Double-diffusive erosion of the core of Jupiter

We present Direct Numerical Simulations of the transport of heat and heavy elements across a double-diffusive interface or a double-diffusive staircase, in conditions that are close to those one may expect to find near the boundary between the heavy-element rich core and the hydrogen-helium envelope of giant planets such as Jupiter. We find that the non-dimensional ratio of the buoyancy flux associated with heavy element transport to the buoyancy flux associated with heat transport lies roughly between 0.5 and 1, which is much larger than previous estimates derived by analogy with geophysical double-diffusive convection. Using these results in combination with a core-erosion model proposed by Guillot et al. (2004), we find that the entire core of Jupiter would be eroded within less than 1Myr assuming that the core-envelope boundary is composed of a single interface. We also propose an alternative model that is more appropriate in the presence of a well-established double-diffusive staircase, and find that in this limit a large fraction of the core could be preserved. These findings are interesting in the context of Juno's recent results, but call for further modeling efforts to better understand the process of core erosion from first principles.Comment: Accepted for publication in Ap

The Sun's meridional circulation and interior magnetic field

To date, no self-consistent numerical simulation of the solar interior has succeeded in reproducing the observed thinness of the solar tachocline, and the persistence of uniform rotation beneath it. Although it is known that the uniform rotation can be explained by the presence of a global-scale confined magnetic field, numerical simulations have thus far failed to produce any solution where such a field remains confined against outward diffusion. We argue that the problem lies in the choice of parameters for which these numerical simulations have been performed. We construct a simple analytical magneto-hydrodynamic model of the solar interior and identify several distinct parameter regimes. For realistic solar parameter values, our results are in broad agreement with the tachocline model of Gough & McIntyre. In this regime, meridional flows driven at the base of the convection zone are of sufficient amplitude to hold back the interior magnetic field against diffusion. For the parameter values used in existing numerical simulations, on the other hand, we find that meridional flows are significantly weaker and, we argue, unable to confine the interior field. We propose a method for selecting parameter values in future numerical models.Comment: 49 pages, 11 figures, in press in the Astrophysical Journa

A practical model of convective dynamics for stellar evolution calculations

Turbulent motions in the interior of a star play an important role in its evolution, since they transport chemical species, thermal energy and angular momentum. Our overall goal is to construct a practical turbulent closure model for convective transport that can be used in a multi-dimensional stellar evolution calculation including the effects of rotation, shear and magnetic fields. Here, we focus on the first step of this task: capturing the well-known transition from radiative heat transport to turbulent convection with and without rotation, as well as the asymptotic relationship between turbulent and radiative transport in the limit of large Rayleigh number. We extend the closure model developed by Ogilvie (2003) and Garaud and Ogilvie (2005) to include heat transport and compare it with experimental results of Rayleigh-Benard convection.Comment: Conference proceeding for poster at conference "Unsolved problems in Stellar Physics

Global shallow water magnetohydrodynamic waves in the solar tachocline

We derive analytical solutions and dispersion relations of global magnetic Poincar\'e (magneto-gravity) and magnetic Rossby waves in the approximation of shallow water magnetohydrodynamics. The solutions are obtained in a rotating spherical coordinate system for strongly and weakly stable stratification separately in the presence of toroidal magnetic field. In both cases magnetic Rossby waves split into fast and slow magnetic Rossby modes. In the case of strongly stable stratification (valid in the radiative part of the tachocline) all waves are slightly affected by the layer thickness and the toroidal magnetic field, while in the case of weakly stable stratification (valid in the upper overshoot layer of the tachocline) magnetic Poincar\'e and fast magnetic Rossby waves are found to be concentrated near the solar equator, leading to equatorially trapped waves. However, slow magnetic Rossby waves tend to concentrate near the poles, leading to polar trapped waves. The frequencies of all waves are smaller in the upper weakly stable stratification region than in the lower strongly stable stratification one

Individual and collective behavior of dust particles in a protoplanetary nebula

We study the interaction between gas and dust particles in a protoplanetary disk, comparing analytical and numerical results. We first calculate analytically the trajectories of individual particles undergoing gas drag in the disk, in the asymptotic cases of very small particles (Epstein regime) and very large particles (Stokes regime). Using a Boltzmann averaging method, we then infer their collective behavior. We compare the results of this analytical formulation against numerical computations of a large number of particles. Using successive moments of the Boltzmann equation, we derive the equivalent fluid equations for the average motion of the particles; these are intrinsically different in the Epstein and Stokes regimes. We are also able to study analytically the temporal evolution of a collection of particles with a given initial size-distribution provided collisions are ignored.Comment: 15 pages, 9 figures, submitted to Ap

Dynamics of the solar tachocline II: the stratified case

We present a detailed numerical study of the Gough & McIntyre model for the solar tachocline. This model explains the uniformity of the rotation profile observed in the bulk of the radiative zone by the presence of a large-scale primordial magnetic field confined below the tachocline by flows originating from within the convection zone. We attribute the failure of previous numerical attempts at reproducing even qualitatively Gough & McIntyre's idea to the use of boundary conditions which inappropriately model the radiative--convective interface. We emphasize the key role of flows downwelling from the convection zone in confining the assumed internal field. We carefully select the range of parameters used in the simulations to guarantee a faithful representation of the hierarchy of expected lengthscales. We then present, for the first time, a fully nonlinear and self-consistent numerical solution of the Gough & McIntyre model which qualitatively satisfies the following set of observational constraints: (i) the quenching of the large-scale differential rotation below the tachocline - including in the polar regions - as seen by helioseismology (ii) the confinement of the large-scale meridional flows to the uppermost layers of the radiative zone as required by observed light element abundances and suggested by helioseismic sound-speed data.Comment: 21 pages, 15 figures, submitted to MNRA