The Sun's Preferred Longitudes and the Coupling of Magnetic Dynamo Modes

Observations show that solar activity is distributed non-axisymmetrically, concentrating at "preferred longitudes". This indicates the important role of non-axisymmetric magnetic fields in the origin of solar activity. We investigate the generation of the non-axisymmetric fields and their coupling with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model operating in a sphere includes solar differential rotation, which approximates the differential rotation obtained by inversion of helioseismic data, modelled distributions of the turbulent resistivity, non-axisymmetric mean helicity, and meridional circulation in the convection zone. We find that (1) the non-axisymmetric modes are localised near the base of the convection zone, where the formation of active regions starts, and at latitudes around $30^{\circ}$; (2) the coupling of non-axisymmetric and axisymmetric modes causes the non-axisymmetric mode to follow the solar cycle; the phase relations between the modes are found. (3) The rate of rotation of the first non-axisymmetric mode is close to that determined in the interplanetary space.Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical Journa

Coupled spin models for magnetic variation of planets and stars

Geomagnetism is characterized by intermittent polarity reversals and rapid fluctuations. We have recently proposed a coupled macro-spin model to describe these dynamics based on the idea that the whole dynamo mechanism is described by the coherent interactions of many small dynamo elements. In this paper, we further develop this idea and construct a minimal model for magnetic variations. This simple model naturally yields many of the observed features of geomagnetism: its time evolution, the power spectrum, the frequency distribution of stable polarity periods, etc. This model has coexistent two phases; i.e. the cluster phase which determines the global dipole magnetic moment and the expanded phase which gives random perpetual perturbations that yield intermittent polarity flip of the dipole moment. This model can also describe the synchronization of the spin oscillation. This corresponds to the case of sun and the model well describes the quasi-regular cycles of the solar magnetism. Furthermore, by analyzing the relevant terms of MHD equation based on our model, we have obtained a scaling relation for the magnetism for planets, satellites, sun, and stars. Comparing it with various observations, we can estimate the scale of the macro-spins.Comment: 16 pages, 9 figure

Analytical determination of coronal parameters using the period ratio P₁/2P₂

<p>Context. In transverse coronal loop oscillations, two periodicities have been measured simultaneously and are interpreted as the fundamental kink mode (with period P1) and the first harmonic (with period P2). Deviations of the period ratio P1/2P2 from unity provide information about the extent of longitudinal structuring within the loop.</p> <p>Aims. Here we develop an analytical approximation that describes the shift in P1/2P2 in terms of the ratio L/Λc of the length 2L of a coronal loop and the density scale height Λc.</p> <p>Methods. We study the MHD wave equations in a low β plasma using the thin tube approximation. Disturbances are described by a differential equation which may be solved for various equilibrium density profiles, obtaining dispersion relations in terms of Bessel functions. These dispersion relations may be used to obtain analytical approximations to the periods P1 and P2. We also present a variational approach to determining the period ratio and show how the WKB method may be used.</p> <p>Results. Analytical approximations to the period ratio P1/2P2 are used to shed light on the magnitude of longitudinal structuring in a loop, leading to a determination of the density scale height. We apply our formula to the observations in Verwichte et al. (2004) and Van Doorsselaere et al. (2007), obtaining the coronal density scale height.</p> <p>Conclusions. Our simple formula and approximate approaches highlight a useful analytical tool for coronal seismology. We demonstrate that P1/2P2 is linked to the density scale height, with no need for estimates of other external parameters. Given the accuracy of current observations, our formula provides a convenient means of determining density scale heights.</p&gt

Alpha effect due to buoyancy instability of a magnetic layer

A strong toroidal field can exist in form of a magnetic layer in the overshoot region below the solar convection zone. This motivates a more detailed study of the magnetic buoyancy instability with rotation. We calculate the alpha effect due to helical motions caused by a disintegrating magnetic layer in a rotating density-stratified system with angular velocity Omega making an angle theta with the vertical. We also study the dependence of the alpha effect on theta and the strength of the initial magnetic field. We carry out three-dimensional hydromagnetic simulations in Cartesian geometry. A turbulent EMF due to the correlations of the small scale velocity and magnetic field is generated. We use the test-field method to calculate the transport coefficients of the inhomogeneous turbulence produced by the layer. We show that the growth rate of the instability and the twist of the magnetic field vary monotonically with the ratio of thermal conductivity to magnetic diffusivity. The resulting alpha effect is inhomogeneous and increases with the strength of the initial magnetic field. It is thus an example of an "anti-quenched" alpha effect. The alpha effect is nonlocal, requiring around 8--16 Fourier modes to reconstruct the actual EMF based on the actual mean field.Comment: 14 pages, 19 figures 3 tables (submitted to A & A

Instability-driven interfacial dynamo in protoneutron stars

The existence of a tachocline in the Sun has been proven by helioseismology. It is unknown whether a similar shear layer, widely regarded as the seat of magnetic dynamo action, also exists in a protoneutron star. Sudden jumps in magnetic diffusivity $\eta$ and turbulent vorticity $\alpha$, for example at the interface between the neutron-finger and convective zones, are known to be capable of enhancing mean-field dynamo effects in a protoneutron star. Here we apply the well-known, plane-parallel, MacGregor-Charbonneau analysis of the Solar interfacial dynamo to the protoneutron star problem and calculate the growth rate analytically under a range of conditions. It is shown that, like the Solar dynamo, it is impossible to achieve self-sustained growth if the discontinuities in $\alpha$, $\eta$, and shear are coincident and the magnetic diffusivity is isotropic. In contrast, when the jumps in $\eta$ and $\alpha$ are situated away from the shear layer, self-sustained growth is possible for $P\lesssim 49.8$ ms (if the velocity shear is located at $0.3R$) or $P\lesssim 83.6$ ms (if the velocity shear is located at $0.6R$). This translates into stronger shear and/or $\alpha$-effect than in the Sun. Self-sustained growth is also possible if the magnetic diffusivity if anisotropic, through the ${\bf{\Omega}}\times{\bf{J}}$ effect, even when the $\alpha$, $\eta$, and shear discontinuities are coincident.Comment: 14 pages, 5 figures, 1 tabl

Magnetoconvection and dynamo coefficients: Dependence of the alpha-effect on rotation and magnetic field

We present numerical simulations of three-dimensional compressible magnetoconvection in a rotating rectangular box that represents a section of the solar convection zone. The box contains a convectively unstable layer, surrounded by stably stratified layers with overshooting convection. The magnetic Reynolds number, Rm, is chosen subcritical, thus excluding spontaneous growth of the magnetic field through dynamo action, and the magnetic energy is maintained by introducing a constant magnetic field into the box, once convection has attained a statistically stationary state. Under the influence of the Coriolis force, the advection of the magnetic field results in a non-vanishing contribution to the mean electric field, given by uxb. From this electric field, we calculate the alpha-effect, separately for the stably and the unstably stratified layers, by averaging over time and over suitably defined volumes. From the variation of alpha we derive an error estimate, and the dependence of alpha on rotation and magnetic field strength is studied. Evidence is found for rotational quenching of the vertical alpha-effect, and for a monotonic increase of the horizontal alpha-effect with increasing rotation. For Rm~30, our results for both vertical and horizontal alpha-effect are consistent with magnetic quenching by a factor 1/[1+Rm(B_0/B_eq)^2]. The signs of the small-scale current helicity and of the vertical component of alpha are found to be opposite to those for isotropic turbulence.Comment: 14 pages, 11 figures; to appear in Astronomy & Astrophysics (accepted