2025
Journal articles
- titre
- Tayler-Spruit dynamo in stably stratified rotating fluids: Application to proto-magnetars
- auteur
- P. Barrère, J. Guilet, R. Raynaud, A. Reboul-Salze
- article
- Astronomy & Astrophysics - A&A, 2025, 695, pp.A183. ⟨10.1051/0004-6361/202451337⟩
- resume
- The formation of highly magnetized young neutron stars, called magnetars, is still a strongly debated topic. One promising scenario invokes the amplification of the magnetic field by the Tayler-Spruit dynamo in a proto-neutron star (PNS) that is spun up by fall-back. Our previous numerical study supports this scenario by demonstrating that this dynamo can generate magnetar-like magnetic fields in stably stratified Boussinesq models of a PNS interior. To further investigate the Tayler-Spruit dynamo, we performed 3D magnetohydrodynamic (MHD) numerical simulations with the MagIC code, varying the ratio between the Brunt-Väisälä frequency and the rotation rate. We first demonstrated that a self-sustained dynamo process can be maintained for a Brunt-Väisälä frequency about four times higher than the angular rotation frequency. The generated magnetic fields and angular momentum transport follow the scaling laws derived in prior analytical investigations, confirming our earlier results. We also report, for the first time, the existence of an intermittent Tayler-Spruit dynamo. For a typical PNS Brunt-Väisälä frequency of 1 kHz, the axisymmetric toroidal and dipolar magnetic fields range between 1.2 × 10 15 –2 × 10 16 G and 1.4 × 10 13 –3 × 10 15 G, for rotation periods of 1 − 10 ms. Moreover, the total magnetic field remains ≳10 14 G for periods of ≲60 ms. Thus, our results suggest that our scenario is promising to form classical fast-rotating magnetars and magnetars with weaker magnetic dipoles for slower rotations. We offer a calibration of the analytical scaling laws based on our simulations, with a dimensionless normalisation factor of the order of 10 −2 . As the Tayler-Spruit dynamo is often invoked for the angular momentum transport in stellar radiative zones, our results are of particular significance to asteroseismology as well.
- DOI
- DOI : 10.1051/0004-6361/202451337
- Accès au texte intégral et bibtex
-
2023
Journal articles
- titre
- Numerical simulations of the Tayler–Spruit dynamo in proto-magnetars
- auteur
- Paul Barrère, Jérôme Guilet, Raphaël Raynaud, Alexis Reboul-Salze
- article
- Monthly Notices of the Royal Astronomical Society: Letters, 2023, 526 (1), pp.L88-L93. ⟨10.1093/mnrasl/slad120⟩
- resume
- The Tayler–Spruit dynamo is one of the most promising mechanisms proposed to explain angular momentum transport during stellar evolution. Its development in proto-neutron stars spun-up by supernova fallback has also been put forward as a scenario to explain the formation of very magnetized neutron stars called magnetars. Using three-dimensional direct numerical simulations, we model the proto-neutron star interior as a stably stratified spherical Couette flow with the outer sphere that rotates faster than the inner one. We report the existence of two subcritical dynamo branches driven by the Tayler instability. They differ by their equatorial symmetry (dipolar or hemispherical) and the magnetic field scaling, which is in agreement with different theoretical predictions (by Fuller and Spruit, respectively). The magnetic dipole of the dipolar branch is found to reach intensities compatible with observational constraints on magnetars.
- DOI
- DOI : 10.1093/mnrasl/slad120
- Accès au texte intégral et bibtex
-
2022
Journal articles
- titre
- MRI-driven dynamo at very high magnetic Prandtl numbers
- auteur
- Jérôme Guilet, Alexis Reboul-Salze, Raphaël Raynaud, Matteo Bugli, Basile Gallet
- article
- Monthly Notices of the Royal Astronomical Society, 2022, 516, pp.4346 - 4353. ⟨10.1093/mnras/stac2499⟩
- resume
- The dynamo driven by the magnetorotational instability (MRI) is believed to play an important role in the dynamics of accretion discs and may also explain the origin of the extreme magnetic fields present in magnetars. Its saturation level is an important open question known to be particularly sensitive to the diffusive processes through the magnetic Prandtl number Pm (the ratio of viscosity to resistivity). Despite its relevance to proto-neutron stars and neutron star merger remnants, the numerically challenging regime of high Pm is still largely unknown. Using zero-net flux shearing box simulations in the incompressible approximation, we studied MRI-driven dynamos at unprecedentedly high values of Pm reaching 256. The simulations show that the stress and turbulent energies are proportional to Pm up to moderately high values (Pm ∼ 50). At higher Pm, they transition to a new regime consistent with a plateau independent of Pm for Pm 100. This trend is independent of the Reynolds number, which may suggest an asymptotic regime where the energy injection and dissipation are independent of the dif fusi ve processes. Interestingly, large values of Pm not only lead to intense small-scale magnetic fields but also to a more efficient dynamo at the largest scales of the box.
- DOI
- DOI : 10.1093/mnras/stac2499
- Accès au texte intégral et bibtex
-
- titre
- Gravitational wave signature of proto-neutron star convection: I. MHD numerical simulations
- auteur
- Raphaël Raynaud, Pablo Cerdá-Durán, Jérôme Guilet
- article
- Monthly Notices of the Royal Astronomical Society, 2022, 509 (3), pp.3410-3426. ⟨10.1093/mnras/stab3109⟩
- resume
- Gravitational waves provide a unique and powerful opportunity to constrain the dynamics in the interior of proto-neutron stars during core collapse supernovae. Convective motions play an important role in generating neutron stars magnetic fields, which could explain magnetar formation in the presence of fast rotation. We compute the gravitational wave emission from proto-neutron star convection and its associated dynamo, by post-processing three-dimensional MHD simulations of a model restricted to the convective zone in the anelastic approximation. We consider two different proto-neutron star structures representative of early times (with a convective layer) and late times (when the star is almost entirely convective). In the slow rotation regime, the gravitational wave emission follows a broad spectrum peaking at about three times the turnover frequency. In this regime, the inclusion of magnetic fields slightly decreases the amplitude without changing the spectrum significantly compared to a non-magnetised simulation. Fast rotation changes both the amplitude and spectrum dramatically. The amplitude is increased by a factor of up to a few thousands. The spectrum is characterized by several peaks associated to inertial modes, whose frequency scales with the rotation frequency. Using simple physical arguments, we derive scalings that reproduce quantitatively several aspects of these numerical results. We also observe an excess of low-frequency gravitational waves, which appears at the transition to a strong field dynamo characterized by a strong axisymmetric toroidal magnetic field. This signature of dynamo action could be used to constrain the dynamo efficiency in a proto-neutron star with future gravitational wave detections.
- DOI
- DOI : 10.1093/mnras/stab3109
- Accès au texte intégral et bibtex
-
2021
Journal articles
- titre
- De quoi les magnétoiles sont-elles coupables ?
- auteur
- Jérôme Guilet, Raphaël Raynaud
- article
- La Recherche, 2021, 565
- resume
- Étoiles à neutrons aux champs magnétiques colossaux, les magnétoiles défient l'imagination. La naissance de ces astres denses pourrait donner lieu à de puissantes explosions stellaires, comme des hypernovae. Des simulations numériques reproduisent pour la première fois la genèse de leur champ magnétique et apportent de nouveaux indices sur leur naissance cataclysmique.
- Accès au bibtex
-
- titre
- A global model of the magnetorotational instability in protoneutron stars
- auteur
- A. Reboul-Salze, J. Guilet, R. Raynaud, M. Bugli
- article
- Astronomy & Astrophysics - A&A, 2021, 645, pp.A109. ⟨10.1051/0004-6361/202038369⟩
- resume
- Context. Magnetars are isolated neutron stars characterized by their variable high-energy emission, which is powered by the dissipation of enormous internal magnetic fields. The measured spin-down of magnetars constrains the magnetic dipole to be in the range of 1014 − 1015 G. The magnetorotational instability (MRI) is considered to be a promising mechanism to amplify the magnetic field in fast-rotating protoneutron stars and form magnetars. This scenario is supported by many local studies that have shown that magnetic fields could be amplified by the MRI on small scales. However, the efficiency of the MRI at generating a dipole field is still unknown.Aims. To answer this question, we study the MRI dynamo in an idealized global model of a fast rotating protoneutron star with differential rotation.Methods. Using the pseudo-spectral code MagIC, we performed three-dimensional incompressible magnetohydrodynamics simulations in spherical geometry with explicit diffusivities where the differential rotation is forced at the outer boundary. We performed a parameter study in which we varied the initial magnetic field and investigated different magnetic boundary conditions. These simulations were compared to local shearing box simulations performed with the code Snoopy.Results. We obtain a self-sustained turbulent MRI-driven dynamo, whose saturated state is independent of the initial magnetic field. The MRI generates a strong turbulent magnetic field of B ≥ 2 × 1015 G and a nondominant magnetic dipole, which represents systematically about 5% of the averaged magnetic field strength. Interestingly, this dipole is tilted toward the equatorial plane. By comparing these results with shearing box simulations, we find that local models can reproduce fairly well several characteristics of global MRI turbulence such as the kinetic and magnetic spectra. The turbulence is nonetheless more vigorous in the local models than in the global ones. Moreover, overly large boxes allow for elongated structures to develop without any realistic curvature constraint, which may explain why these models tend to overestimate the field amplification.Conclusions. Overall, our results support the ability of the MRI to form magnetar-like large-scale magnetic fields. They furthermore predict the presence of a stronger small-scale magnetic field. The resulting magnetic field could be important to power outstanding stellar explosions, such as superluminous supernovae and gamma-ray bursts.
- DOI
- DOI : 10.1051/0004-6361/202038369
- Accès au texte intégral et bibtex
-
Conference papers
- titre
- Gravitational wave signature of magnetar formation
- auteur
- Raphaël Raynaud
- article
- IAU Symposium 363: Neutron Star Astrophysics at the Crossroads: Magnetars and the Multimessenger Revolution, Nov 2021, L'Aquila, Italy
- Accès au bibtex
-
- titre
- Gravitational wave signature of proto-neutron star convection
- auteur
- Raphaël Raynaud, Pablo Cerdá-Durán, Jérôme Guilet
- article
- 11th Iberian Gravitational Waves Meeting, Universitat de Valencia, Jun 2021, Valencia, Spain
- Accès au bibtex
-
- titre
- Gravitational wave signature of proto-neutron star convection
- auteur
- Raphaël Raynaud, Pablo Cerdá-Durán, Jérôme Guilet
- article
- Gravitational waves: a new messenger to explore the universe, Groupement de Recherche "Ondes Gravitationnelles", Mar 2021, Paris, France
- resume
- Gravitational waves provide a unique opportunity to better constrain the dynamics in the interior of proto-neutron stars during core collapse supernovae. Convective motions inside the proto-neutron star play an important role in determining neutron star magnetic fields. In paticular, numerical models suggest that a convective dynamo could explain magnetar formation in presence of fast rotation. Using 3D MHD simulations of proto-neutron star convective zones, we compute the gravitational wave emission from turbulent convection and study the impacts of both rotation and dynamo action. We derive physical scalings that reproduce quantitatively several aspects of the numerical results. Given the potentially long duration of the signal, we find that the typical strain and frequency range could allow its detection by current GW detectors in a nearby supernova explosion, and may be a primary target for next generation of GW detectors. In some cases, the signal may even capture the growth of a magnetic field due to dynamo action.
- Accès au bibtex
-
2020
Journal articles
- titre
- Magnetar formation through a convective dynamo in protoneutron stars
- auteur
- Raphaël Raynaud, Jérôme Guilet, Hans-Thomas Janka, Thomas Gastine
- article
- Science Advances , 2020, 6 (eaay2732), ⟨10.1126/sciadv.aay2732⟩
- resume
- The release of spin-down energy by a magnetar is a promising scenario to power several classes of extreme explosive transients. However, it lacks a firm basis because magnetar formation still represents a theoretical challenge. Using the first three-dimensional simulations of a convective dynamo based on a protoneutron star interior model, we demonstrate that the required dipolar magnetic field can be consistently generated for sufficiently fast rotation rates. The dynamo instability saturates in the magnetostrophic regime with the magnetic energy exceeding the kinetic energy by a factor of up to 10. Our results are compatible with the observational constraints on galactic magnetar field strength and provide strong theoretical support for millisecond protomagnetar models of gamma-ray burst and superluminous supernova central engines.
- DOI
- DOI : 10.1126/sciadv.aay2732
- Accès au texte intégral et bibtex
-
2019
Conference papers
- titre
- Magnetar formation through convective dynamos in protoneutron stars
- auteur
- Raphaël Raynaud, Jérôme Guilet, Hans-Thomas Janka, Thomas Gastine
- article
- Multi-Messenger Astrophysics in the Gravitational Wave Era, Yukawa Institute for Theoretical Physics, Sep 2019, Kyoto, Japan
- Accès au bibtex
-
- titre
- Protoneutron star dynamos
- auteur
- Raphaël Raynaud, Jérôme Guilet
- article
- Gamma-ray bursts and supernovae: from the central engines to the observer, PSI2 thematic program, Jun 2019, Orsay, France
- Accès au bibtex
-
- titre
- Convection and dynamo modeling in protoneutron stars
- auteur
- Raphaël Raynaud
- article
- Bursting the Bubble: Connecting Thermonuclear Burst Research to a Wider Community, Lorentz Center, Jun 2019, Leiden, Netherlands
- resume
- If the Boussinesq approximation performs well in modeling convection in laboratory experiments, it is however unsatisfactory for large natural systems, the lower part of which is compressed by the overlying material. The anelastic approximation enables us to overcome this difficulty by taking into account the mean stratification of the system, while filtering out sound waves for a faster numerical integration. It has been successfully used to study planetary or stellar convection and I will show how it can be further adapted to develop a realistic interior model of a newborn neutron star.
- Accès au bibtex
-
- titre
- Magnetar formation through convective dynamos in protoneutron stars
- auteur
- Raphaël Raynaud, Jérôme Guilet, Hans-Thomas Janka, Thomas Gastine
- article
- Journées de la SF2A 2019, Société Francaise d’Astronomie et d’Astrophysique, May 2019, Nice, France
- Accès au bibtex
-
- titre
- A global model of the magnetorotational instability in proto-neutron stars
- auteur
- Alexis Reboul-Salze, Jérôme Guilet, Raphaël Raynaud, Matteo Bugli
- article
- Journées de la SF2A, Société Francaise d’Astronomie et d’Astrophysique, May 2019, Nice, France
- resume
- The magnetorotational instability (MRI) is a promising mechanism to amplify the magnetic field in fast-rotating proto-neutron stars. Many local studies have shown that the magnetic field could be amplified on small scales. However, the efficiency of the MRI at generating a large-scale field similar to the dipolar magnetic field of magnetars (10 14 − 10 15 G) is still unknown. We used a three dimensional pseudo-spectral code to develop an idealized global model of the MRI in a proto-neutron star. We show that a dipole field strength consistent with the values of magnetar field intensity can be generated by the MRI, even though it is lower than the small-scale magnetic field. Overall, our results support the ability of the MRI to form magnetar-like dipolar magnetic fields.
- Accès au texte intégral et bibtex
-
Proceedings
- titre
- Dipole collapse in rotating stratified dynamos
- auteur
- Ludovic Petitdemange, Raphaël Raynaud
- article
- 2019, ⟨10.1051/eas/1982031⟩
- resume
- Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields, but the relevance of these results remains to be assessed for highly stratified systems, like gas planets and stars. The common approach is then to rely on the anelastic approximation to model the background density stratification. A conclusion from different anelastic studies is that dipolar solutions seem more difficult to obtain in presence of a substantial density contrast. We review some important results obtained by Raynaud et al. (2015), who investigated the influence of the density stratification on the stability of dipolar dynamos. This 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. In strongly stratified systems, the force balance may vary with depth, and a local increase of inertia close to the outer surface can explain the loss of the dipolar branch, while volume-averaged measures may underestimate the role of inertia on the field topology.
- DOI
- DOI : 10.1051/eas/1982031
- Accès au texte intégral et bibtex
-
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 & Astrophysics - A&A, 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
- Accès au texte intégral et bibtex
-
Conference papers
- titre
- Convective dynamos in protoneutron stars
- auteur
- Raphaël Raynaud, Jérôme Guilet, Hans-Thomas Janka, Thomas Gastine
- article
- Magnetic field formation and evolution in neutron stars, PHAROS WG4+WG5 meeting and CoCoNuT Meeting, Nov 2018, Saclay, France
- Accès au bibtex
-
- titre
- The pseudo-spectral code MagIC
- auteur
- Raphaël Raynaud
- article
- Multi-Dimensional processes in stellar physics, École Évry Schatzman du PNPS, Oct 2018, Roscoff, France
- Accès au bibtex
-
- titre
- Gravity darkening in late-type stars
- auteur
- Raphaël Raynaud, Michel Rieutord, Ludovic Petitdemange, Thomas Gastine, Bertrand Putigny
- article
- 7th BCool meeting, Apr 2018, Dublin, Ireland
- Accès au bibtex
-
Proceedings
- titre
- Supermodulation of the solar cycle
- auteur
- Raphaël Raynaud, Steven M. Tobias
- article
- Journées de la SF2A, Jul 2018, Bordeaux, France. 2018
- resume
- There is evidence from record of cosmogenic radionuclides that the Sun's activity switches between periods of strong modulation with clusters of deep grand minima and periods of weaker modulation. By considering dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell, we demonstrate how interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle of an oscillatory dynamo. 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 characteristic of the long term modulation of the solar activity.
- Accès au texte intégral et bibtex
-
- titre
- Gravity darkening in late-type stars
- auteur
- Raphaël Raynaud, Michel Rieutord, Ludovic Petitdemange, T. Gastine, Bertrand Putigny
- article
- Journées de la SF2A, Jul 2018, Bordeaux, France. 2018
- resume
- 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.
- Accès au texte intégral et bibtex
-
2017
Conference papers
- titre
- Latitudinal flux variations of thermal anelastic convection in a rotating spherical shell
- auteur
- Raphaël Raynaud, Michel Rieutord, Ludovic Petitdemange, Thomas Gastine, Bertrand Putigny
- article
- Compressible Convection Conference, Sep 2017, Lyon, France
- resume
- Following interferometric observations of fast rotating stars, which now give new constraints on the latitudinal heat flux distribution, we investigate the influence of rotation on this quantity in solar-type stars, which own an outer convective envelope. To that end, we carried 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 shells with different degrees of stratification. We measure the heat transfer efficiency in terms of the Nusselt number, defined as the output luminosity normalised by the conductive state luminosity. 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 luminosity contrast is mainly controlled by the surface value of the local Rossby number: when the Coriolis force dominates the force balance, 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. But in presence of a strong background stratification, the radial dependence of the conductive entropy profile favours the sharp increase of the local Rossby number in the outer layers, which ultimately leads to the uniformisation of the surface heat flux distribution.
- Accès au bibtex
-
- titre
- Dynamo theory
- auteur
- Raphaël Raynaud
- article
- 10th National Meeting on Astronomy and Astrophysics, Iranian Astronomical Society, Jan 2017, Zahedan, Iran
- Accès au bibtex
-
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).
- Accès au texte intégral et bibtex
-
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, 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
- Accès au texte intégral et bibtex
-
- titre
- Convective dynamo action in a spherical shell: symmetries and modulation
- auteur
- Raphaël Raynaud, Steven M. Tobias
- article
- Journal of Fluid Mechanics, 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
- Accès au texte intégral et bibtex
-
Conference papers
- titre
- Convective dynamos: symmetries and modulation
- auteur
- Raphaël Raynaud, Steven M. Tobias
- article
- Advances in Geophysical and Astrophysical Turbulence, Jul 2016, Cargèse, France
- Accès au bibtex
-
- titre
- Convective dynamos: symmetries and modulation
- auteur
- Raphaël Raynaud, Steven M. Tobias
- article
- European GdR Dynamo, Jun 2016, Barcelone, Spain
- Accès au bibtex
-
- titre
- New insights into the modulation of the Sun activity
- auteur
- Raphaël Raynaud, Steven M. Tobias
- article
- 19th Meeting on Research in Astronomy, Institute for Advanced Studies in Basic Sciences (IASBS), May 2016, Zanjan, Iran
- Accès au bibtex
-
2015
Journal articles
- titre
- Dipolar dynamos in stratified systems
- auteur
- Raphaël Raynaud, Ludovic Petitdemange, Emmanuel Dormy
- article
- Monthly Notices of the Royal Astronomical Society, 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
- Accès au texte intégral et bibtex
-
Conference papers
- titre
- Dipolar dynamos in stratified systems
- auteur
- Raphaël Raynaud, Ludovic Petitdemange, Emmanuel Dormy
- article
- Stellar and planetary dynamos, May 2015, Goettingen, Germany
- resume
- Observations of low-mass stars reveal a variety of magnetic topologies ranging from large-scale, axial dipoles to more complex magnetic fields. Spherical simulations of convectivedynamos reproduce a similar diversity, either with Boussinesq or anelastic models taking intoaccount the variation of the density with depth throughout the convection zone. A conclusionfrom anelastic studies is that dipolar solutions are difficult to obtain as soon as substantialstratifications are considered. We rely on a systematic parameter study to investigate inmore detail the impact of the density stratification both on the dynamo onset and thedipole collapse. Our study indicates that the loss of the dipolar branch does not ensue froma modification of the dynamo mechanisms related to the background stratification, butcould instead result from a bias as our observations naturally favour a certain domain in theparameter space characterized by moderate values of the Ekman number, owing to currentcomputational limitations. We also show that the critical magnetic Reynolds number ofthe dipolar branch is scarcely modified, which provides an important insight into the globalunderstanding of the impact of the density stratification on the stability domain of thedipolar dynamo branch.
- Accès au bibtex
-
Theses
- titre
- Numerical modelling of the solar and stellar magnetism
- auteur
- Raphaël Raynaud
- article
- Physique [physics]. Observatoire de Paris, 2015. Français. ⟨NNT : ⟩
- resume
- Cette thèse traite de la génération d’un champ magnétique par l’écoulement d’un fluide conducteur de l’électricité, connu sous le nom d’effet dynamo. De nombreuses études numériques ont ainsi cherché à comprendre l’origine du champ magnétique terrestre par l’analyse des champs magnétiques engendrés par les mouvements de convection d’un fluide conducteur contenu dans une coquille sphérique en rotation. La plupart de ces modèles simplifiés du noyau externe de fer liquide font communément usage de l’approximation dite de Boussinesq ; cette approximation n’est cependant pas adaptée pour décrire la convection dans des systèmes fortement stratifiés tels que les intérieurs stellaires, dont la zone convective est potentiellement mieux modélisée en ayant recours à l’approximation anélastique qui considère la convection comme une perturbation par rapport à un état de référence stratifié adiabatiquement. À l’aide de simulations numériques directes, nous étudions l’influence de la stratification en densité du système sur les propriétés des champs magnétiques engendrés par effet dynamo. Nos analyses tendent à souligner la robustesse des résultats de géodynamo sur la structure et l’intensité du champ magnétique, lesquels semblent ainsi rester pertinents dans le cadre de l’étude des dynamos stellaires.
- Accès au texte intégral et bibtex
-
2014
Journal articles
- titre
- Influence of the mass distribution on the magnetic field topology
- auteur
- Raphaël Raynaud, Ludovic Petitdemange, Emmanuel Dormy
- article
- Astronomy & Astrophysics - A&A, 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
- Accès au texte intégral et bibtex
-
- titre
- Topology and field strength in spherical, anelastic dynamo simulations
- auteur
- Martin Schrinner, Ludovic Petitdemange, Raphaël Raynaud, Emmanuel Dormy
- article
- Astronomy & Astrophysics - A&A, 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
- Accès au texte intégral et bibtex
-
Poster communications
- titre
- Topology and field strength in spherical, anelastic dynamo simulations
- auteur
- Raphaël Raynaud, Martin Schrinner, Ludovic Petitdemange, Emmanuel Dormy
- article
- AGU Fall Meeting, Dec 2014, San Francisco, United States.
- 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 magnetic fields of stars and planets. Intensive and systematic parameter 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. We present the results of a systematic parameter study of spherical anelastic dynamo models, and compare them with previous results obtained in the Boussinesq approximation. We discuss the influence of the stratification on the field geometry and the field strength, and also compare the different scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux.
- Accès au texte intégral et bibtex
-
- titre
- Spherical, anelastic dynamo simulations
- auteur
- Raphaël Raynaud
- article
- Magnetic fields from the Sun to black holes - In memory of Jean Heyvaerts, Nov 2014, Paris, France
- Accès au bibtex
-
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
- 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.
- Accès au texte intégral et bibtex
-
2013
Journal articles
- titre
- Intermittency in spherical Couette dynamos
- auteur
- Raphaël Raynaud, Emmanuel Dormy
- article
- Physical Review Online Archive (PROLA), 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
- Accès au texte intégral et bibtex
-
Conference papers
- titre
- The convective approximations
- auteur
- Raphaël Raynaud
- article
- Differential Rotation and Magnetism across the HR Diagram, Nordita Scientific Program, Apr 2013, Stockholm, Sweden
- Accès au bibtex
-
Poster communications
- titre
- The convective approximations
- auteur
- Raphaël Raynaud, Ludovic Petitdemange, Emmanuel Dormy
- article
- European GdR Dynamo, Jul 2013, Ascona, Switzerland
- resume
- Convection can occur in a shallow layer of fluid with a small temperature contrast across the layer. Thus, it is natural to hope for a simpler description of buoyantly driven flows via an expansion of the fully compressible equations. The Boussinesq approximation performs well in modeling convection in laboratory experiments, but it is however unsatisfactory for large stratified systems, the lower part of which is compressed by the overlying material. More general approximations are then required to describe convection in natural systems like oceans, stars or planetary cores.
- Accès au texte intégral et bibtex
-
2012
Poster communications
- titre
- On-off intermittency in spherical Couette flow
- auteur
- Raphaël Raynaud, Stephan Fauve, Emmanuel Dormy
- article
- European GDR Dynamo, Oct 2012, Nice, France
- resume
- We perform 3D numerical simulations of dynamos in a Couette flow generated by two contra-rotating spheres. We show that the magnetic field may display on-off inter- mittency at relatively low magnetic Prandtl number, close to the onset of dynamo ac- tion. The basic signature of this phe- nomenon lies in series of short bursts of the magnetic energy (“on” phases) separated by low energy phases (“off” phases). The length of the “off” phases increases as the system gets closer to the threshold. We successfully compare our observations to predictions based on a canonical model and find it provides an accurate estimate of the threshold.
- Accès au texte intégral et bibtex
-