The effect of random alpha-fluctuations and the global properties of the solar magnetic field.
Abstract
We study the effect of rapid random fluctuations in the dynamo parameter α in a simple axisymmetric mean-field dynamo. The model is 1D; it is a shell with latitude-dependent fields. Radial turbulent diffusion is modeled by a prescribed factor exp(imagkr)/r in the field potentials. We consider mainly linear models. The fluctuations excite overtones of the fundamental mode which are otherwise damped. Butterfly diagrams and frequency spectra S_l_(ν) of the Legendre expansion coefficients c_l_(t) of the toroidal mean field [B(θ,t)={SIGMA}_l_c_l_(t)P_l_(cos θ)] are compared with observations of the solar magnetic field. The results are: (1). The model accounts for the observed relative phases of the coefficients c_l_(t) for odd l at the frequency 1/(22yr) of the fundamental mode, and potentially also for their relative amplitudes. (2). The spectra S_l_(ν) are broad and featureless for even l, while for odd l the frequency 1/(22yr) of the fundamental mode dominates. They agree qualitatively with the results of Gokhale and coworkers. It is unlikely that the modal structure in the surface field for even l found by Stenflo and colleagues can be produced by mean field models with random α-fluctuations. (3). Butterfly diagrams have a solar-type structure for 1<~kR<~5 (R = position of the bottom of the convection zone). The fluctuations generate many phenomena also seen in the solar cycle, such as slow activity modulations due to mode beating, accidental disappearances of the activity, transequatorial activity, and sometimes quite persistent North-South asymmetries in the butterfly diagram. The character of the latter depends sensitively on the value of kR. (4). The amplitudes of the eigenmodes are shown to behave as randomly excited coupled oscillators, which allows us to explain the excitation levels of the overtones, their frequency spectra and the structure of the North-South asymmetries. (5). In the latitude region where the dynamo operates the local fluctuations in ({vec}(u).∇ x {vec}(u))τ_c_ are ~60 to 70 times larger than the mean value of ({vec}(u).∇ x {vec}(u))τ_c_, and the fluctuations in α are 6 to 7 times larger than the mean value of α.
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- September 1994
- Bibcode:
- 1994A&A...289..265H
- Keywords:
-
- Dynamo Theory;
- Magnetic Variations;
- Magnetohydrodynamics;
- Power Spectra;
- Solar Activity;
- Solar Magnetic Field;
- Diffusion;
- Spherical Harmonics;
- Stellar Convection;
- Stellar Models;
- Turbulence;
- Solar Physics;
- CHAOTIC PHENOMENA;
- MHD;
- TURBULENCE;
- METHODS: STATISTICAL;
- SUN: ACTIVITY;
- SUN: MAGNETIC FIELDS