arXiv subjects

M. Rieutord

Publications and source records attributed to M. Rieutord.

At least 19 recordsLinked to original sources

arXiv2026

Phase-space averaging for stellar convection I. Liouvillian dynamics

Convection remains one of the main uncertain links between multidimensional hydrodynamics and one-dimensional stellar evolution. In particular, transition regions such as near-surface layers or convective boundaries require mean-field descriptions that remain connected to the underlying dynamics rather than to a prescribed mixing length. We describe the flow as a distribution of mesoscopic fluid particles in position-velocity space. A conservation law for this distribution defines the average and yields the Reynolds-Favre mean-field equations as velocity-space moments. Under standard interior conditions, the same dynamics can be written in Liouvillian form, which extends the Hamiltonian structure to stratified and dissipative media. The Liouvillian formulation identifies the phase-space divergence, $\{s, T\}$, as a local measure of contraction or expansion of nearby trajectories. In the quasi-adiabatic limit, its sign reduces to the classical Schwarzschild stability criterion. Away from this limit, the diagnostic remains velocity-resolved and can distinguish different parts of the convective population within the same layer, for example in surface and penetration regions. Appendices show how rotation, magnetic fields, and composition changes can be incorporated through modifications of the phase-space structure. Phase-space averaging provides a dynamically grounded route from hydrodynamics to mean-field stellar convection equations. It also supplies a local trajectory-based stability diagnostic and a natural starting point for the maximum-entropy closures constructed in the companion paper.

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arXiv2026

White paper on the relevance of the European Solar Telescope (EST) for the French heliophysics

The project of the European Solar Telescope aims to provide a state-of-the art infrastructure to study the Sun and its interactions with Earth and the heliosphere. This 4.2m aperture telescope will be equipped with multi conjugate adaptive optics, light-polarisation analyser, imaging spectrograph and integral field unit spectrographs. It will provide unprecedented observations of the solar photosphere and chromosphere and of the dynamical events and features that pertains to the low solar atmosphere. The EST project is presently in a phase of crystallisation, aiming at the creation of an European Research Infrastructure Consortium. While the French community has continuously been associated with the development of the EST project, some specific scientific aspects are more particularly relevant for the French astrophysics and heliophysics communities. The present review highlights the scientific research axes of high interest from the French community that shall strongly benefit from EST. The later will not only advance numerous topics of solar physics, as well as solar adaptive optics developments, but will also provide unrivaled datasets of high interest in the framework of space weather. This review also aims to highlight the space weather use that can be done with future EST observations, that will be particularly relevant for French heliophysicists.

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arXiv2026

Phase-space averaging for stellar convection II. Maximum-entropy closures for mixed radiative-convective envelopes

Surface convection in cool stars sets the entropy jump between the atmosphere and the deep convective envelope, and therefore affects the radius and structure of one-dimensional stellar models. In standard local treatments, this entropy jump is controlled through an effective convective efficiency. We develop a phase-space closure that relates the mean stratification to the local distribution of entropy and velocity among convective elements. Our aim is to describe how the surface entropy transition emerges from the statistics of these elements, rather than prescribing it directly. We first construct a maximum-entropy model for the convective bulk, assuming that the realised states are bounded by a deep entropy level $S$. This maximum-entropy construction predicts a one-sided exponential entropy distribution, and its low-entropy tail is recovered in the deep convective part of the three-dimensional radiation-hydrodynamics simulations. Closer to the surface, the distribution is reorganised by radiative cooling and separates into two thermodynamic components. Using a radiative entropy branch, an adiabatically descending cooled branch, and a population fraction controlled by optical depth, the two-population closure reproduces the mean entropy stratification of the four reference simulations over most of the displayed range, without adjusting the entropy profile itself. The surface transition can therefore be interpreted as a continuous population decomposition, rather than as a sharp boundary between radiative and convective layers. This provides a natural route toward one-dimensional stellar models in which the surface entropy jump is determined from the statistical organisation of the flow instead of being set by a calibrated mixing-length efficiency.

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arXiv2026

Kelvin waves over a differentially rotating spherical shell

Context. Be stars are presently viewed as B-type stars surrounded by a disc fueled by the star itself during episodicexcretion events. The origin of these events are poorly understood.Aims. This article aims to determine whether or not surface equatorial Kelvin waves can be unstable and therefore canplay a role in the triggering of the Be phenomenon.Methods. We first derive an analytical expression for gravito-inertial modes in the shallow-water framework. Then, weinvestigate numerically the evolution of equatorial Kelvin modes as system parameters vary. The study is extended tothick-layer configurations with a constant density fluid. We then analyze the stability of these modes under differentialrotation and viscous effects.Results. We show that equatorial Kelvin waves still exist in a spherical shell of finite thickness, but that their equatorialconfinement is weaker. At low azimuthal wavenumbers, Kelvin waves are in the inertial waves frequency band and thusget specificities of inertial waves like shear layers associated with singularities of the Poincaré equation. These shearlayers are new dissipative structures for Kelvin waves. When a radial (shellular) differential rotation is imposed, we showthat equatorial Kelvin waves can be destabilised provided that differential rotation and viscosity are in an appropriaterange. The non-monotonic behaviour of the growth rate of the instability is traced back to the rise of a critical layerwhere the fluid azimuthal velocity equals the phase speed of the surface waves.Conclusions. This study provides new insights into the behavior of equatorial Kelvin waves in astrophysics, particularlyin rapidly rotating stars. The results reinforce the idea that gravito-inertial waves, and more specifically the equatorialKelvin waves, can be unstable and thus be key parts in the mechanisms leading to the Be phenomenon.

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arXiv2025

Is a 1D perturbative method sufficient for asteroseismic modelling of $β$ Cephei pulsators? Implications for measurements of rotation and internal magnetic fields

Asymmetries in the observed rotational splittings of a multiplet contain information about the star's rotation profile and internal magnetic field. However, to exploit this information, highly accurate theoretical predictions are needed. We aim to quantify the difference in the predicted mode asymmetries between a 1D perturbative method, and a 2D method that includes a 2D stellar structure model, which takes rotation into account. We then put these differences in the context of asteroseismic measurements of internal magnetic fields. We couple the 1D pulsation codes GYRE and StORM to the 2D stellar structure code ESTER and compare the oscillation predictions with the results from the 2D TOP pulsation code. We focus on ZAMS models representative of rotating $β$~Cephei pulsators, going up to 20% of the critical rotation rate. We find a generally good agreement between the oscillation frequencies resulting from the 1D and 2D pulsation codes. Since the magnetic asymmetries are small compared to the differences in the rotational asymmetries resulting from the 1D and 2D predictions, accurate measurements of the magnetic field are in most cases challenging. Differences in the predicted mode asymmetries between 1D perturbative methods and 2D non-perturbative methods can greatly hinder accurate measurements of internal magnetic fields in main-sequence pulsators with low-order modes. Nevertheless, reasonably accurate measurements could be possible with $n_{pg} \ge 2$ modes if the internal rotation is roughly below 10% of the critical rotation frequency for (aligned) magnetic fields on the order of a few hundred kG. While the differences between the 1D and 2D predictions are mostly too large for internal magnetic field detections, the rotational asymmetries predicted by StORM are in general accurate enough for asteroseismic modelling of the stellar rotation in main-sequence stars.

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arXiv2024

Coriolis darkening in late-type stars II. Effect of self-sustained magnetic fields in stratified convective envelope

Modeling the surface brightness distribution of stars is of prime importance to interpret observations. Nevertheless, this remains quite challenging for cool stars as it requires one to model the MHD turbulence that develops in their convective envelope. In Paper I, the effect of the Coriolis acceleration on the surface heat flux has been studied by means of hydrodynamic simulations. In this paper, we aim to investigate the additional effect of dynamo magnetic fields. We focus on an envelope thickness that is representative of either a $\sim0.35~M_\odot$ M dwarf, a young red giant star or a pre-main sequence star. We performed a parametric study using numerical MHD simulations of anelastic convection in thick rotating spherical shells. For each model, we computed the mean surface distribution of the heat flux, and examined the leading-order effect of the magnetic field on the obtained latitudinal luminosity profile. We identify three different regimes. Close to the onset of convection, while the first unstable modes tend to convey heat more efficiently near the equator, magnetic fields are shown to generally enhance the mean heat flux close to the polar regions (and the tangent cylinder). By progressively increasing the Rayleigh number, the development of a prograde equatorial jet was previously shown to make the equator darker when no magnetic field is taken into account. For moderate Rayleigh numbers, magnetic fields can instead inverse the mean pole-equator brightness contrast (which means going from a darker to a brighter equator when a dynamo sets in) and finally induce a similar regime to that found close to the onset of convection. For more turbulent models with larger Rayleigh numbers, magnetic fields alternatively tend to smooth out the brightness contrast. This general behavior is shown to be related to the quenching of the surface differential rotation by magnetic fields.

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arXiv2022

Spectroscopic detection of Altair's non-radial pulsations

Context: Rapid rotation is a common feature of early-type stars but which remains a challenge for the models. The understanding of its effect on stellar evolution is however imperative to interpret the observed properties of numerous stars. Aims: We wish to bring more observational constraints on the properties of fast rotating stars, especially on their oscillation modes. Methods: We focus on the nearby star Altair which is known as a very rapidly rotating star with an equatorial velocity estimated recently at 313 km/s. We observed this star with the high-resolution spectropolarimeter Neo-Narval during six nights, with one night of interruption, in September 2020. Results: We detect significant line profile variations on the mean line profile of the spectra. Their time-frequency analysis shows that these variations are induced by gravito-inertial waves propagating at Altair's surface with azimuthal wavenumbers of order $m=10-15$. With a preliminary computation of the eigenspectrum using the most recent concordance model of Altair we can give a first modelling of the observed waves. Conclusions: Altair was known as the brightest $δ$ Scuti star. We now see that it is the brightest hybrid oscillating star with excited gravito-inertial waves and acoustic waves. Clearly, more observations and more advanced models are needed to explain the observations in greater details

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arXiv2020

Oscillations of 2D ESTER models. I. The adiabatic case

Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula and recent observations of pulsations in rapidly rotating delta Scuti stars seem to match these expectations. However, a key question is whether strong gradients or discontinuities can adversely affect this 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. Accordingly, we numerically calculate pulsation modes in continuous and discontinuous rapidly rotating models produced by the 2D ESTER (Evolution STEllaire en Rotation) code. This spectral multi-domain code self-consistently calculates the rotation profile based on baroclinic effects and allows us to introduce discontinuities without loss of numerical accuracy. Pulsations are calculated using an adiabatic version of the Two-dimensional Oscillation Program (TOP) code. The variational principle is used to confirm the high accuracy of the pulsation frequencies and to derive an integral formula that closely matches the generalised rotational splittings, except when modes are involved in avoided crossings. This potentially allows us to probe the the rotation profile using inverse theory. Acoustic glitch theory, applied along the island mode orbit deduced from ray dynamics, can correctly predict the periodicity of the glitch frequency pattern produced by a discontinuity or the Gamma1 dip related to the He II ionisation zone in some of the models. The asymptotic frequency pattern remains sufficiently well preserved to potentially allow its detection in observed stars.

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arXiv2019

A realistic two-dimensional model of Altair

Fast rotation is responsible for important changes in the structure and evolution of stars. Optical long baseline interferometry now permits the study of its effects on the stellar surface, mainly gravity darkening and flattening. We aim to determine the fundamental parameters of the fast-rotating star Altair, in particular its evolutionary stage, mass, and differential rotation, using state-of-the-art stellar interior and atmosphere models together with interferometric, spectroscopic, and asteroseismic observations. We use ESTER 2D 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 MCMC algorithm Emcee. We determined Altair's equatorial radius to be 2.008 +/- 0.006 Rsun, the position angle 301.1 +/- 0.3 degrees, the inclination 50.7 +/- 1.2 degrees, and the equatorial angular velocity 0.74 +/- 0.01 times the Keplerian angular velocity. This angular velocity leads to a flattening of 0.220 +/- 0.003. We also deduce from the spectroscopically derived vsini ~ 243 km/s, a true equatorial velocity of ~314 km/s corresponding to a rotation period of 7h46m (~3 c/d). The data also impose a strong correlation between mass, metallicity, hydrogen abundance, and core evolution. Thanks to asteroseismic data, we constrain the mass of Altair to 1.86 +/- 0.03 Msun 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 ~100 Myrs 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%.

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arXiv2019

The first view of $δ$ Scuti and $γ$ Doradus stars with the TESS mission

We present the first asteroseismic results for $δ$ Scuti and $γ$ Doradus stars observed in Sectors 1 and 2 of the TESS mission. We utilise 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% 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.

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arXiv2019

Evolution of rotation in rapidly rotating early-type stars during the main sequence with 2D models

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 $7~M_\odot$ 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 $\dot{M}-T_{\rm eff}$ 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-winds-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.

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arXiv2019

Critical angular velocity and anisotropic mass loss of rotating stars with radiation-driven winds

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. 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? 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. We find that radiative acceleration only mildly influences the critical angular velocity, at least for stars with masses lower than 40 Msun. 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 $\dot{M}-T_{\rm eff}$ 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.

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arXiv2018

Large-scale photospheric motions determined from granule tracking and helioseismology from SDO/HMI data

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 and few m/s , respectively. These flows also have a cycle related components, namely the torsional oscillations. 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. 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. 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 three days of data and after averaging between + and -15 degrees in longitude. 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.

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arXiv2017

The 2D dynamics of radiative zones of low-mass stars

In the context of secular evolution, we describe the dynamics of the radiative core of low-mass stars to understand the internal transport of angular momentum in such stars which results in a solid rotation in the Sun from 0.7R_sun to 0.2R_sun 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. We build 2D numerical models of a radiative core on the top of which we impose a latitudinal shear so as to reproduce a cylindrical differential rotation in a convective envelope. We perform a systematic study over the Rossby number measuring the latitudinal differential rotation at the radiative-convective interface. The imposed shear generates a geostrophic flow implying a cylindrical differential rotation. 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 with a cylindrical rotation profile. For low Rossby numbers, the baroclinic solution dominates with a quasi-shellular rotation profile. Using scaling laws from 3D simulations, we show that slow rotators are expected to have a cylindrical rotation profile. Fast rotators may have a shellular profile at the beginning of the main-sequence in stellar radiative zones. This study enables us to predict different types of differential rotation and emphasizes the need of 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. But, 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.

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arXiv2017

Gravity darkening in stars with surface differential rotation

The interpretation of stellar apparent fundamental parameters must be treated consistently with the characteristics of their surface rotation law. We develop a model to determine the distribution of the effective temperature and gravity, which depend on the surface differential rotation law and on the stellar external geometry. The basic assumptions are: a) the atmosphric layers are in radiative equilibrium; b) the bolometric flux is anti-parallel with the effective gravity; c) the angular velocity in the surface is Omega=Omega(theta,alpha,k)] where (alpha,k) are free parameters. The effective temperature varies with co-latitude `theta' and on the differential-rotation law through the 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 ofcharacteristic curves', on which the determination of the GDF relies, are obtained. The effects of the quantities (eta,alpha,k) (eta=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 (eta,alpha,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 $β_1$ 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,alpha). 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 classical pair (eta,beta1), it would be more useful to determine the quantities (eta,alpha,i) to characterize stellar rotation.

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arXiv2017

Supergranulation and multiscale flows in the solar photosphere: Global observations vs. a theory of anisotropic turbulent convection

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.

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arXiv2016

An algorithm for computing the 2D structure of fast rotating stars

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 preconditionner of the Jacobian matrix.

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arXiv2016

Relation between trees of fragmenting granules and supergranulation evolution

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. Method: To probe the superganule interior cell, we used the Trees of Fragmenting Granules (TFG) evolution and their relations to horizontal 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 hours) over a scale up to 12\arcsec. 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 hours, 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.

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