arXiv subjects

M. Rieutord

Publications and source records attributed to M. Rieutord.

At least 55 records · Page 3Linked to original sources

arXiv2009

Viscous dissipation by tidally forced inertial modes in a rotating spherical shell

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).

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arXiv2009

Mesoscale dynamics on the Sun's surface from HINODE observations

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. Method: We analyse a 48h 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 \arcsec$\times$ 100 \arcsec, 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 $430 \mathrm{km}^2 \mathrm{s}^{-1}$. 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.

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arXiv2008

Regular patterns in the acoustic spectrum of rapidly rotating stars

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 third order perturbative method valid at low rotation rates.

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arXiv2007

Large-scale horizontal flows in the solar photosphere III: Effects on filament destabilization

We study the influence of large-scale photospheric motions on the estabilization 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 were invetigated 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. 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. We conclude that there is probably a link between changes in surface flow and the disappearance of the eruptive filament.

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arXiv2007

Tracking granules on the Sun's surface and reconstructing horizontal velocity fields: I. the CST algorithm

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. 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. 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.

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arXiv2007

Tracking granules at the Sun's surface and reconstructing velocity fields. II. Error analysis

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. 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. We use the coherent structure tracking algorithm developed recently and apply it to two independent series of images that contain the same solar signal. We first show that a k-ωfiltering 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. 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.

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arXiv2007

The dynamics of a fully radiative rapidly rotating star

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.

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arXiv2007

Modeling rapidly rotating stars

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.

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arXiv2006

Mesoscale flows in large aspect ratio simulations of turbulent compressible convection

We present the results of a very large aspect ratio (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 Cattaneo et al. (2001), 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.

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arXiv2006

Acoustic oscillations of rapidly rotating polytropic stars. II. Effects of the Coriolis and centrifugal accelerations

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. Method: 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 for a R = 2.3 R_\odot, M = 1.9 M_\odot polytropic star. Furthermore, it is shown that the main differences between complete and perturbative calculations come essentially from the centrifugal distortion.

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arXiv2006

On the dynamics of radiative zones in rotating stars

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 thoroughly 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.

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arXiv2006

Acoustic oscillations in rapidly rotating polytropic stars I. Effects of the centrifugal distortion

A new non-perturbative method to compute accurate oscillation modes in rapidly rotating stars is presented. In this paper, 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. 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 with 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 then discussed.

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arXiv2005

The magnetism of the solar interior for a complete MHD solar vision

The solar magnetism is no more considered as a purely superficial phenomenon. The SoHO community has shown that the length of the solar cycle depends on the transition region between radiation and convection. Nevertheless, the internal solar (stellar) magnetism stays poorly known. Starting in 2008, the American instrument HMI/SDO and the European microsatellite PICARD will enrich our view of the Sun-Earth relationship. Thus obtaining a complete MHD solar picture is a clear objective for the next decades and it requires complementary observations of the dynamics of the radiative zone. For that ambitious goal, space prototypes are being developed to improve gravity mode detection. The Sun is unique to progress on the topology of deep internal magnetic fields and to understand the complex mechanisms which provoke photospheric and coronal magnetic changes and possible longer cycles important for human life. We propose the following roadmap in Europe to contribute to this "impressive" revolution in Astronomy and in our Sun-Earth relationship: SoHO (1995-2007), PICARD (2008-2010), DynaMICS (2009-2017) in parallel to SDO (2008-2017) then a world-class mission located at the L1 orbit or above the solar poles.

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arXiv2004

Oscillations of magnetic stars: II. Axisymmetric toroidal and non-axisymmetric shear Alfven modes in a spherical shell

We carry out numerical and mathematical investigations of shear Alfven 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.

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arXiv2003

Statistical mechanics and phase diagrams of rotating self-gravitating fermions

We compute statistical equilibrium states of rotating self-gravitating systems enclosed within a box by maximizing the Fermi-Dirac entropy at fixed mass, energy and angular momentum. 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 and angular velocity. We argue that systems described by the Fermi-Dirac distribution in phase space do not bifurcate to non-axisymmetric structures, in continuity with the case of polytropes with index n>0.808 (the Fermi gas at T=0 corresponds to n=3/2). This contrasts with the study of Votyakov et al. (2002) who consider a Fermi-Dirac distribution in configuration space and find ``double star'' structures (their model at T=0 corresponds to n=0). We also discuss the influence of rotation on the onset of the gravothermal catastrophe for globular clusters. 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 and Dirac peaks (or massive condensates) in the canonical ensemble. We also describe an hysteretic cycle between the gaseous phase and the condensed phase that are connected by a ``collapse'' or an ``explosion''. This notion of hysteresis in self-gravitating systems is new.

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arXiv2002

A simulation of solar convection at supergranulation scale

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$82, which is used to investigate the dynamics of scales larger than granulation. No structure resembling supergranulation is present; possibly higher Reynolds numbers (i.e. higher numerical resolution), or magnetic fields, or greater depth are necessary. The results also show interesting aspects of granular dynamics which are briefly presented, like extensive p-mode ridges in the k-$ω$ 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.

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arXiv2002

More concerning the anelastic and subseismic approximations for low-frequency modes in stars

Two approximations, namely the subseismic approximation and the anelastic approximation, are presently used to filter out the acoustic modes when computing low frequency modes of a star (gravity modes or inertial modes). In a precedent paper (Dintrans & Rieutord 2001), 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 due to 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-Vaisala frequency as asymptotically small and makes no assumption on 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.

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arXiv2001

Acoustic modes in spheroidal cavities

Oscillation modes of rapidly rotating stars have not yet been calculated with precision, rotational effects being generally approximated by perturbation methods. We are developing a numerical method able to account for the deformation of the star by the centrifugal force and, as a first step, we determined the acoustic modes of a uniform density spheroid and studied how the spheroid flatness affects these modes.

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