Michel Rieutord

Magnetic structures in a dynamo simulation

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.

Are granules good tracers of solar surface velocity fields

Using a numerical simulation of compressible convection with radiative transfer mimicking the solar photosphere, we compare the velocity eld derived from granule motions to the actual velocity eld of the plasma. We thus test the idea that granules may be used to trace large-scale velocity elds at the suns surface. Our results show that this is indeed the case provided the scale separation is sucient. We thus estimate that neither velocity elds 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 coecients up to0.9.

Slichter modes of the Earth revisited

Abstract 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.

Families of fragmenting granules and their relation to meso- and supergranular flow fields

D 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.

Adiabatic oscillations of non-rotating superfluid neutron stars

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 ofg-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 eective one-fluid case we find the usual singlet f -a ndp-modes, and we also find the expectedg-modes of stratified neutron star models.

Statistical mechanics and phase diagrams of rotating self-gravitating fermions

We compute statistical equilibrium states of rotating self-gravitating fermions by maximizing the Fermi-Dirac en- tropy 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 rotat- ing 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. (2002) who consider a Fermi-Dirac distribution in configuration space appropriate to stellar formation and find double star structures (their model at T = 0c or- responds 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.

Inertial modes in the liquid core of the Earth

Abstract 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).

Ekman Layers and the Damping of Inertial r-Modes in a Spherical Shell: Application to Neutron Stars

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 by fluid dynamicists. 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.

Oscillations of magnetic stars: I. Axisymmetric shear Alfvén modes of a spherical shell in a dipolar magnetic field

We carry out an investigation of axisymmetric shear Alfven 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 Alfvenic 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 Alfven waves provide a good instance of non-perturbative effects due to the strong magnetic field of such stars.

Temporal height properties of the exploding granules

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 Plumeslocated 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.