Magnetic energy cascade in spherical geometry: I. The stellar convective dynamo case

We present a method to characterize the spectral transfers of magnetic energy between scales in simulations of stellar convective dynamos. The full triadic transfer functions are computed thanks to analytical coupling relations of spherical harmonics based on the Clebsch-Gordan coefficients. The method is applied to mean field $\alpha\Omega$ dynamo models as benchmark tests. From the physical standpoint, the decomposition of the dynamo field into primary and secondary dynamo families proves very instructive in the $\alpha\Omega$ case. The same method is then applied to a fully turbulent dynamo in a solar convection zone, modeled with the 3D MHD ASH code. The initial growth of the magnetic energy spectrum is shown to be non-local. It mainly reproduces the kinetic energy spectrum of convection at intermediate scales. During the saturation phase, two kinds of direct magnetic energy cascades are observed in regions encompassing the smallest scales involved in the simulation. The first cascade is obtained through the shearing of magnetic field by the large scale differential rotation that effectively cascades magnetic energy. The second is a generalized cascade that involves a range of local magnetic and velocity scales. Non-local transfers appear to be significant, such that the net transfers cannot be reduced to the dynamics of a small set of modes. The saturation of the large scale axisymmetric dipole and quadrupole are detailed. In particular, the dipole is saturated by a non-local interaction involving the most energetic scale of the magnetic energy spectrum, which points out the importance of the magnetic Prandtl number for large-scale dynamos.Comment: 21 pages, 14 figures, 1 table, accepted for publication in the Astrophysical Journa

A simple model of quantum trajectories

Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. In this paper I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different ``unravelings'' of a mixed state master equation. I also comment briefly on the relationship of the theory to the Consistent Histories formalism and to spontaneous collapse models.Comment: 42 pages RevTeX including four figures in encapsulated postscript. Submitted to special issue of American Journal of Physic

Influence of the Tachocline on Solar Evolution

Recently helioseismic observations have revealed the presence of a shear layer at the base of the convective zone related to the transition from differential rotation in the convection zone to almost uniform rotation in the radiative interior, the tachocline. At present, this layer extends only over a few percent of the solar radius and no definitive explanations have been given for this thiness. Following Spiegel and Zahn (1992, Astron. Astrophys.), who invoke anisotropic turbulence to stop the spread of the tachocline deeper in the radiative zone as the Sun evolves, we give some justifications for their hypothesis by taking into account recent results on rotating shear instability (Richard and Zahn 1999, Astron. Astrophys.). We study the impact of the macroscopic motions present in this layer on the Sun's structure and evolution by introducing a macroscopic diffusivity $D_T$ in updated solar models. We find that a time dependent treatment of the tachocline significantly improves the agreement between computed and observed surface chemical species, such as the $^7$Li and modify the internal structure of the Sun (Brun, Turck-Chi\`eze and Zahn, 1999, in Astrophys. J.).Comment: to appear in Annals of the New York Academy of Sciences, vol 898. Postscript file, 9 pages and 5 figures New Email Address for A. S. Brun: [email protected]

Magnetic games between a planet and its host star: the key role of topology

Magnetic interactions between a star and a close-in planet are postulated to be a source of enhanced emissions and to play a role in the secular evolution of the orbital system. Close-in planets generally orbit in the sub-alfv\'enic region of the stellar wind, which leads to efficient transfers of energy and angular momentum between the star and the planet. We model the magnetic interactions occurring in close-in star-planet systems with three-dimensional, global, compressible magneto-hydrodynamic numerical simulations of a planet orbiting in a self-consistent stellar wind. We focus on the cases of magnetized planets and explore three representative magnetic configurations. The Poynting flux originating from the magnetic interactions is an energy source for enhanced emissions in star-planet systems. Our results suggest a simple geometrical explanation for ubiquitous on/off enhanced emissions associated with close-in planets, and confirm that the Poynting fluxes can reach powers of the order of $10^{19}$ W. Close-in planets are also showed to migrate due to magnetic torques for sufficiently strong stellar wind magnetic fields. The topology of the interaction significantly modifies the shape of the magnetic obstacle that leads to magnetic torques. As a consequence, the torques can vary by at least an order of magnitude as the magnetic topology of the interaction varies.Comment: 15 pages, 6 figures, accepted for publication in The Astrophysical Journa

Global Dynamics of Subsurface Solar Active Regions

We present three-dimensional numerical simulations of a magnetic loop evolving in either a convectively stable or unstable rotating shell. The magnetic loop is introduced in the shell in such a way that it is buoyant only in a certain portion in longitude, thus creating an \Omega-loop. Due to the action of magnetic buoyancy, the loop rises and develops asymmetries between its leading and following legs, creating emerging bipolar regions whose characteristics are similar to the ones of observed spots at the solar surface. In particular, we self-consistently reproduce the creation of tongues around the spot polarities, which can be strongly affected by convection. We moreover emphasize the presence of ring-shaped magnetic structures around our simulated emerging regions, which we call "magnetic necklace" and which were seen in a number of observations without being reported as of today. We show that those necklaces are markers of vorticity generation at the periphery and below the rising magnetic loop. We also find that the asymmetry between the two legs of the loop is crucially dependent on the initial magnetic field strength. The tilt angle of the emerging regions is also studied in the stable and unstable cases and seems to be affected both by the convective motions and the presence of a differential rotation in the convective cases.Comment: 23 pages (ApJ 2-column format), 19 figures, accepted for publication in Ap