclude that there is probably a link between changes in surface flow and the disappearance of the eruptive filament. Title: Solar supergranulation revealed by granule tracking Authors: Rieutord, M.; Meunier, N.; Roudier, T.; Rondi, S.; Beigbeder, F.; Parès, L. Bibcode: 2008A&A...479L..17R Altcode: 2008arXiv0801.1369R Context: Supergranulation is a pattern of the velocity field at the surface of the Sun, which has been known about for more than fifty years, however, no satisfactory explanation of its origin has been proposed.
Aims: New observational constraints are therefore needed to guide theoretical approaches which hesitate between scenarios that either invoke a large-scale instability of the surface turbulent convection or a direct forcing by buoyancy.
Methods: Using the 14-Mpixel CALAS camera at the Pic-du-Midi observatory, we obtained a 7.5 h-long sequence of high resolution images with unprecedented field size. Tracking granules, we have determined the velocity field at the Sun's surface in great detail from a scale of 2.5 Mm up to 250 Mm.
Results: The kinetic energy density spectrum shows that supergranulation peaks at 36 Mm and spans on scales ranging between 20 Mm and 75 Mm. The decrease of supergranular flows in the small scales is close to a k-2-power law, steeper than the equipartition Kolmogorov one. The probability distribution function of the divergence field shows the signature of intermittency of the supergranulation and thus its turbulent nature.
Conclusions: Title: The dynamics of rotating fluids and binary stars Authors: Rieutord, M. Bibcode: 2008EAS....29..127R Altcode: In this lecture I try to explain the basic concepts related to fluid motions when a background rotation dominates the flows. In particular, the notions of geostrophic flow, Ekman layer, Ekman circulation are explained. However, the main focus of this lecture is on the eigenmodes which occur in such a context and I emphasize here the special effects conveyed to inertial and gravito-inertial modes by the hyperbolic nature of the governing operators. A final section introduces the case of the elliptic instability which I recently suggested as one of the processes of binary synchronization. Title: HINODE SOT Observations - First Preliminary Analysis Authors: Hanslmeier, A.; Müller, R.; Roudier, Th.; Rieutord, M. Bibcode: 2008CEAB...32...25H Altcode: In this paper we present some preliminary analysis of Hinode-SOT data: time series as well as synoptic data. We show that the data are influenced by periodic intensity variations as well as bad images appear. This should be taken into account when analysing the data. Title: The dynamics of a fully radiative rapidly rotating star enclosed within a spherical box Authors: Espinosa Lara, F.; Rieutord, M. Bibcode: 2007A&A...470.1013E Altcode: Context: Recent results from interferometry and asteroseismology require models of rapidly rotating stars that are more and more precise.
Aims: We describe the basic structure and the hydrodynamics of a fully radiative star as a preliminary step towards more realistic models of rotating stars.
Methods: We consider a solar mass of perfect gas enclosed in a spherical container. The gas is self-gravitating and rotating, and is the seat of nuclear heating, and heat diffusion is due to radiative diffusion with Kramers type opacities. Equations are solved numerically with spectral methods in two dimensions with a radial Gauss-Lobatto grid and spherical harmonics.
Results: We computed the centrifugally flattened structure of such a star: the von Zeipel model, which says that the energy flux is proportional to the local effective gravity is tested. We show that it overestimates the ratio of the polar to the equatorial energy flux by almost a factor 2. We also determine the Brunt-Väisälä frequency distribution and show that outer equatorial regions in a radiative zone are convectively unstable when the rotation is fast enough. We compute the differential rotation and meridional circulation stemming from the baroclinicity of the star and show that, in such radiative zones, equatorial regions rotate faster than polar ones. The surface differential rotation is also shown to reach a universal profile when rotation is slow enough (less than 36% of the breakup one), as long as viscosity and Prandlt number remain small. Title: Convergence and round-off errors in a two-dimensional eigenvalue problem using spectral methods and Arnoldi-Chebyshev algorithm Authors: Valdettaro, Lorenzo; Rieutord, Michel; Braconnier, Thierry; Fraysse, Valerie Bibcode: 2007JCoAM.205..382V Altcode: 2006physics...4219V An efficient way of solving 2D stability problems in fluid mechanics is to use, after discretization of the equations that cast the problem in the form of a generalized eigenvalue problem, the incomplete Arnoldi-Chebyshev method. This method preserves the banded structure sparsity of matrices of the algebraic eigenvalue problem and thus decreases memory use and CPU time consumption. The errors that affect computed eigenvalues and eigenvectors are due to the truncation in the discretization and to finite precision in the computation of the discretized problem. In this paper we analyze those two errors and the interplay between them. We use as a test case the 2D eigenvalue problem yielded by the computation of inertial modes in a spherical shell. This problem contains many difficulties that make it a very good test case. It turns out that single modes (especially most-damped modes i.e. with high spatial frequency) can be very sensitive to roundoff errors, even when apparently good spectral convergence is achieved. The influence of roundoff errors is analyzed using the spectral portrait technique and by comparison of double precision and extended precision computations. Through the analysis we give practical recipes to control the truncation and roundoff errors on eigenvalues and eigenvectors. Title: Tracking granules on the Sun's surface and reconstructing velocity fields. I. The CST algorithm Authors: Rieutord, M.; Roudier, T.; Roques, S.; Ducottet, C. Bibcode: 2007A&A...471..687R Altcode: 2007arXiv0707.1991R Aims:Determination of horizontal velocity fields on the solar surface is crucial for understanding the dynamics of structures like mesogranulation or supergranulation or simply the distribution of magnetic fields.
Methods: We pursue here the development of a method called CST for coherent structure tracking, which determines the horizontal motion of granules in the field of view.
Results: We first devise a generalization of Strous method for the segmentation of images and show that when segmentation follows the shape of granules more closely, granule tracking is less effective for large granules because of increased sensitivity to granule fragmentation. We then introduce the multi-resolution analysis on the velocity field, based on Daubechies wavelets, which provides a view of this field on different scales. An algorithm for computing the field derivatives, like the horizontal divergence and the vertical vorticity, is also devised. The effects from the lack of data or from terrestrial atmospheric distortion of the images are also briefly discussed. Title: Tracking granules on the Sun's surface and reconstructing velocity fields. II. Error analysis Authors: Tkaczuk, R.; Rieutord, M.; Meunier, N.; Roudier, T. Bibcode: 2007A&A...471..695T Altcode: 2007arXiv0707.1994T Context: The determination of horizontal velocity fields at the solar surface is crucial to understanding the dynamics and magnetism of the convection zone of the sun. These measurements can be done by tracking granules.
Aims: Tracking granules from ground-based observations, however, suffers from the Earth's atmospheric turbulence, which induces image distortion. The focus of this paper is to evaluate the influence of this noise on the maps of velocity fields.
Methods: We use the coherent structure tracking algorithm developed recently and apply it to two independent series of images that contain the same solar signal.
Results: We first show that a k-ω filtering of the times series of images is highly recommended as a pre-processing to decrease the noise, while, in contrast, using destretching should be avoided. We also demonstrate that the lifetime of granules has a strong influence on the error bars of velocities and that a threshold on the lifetime should be imposed to minimize errors. Finally, although solar flow patterns are easily recognizable and image quality is very good, it turns out that a time sampling of two images every 21 s is not frequent enough, since image distortion still pollutes velocity fields at a 30% level on the 2500 km scale, i.e. the scale on which granules start to behave like passive scalars.
Conclusions: The coherent structure tracking algorithm is a useful tool for noise control on the measurement of surface horizontal solar velocity fields when at least two independent series are available. Title: The dynamics of a fully radiative rapidly rotating star Authors: Espinosa Lara, F.; Rieutord, M. Bibcode: 2007astro.ph..2255E Altcode: Recent results from interferometry and asteroseismology require models of rapidly rotating stars that are more and more precise. We describe the basic structure and the hydrodynamics of a fully radiative star as a preliminary step towards more realistic models of rotating stars. We consider a solar mass of perfect gas enclosed in a spherical container. The gas is self-gravitating and rotating, and is the seat of nuclear heating, and heat diffusion is due to radiative diffusion with Kramers type opacities. Equations are solved numerically with spectral methods in two dimensions with a radial Gauss-Lobatto grid and spherical harmonics. We computed the centrifugally flattened structure of such a star: the von Zeipel model, which says that the energy flux is proportional to the local effective gravity is tested. We show that it overestimates the ratio of the polar to the equatorial energy flux by almost a factor 2. We also determine the Brunt-Vaisala frequency distribution and show that outer equatorial regions in a radiative zone are convectively unstable when the rotation is fast enough. We compute the differential rotation and meridional circulation stemming from the baroclinicity of the star and show that, in such radiative zones, equatorial regions rotate faster than polar ones. The surface differential rotation is also shown to reach a universal profile when rotation is slow enough (less than 36% of the breakup one), as long as viscosity and Prandlt number remain small. Title: Modeling rapidly rotating stars Authors: Rieutord, M. Bibcode: 2007astro.ph..2384R Altcode: We review the quest of modeling rapidly rotating stars during the past 40 years and detail the challenges to be taken up by models facing new data from interferometry, seismology, spectroscopy... We then present the progress of the ESTER project aimed at giving a physically self-consistent model for the structure and evolution of rapidly rotating stars. Title: Photospheric flows around a quiescent filament and CALAS first results . Authors: Rondi, S.; Roudier, Th.; Molodij, G.; Bommier, V.; Malherbe, J. M.; Schmieder, B.; Meunier, N.; Rieutord, M.; Beigbeder., F. Bibcode: 2007MmSAI..78..114R Altcode: The horizontal photospheric flows below and around a filament are one of the components in the formation and evolution of filaments. Few studies have been done so far because this requires multiwalength time sequences with high spatial resolution. We present observations obtained in 2004 during the international JOP 178 campaign in which eleven instruments were involved, from space and ground based observatories. Several supergranulation cells are crossing the Polarity Inversion Line (PIL) allowing the transport of magnetic flux through the PIL, in particular the parasitic polarities. Before the filament eruptive phase, parasitic and normal polarities are swept by a continuous diverging horizontal flow located in the filament gap where the disappearance of the filament starts. In the future, observations at high spatial resolution on a large field-of-view would be very useful to study filaments, as they are very large structures. We also present the first images obtained with the use of our new 14 MPixel camera CALAS (CAmera for the LArge Scales of the Solar Surface) (10 arcmin× 6.7 arcmin) . These are the first large-scale and high-resolution images of the solar surface ever made. Title: Velocities and divergences as a function of supergranule size Authors: Meunier, N.; Tkaczuk, R.; Roudier, Th.; Rieutord, M. Bibcode: 2007A&A...461.1141M Altcode: Context: The origin of supergranulation is not understood yet and many scenarios, which range from large-scale deep convection to large-scale instabilities of surface granular flows, are possible.
Aims: We characterize the velocities and divergences in supergranulation cells as a function of their size.
Methods: Using local correlation tracking, we determine the horizontal flow fields from MDI intensity maps and derive the divergences. The smoothed divergences are used to determine the cells for various spatial smoothings, in particular at the supergranular scale.
Results: We find evidence of intermittency in the supergranular range and a correlation between the size of supergranules and the strength of the diverging flow. We also show that the relation between rms velocities and scale (the supergranule radius R) can be represented by a law V_rms∼ R0.66.
Conclusions: . The results issued from our data point towards a scenario where supergranulation is a surface phenomenon of the sun, probably the consequence of a large-scale instability triggered by strong positive correlated rising flows. Title: The Seismology Programme of CoRoT Authors: Michel, E.; Baglin, A.; Auvergne, M.; Catala, C.; Aerts, C.; Alecian, G.; Amado, P.; Appourchaux, T.; Ausseloos, M.; Ballot, J.; Barban, C.; Baudin, F.; Berthomieu, G.; Boumier, P.; Bohm, T.; Briquet, M.; Charpinet, S.; Cunha, M. S.; De Cat, P.; Dupret, M. A.; Fabregat, J.; Floquet, M.; Fremat, Y.; Garrido, R.; Garcia, R. A.; Goupil, M. -J.; Handler, G.; Hubert, A. -M.; Janot-Pacheco, E.; Lambert, P.; Lebreton, Y.; Lignieres, F.; Lochard, J.; Martin-Ruiz, S.; Mathias, P.; Mazumdar, A.; Mittermayer, P.; Montalban, J.; Monteiro, M. J. P. F. G.; Morel, P.; Mosser, B.; Moya, A.; Neiner, C.; Nghiem, P.; Noels, A.; Oehlinger, J.; Poretti, E.; Provost, J.; Renan de Medeiros, J.; De Ridder, J.; Rieutord, M.; Roca-Cortes, T.; Roxburgh, I.; Samadi, R.; Scuflaire, R.; Suarez, J. C.; Theado, S.; Thoul, A.; Toutain, T.; Turck-Chieze, S.; Uytterhoeven, K.; Vauclair, G.; Vauclair, S.; Weiss, W. W.; Zwintz, K. Bibcode: 2006ESASP1306...39M Altcode: 2008arXiv0811.1080M We introduce the main lines and specificities of the CoRoT Seismology Core Programme. The development and consolidation of this programme has been made in the framework of the CoRoT Seismology Working Group. With a few illustrative examples, we show how CoRoT data will help to address various problems associated with present open questions of stellar structure and evolution. Title: The DynaMICS perspective Authors: Turck-Chièze, S.; Schmutz, W.; Thuillier, G.; Jefferies, S.; Pallé; Dewitt, S.; Ballot, J.; Berthomieu, G.; Bonanno, A.; Brun, A. S.; Christensen-Dalsgaard, J.; Corbard, T.; Couvidat, S.; Darwich, A. M.; Dintrans, B.; Domingo, V.; Finsterle, W.; Fossat, E.; Garcia, R. A.; Gelly, B.; Gough, D.; Guzik, J.; Jiménez, A. J.; Jiménez-Reyes, S.; Kosovichev, A.; Lambert, P.; Lefebvre, S.; Lopes, I.; Martic, M.; Mathis, S.; Mathur, S.; Nghiem, P. A. P.; Piau, L.; Provost, J.; Rieutord, M.; Robillot, J. M.; Rogers, T.; Roudier, T.; Roxburgh, I.; Rozelot, J. P.; Straka, C.; Talon, S.; Théado, S.; Thompson, M.; Vauclair, S.; Zahn, J. P. Bibcode: 2006ESASP.624E..24T Altcode: 2006soho...18E..24T No abstract at ADS Title: Acoustic oscillations of rapidly rotating polytropic stars. II. Effects of the Coriolis and centrifugal accelerations Authors: Reese, D.; Lignières, F.; Rieutord, M. Bibcode: 2006A&A...455..621R Altcode: 2006astro.ph..5503R Context.With the launch of space missions devoted to asteroseismology (like COROT), the scientific community will soon have accurate measurements of pulsation frequencies in many rapidly rotating stars.
Aims.The present work focuses on the effects of rotation on pulsations of rapidly rotating stars when both the Coriolis and centrifugal accelerations require a non-perturbative treatment.
Methods.We develop a 2-dimensional spectral numerical approach which allows us to compute acoustic modes in centrifugally distorted polytropes including the full influence of the Coriolis force. This method is validated through comparisons with previous studies, and the results are shown to be highly accurate.
Results.In the frequency range considered and with COROT's accuracy, we establish a domain of validity for perturbative methods, thus showing the need for complete calculations beyond v sin i=50 km s-1 for a R = 2.3 R_⊙, M=1.9 M_⊙ polytropic star. Furthermore, it is shown that the main differences between complete and perturbative calculations come essentially from the centrifugal distortion.
Title: Acoustic oscillations of rapidly rotating polytropic stars. I. Effects of the centrifugal distortion Authors: Lignières, F.; Rieutord, M.; Reese, D. Bibcode: 2006A&A...455..607L Altcode: 2006astro.ph..4312L Aims.A new non-perturbative method to compute accurate oscillation modes in rapidly rotating stars is presented.
Methods.The effect of the centrifugal force is fully taken into account while the Coriolis force is neglected. This assumption is valid when the time scale of the oscillation is much shorter than the inverse of the rotation rate and is expected to be suitable for high radial order p-modes of δ Scuti stars. Axisymmetric p-modes have been computed in uniformly rotating polytropic models of stars.
Results.In the frequency and rotation range considered, we found that as rotation increases (i) the asymptotic structure of the non-rotating frequency spectrum is first destroyed then replaced by a new form of organization (ii) the mode amplitude tends to concentrate near the equator (iii) differences to perturbative methods become significant as soon as the rotation rate exceeds about fifteen percent of the Keplerian limit. The implications for the seismology of rapidly rotating stars are discussed.
Title: Scientific Objectives of the Novel Formation Flying Mission Aspiics Authors: Turck-Chièze, S.; Schmutz, W.; Thuillier, G.; Jefferies, S.; Pallé; Dewitt, S.; Ballot, J.; Berthomieu, G.; Bonanno, A.; Brun, A. S.; Christensen-Dalsgaard, J.; Corbard, T.; Couvidat, S.; Darwich, A. M.; Dintrans, B.; Domingo, V.; Finsterle, W.; Fossat, E.; Garcia, R. A.; Gelly, B.; Gough, D.; Guzik, J.; Jiménez, A. J.; Jiménez-Reyes, S.; Kosovichev, A.; Lambert, P.; Lefebvre, S.; Lopes, I.; Martic, M.; Mathis, S.; Mathur, S.; Nghiem, P. A. P.; Piau, L.; Provost, J.; Rieutord, M.; Robillot, J. M.; Rogers, T.; Roudier, T.; Roxburgh, I.; Rozelot, J. P.; Straka, C.; Talon, S.; Théado, S.; Thompson, M.; Vauclair, S.; Zahn, J. P. Bibcode: 2006ESASP.617E.164L Altcode: 2006soho...17E.164L No abstract at ADS Title: The EUV Variability Experiment (EVE) on the Solar Dynamics Observatory (SDO): Science Plan and Instrument Overview Authors: Turck-Chièze, S.; Schmutz, W.; Thuillier, G.; Jefferies, S.; Pallé; Dewitt, S.; Ballot, J.; Berthomieu, G.; Bonanno, A.; Brun, A. S.; Christensen-Dalsgaard, J.; Corbard, T.; Couvidat, S.; Darwich, A. M.; Dintrans, B.; Domingo, V.; Finsterle, W.; Fossat, E.; Garcia, R. A.; Gelly, B.; Gough, D.; Guzik, J.; Jiménez, A. J.; Jiménez-Reyes, S.; Kosovichev, A.; Lambert, P.; Lefebvre, S.; Lopes, I.; Martic, M.; Mathis, S.; Mathur, S.; Nghiem, P. A. P.; Piau, L.; Provost, J.; Rieutord, M.; Robillot, J. M.; Rogers, T.; Roudier, T.; Roxburgh, I.; Rozelot, J. P.; Straka, C.; Talon, S.; Théado, S.; Thompson, M.; Vauclair, S.; Zahn, J. P. Bibcode: 2006ESASP.617E.165W Altcode: 2006soho...17E.165W No abstract at ADS Title: The Dynamics Project Authors: Turck-Chièze, S.; Schmutz, W.; Thuillier, G.; Jefferies, S.; Pallé; Dewitt, S.; Ballot, J.; Berthomieu, G.; Bonanno, A.; Brun, A. S.; Christensen-Dalsgaard, J.; Corbard, T.; Couvidat, S.; Darwich, A. M.; Dintrans, B.; Domingo, V.; Finsterle, W.; Fossat, E.; Garcia, R. A.; Gelly, B.; Gough, D.; Guzik, J.; Jiménez, A. J.; Jiménez-Reyes, S.; Kosovichev, A.; Lambert, P.; Lefebvre, S.; Lopes, I.; Martic, M.; Mathis, S.; Mathur, S.; Nghiem, P. A. P.; Piau, L.; Provost, J.; Rieutord, M.; Robillot, J. M.; Rogers, T.; Roudier, T.; Roxburgh, I.; Rozelot, J. P.; Straka, C.; Talon, S.; Théado, S.; Thompson, M.; Vauclair, S.; Zahn, J. P. Bibcode: 2006ESASP.617E.162T Altcode: 2006soho...17E.162T No abstract at ADS Title: The dynamics of the radiative envelope of rapidly rotating stars. I. A spherical Boussinesq model Authors: Rieutord, M. Bibcode: 2006A&A...451.1025R Altcode: 2006astro.ph..2040R Context.The observations of rapidly rotating stars are increasingly detailed and precise thanks to interferometry and asteroseismology; two-dimensional models taking into account the hydrodynamics of these stars are very much needed.
Aims.A model to study the dynamics of baroclinic stellar envelopes is presented.
Methods.This model treats the stellar fluid with the Boussinesq approximation and assumes that it is contained in a rigid spherical domain. The temperature field and the rotation of the system generate the baroclinic flow.
Results.We give an analytical solution to the asymptotic problem at small Ekman and Prandtl numbers. We show that, provided the Brunt-Väisälä frequency profile is smooth enough, differential rotation of a stably stratified envelope takes the form a fast rotating pole and a slow equator while it is the opposite in a convective envelope. We also show that at low Prandtl numbers and without μ-barriers, the jump in viscosity at the core-envelope boundary generates a shear layer staying along the tangential cylinder of the core. Its role in mixing processes is discussed.
Conclusions.Such a model provides an interesting tool to investigate the fluid dynamics of rotating stars in particular for the study of the various instabilities affecting baroclinic flows or a dynamo effect. Title: Modeling rapidly rotating stars Authors: Rieutord, M. Bibcode: 2006sf2a.conf..501R Altcode: We review the quest of modeling rapidly rotating stars during the past 40 years and detail the challenges to be taken up by models facing new data from interferometry, seismology, spectroscopy... We then present the progress of the ESTER project aimed at giving a physically self-consistent model for the structure and evolution of rapidly rotating stars. Title: A CMOS Sensor for Solar Observation Authors: Beigbeder, Francis; Rondi, Sylvain; Meunier, Nadège; Rieutord, Michel Bibcode: 2006ASSL..336..123B Altcode: 2006sda..conf..123B No abstract at ADS Title: Preface Authors: Rieutord, M.; Dubrulle, B. Bibcode: 2006EAS....21D...3R Altcode: No abstract at ADS Title: On the dynamics of radiative zones in rotating stars Authors: Rieutord, M. Bibcode: 2006EAS....21..275R Altcode: 2006astro.ph..8431R In this lecture I try to explain the basic dynamical processes at work in a radiative zone of a rotating star. In particular, the notion of baroclinicity is thoroughtly discussed. Attention is specially directed to the case of circulations and the key role of angular momentum conservation is stressed. The specific part played by viscosity is also explained. The old approach of Eddington and Sweet is reviewed and criticized in the light of the seminal papers of Busse (1981) and Zahn (1992). Other examples taken in the recent literature are also presented; finally, I summarize the important points. Title: An introduction to thermal convection Authors: Rieutord, M. Bibcode: 2006EAS....21....5R Altcode: In this lecture I propose a little tour of thermal convection and its applications in astrophysics. The first part of the lecture is devoted to a qualitative introduction to the convective instability using the Schwarzschild criterion; then, concentrating on the equations governing the fluid motions, I introduce the Boussinesq and anelastic approximations which are so often used in these problems. The following part focuses on the Rayleigh-Bénard model which is worked out in detail up to the Landau equation and the Lorenz strange attractor. Finally, I briefly sketch out some results on turbulent convection and end the lecture with the case of stellar convection. Title: Oscillations of rapidly rotating stars Authors: Reese, D.; Lignieres, F.; Rieutord, M. Bibcode: 2006CoAst.147...65R Altcode: The effects of rapid rotation on stellar pulsation is examined using an accurate 2D numerical method. We compare the results of these non-perturbative calculations with those of perturbative methods and find that frequency differences exceed 0.08 muHz on half of the modes when the rotation rate is 15% of the keplerian (break-up) limit. The differences between the two results is mainly attributed to the approximate treatment of the centrifugal force in perturbative methods. We also explore different levels of approximation for the Coriolis force. Title: Acoustic oscillations in centrifugally flattened polytropic star . Authors: Lignières, F.; Rieutord, M.; Reese, D. Bibcode: 2006MmSAI..77..425L Altcode: We present numerical calculations of axisymmetric acoustic modes in polytropic models of star deformed by the centrifugal force. In the range of flatness and frequencies considered, we found that, as flatness increases, (i) differences with perturbative methods becomes rapidly significant (ii) the structure of the spectrum is strongly modified (iii) the mode amplitude at the surface tends to concentrate near the equator. Title: Stellar fluid dynamics and numerical simulations : from the sun to neutron stars Authors: Rieutord, Michel; Dubrulle, Berengere Bibcode: 2006EAS....21.....R Altcode: No abstract at ADS Title: The foundations of fluid dynamics Authors: Rieutord, M. Bibcode: 2006EAS....21....3R Altcode: In this lecture I introduce the basic concepts needed to understand fluid motions at a macroscopic level. Hence, the idea of a continuous medium and its kinematical properties are presented. Then the physical laws governing the motion (mass, momentum and energy equation) are derived and discussed. The concept of rheological law is introduced and illustrated. I end this lecture with a discussion of the boundary conditions that are needed to complete the equations of motion. Title: CALAS, A Camera for the Large-scale of the Solar Surface Authors: Meunier, N.; Rondi, S.; Tkaczuk, R.; Rieutord, M.; Beigbeder, F. Bibcode: 2005ASPC..346...53M Altcode: The origin of supergranulation (convective or not) is still much debated. Among various possible approaches, one way to study supergranulation is to observe the horizontal motions of granules. A combination of a very large field-of-view (in order to see as many supergranules as possible), a very high spatial resolution (to sample granules with a high accuracy, even the small ones) and a high cadence is necessary to study this pattern in detail. We plan to implement a 4k×4k CMOS camera at the Lunette Jean Rösch (previously Coupole Tourelle) at the Pic du Midi Observatory (a 50 cm diameter refractor). The main objective of the camera, CALAS (Camera for the Large Scale of the Solar Surface), is the study of supergranulation. This will allow to sample granules with a high spatial resolution on a 10'×10' field-of-view (∼ 100 supergranules). We present our objectives, the instrumental set-up and organization, and the status of the instrument. Title: The ESTER project Authors: Rieutord, M.; Dintrans, B.; Lignières, F.; Corbard, T.; Pichon, B. Bibcode: 2005sf2a.conf..759R Altcode: The ESTER project aims at building a stellar evolution code in two dimensions of space for the study of effects of rotation. The numerical scheme is based on spectral methods with a spherical harmonic decomposition in the horizontal direction and a Chebyshev polynomial expansion in the vertical direction. Coordinates adapted to the centrifugally distorted shape are mapped to spherical coordinates. First tests on rotating polytropes are presented. Title: Mesoscale flows in large aspect ratio simulations of turbulent compressible convection Authors: Rincon, F.; Lignières, F.; Rieutord, M. Bibcode: 2005A&A...430L..57R Altcode: 2006astro.ph.11843R We present the results of a very large aspect ratio (A=42.6) numerical simulation of fully compressible turbulent convection in a polytropic atmosphere, and focus on the properties of large-scale flows. Mesoscale patterns dominate the turbulent energy spectrum. We show that these structures, which had already been observed in Boussinesq simulations by \cite{cattaneo01}, have a genuine convective origin and do not result directly from collective interactions of the smaller scales of the flow, even though their growth is strongly affected by nonlinear transfers. If this result is relevant to the solar photosphere, it suggests that the dominant convective mode below the Sun's surface may be at mesoscales. Title: Shear Alfvén modes in magnetized spherical shells Authors: Reese, D.; Rincon, F.; Rieutord, M. Bibcode: 2004sf2a.conf..267R Altcode: 2004sf2a.confE.300R An investigation of shear Alfvén waves inside a spherical shell is carried out, in which the background magnetic field is dipolar and resistive effects are taken into account. Numerical results indicate two basic behaviours for both the axisymmetric and non-axisymmetric cases. Poloidal modes appear to remain regular, except for internal shear layers, when kinetic and magnetic diffusivities become arbitrarily small, whereas toroidal modes become singular. Analytical results are provided for the axisymmetric toroidal case. The corresponding eigenvalues also exhibit different behaviours in the two cases. Title: Oscillations of magnetic stars. II. Axisymmetric toroidal and non-axisymmetric shear Alfvén modes in a spherical shell Authors: Reese, D.; Rincon, F.; Rieutord, M. Bibcode: 2004A&A...427..279R Altcode: 2004astro.ph..9120R We carry out numerical and mathematical investigations of shear Alfvén waves inside of a spherical shell filled with an incompressible conducting fluid, and bathed in a strong dipolar magnetic field. We focus on axisymmetric toroidal and non-axisymmetric modes, in continuation of a previous work by Rincon & Rieutord (2003, A&A, 398, 663). Analytical expressions are obtained for toroidal eigenmodes and their corresponding frequencies at low diffusivities. These oscillations behave like magnetic shear layers, in which the magnetic poles play a key role, and hence become singular when diffusivities vanish. It is also demonstrated that non-axisymmetric modes are split into two categories, namely poloidal or toroidal types, following similar asymptotic behaviours as their axisymmetric counterparts when the diffusivities become arbitrarily small.

Appendices are only available in electronic form at http://www.edpsciences.org Title: Evolution of Rotation in Binaries: Physical Processes (Invited Review) Authors: Rieutord, M. Bibcode: 2004IAUS..215..394R Altcode: No abstract at ADS Title: Oscillations of Fast Rotating Stars: p-Modes in Centrifugally Flattened Polytropes Authors: Lignières, F.; Rieutord, M. Bibcode: 2004IAUS..215..414L Altcode: No abstract at ADS Title: Statistical mechanics and phase diagrams of rotating self-gravitating fermions Authors: Chavanis, P. H.; Rieutord, M. Bibcode: 2003A&A...412....1C Altcode: 2003astro.ph..2594C We compute statistical equilibrium states of rotating self-gravitating fermions by maximizing the Fermi-Dirac entropy at fixed mass, energy and angular momentum. We describe the phase transition from a gaseous phase to a condensed phase (corresponding to white dwarfs, neutron stars or fermion balls in dark matter models) as we vary energy and temperature. We increase the rotation up to the Keplerian limit and describe the flattening of the configuration until mass shedding occurs. At the maximum rotation, the system develops a cusp at the equator. We draw the equilibrium phase diagram of the rotating self-gravitating Fermi gas and discuss the structure of the caloric curve as a function of degeneracy parameter (or system size) and angular velocity. We argue that systems described by the Fermi-Dirac distribution in phase space do not bifurcate to non-axisymmetric structures when rotation is increased, in continuity with the case of polytropes with index n>0.808 (the Fermi gas at T=0 corresponds to n=3/2). This differs from the study of Votyakov et al. (\cite{Votyakov2002}) who consider a Fermi-Dirac distribution in configuration space appropriate to stellar formation and find ``double star'' structures (their model at T=0 corresponds to n=0). We also consider the case of classical objects described by the Boltzmann entropy and discuss the influence of rotation on the onset of gravothermal catastrophe (for globular clusters) and isothermal collapse (for molecular clouds). On general grounds, we complete previous investigations concerning the nature of phase transitions in self-gravitating systems. We emphasize the inequivalence of statistical ensembles regarding the formation of binaries (or low-mass condensates) in the microcanonical ensemble (MCE) and Dirac peaks (or massive condensates) in the canonical ensemble (CE). We also describe an hysteretic cycle between the gaseous phase and the condensed phase that are connected by a ``collapse'' or an ``explosion''. Title: Families of fragmenting granules and their relation to meso- and supergranular flow fields Authors: Roudier, Th.; Lignières, F.; Rieutord, M.; Brandt, P. N.; Malherbe, J. M. Bibcode: 2003A&A...409..299R Altcode: 3D analysis (x,y,t) of the granular intensity field (11-hour time sequence from the Swedish Vacuum Solar Telescope on La Palma, Canary Islands), demonstrates that a significant fraction of the granules in the photosphere are organized in the form of ``Trees of Fragmenting Granules" (TFGs). A TFG consists of a family of repeatedly splitting granules, originating from a single granule at its beginning. A striking result is that TFGs can live much longer (up to 8 h) than individual granules (10 min). We find that 62% of the area covered by granules belongs to TFGs of a lifetime >1.5 h. When averaged in time, such long-lived TFGs correspond to coherent diverging flows which may be identified as mesogranules. We also find a correlation between the network and the spatial distribution of TFGs. Title: Evolution of rotation in binaries: physical processes Authors: Rieutord, Michel Bibcode: 2003astro.ph..8313R Altcode: In this review, we describe the physical processes driving the dynamical evolution of binary stars, namely the circularization of the orbit and the synchronization of their spin and orbital rotation. We also discuss the possible role of the elliptic instability which turns out to be an unavoidable ingredient of the evolution of binary stars. Title: Oscillations of magnetic stars: I. Axisymmetric shear Alfvén modes of a spherical shell in a dipolar magnetic field Authors: Rincon, F.; Rieutord, M. Bibcode: 2003A&A...398..663R Altcode: We carry out an investigation of axisymmetric shear Alfvén waves in a spherical layer of an incompressible resistive fluid when a strong dipolar magnetic field is applied. A decomposition on the spherical harmonics base is used to compute the eigenmodes of the system. Numerical results show that the least-damped Alfvénic modes naturally concentrate near the magnetic polar axis. These modes also show internal shear/magnetic layers associated with resonant field lines. This model is useful when modelling planetary cores sustaining a dynamo, magnetic neutron stars or to the magnetic layer of roAp stars. In this latter case, it shows that shear Alfvén waves provide a good instance of non-perturbative effects due to the strong magnetic field of such stars. Title: A Study of Shear Alfvén Waves in Magnetic Stars: the Spherical Shell Model Authors: Rincon, F.; Rieutord, M. Bibcode: 2003aahd.conf..561R Altcode: No abstract at ADS Title: Stability of a compressible fluid layer in a magnetic field: a simple model for supergranulation Authors: Rincon, F.; Rieutord, M. Bibcode: 2003sf2a.conf..103R Altcode: 2003sf2a.confE..33R We investigate the onset of steady Rayleigh-Benard magnetoconvection enclosed between two thermally insulating plates in a polytropic layer of index 1. In a non-magnetic Boussinesq context, such boundary conditions, also called fixed flux conditions, are known to favor an infinite horizontal scale as the first unstable mode. We show that the situation can be very different when compressibility and magnetic field combine, giving birth to a finite horizontal scale in most cases. We explore different regimes and demonstrate in particular that the transition to a non-zero wave number occurs for a Chandrasekhar number Q=394.3 in the Boussinesq limit, while compressibility tends to reduce this critical value. We discuss these results in the context of large scale stellar convection such as supergranulation where fixed flux conditions are physically relevant and for which the effects of magnetic fields and stratification cannot be bypassed. Title: Recurrence of fragmenting granules and their relation to meso- and supergranular flow fields Authors: Roudier, Th.; Lignières, F.; Rieutord, M.; Brandt, P. N.; Malherbe, J. -M. Bibcode: 2003EAS.....9..371R Altcode: The 3D analysis (x, y, t) of the granulation intensity field (11-hour time sequence from Swedish Vacuum Solar Telescope on La Palma, Canary Islands), demonstrated that the granules in the phostosphere are organized in ``Trees of Fragmenting Granules" (TFGs). A TFG consists of a family of repeatedly splitting granules, issued from one granule at its beginning. A striking result is that TFGs can live much longer (up to 8h10) than individual granules (10 mn). When averaged in time, such long-lived TFGs can be identified to the mesogranules. We also found a correlation between the network and the spatial distribution of TFGs. Title: CALAS: a CAmera for the LArge Scales of the solar surface Authors: Meunier, N.; Rieutord, M.; Beigbeder, F. Bibcode: 2003sf2a.conf...93M Altcode: 2003sf2a.confE..29M Supergranulation is constituted of cells of horizontal outflows with a typical size of 30000 km at the surface of the Sun. The origin of this pattern (convection or not) is still controversial. Usually observed using Doppler shifts at the photospheric level, it can also be studied using horizontal motions of solar granules. A combination of a large field of view (containing as many supergranules as possible) and a high spatial resolution (to sample granules with a high accuracy, even the small ones) is then necessary to study this process in more details. Our project is to implement a large scale CMOS camera, CALAS (CAmera for the LArge Scales of the solar surface) at the Coupole Tourelle at the Pic du Midi. The field of view will be 10'x10', allowing to sample 100 hundred supergranules. We will present the scientific objectives and the organisation of our project. Title: The oscillations of rapidly rotating stars Authors: Rieutord, Michel Bibcode: 2003safd.book...99R Altcode: We review the effects of rotation on the oscillation spectrum of rapidly rotating stars. We particularly stress the novelties introduced by rotation: for instance, the disappearance of modes in the low frequency band due to the ill-posed natured of the underlying mathematical problem. This is mainly an effect of the Coriolis acceleration. The centrifugal effect changes the shape of the star in the first place. The possible consequences of this deformation on the oscillation spectrum are briefly analyzed. We also describe other possibly important effects of the centrifugal acceleration which come about on the time scale of star evolution. Title: More concerning the anelastic and subseismic approximations for low-frequency modes in stars Authors: Rieutord, Michel; Dintrans, Boris Bibcode: 2002MNRAS.337.1087R Altcode: 2002astro.ph..6357R Two approximations, namely the subseismic approximation and the anelastic approximation, are used to filter out the acoustic modes when computing low-frequency modes of a star (gravity modes or inertial modes). In a previous paper, we observed that the anelastic approximation gave eigenfrequencies much closer to the exact ones than the subseismic approximation. Here, we try to clarify this behaviour and show that it is a result of the different physical approach taken by each approximation. On the one hand, the subseismic approximation considers the low-frequency part of the spectrum of (say) gravity modes and turns out to be valid only in the central region of a star; on the other hand, the anelastic approximation considers the Brunt-Väisälä frequency to be asymptotically small and makes no assumption concerning the order of the modes. Both approximations fail to describe the modes in the surface layers but eigenmodes issued from the anelastic approximation are closer to those including acoustic effects than their subseismic equivalent. We conclude that, as far as stellar eigenvalue problems are concerned, the anelastic approximation is better suited for simplifying the eigenvalue problem when low-frequency modes of a star are considered, while the subseismic approximation is a useful concept when analytic solutions of high-order low-frequency modes are needed in the central region of a star. Title: Adiabatic oscillations of non-rotating superfluid neutron stars Authors: Prix, R.; Rieutord, M. Bibcode: 2002A&A...393..949P Altcode: 2002astro.ph..4520P We present results concerning the linear (radial and non-radial) oscillations of non-rotating superfluid neutron stars in Newtonian physics. We use a simple two-fluid model to describe the superfluid neutron star, where one fluid consists of the superfluid neutrons, while the second fluid contains all the remaining constituents (protons, electrons). The two fluids are assumed to be ``free'' in the sense of absence of vortex-mediated forces like mutual friction or pinning, but they can be coupled by the equation of state, in particular by entrainment. We calculate numerically the eigen-frequencies and -modes of adiabatic oscillations, neglecting beta-reactions that would lead to dissipation. We find a doubling of all acoustic-type modes (f-modes, p-modes), and confirm the absence of g-modes in these superfluid models. We show analytically and numerically that only in the case of non-stratified background models (i.e. with no composition gradient) can these acoustic modes be separated into two distinct families, which are characterized by either co- or counter-moving fluids respectively, and which are sometimes referred to as ``ordinary'' and ``superfluid'' modes. In the general, stratified case, however, this separation is not possible, and these acoustic modes can not be classified as being either purely ``ordinary'' or ``superfluid''. We show how the properties of the two-fluid modes change as functions of the coupling by entrainment. We find avoided mode-crossings for the stratified models, while the crossings are not avoided in the non-stratified, separable case. The oscillations of normal-fluid neutron stars are recovered as a special case simply by locking the two fluids together. In this effective one-fluid case we find the usual singlet f- and p-modes, and we also find the expected g-modes of stratified neutron star models. Title: A simulation of solar convection at supergranulation scale Authors: Rieutord, M.; Ludwig, H. -G.; Roudier, T.; Nordlund, .; Stein, R. Bibcode: 2002NCimC..25..523R Altcode: 2001astro.ph.10208R We present here numerical simulations of surface solar convection which cover a box of 30$\times30\times$3.2 Mm$^3$ with a resolution of 315$\times315\times$82, which is used to investigate the dynamics of scales larger than granulation. No structure resembling supergranulation is present; possibly higher Reynolds numbers (i.e. higher numerical resolution), or magnetic fields, or greater depth are necessary. The results also show interesting aspects of granular dynamics which are briefly presented, like extensive p-mode ridges in the k-$\omega$ diagram and a ringlike distribution of horizontal vorticity around granules. At large scales, the horizontal velocity is much larger than the vertical velocity and the vertical motion is dominated by p-mode oscillations. Title: Slichter modes of the Earth revisited Authors: Rieutord, Michel Bibcode: 2002PEPI..131..269R Altcode: Using the simple model of a spherical solid inner core oscillating in a rotating liquid outer core, we compute the frequencies of the Slichter modes of the earth. The fluid is assumed neutrally stratified (but with a radially varying density) and viscous, viscosity being taken into account non-perturbatively. The parameters are those given by earth models like PREM, 1066A or CORE11. The computed resonant frequencies are compared to those observed by Courtier et al. (2000) and claimed to be the Slichter frequencies. We show that our model cannot reproduce these frequencies and that previous models which did reproduce them are not consistent with the observed quality factors of the resonances. Title: Photospheric flows measured with TRACE Authors: Krijger, J. M.; Roudier, T.; Rieutord, M. Bibcode: 2002A&A...387..672K Altcode: We analyse white-light image sequences taken with the Transition Region and Coronal Explorer (TRACE) using an optimised local correlation tracking (LCT) method to measure the horizontal flows in the quiet solar photosphere with high spatial (1 arcsec) and temporal (5 min) resolution. Simultaneously taken near-ultraviolet images from TRACE confirm that our LCT-determined flows recover the actual supergranulation pattern, thus proving that the topology of the horizontal flow distribution and network assembly may be studied from long-duration TRACE white-light sequences with our method. Title: On the Theory of Oscillations of Rapidly Rotating Stars Authors: Rieutord, M.; Lignières, F. Bibcode: 2002ASPC..259..190R Altcode: 2002rnpp.conf..190R; 2002IAUCo.185..190R No abstract at ADS Title: A Comparison of the Anelastic and Subseismic Approximations for Low-Frequency Stellar Oscillations: an Application to Rapidly Rotating Stars Authors: Dintrans, B.; Rieutord, M. Bibcode: 2002ASPC..259..186D Altcode: 2002IAUCo.185..186D; 2002rnpp.conf..186D; 2001astro.ph.11446D After showing that the anelastic approximation is better than the subseismic one to filter out acoustic waves when studying low-frequency stellar oscillations, we compute gravito-inertial modes of a typical Gamma-Doradus star using this approximation. We show that eigenmodes can be regular or singular, according to the possible focusing towards attractors of the underlying characteristics. Consequences on the oscillations spectrum are then discussed. Title: Are granules good tracers of solar surface velocity fields? Authors: Rieutord, M.; Roudier, T.; Ludwig, H. -G.; Nordlund, Å.; Stein, R. Bibcode: 2001A&A...377L..14R Altcode: 2001astro.ph..8284R Using a numerical simulation of compressible convection with radiative transfer mimicking the solar photosphere, we compare the velocity field derived from granule motions to the actual velocity field of the plasma. We thus test the idea that granules may be used to trace large-scale velocity fields at the sun's surface. Our results show that this is indeed the case provided the scale separation is sufficient. We thus estimate that neither velocity fields at scales less than 2500 km nor time evolution at scales shorter than 0.5 hr can be faithfully described by granules. At larger scales the granular motions correlate linearly with the underlying fluid motions with a slope of ≲2 reaching correlation coefficients up to ~ 0.9. Title: Erratum: Ekman Layers and the Damping of Inertial r-Modes in a Spherical Shell: Application to Neutron Stars Authors: Rieutord, Michel Bibcode: 2001ApJ...557..493R Altcode: In the paper ``Ekman Layers and the Damping of Inertial r-Modes in a Spherical Shell: Application to Neutron Stars'' by Michel Rieutord (ApJ, 550, 443 [2001]), Figure 2 was erroneously reproduced as Figure 1. The correct Figure 1 appears below. The Press sincerely regrets this error. Title: A comparison of the anelastic and subseismic approximations for low-frequency gravity modes in stars Authors: Dintrans, B.; Rieutord, M. Bibcode: 2001MNRAS.324..635D Altcode: 2000astro.ph.11273D A comparative study of the properties of the anelastic and subseismic approximations is presented. The anelastic approximation is commonly used in astrophysics in compressible convection studies, whereas the subseismic approximation comes from geophysics where it is used to describe long-period seismic oscillations propagating in the Earth's outer fluid core. Both approximations aim to filter out the acoustic waves while retaining the density variations of the equilibrium configuration. However, they disagree on the form of the equation of mass conservation. We show here that the anelastic approximation is in fact the only consistent approximation as far as stellar low-frequency oscillations are concerned. We also show that this approximation implies Cowling's approximation which neglects perturbations of the gravity field. Examples are given to demonstrate the efficiency of the anelastic approximation. Title: Acoustic modes in spheroidal cavities Authors: Lignières, Francois; Rieutord, M.; Valdettaro, L. Bibcode: 2001sf2a.conf..127L Altcode: 2001astro.ph.10214L The calculation of the oscillation modes of a star in fast rotation has not yet been carried out with precision, the effect of rotation has been considered only by means of perturbation developpements. We develop a numerical method able to fully take into account the deformation of the star by the centrifugal force and, in a first step, we have determined the acoustic modes of an ellipsoid of uniform density and studied the effect of the ellipticity on these modes. The consequences of these first results for the seismology of stars in fast rotation as the delta Scuti delta will be discussed. Title: Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum Authors: Rieutord, M.; Georgeot, B.; Valdettaro, L. Bibcode: 2001JFM...435..103R Altcode: 2000physics...7007R We investigate the asymptotic properties of inertial modes confined in a spherical shell when viscosity tends to zero. We first consider the mapping made by the characteristics of the hyperbolic equation (Poincaré's equation) satisfied by inviscid solutions. Characteristics are straight lines in a meridional section of the shell, and the mapping shows that, generically, these lines converge towards a periodic orbit which acts like an attractor (the associated Lyapunov exponent is always negative or zero). We show that these attractors exist in bands of frequencies the size of which decreases with the number of reflection points of the attractor. At the bounding frequencies the associated Lyapunov exponent is generically either zero or minus infinity. We further show that for a given frequency the number of coexisting attractors is finite. Title: Ekman Layers and the Damping of Inertial R-Modes in a Spherical Shell: Application to Neutron Stars Authors: Rieutord, Michel Bibcode: 2001ApJ...550..443R Altcode: 2000astro.ph..3171R Recently, eigenmodes of rotating fluids, namely, inertial modes, have received much attention in relation to their destabilization when coupled to gravitational radiation within neutron stars. However, these modes have been known for a long time in fluid dynamics. We give a short account of their history and review our present understanding of their properties. Considering the case of a spherical container, we then give the exact solution of the boundary (Ekman) layer flow associated with inertial r-modes and show that previous estimations all underestimated the dissipation by these layers. We also show that the presence of an inner core has little influence on this dissipation. As a conclusion, we compute the window of instability in the temperature/rotation plane for a crusted neutron star when it is modeled by an incompressible fluid. Title: Temporal height properties of the exploding granules Authors: Roudier, Th.; Eibe, M. T.; Malherbe, J. M.; Rieutord, M.; Mein, P.; Mein, N.; Faurobert, M. Bibcode: 2001A&A...368..652R Altcode: Based on time series of 2D MSDP spectrograms, taken at the Turret Dome in Pic du Midi, we present the temporal evolution of exploding granules in intensity and Doppler velocity through the solar photosphere. We describe the penetration of exploding granules in the solar photosphere during their lifes and the related phenomena like the ``Bright Plumes'' located in the downflowing plasma just on the edge of the granule. We suggest a possible scenario of the exploding granule evolution in the solar photosphere. Title: Wave Attractors in Rotating Fluids: A Paradigm for Ill-Posed Cauchy Problems Authors: Rieutord, M.; Georgeot, B.; Valdettaro, L. Bibcode: 2000PhRvL..85.4277R Altcode: 2000physics..11031R In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincaré equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behavior of the eigenmodes and eigenspectrum in the physically relevant régime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields. Title: On mesogranulation, network formation and supergranulation Authors: Rieutord, M.; Roudier, T.; Malherbe, J. M.; Rincon, F. Bibcode: 2000A&A...357.1063R Altcode: We present arguments which show that in all likelihood mesogranulation is not a true scale of solar convection but the combination of the effects of both highly energetic granules, which give birth to strong positive divergences (SPDs) among which we find exploders, and averaging effects of data processing. The important role played by SPDs in horizontal velocity fields appears in the spectra of these fields where the scale ~ 4 Mm is most energetic; we illustrate the effect of averaging with a one-dimensional toy model which shows how two independent non-moving (but evolving) structures can be transformed into a single moving structure when time and space resolution are degraded. The role of SPDs in the formation of the photospheric network is shown by computing the advection of floating corks by the granular flow. The coincidence of the network bright points distribution and that of the corks is remarkable. We conclude with the possibility that supergranulation is not a proper scale of convection but the result of a large-scale instability of the granular flow, which manifests itself through a correlation of the flows generated by SPDs. Title: Oscillations of a rotating star: a non-perturbative theory Authors: Dintrans, Boris; Rieutord, Michel Bibcode: 2000A&A...354...86D Altcode: Nonradial gravity modes of a 1.5 Mscriptstyleun rotating ZAMS star are investigated using the anelastic approximation. Formulating the oscillation equations as a generalized eigenvalue problem, we first show that the usual second-order perturbative theory reaches its limits for rotation periods of about three days. Studying the rapid rotation régime, we develop a geometric formalism based on the integration of the characteristics of the governing mixed-type operator. These characteristics propagate in the star interior and the resulting web can be either ergodic (the web fills the whole domain) or periodic (the web reduces to an attractor along which characteristics focus). We further show the deep relation existing between the orbits of characteristics and the corresponding eigenmodes: {(i)} with ergodic orbits are associated regular eigenmodes which are similar to the usual gravity modes; {(ii)} with periodic orbits are associated singular eigenmodes for which the velocity diverges along the attractor. If diffusivity is taken into account, this singularity turns into internal shear layers tracing the attractor. As a consequence, the classical organization of eigenvalues along families with fixed (l,n) disappears and leaves the place to an intricate low-frequency spectrum. Title: Oscillations of Rapidly Rotating Stars Authors: Dintrans, B.; Rieutord, M. Bibcode: 2000ASPC..203..373D Altcode: 2001astro.ph.11453D; 2000IAUCo.176..373D; 2000ilss.conf..373D We present numerical simulations of gravito-inertial waves propagating in radiative zones of rapidly rotating stars. A first model, using the Boussinesq approximation, allows us to study the oscillations of a quasi-incompressible stratified fluid embedded in a rapidly rotating sphere or spherical shell. In a second step, we investigate the case of a γ Doradus-type star using the anelastic approximation. Some fascinating features of rapidly rotating fluids, such as wave attractors, appear in both cases. Title: A note on inertial modes in the core of the Earth Authors: Rieutord, Michel Bibcode: 2000PEPI..117...63R Altcode: We analyse the consequences of the singular (at zero viscosity) nature of inertial modes in a spherical shell for the dynamics of the Earth's liquid core on the time scale of a day. We show that the singularities, essentially appearing as internal shear layers, although increasing the damping rates of the modes, cannot be invoked to rule out the possible role of the elliptical instability in the geodynamo. We also show that the search for core modes in the spectrum of oscillations of the Earth should be guided by the Lyapunov exponents associated with the maps built up by characteristics propagating in the shell. Title: Determination of horizontal velocity fields at the sun's surface with high spatial and temporal resolution Authors: Roudier, Th.; Rieutord, M.; Malherbe, J. M.; Vigneau, J. Bibcode: 1999A&A...349..301R Altcode: We analyse the two algorithms which have been used in the past few years to determine the horizontal flow fields at the Sun's surface, namely the Local Correlation Tracking (LCT) of L. November and the Feature Tracking of L. Strous. Analysing the systematic errors introduced by LCT, we show that these errors come from the averaging processes. More precisely, they arise from the interpolating step of the algorithm: granules' motions determine the flow on an irregular grid which is then interpolated to derive quantities such as horizontal divergence or vertical vorticity. Interpolation is therefore a crucial step since mesoscale structures have mainly been studied through divergences and vorticities. We conclude that a reliable algorithm should be based on the tracking of coherent structures, like granules, since they are representative of the fluid motion, and should contain an interpolator which keeps track of the errors introduced either by location of the data (the shape of the irregular grid) or by the noise in the data. Title: Internal intermittency on the Sun surface? Authors: Roudier, T.; Rieutord, M.; Malherbe, J. M.; Vigneau, J. Bibcode: 1999joso.proc..197R Altcode: An improved version of LCT and FT is presented and used to determine high spatial and temporal resolution horizontal flow fields at the Sun's surface. The granule diplacements and group evolution can be followed. The horizontal flow fields calculated by these methods show a structured flow at mean scale (4 to 8 arcsec) by a group of granules which is probably related to the local intermittency. Title: Ekman Pumping and Tidal Dissipation in Close Binaries: A Refutation of Tassoul's Mechanism Authors: Rieutord, Michel; Zahn, Jean-Paul Bibcode: 1997ApJ...474..760R Altcode: We show that the existence of an Ekman boundary layer does not enhance the tidal dissipation in a close binary star because the tides do not exert a stress on the stellar surface. The synchronization timescale is of order (ɛT)-2tadj, where tadj is the (global) viscous damping time and ɛT is the tidal deformation caused by the companion (Darwin 1879; Zahn 1966; Scharlemann 1982; Rieutord & Bonazzola 1987). We thus refute the claim made by Tassoul (1987), who thought to have found a very efficient mechanism for the synchronization and circularization of binary systems. We analyze the paper by Tassoul & Tassoul (1992b) and prove that the alleged magnitude of their Ekman pumping is due to an improper treatment of the surface boundary conditions. Their mechanism would have dramatic, yet unverified consequences, as illustrated by two examples of tidal interaction: between Io and Jupiter, and in the newly discovered planetary system 51 Peg. Title: On the internal dynamics of turbulent plumes in the context of stellar convection. Authors: Bonin, P.; Rieutord, M. Bibcode: 1996A&A...310..221B Altcode: We investigate in some details the modeling of turbulent plumes which have been proposed by Rieutord and Zahn to represent the downflows in a stellar convective zone. We show in particular the limits of Taylor's hypothesis about turbulent entrainment and emphasize its connection with the flow's self-similarity. The role of the dissipation is shown to be important in the choice of the final asymptotic regime. This is illustrated by a paradox which is solved when dissipation is correctly taken into account. It is concluded that in stellar conditions, the lack of self-similarity implies the replacement of Taylor's hypothesis by a proper closure of the mean-field equations in order to obtain a reliable prediction on the large-scale dynamics. Title: Magnetic structures in a dynamo simulation Authors: Brandenburg, A.; Jennings, R. L.; Nordlund, Å.; Rieutord, M.; Stein, R. F.; Tuominen, I. Bibcode: 1996JFM...306..325B Altcode: We use three-dimensional simulations to study compressible convection in a rotating frame with magnetic fields and overshoot into surrounding stable layers. The, initially weak, magnetic field is amplified and maintained by dynamo action and becomes organized into flux tubes that are wrapped around vortex tubes. We also observe vortex buoyancy which causes upward flows in the cores of extended downdraughts. An analysis of the angles between various vector fields shows that there is a tendency for the magnetic field to be parallel or antiparallel to the vorticity vector, especially when the magnetic field is strong. The magnetic energy spectrum has a short inertial range with a slope compatible with k(+1/3) during the early growth phase of the dynamo. During the saturated state the slope is compatible with k(-1). A simple analysis based on various characteristic timescales and energy transfer rates highlights important qualitative ideas regarding the energy budget of hydromagnetic dynamos. Title: Turbulent plumes in stellar convective envelopes. Authors: Rieutord, M.; Zahn, J. -P. Bibcode: 1995A&A...296..127R Altcode: Recent numerical simulations of compressible convection in a stratified medium suggest that strong downwards directed flows may play an important role in stellar convective envelopes, both in the dynamics and in the energy transport. We transpose this idea to stellar convective envelopes by assuming that these plumes are turbulent plumes which may be described by Taylor's entrainment hypothesis, whose validity is well established in various geophysical conditions. We consider first the ideal case of turbulent plumes occurring in an isentropic atmosphere, and ignore all types of feedback. Thereafter we include the effect of the backflow generated by the plumes, and take into account the contribution of the radiative flux. The main result is that plumes originating from the upper layers of a star are able to reach the base of its convective envelope. Their number is necessarily limited because of their conical shape; the backflow further reduces their number to a maximum of about 1000. In these plumes the flux of kinetic energy is directed downwards, but it is less than the upwards directed enthalpy flux, so that the plumes always carry a net energy flux towards the surface. Our plume model is not applicable near the surface, where the departures from adiabaticity become important due to radiative leaking; therefore it cannot predict the depth of the convection zone, which is determined mainly by the transition from the radiative regime above to the nearly adiabatic conditions below. Neither does it permit to evaluate the extent of penetration, which strongly depends on the (unknown) number of plumes. We conclude that, to be complete, a phenomenological model of stellar convection must have a dual character: it should include both the advective transport through diving plumes, which is outlined in this paper, and the turbulent diffusion achieved by the interstitial medium. Only the latter process is apprehended by the familiar mixing-length treatment. Title: Turbulent Jets: Reichardt's Inductive Theory and Intermittency Corrections Authors: Bonin, P.; Rieutord, M. Bibcode: 1995LNP...462..165B Altcode: 1995ssst.conf..165B We investigate the so-called inductive closure relation given by Reichardt for mean turbulent momentum transport in jets (1941). It is shown to be in good agreement with measurements in the axisymmetric jet by Panchapakesan and Lumley (1993). Despite these results, it is conjectured that there is a lack of account for intermittency effects which is hidden by the experimental procedure of Panchapakesan and Lumley. Intermittency corrections are then proposed, based on the classical concept of intermittency factor and the corrected model is compared with the results of Bradbury (1965) for the plane jet. The agreement with experimental measurements appears to be very good. The underlying picture of the Reichardt 1941 model is discussed, mainly the fact that it expresses the self-injection of kinetic energy by the jet and the conversion of longitudinal into lateral momentum thus providing entrainment of the surrounding fluid. Title: Inertial modes in the liquid core of the Earth Authors: Rieutord, Michel Bibcode: 1995PEPI...91...41R Altcode: Using the simple model of an incompressible fluid, we have computed the eigenfrequencies of the lowest-order inertial modes (azimuthal wavenumber m = 0,1,2) in a spherical shell with the same aspect ratio as the liquid core of the Earth. The computed eigenfunctions show that all inertial modes have strong oscillating shear layers. For the very low Ekman number appropriate to the core, these layers might be the origin of some small-scale turbulence through shear instabilities. We have also studied the effect of a thin stable layer lying just below the core-mantle boundary, with the remainder of the core being neutrally stratified, as suggested by recent work. For plausible Nusselt numbers (0.8-0.9), the frequencies of the large-scale modes are only slightly increased (at best by 10 -4). Title: Reynolds stresses and differential rotation in Boussinesq convection in a rotating spherical shell. Authors: Rieutord, Michel; Brandenburg, Axel; Mangeney, Andre; Drossart, Pierre Bibcode: 1994A&A...286..471R Altcode: We consider the problem of how numerical simulations of convection in a spherical shell can be used to estimate turbulent transport coefficients that may be used in mean field theory. For this purpose we analyse data from simulations of three dimensional Boussinesq convection. The rotational influence on convection is described in terms of the {LAMBDA}-effect and anisotropic eddy conductivity. When the resulting transport coefficients are used in a mean field model, the original rotation law is recovered approximately. We thus conclude that the flow can be described in terms of a {LAMBDA}-effect. Our results are also compared with analytical theories and observations. Title: Does solar differential rotation ARISE from a large scale instability?. Authors: Tuominen, Ilkka; Brandenburg, Axel; Moss, David; Rieutord, Michel Bibcode: 1994A&A...284..259T Altcode: The suggestion by several authors that the solar differential rotation is caused by a large scale instability of the basic convective state is examined. We find that the proposed mean-field models are unstable to a Rayleigh-Benard type instability, but argue that this cannot explain the differential rotation of the Sun, because such a flow would become nonaxisymmetric. We discuss the applicability of the mean-field equations to the problem. hydrodynamics - Sun: rotation Title: Non linear stability of slender accretion disks by bifurcation method Authors: Dubrulle, B.; Chomaz, J. M.; Kumar, S.; Rieutord, M. Bibcode: 1993GApFD..70..235D Altcode: The nonlinear evolution of a constant angular momentum accretion disk subject to Papaloizou and Pringle (1984; hereafter PP) instability is investigated. The analysis is performed on an inviscid incompressible two-dimensional model using a formalism suitable for Hamiltonian systems. Only the most unstable modes are taken into account. It is found that relevant nonlinear terms have a stabilizing influence on the system. This supports recent numerical experiments showing a transition towards a quasi-stable planet configuration. The extension of the method to fat disk instabilities, more relevant to AGN disks, is discussed. Title: Coherent Structures and the Differential Rotation of the Sun Authors: Rieutord, M. Bibcode: 1993ASPC...42...65R Altcode: 1993gong.conf...65R No abstract at ADS Title: Ekman circulation and the synchronization of binary stars Authors: Rieutord, M. Bibcode: 1992A&A...259..581R Altcode: We show that large-scale flows driven by Ekman pumping in the spin-up/down of a tidally distorted star is not efficient enough to reduce the synchronization time. This latter time remains of the order of the viscous time, if the star is made of an incompressible viscous fluid. The computation of the synchronization time scale of early-type binaries should follow the approach proposed by Zahn and recently improved by Rocca, and Goldreich and Nicholson. Title: Dynamo Action in Stratified Convection with Overshoot Authors: Nordlund, Ake; Brandenburg, Axel; Jennings, Richard L.; Rieutord, Michel; Ruokolainen, Juha; Stein, Robert F.; Tuominen, Ilkka Bibcode: 1992ApJ...392..647N Altcode: Results are presented from direct simulations of turbulent compressible hydromagnetic convection above a stable overshoot layer. Spontaneous dynamo action occurs followed by saturation, with most of the generated magnetic field appearing as coherent flux tubes in the vicinity of strong downdrafts, where both the generation and destruction of magnetic field is most vigorous. Whether or not this field is amplified depends on the sizes of the magnetic Reynolds and magnetic Prandtl numbers. Joule dissipation is balanced mainly by the work done against the magnetic curvature force. It is this curvature force which is also responsible for the saturation of the dynamo. Title: Ekman layers and tidal synchronization of binary stars. Authors: Rieutord, M. Bibcode: 1992btsf.work..229R Altcode: 1992bats.proc..229R No abstract at ADS Title: Linear theory of rotating fluids using spherical harmonics part II, time-periodic flows Authors: Rieutord, Michel Bibcode: 1991GApFD..59..185R Altcode: Expansion in spherical harmonics is used to solve linear equations of flows of homogeneous viscous fluids in a rotating frame. For a truncated series, analytical solutions are obtained for the radial functions. These solutions are used to investigate the modal properties of a viscous incompressible fluid in a spherical shell. The results are compared to the experimental data of Aldridge. The problem of identification of inertial modes in the Earth's outer core is also discussed. Title: αΛ-dynamos Authors: Brandenburg, A.; Moss, D.; Rieutord, M.; Rüdiger, G.; Tuominen, I. Bibcode: 1991LNP...380..147B Altcode: 1991sacs.coll..147B; 1991IAUCo.130..147B In contrast to -dynamos, where the angular velocity is arbitrarily prescribed, we consider here -dynamos, for which the differential rotation and meridional circulation are solutions of the momentum equation. The non-diffusive parts of the Reynolds stress tensor are parameterized by the -effect. In earlier investigations we have shown that the turbulent magnetic diffusivity has to be much smaller than the eddy viscosity, otherwise the dynamo is not oscillatory or else the contours of constant angular velocity are cylindrical, contrary to observations. In the present paper we investigate the effects of compressibility. Title: Large scale convection in stars : Towards a model for the action of coherent structures Authors: Rieutord, Michel; Zahn, Jean-Paul Bibcode: 1991LNP...380...33R Altcode: 1991sacs.coll...33R; 1991IAUCo.130...33R We show that, representing the descending fluid in a convection zone by a porous medium, the differential rotation of the (rising) fluid is very close to that in an axisymmetric model of the convection zone with anisotropic viscosity Title: Tidal heating in close binary stellar systems Authors: Rieutord, Michel; Bonazzola, Silvano Bibcode: 1987MNRAS.227..295R Altcode: The present consideration of tidal heating in a close binary system's low-mass star due to the conjugate effect of angular momentum loss and tidal action, with attention to the flow within the secondary, notes in the case of cataclismic binaries that viscous dissipation is at most one-thousandth of the nuclear luminosity of a star, thereby confirming by a more exact model the results of Verbunt and Hut (1981). It is shown, however, that the dissipation is very sensitive to the turbulent viscosity of the secondary's envelope. Attention is also given to the case of very close pairs of white dwarfs, which may dissipate a power as great as 10 to the 38th erg/sec if they reach synchronization, but whose detection will be very difficult. Title: Contribution à l'étude de l'évolution des étoiles doubles serrées : étude du spin-up par effet de marée Title: Contribution à l'étude de l'évolution des étoiles doubles serrées : étude du spin-up par effet de marée Title: Contribution to the study of the evolution of close binary stars: study of the spin-up by tidal effect; Authors: Rieutord, Michel Bibcode: 1987PhDT.......152R Altcode: No abstract at ADS Title: Linear theory of rotating fluids using spherical harmonics part I: Steady flows Authors: Rieutord, Michel Bibcode: 1987GApFD..39..163R Altcode: It is shown that a systematic development of physical quantities using spherical harmonics provides analytical solutions to a whole class of linear problems of rotating fluids. These solutions are regular throughout the whole domain of the fluid and are not much affected by the equatorial singularity of steady boundary layers in spherical geometries. A comparison between this method and the one based on boundary layer theory is carried out in the case of the steady spin-up of a fluid inside a sphere.