2018

Journal articles

- titre
- Gravity darkening in late-type stars. I. The Coriolis effect
- auteur
- Raphaël Raynaud, Michel Rieutord, Ludovic Petitdemange, Thomas Gastine, Bertrand Putigny
- article
*Astronomy and Astrophysics - A&A*, EDP Sciences, 2018, 609 (A124), ⟨10.1051/0004-6361/201731729⟩- resume
- 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. Aims. 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.
- DOI
- DOI : 10.1051/0004-6361/201731729
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2017

Poster communications

- titre
- Magnetars
- auteur
- Raphaël Raynaud, Jérôme Guilet
- article
*GDRI Dynamo Meeting*, Nov 2017, Paris, France- resume
- What is the origin of neutron star magnetic fields ? Although the fossil field hypothesis (i.e. the amplification of the neutron star progenitor field by flux conservation) would be the simplest mechanism, it seems unlikely to explain the existence of magnetars, which are a peculiar type of neutron stars endowed with unusually strong dipolar magnetic fields. Their intensity is currently deduced from stellar spin-down rate measurements and estimated to be in the order of $10^{15}$ Gauss, which makes them the strongest magnetic fields ever observed in the Universe. Understanding the formation process of magnetars is of particular importance, since they are believed to power a variety of outstanding explosive events observed with ongoing and future transient surveys (LSST, SVOM).
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2016

Journal articles

- titre
- Multi-stage high order semi-Lagrangian schemes for incompressible flows in Cartesian geometries
- auteur
- Alexandre Cameron, Raphaël Raynaud, Emmanuel Dormy
- article
*International Journal for Numerical Methods in Fluids*, Wiley, 2016, ⟨10.1002/fld.4245⟩- resume
- Efficient transport algorithms are essential to the numerical resolution of incompressible fluid flow problems. Semi-Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi-stage procedure which can easily be used to increase the order of accuracy of a code based on multi-linear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont & Liu (2003, 2007). This multi-stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communications pattern is identical to that of the multi-linear scheme. We show how a combination of a forward and backward error correction can provide a third-order accurate scheme, thus significantly reducing diffusive effects while retaining a non-dispersive leading error term.
- DOI
- DOI : 10.1002/fld.4245
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- titre
- Convective dynamo action in a spherical shell: symmetries and modulation
- auteur
- Raphaël Raynaud, Steven Tobias
- article
*Journal of Fluid Mechanics*, Cambridge University Press (CUP), 2016, 799 (R6), ⟨10.1017/jfm.2016.407⟩- resume
- We consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and demonstrate how complicated interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle. For some parameters, Type 1 modulation occurs by the transfer of energy between modes of different symmetries with little change in the overall amplitude; for other parameters, the modulation is of Type 2, where the amplitude is significantly affected (leading to grand minima in activity) without significant changes in symmetry. Most importantly, we identify the presence of 'supermodulation' in the solutions, where the activity switches chaotically between Type 1 and Type 2 modulation; this is believed to be an important process in solar activity.
- DOI
- DOI : 10.1017/jfm.2016.407
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2015

Journal articles

- titre
- Dipolar dynamos in stratified systems
- auteur
- Raphaël Raynaud, Ludovic Petitdemange, Emmanuel Dormy
- article
*Monthly Notices of the Royal Astronomical Society*, Oxford University Press (OUP): Policy P - Oxford Open Option A, 2015, 448, pp.2055-2065. ⟨10.1093/mnras/stv122⟩- resume
- Observations of low-mass stars reveal a variety of magnetic field topologies ranging from large-scale, axial dipoles to more complex magnetic fields. At the same time, three-dimensional spherical simulations of convectively driven dynamos reproduce a similar diversity, which is commonly obtained either with Boussinesq models or with more realistic models based on the anelastic approximation, which take into account the variation of the density with depth throughout the convection zone. Nevertheless , a conclusion from different anelastic studies is that dipolar solutions seem more difficult to obtain as soon as substantial stratifications are considered. In this paper, we aim at clarifying this point by investigating in more detail the influence of the density stratification on dipolar dynamos. To that end, we rely on a systematic parameter study that allows us to clearly follow the evolution of the stability domain of the dipolar branch as the density stratification is increased. The impact of the density stratification both on the dynamo onset and the dipole collapse is discussed and compared to previous Boussinesq results. Furthermore, our study indicates that the loss of the dipolar branch does not ensue from a specific modification of the dynamo mechanisms related to the background stratification, but could instead result from a bias as our observations naturally favour a certain domain in the parameter space characterized by moderate values of the Ekman number, owing to current computational limitations. Moreover, we also show that the critical magnetic Reynolds number of the dipolar branch is scarcely modified by the increase of the density stratification, which provides an important insight into the global understanding of the impact of the density stratification on the stability domain of the dipolar dynamo branch.
- DOI
- DOI : 10.1093/mnras/stv122
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Theses

- titre
- Modélisation numérique du magnétisme solaire et stellaire
- auteur
- Raphaël Raynaud
- article
- Physique [physics]. Observatoire de Paris, 2015. Français
- resume
- Dynamo action, i.e. the self-amplification of a magnetic field by the flow of an electrically conducting fluid, is considered to be the main mechanism for the generation of the magnetic fields of stars and planets. Intensive and systematic param- eter studies by direct numerical simulations using the Boussinesq approximation revealed fundamental properties of these models. However, this approximation considers an incompressible conducting fluid, and is therefore not adequate to describe convection in highly stratified systems like stars or gas giants. A common approach to overcome this difficulty is then to use the anelastic approximation, that allows for a reference density profile while filtering out sound waves for a faster numerical integration. Through a systematic parameter study of spherical anelastic dynamo models, we investigate the influence of the stratification on the dynamo mechanisms, and compare them with previous results obtained in the Boussinesq approximation. We discuss the influence of the density stratification on the field geometry and the field strength. Our results are in overall agreeement with the previous geodynamo studies, and thus the main established results seem to be still relevant to the study of stellar dynamos.
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2014

Journal articles

- titre
- Topology and field strength in spherical, anelastic dynamo simulations
- auteur
- Martin Schrinner, Ludovic Petitdemange, Raphaël Raynaud, Emmanuel Dormy
- article
*Astronomy and Astrophysics - A&A*, EDP Sciences, 2014, 564 (A78), ⟨10.1051/0004-6361/201322801⟩- resume
- Context: Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid of constant density, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation. Aims: The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular, with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Methods: Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. Results: The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings.
- DOI
- DOI : 10.1051/0004-6361/201322801
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- titre
- Influence of the mass distribution on the magnetic field topology
- auteur
- Raphaël Raynaud, Ludovic Petitdemange, Emmanuel Dormy
- article
*Astronomy and Astrophysics - A&A*, EDP Sciences, 2014, 567 (A107), ⟨10.1051/0004-6361/201423902⟩- resume
- Context. Three-dimensional spherical dynamo simulations carried out within the framework of the anelastic approximation have revealed that the established distinction between dipolar and multipolar dynamos tends to be less clear than it was in Boussinesq studies. This result was first interpreted as a direct consequence of the existence of a larger number of models with a high equatorial dipole contribution, together with an intermediate dipole field strength. However, this finding has not been clearly related to specific changes that would have been introduced by the use of the anelastic approximation. Aims. In this paper, we primarily focus on the effects of choosing a different mass distribution. Indeed, it is likely to have as large consequences as taking a stratified reference state into account would, especially when comparing our results to previous Boussinesq studies. Methods. Our investigation is based on a systematic parameter study of weakly stratified anelastic dynamo models. Results. We show that the tendencies highlighted in previous anelastic dynamo simulations are already present in the Boussinesq limit. Thus they cannot be systematically related to anelastic effects. Actually, a central mass distribution can result in changes in the magnetic field topology that are mainly due to the concentration of convective cells close to the inner sphere.
- DOI
- DOI : 10.1051/0004-6361/201423902
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Directions of work or proceedings

- titre
- Influence of the mass distribution on the magnetic field topology in spherical, anelastic dynamo simulations
- auteur
- Raphaël Raynaud, Ludovic Petitdemange, Emmanuel Dormy
- article
- J. Ballet, F. Bournaud, F. Martins, R. Monier et C. Reylé.
*Journées de la SF2A*, Jun 2014, Paris, France. 2014 - resume
- Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields. However, Boussinesq models are not adequate for describing convection in stratified systems, and thus the validity of these previous results remains to be assessed for gas giants and stars. To that end, we carried out a systematic parameter study of spherical dynamo models in the so-called anelastic approximation, which allows for a reference density profile while filtering out sound waves for faster numerical integration. We show that the dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is still present in anelastic models, and dipolar dynamos require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the established distinction between dipolar and multipolar dynamos tends to be less clear than it was in Boussinesq studies, since we found a large number of models with a considerable equatorial dipole contribution together with an intermediate overall dipole field strength. This tendency can be found in very weakly stratified models, but it was not reported for previous Boussinesq models assuming a homogeneous mass distribution. In contrast, anelastic models usually assume a central mass distribution, which leads to a gravity profile proportional to 1/r**2. Actually, we show that this choice can result in changes in the magnetic field topology that are mainly due to the concentration of convective cells close to the inner sphere.
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2013

Journal articles

- titre
- Intermittency in spherical Couette dynamos
- auteur
- Raphaël Raynaud, Emmanuel Dormy
- article
*Physical Review Online Archive (PROLA)*, American Physical Society, 2013, 87 (033011), ⟨10.1103/PhysRevE.87.033011⟩- resume
- We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic energy separated by low-energy phases. We show that this behavior corresponds to the so-called on-off intermittency. This behavior is here reported for dynamo action with realistic boundary conditions. We investigate the role of magnetic boundary conditions in this phenomenon.
- DOI
- DOI : 10.1103/PhysRevE.87.033011
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