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We use 123 three dimensional direct numerical simulations to study fingering convection in non-rotating spherical shells. We investigate the scaling behaviour of the flow lengthscale, the non-dimensional heat and compositional fluxes $Nu$ and $Sh$ and the mean convective velocity over the fingering convection instability domain defined by $1 \leq R_\rho < Le$, $R_\rho$ being the ratio of density perturbations of thermal and compositional origins and $Le$ the Lewis number. We show that the chemical boundary layers are marginally unstable and adhere to the laminar Prandtl-Blasius model, hence explaining the asymmetry between the inner and outer spherical shell boundary layers. We develop scaling laws for two asymptotic regimes close to the two edges of the instability domain, namely $R_\rho \lesssim Le$ and $R_\rho \gtrsim 1$. For the former, we develop novel power laws of a small parameter $\epsilon$ measuring the distance to onset, which differ from theoretical laws published to date in Cartesian geometry. For the latter, we find that the Sherwood number $Sh$ gradually approaches a scaling $Sh\sim Ra_\xi^{1/3}$ when $Ra_\xi \gg 1$; and that the P\'eclet number accordingly follows $Pe \sim Ra_\xi^{2/3} |Ra_T|^{-1/4}$, $Ra_\xi$ being the chemical Rayleigh number. When the Reynolds number exceeds a few tens, we report on a secondary instability which takes the form of large-scale toroidal jets which span the entire spherical domain. Jets distort the fingers resulting in Reynolds stress correlations, which in turn feed the jet growth until saturation. This nonlinear phenomenon can yield relaxation oscillation cycles., Comment: 45 pages, 21 figures, 3 tables, accepted for publication in JFM

Convection occurs ubiquitously on and in rotating geophysical and astrophysical bodies. Prior spherical shell studies have shown that the convection dynamics in polar regions can differ significantly from the lower latitude, equatorial dynamics. Yet most spherical shell convective scaling laws use globally-averaged quantities that erase latitudinal differences in the physics. Here we quantify those latitudinal differences by analyzing spherical shell simulations in terms of their regionalized convective heat transfer properties. This is done by measuring local Nusselt numbers in two specific, latitudinally separate, portions of the shell, the polar and the equatorial regions, $Nu_p$ and $Nu_e$, respectively. In rotating spherical shells, convection first sets in outside the tangent cylinder such that equatorial heat transfer dominates at small and moderate supercriticalities. We show that the buoyancy forcing, parameterized by the Rayleigh number $Ra$, must exceed the critical equatorial forcing by a factor of $\approx 20$ to trigger polar convection within the tangent cylinder. Once triggered, $Nu_p$ increases with $Ra$ much faster than does $Nu_e$. The equatorial and polar heat fluxes then tend to become comparable at sufficiently high $Ra$. Comparisons between the polar convection data and Cartesian numerical simulations reveal quantitative agreement between the two geometries in terms of heat transfer and averaged bulk temperature gradient. This agreement indicates that spherical shell rotating convection dynamics are accessible both through spherical simulations and via reduced investigatory pathways, be they theoretical, numerical or experimental., Comment: 11 pages, 6 figures, accepted for publication in JFM

Observations of surface magnetic fields of cool stars reveal a large diversity of configurations. Although there is now a consensus that these fields are generated through dynamo processes occurring within the convective zone, the physical mechanism driving such a variety of field topologies is still debated. This paper discusses the possible origins of dipole and multipole-dominated morphologies using three-dimensional numerical simulations of stratified systems where the magnetic feedback on the fluid motion is significant. Our main result is that dipolar solutions are found at Rossby numbers up to 0.4 in strongly stratified simulations, where previous works suggested that only multipolar fields should exist. We argue that these simulations are reminiscent of the outlier stars observed at Rossby numbers larger than 0.1, whose large-scale magnetic field is dominated by their axisymmetric poloidal component. As suggested in previous Boussinesq calculations, the relative importance of inertial over Lorentz forces is again controlling the dipolar to multipolar transition. Alternatively, we find that the ratio of kinetic to magnetic energies can equally well capture the transition in the field morphology. We test the ability of this new proxy to predict the magnetic morphology of a few M-dwarf stars whose internal structure matches that of our simulations and for which homogeneous magnetic field characterization is available. Finally, the magnitude of the differential rotation obtained in our simulations is compared to actual measurements reported in the literature for M-dwarfs. In our simulations, we find a clear relationship between anti-solar differential rotation and the emergence of dipolar fields., Comment: 15 pages, 15 figures, accepted for publication in MNRAS

Rayleigh-B\'enard convection in rotating spherical shells can be considered as a simplified analogue of many astrophysical and geophysical fluid flows. Here, we use three-dimensional direct numerical simulations to study this physical process. We construct a dataset of more than 200 numerical models that cover a broad parameter range with Ekman numbers spanning $3\times 10^{-7} \leq E \leq 10^{-1}$, Rayleigh numbers within the range $10^3 < Ra < 2\times 10^{10}$ and a Prandtl number unity. We investigate the scaling behaviours of both local (length scales, boundary layers) and global (Nusselt and Reynolds numbers) properties across various physical regimes from onset of rotating convection to weakly-rotating convection. Close to critical, the convective flow is dominated by a triple force balance between viscosity, Coriolis force and buoyancy. For larger supercriticalities, a subset of our numerical data approaches the asymptotic diffusivity-free scaling of rotating convection $Nu\sim Ra^{3/2}E^{2}$ in a narrow fraction of the parameter space delimited by $6\,Ra_c \leq Ra \leq 0.4\,E^{-8/5}$. Using a decomposition of the viscous dissipation rate into bulk and boundary layer contributions, we establish a theoretical scaling of the flow velocity that accurately describes the numerical data. In rapidly-rotating turbulent convection, the fluid bulk is controlled by a triple force balance between Coriolis, inertia and buoyancy, while the remaining fraction of the dissipation can be attributed to the viscous friction in the Ekman layers. Beyond $Ra \simeq E^{-8/5}$, the rotational constraint on the convective flow is gradually lost and the flow properties vary to match the regime changes between rotation-dominated and non-rotating convection. The quantity $Ra E^{12/7}$ provides an accurate transition parameter to separate rotating and non-rotating convection., Comment: 42 pages, 20 figures, 3 tables, accepted for publication in JFM

We simulate numerically Boussinesq convection in non-rotating spherical shells for a fluid with a unity Prandtl number and Rayleigh numbers up to $10^9$. In this geometry, curvature and radial variations of the gravitationnal acceleration yield asymmetric boundary layers. A systematic parameter study for various radius ratios (from $\eta=r_i/r_o=0.2$ to $\eta=0.95$) and gravity profiles allows us to explore the dependence of the asymmetry on these parameters. We find that the average plume spacing is comparable between the spherical inner and outer bounding surfaces. An estimate of the average plume separation allows us to accurately predict the boundary layer asymmetry for the various spherical shell configurations explored here. The mean temperature and horizontal velocity profiles are in good agreement with classical Prandtl-Blasius laminar boundary layer profiles, provided the boundary layers are analysed in a dynamical frame, that fluctuates with the local and instantaneous boundary layer thicknesses. The scaling properties of the Nusselt and Reynolds numbers are investigated by separating the bulk and boundary layer contributions to the thermal and viscous dissipation rates using numerical models with $\eta=0.6$ and a gravity proportional to $1/r^2$. We show that our spherical models are consistent with the predictions of Grossmann \& Lohse's (2000) theory and that $Nu(Ra)$ and $Re(Ra)$ scalings are in good agreement with plane layer results., Comment: 43 pages, 25 figures, 2 tables, accepted for publication in JFM

Stellar magnetic field measurements obtained from spectropolarimetry offer key data for activity and dynamo studies, and we present the results of a major high-resolution spectropolarimetric Bcool project magnetic snapshot survey of 170 solar-type stars from observations with the Telescope Bernard Lyot and the Canada-France-Hawaii Telescope. For each target star a high signal-to-noise circularly polarised Stokes V profile has been obtained using Least-Squares Deconvolution, and used to detect surface magnetic fields and measure the corresponding mean surface longitudinal magnetic field ($B_{l}$). Chromospheric activity indicators were also measured. Surface magnetic fields were detected for 67 stars, with 21 of these stars classified as mature solar-type stars, a result that increases by a factor of four the number of mature solar-type stars on which magnetic fields have been observed. In addition, a magnetic field was detected for 3 out of 18 of the subgiant stars surveyed. For the population of K-dwarfs the mean value of $B_{l}$ ($|B_{l}|_{mean}$) was also found to be higher (5.7 G) than $|B_{l}|_{mean}$ measured for the G-dwarfs (3.2 G) and the F-dwarfs (3.3 G). For the sample as a whole $|B_{l}|_{mean}$ increases with rotation rate and decreases with age, and the upper envelope for $|B_{l}|$ correlates well with the observed chromospheric emission. Stars with a chromospheric S-index greater than about 0.2 show a high magnetic field detection rate and so offer optimal targets for future studies. This survey constitutes the most extensive spectropolarimetric survey of cool stars undertaken to date, and suggests that it is feasible to pursue magnetic mapping of a wide range of moderately active solar-type stars to improve understanding of their surface fields and dynamos., Comment: 36 pages, 26 figures, 7 tables, submitted to MNRAS

Stellar differential rotation can be separated into two main regimes: solar-like when the equator rotates faster than the poles and anti-solar when the polar regions rotate faster than the equator. We investigate the transition between these two regimes with 3-D numerical simulations of rotating spherical shells. We conduct a systematic parameter study which also includes models from different research groups. We find that the direction of the differential rotation is governed by the contribution of the Coriolis force in the force balance, independently of the model setup (presence of a magnetic field, thickness of the convective layer, density stratification). Rapidly-rotating cases with a small Rossby number yield solar-like differential rotation, while weakly-rotating models sustain anti-solar differential rotation. Close to the transition, the two kinds of differential rotation are two possible bistable states. This study provides theoretical support for the existence of anti-solar differential rotation in cool stars with large Rossby numbers., Comment: 5 pages, 6 figures, accepted for publication in MNRAS

Observations of active M dwarfs show a broad variety of large-scale magnetic fields encompassing dipole-dominated and multipolar geometries. We detail the analogy between some anelastic dynamo simulations and spectropolarimetric observations of 23 M stars. In numerical models, the relative contribution of inertia and Coriolis force in the global force balance -estimated by the so-called local Rossby number- is known to have a strong impact on the magnetic field geometry. We discuss the relevance of this parameter in setting the large-scale magnetic field of M dwarfs., Comment: 4 pages, 3 figures, conference proceeding, IAUS 302 'Magnetic Fields Throughout the Stellar Evolution', (26-30 Aug 2013, Biarritz, France)

Context: observations of rapidly rotating M dwarfs show a broad variety of large-scale magnetic fields encompassing dipole-dominated and multipolar geometries. In dynamo models, the relative importance of inertia in the force balance -- quantified by the local Rossby number -- is known to have a strong impact on the magnetic field geometry. Aims: we aim to assess the relevance of the local Rossby number in controlling the large-scale magnetic field geometry of M dwarfs. Methods: we explore the similarities between anelastic dynamo models in spherical shells and observations of active M-dwarfs, focusing on field geometries derived from spectropolarimetric studies. To do so, we construct observation-based quantities aimed to reflect the diagnostic parameters employed in numerical models. Results: the transition between dipole-dominated and multipolar large-scale fields in early to mid M dwarfs is tentatively attributed to a Rossby number threshold. We interpret late M dwarfs magnetism to result from a dynamo bistability occurring at low Rossby number. By analogy with numerical models, we expect different amplitudes of differential rotation on the two dynamo branches., Comment: 4 pages, 4 figures, accepted for publication in A&A

The surface zonal winds observed in the giant planets form a complex jet pattern with alternating prograde and retrograde direction. While the main equatorial band is prograde on the gas giants, both ice giants have a pronounced retrograde equatorial jet. We use three-dimensional numerical models of compressible convection in rotating spherical shells to explore the properties of zonal flows in different regimes where either rotation or buoyancy dominates the force balance. We conduct a systematic parameter study to quantify the dependence of zonal flows on the background density stratification and the driving of convection. We find that the direction of the equatorial zonal wind is controlled by the ratio of buoyancy and Coriolis force. The prograde equatorial band maintained by Reynolds stresses is found in the rotation-dominated regime. In cases where buoyancy dominates Coriolis force, the angular momentum per unit mass is homogenised and the equatorial band is retrograde, reminiscent to those observed in the ice giants. In this regime, the amplitude of the zonal jets depends on the background density contrast with strongly stratified models producing stronger jets than comparable weakly stratified cases. Furthermore, our results can help to explain the transition between solar-like and "anti-solar" differential rotations found in anelastic models of stellar convection zones. In the strongly stratified cases, we find that the leading order force balance can significantly vary with depth (rotation-dominated inside and buoyancy-dominated in a thin surface layer). This so-called "transitional regime" has a visible signature in the main equatorial jet which shows a pronounced dimple where flow amplitudes notably decay towards the equator. A similar dimple is observed on Jupiter, which suggests that convection in the planet interior could possibly operate in this regime., Comment: 20 pages, 15 figures, 4 tables, accepted for publication in Icarus

Context: dynamo action in giant planets and rapidly rotating stars leads to a broad variety of magnetic field geometries including small scale multipolar and large scale dipole-dominated topologies. Previous dynamo models suggest that solutions become multipolar once inertia becomes influential. Being tailored for terrestrial planets, most of these models neglected the background density stratification. Aims: we investigate the influence of the density stratification on convection-driven dynamo models. Methods: three-dimensional nonlinear simulations of rapidly rotating spherical shells are employed using the anelastic approximation to incorporate density stratification. A systematic parametric study for various density stratifications and Rayleigh numbers allows to explore the dependence of the magnetic field topology on these parameters. Results: anelastic dynamo models tend to produce a broad range of magnetic field geometries that fall on two distinct branches with either strong dipole-dominated or weak multipolar fields. As long as inertia is weak, both branches can coexist but the dipolar branch vanishes once inertia becomes influential. The dipolar branch also vanishes for stronger density stratifications. The reason is the concentration of the convective columns in a narrow region close to the outer boundary equator, a configuration that favors non-axisymmetric solutions. In multipolar solutions, zonal flows can become significant and participate in the toroidal field generation. Parker dynamo waves may then play an important role close to onset of dynamo action leading to a cyclic magnetic field behavior. Conclusion: Our simulations also suggest that the fact that late M dwarfs have dipolar or multipolar magnetic fields can be explained in two ways. They may differ either by the relative influence of inertia or fall into the regime where both types of solutions coexist., Comment: 13 pages, 13 figures, 2 tables, accepted for publication in A&A

In cold Cepheids close to the red edge of the classical instability strip, a strong coupling between the stellar pulsations and the surface convective motions occurs. This coupling is by now poorly described by 1-D models of convection, the so-called "time-dependent convection models" (TDC). The intrinsic weakness of such models comes from the large number of unconstrained free parameters entering in the description of turbulent convection. A way to overcome these limits is to compute two-dimensional direct simulations (DNS), in which all the nonlinearities are correctly solved. Two-dimensional DNS of the convection-pulsation coupling are presented here. In an appropriate parameter regime, convective motions can actually quench the radial pulsations of the star, as suspected in Cepheids close to the red edge of the instability strip. These nonlinear simulations can also be used to determine the limits and the relevance of the TDC models., Comment: 5 pages, 3 figures, sf2a proceeding

Aims. We aim to investigate the long-term temporal evolution of the magnetic field of the solar-type star \xi Bootis A, both from direct magnetic field measurements and from the simultaneous estimate of indirect activity indicators. Methods. We obtained seven epochs of high-resolution, circularly-polarized spectra from the NARVAL spectropolarimeter between 2007 and 2011, for a total of 76 spectra. Using approximately 6,100 photospheric spectral lines covering the visible domain, we employed a cross-correlation procedure to compute a mean polarized line profile from each spectrum. The large-scale photospheric magnetic field of the star was then modelled by means of Zeeman-Doppler Imaging, allowing us to follow the year-to-year evolution of the reconstructed magnetic topology. Simultaneously, we monitored the width of several magnetically sensitive spectral lines, the radial velocity, the line asymmetry of intensity line profiles, and the chromospheric emission in the cores of the Ca II H and Halpha lines. Results. During the highest observed activity states, in 2007 and 2011, the large-scale field of \xi Boo A is almost completely axisymmetric and is dominated by its toroidal component. The magnetic topologies reconstructed for these activity maxima are very similar, suggesting a form of short cyclicity in the large-scale field distribution. Correlated temporal evolution, due to both rotational modulation and seasonal variability, is observed between the Ca II emission, the Halpha emission and the width of magnetically sensitive lines. When measurable, the differential rotation reveals a strong latitudinal shear in excess of 0.2 rad/d., Comment: 16 pages, 8 figures, accepted for publication in A&A, abstract shortened to respect the 1920 characters required

Context: In Cepheids close to the red edge of the classical instability strip, a coupling occurs between the acoustic oscillations and the convective motions close to the surface.The best topical models that account for this coupling rely on 1-D time-dependent convection (TDC) formulations. However, their intrinsic weakness comes from the large number of unconstrained free parameters entering in the description of turbulent convection. Aims: We compare two widely used TDC models with the first two-dimensional nonlinear direct numerical simulations (DNS) of the convection-pulsation coupling in which the acoustic oscillations are self-sustained by the kappa-mechanism. Methods: The free parameters appearing in the Stellingwerf and Kuhfuss TDC recipes are constrained using a chi2-test with the time-dependent convective flux that evolves in nonlinear simulations of highly-compressible convection with kappa-mechanism. Results: This work emphasises some inherent limits of TDC models, that is, the temporal variability and non-universality of their free parameters. More importantly, within these limits, Stellingwerf's formalism is found to give better spatial and temporal agreements with the nonlinear simulation than Kuhfuss's one. It may therefore be preferred in 1-D TDC hydrocodes or stellar evolution codes., Comment: 7 pages, 5 figures, 2 tables, accepted for publication in A&A

Phase-resolved observations of the solar-type star Ksi Bootis A were obtained using the NARVAL spectropolarimeter at the Telescope Bernard Lyot (Pic du Midi, France) during years 2007, 2008, 2009 and 2010. The data sets enable us to study both the rotational modulation and the long-term evolution of various magnetic and activity tracers. Here, we focus on the large-scale photospheric magnetic field (reconstructed by Zeeman-Doppler Imaging), the Zeeman broadening of the FeI 846.84 nm magnetic line, and the chromospheric CaII H and H alpha emission., Comment: 6 pages, 4 figures, Cool Stars 16 proceeding

Magnetic fields of cool stars can be directly investigated through the study of the Zeeman effect on photospheric spectral lines using several approaches. With spectroscopic measurement in unpolarised light, the total magnetic flux averaged over the stellar disc can be derived but very little information on the field geometry is available. Spectropolarimetry provides a complementary information on the large-scale component of the magnetic topology. With Zeeman-Doppler Imaging (ZDI), this information can be retrieved to produce a map of the vector magnetic field at the surface of the star, and in particular to assess the relative importance of the poloidal and toroidal components as well as the degree of axisymmetry of the field distribution. The development of high-performance spectropolarimeters associated with multi-lines techniques and ZDI allows us to explore magnetic topologies throughout the Hertzsprung-Russel diagram, on stars spanning a wide range of mass, age and rotation period. These observations bring novel constraints on magnetic field generation by dynamo effect in cool stars. In particular, the study of solar twins brings new insight on the impact of rotation on the solar dynamo, whereas the detection of strong and stable dipolar magnetic fields on fully convective stars questions the precise role of the tachocline in this process., Comment: 6 pages, 2 figures, IAU Symposium 273 "Physics of Sun and Star Spots", 22-26 August 2010

Context: we study the convection-pulsation coupling that occurs in cold Cepheids close to the red edge of the classical instability strip. In these stars, the surface convective zone is supposed to stabilise the radial oscillations excited by the kappa-mechanism. Aims: we study the influence of the convective motions onto the amplitude and the nonlinear saturation of acoustic modes excited by kappa-mechanism. We are interested in determining the physical conditions needed to lead to a quenching of oscillations by convection. Methods: we compute two-dimensional nonlinear simulations (DNS) of the convection-pulsation coupling, in which the oscillations are sustained by a continuous physical process: the kappa-mechanism. Thanks to both a frequential analysis and a projection of the physical fields onto an acoustic subspace, we study how the convective motions affect the unstable radial oscillations. Results: depending on the initial physical conditions, two main behaviours are obtained: (i) either the unstable fundamental acoustic mode has a large amplitude, carries the bulk of the kinetic energy and shows a nonlinear saturation similar to the purely radiative case; (ii) or the convective motions affect significantly the mode amplitude that remains very weak. In this second case, convection is quenching the acoustic oscillations. We interpret these discrepancies in terms of the difference in density contrast: larger stratification leads to smaller convective plumes that do not affect much the purely radial modes, while large-scale vortices may quench the oscillations., Comment: 15 pages, 17 figures, 3 tables, accepted for publication in A&A

A strong coupling between convection and pulsations is known to play a major role in the disappearance of unstable modes close to the red edge of the classical Cepheid instability strip. As mean-field models of time-dependent convection rely on weakly-constrained parameters, we tackle this problem by the means of 2-D Direct Numerical Simulations (DNS) of kappa-mechanism with convection. Using a linear stability analysis, we first determine the physical conditions favourable to the kappa-mechanism to occur inside a purely-radiative layer. Both the instability strips and the nonlinear saturation of unstable modes are then confirmed by the corresponding DNS. We next present the new simulations with convection, where a convective zone and the driving region overlap. The coupling between the convective motions and acoustic modes is then addressed by using projections onto an acoustic subspace., Comment: 5 pages, 6 figures, accepted for publication in Astrophysics and Space Science, HELAS workshop (Rome june 2009)