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Register a new userNon-linear and chaotic dynamo regimes
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Axel Brandenburg
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An update is given on the current status of solar and stellar dynamos. At present, it is still unclear why stellar cycle frequencies increase with rotation frequency in such a way that their ratio increases with stellar activity. The small-scale dynamo is expected to operate in spite of a small value of the magnetic Prandtl number in stars. Whether or not the global magnetic activity in stars is a shallow or deeply rooted phenomenon is another open question. Progress in demonstrating the presence and importance of magnetic helicity fluxes in dynamos is briefly reviewed, and finally the role of nonlocality is emphasized in modeling stellar dynamos using the mean-field approach. On the other hand, direct numerical simulations have now come to the point where the models show solar-like equatorward migration that can be compared with observations and that need to be understood theoretically.
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We present a study of the Rayleigh-Taylor unstable regime of accretion onto rotating magnetized stars in a set of high grid resolution three-dimensional (3D) magnetohydrodynamic (MHD) simulations performed in low-viscosity discs. We find that the boundary between the stable and unstable regimes is determined almost entirely by the fastness parameter omega_s=Omega_star/Omega_K(r_m), where Omega_star is the angular velocity of the star and Omega_K(r_m) is the angular velocity of the Keplerian disc at the disc-magnetosphere boundary r=r_m. We found that accretion is unstable if omega_s < 0.6. Accretion through instabilities is present in stars with different magnetospheric sizes. However, only in stars with relatively small magnetospheres, r_m/R_star < 7, do the unstable tongues produce chaotic hot spots on the stellar surface and irregular light-curves. At even smaller values of the fastness parameter, omega_s < 0.45, multiple irregular tongues merge, forming one or two ordered unstable tongues that rotate with the angular frequency of the inner disc. This transition occurs in stars with even smaller magnetospheres, r_m/R_star < 4.2. Most of our simulations were performed at a small tilt of the dipole magnetosphere, Theta=5 degrees, and a small viscosity parameter alpha=0.02. Test simulations at higher alpha values show that many more cases become unstable, and the light-curves become even more irregular. Test simulations at larger tilts of the dipole Theta show that instability is present, however, accretion in two funnel streams dominates if Theta > 15 degrees. The results of these simulations can be applied to accreting magnetized stars with relatively small magnetospheres: Classical T Tauri stars, accreting millisecond X-ray pulsars, and cataclysmics variables.
Though generated deep inside the convection zone, the solar magnetic field has a direct impact on the Earth space environment via the Parker spiral. It strongly modulates the solar wind in the whole heliosphere, especially its latitudinal and longitudinal speed distribution over the years. However the wind also influences the topology of the coronal magnetic field by opening the magnetic field lines in the coronal holes, which can affect the inner magnetic field of the star by altering the dynamo boundary conditions. This coupling is especially difficult to model because it covers a large variety of spatio-temporal scales. Quasi-static studies have begun to help us unveil how the dynamo-generated magnetic field shapes the wind, but the full interplay between the solar dynamo and the solar wind still eludes our understanding. We use the compressible magnetohydrodynamical (MHD) code PLUTO to compute simultaneously in 2.5D the generation and evolution of magnetic field inside the star via an alpha-Omega dynamo process and the corresponding evolution of a polytropic coronal wind over several activity cycles for a young Sun. A multi-layered boundary condition at the surface of the star connects the inner and outer stellar layers, allowing both to adapt dynamically. Our continuously coupled dynamo-wind model allows us to characterize how the solar wind conditions change as a function of the cycle phase, and also to quantify the evolution of integrated quantities such as the Alfven radius. We further assess the impact of the solar wind on the dynamo itself by comparing our results with and without wind feedback.
The Von K{a}rm{a}n Sodium experiment yields a variety of dynamo regimes, when asymmetry is imparted to the flow by rotating impellers at different speed F1 and F2. We show that as the intensity of forcing, measured as F1 + F2, is increased, the transition to a self-sustained magnetic field is always observed via a supercritical bifurcation to a stationary state. For some values of the asymmetry parameter $theta$ = (F1--F2)/(F1+F2), time dependent dynamo regimes develop. They are observed either when the forcing is increased for a given value of asymmetry, or when the amount of asymmetry is varied at sufficiently high forcing. Two qualitatively different transitions between oscillatory and stationary regimes are reported, involving or not a strong divergence of the period of oscillations. These transitions can be interpreted using a low dimensional model based on the interactions of two dynamo modes.
The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time $t$, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases.
In the paper we study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density pattern around the bipolar regions depends on the configuration of the ambient large-scale magnetic field, and in general they show the quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time-latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regions show two bands of sign for the density distribution in each hemisphere. Similar helicity density patterns are provided by the helicity density flux from the emerging bipolar regions subjected to the surface differential rotation. Examining effect of helicity fluxes from the bipolar regions on the large-scale dynamo we find that its effect to the dynamo saturation is negligible.
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