Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

scholarly journals Solar Internal Rotation, the Boundary Layer Dynamo and Latitude Distribution of Activity Belts

1991 ◽  
Vol 130 ◽  
pp. 237-240
Author(s):  
G. Belvedere ◽  
M.R.E. Proctor ◽  
G. Lanzafame
Keyword(s):  
Boundary Layer ◽  
Internal Rotation ◽  
Radial Profile ◽  
Active Regions ◽  
Dynamo Model ◽  
Main Sequence Stars ◽  
Dynamo Action ◽  
Latitude Distribution ◽  
Thin Spherical Shell ◽  
And Migration

Abstract We suggest that the latitude distribution of solar activity belts and the related equatorward or poleward migration of different tracers of the solar cycle are a natural consequence of the internal radial profile of angular velocity via the working of a dynamo in the boundary layer beneath the convection zone. This has been confirmed by the results of a non-linear dynamo model in a very thin spherical shell which show that dynamo action may reasonably take place in the boundary layer and reproduce the observed surface phenomenology.Extending the argument to late main-sequence stars, it is reasonable to think that observations of the latitude distribution and migration of stellar active regions by current sophisticated techniques may make it possible to infer their internal rotation profile in a simple and direct way.

scholarly journals Large-scale dynamo action of magnetized Taylor–Couette flows

2020 ◽  
Vol 493 (1) ◽  
pp. 1249-1260
Author(s):  
G Rüdiger ◽  
M Schultz
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Single Mode ◽  
Eddy Diffusivity ◽  
Magnetic Reynolds Number ◽  
Dynamo Model ◽  
Turbulence Energy ◽  
Dynamo Action ◽  
Taylor Couette

ABSTRACT A conducting Taylor–Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler–Spruit type. The flows are unstable against non-axisymmetric perturbations which form electromotive forces defining α effect and eddy diffusivity. If both degenerated modes with m = ±1 are excited with the same power then the global α effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite α effects if only an isolated mode is considered but this intrinsic helicity of the single-mode is too low for an α2 dynamo. Moreover, an αΩ dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of Rm ≃ 2000 to work. Whether it really works depends on assumptions about the turbulence energy. For a steeper-than-quadratic dependence of the turbulence intensity on the magnetic field, however, dynamos are only excited if the resulting magnetic eddy diffusivity approximates its microscopic value, ηT ≃ η. By basically lower or larger eddy diffusivities the dynamo instability is suppressed.

A mapping method for solving dynamo equations

1995 ◽  
Vol 448 (1932) ◽  
pp. 1-28 ◽  
Keyword(s):  
Magnetic Field ◽  
Decay Rate ◽  
Mapping Method ◽  
Three Dimensions ◽  
New Method ◽  
Dynamo Model ◽  
Dynamo Action ◽  
Electrically Conducting ◽  
Induction Equation ◽  
Conducting Fluids

A new method is presented for integration of the equations of magnetohydrody­namics in rapidly rotating, electrically conducting fluids, and in particular for studying dynamo action in such systems. Tests of the method are reported. The decay rate of magnetic field in a stationary sphere are recovered, as are the results of a number of α 2 - and αω -dynamos. These are solutions of the electrodynamic (induction) equation. An intermediate dynamo model, in which the dynamics are also partly allowed for, is also studied. This is due to Braginsky ( Geomag. Aero­naut . 18, 225 (1978)) and is of ‘model- Z type’. All models considered here are axisymmetric, but the possibility of generalization to three-dimensions is allowed for.

scholarly journals The Sun’s Rotation Near the Interface Between its Convective and Radiative Zones: 1986 to 1990

1993 ◽  
Vol 141 ◽  
pp. 545-548
Author(s):  
Philip R. Goode
Keyword(s):  
Magnetic Field ◽  
Internal Rotation ◽  
Convection Zone ◽  
Solar Observatory ◽  
Private Communication ◽  
Solar Oscillation ◽  
Body Rotation ◽  
Solid Body Rotation ◽  
Temporal And Spatial ◽  
The Magnetic Field

The Sun’s rotation rate near the base of its convection zone might be expected to vary over the solar cycle because of related changes there in the magnetic field. Helioseismic analyses have taught us that much of the Sun’s convection zone rotates with surface-like differential rotation and a transition toward solid body rotation beneath. For a review of what we know about the Sun’s internal rotation, see Goode, et al.(1991). We now have sufficient solar oscillation data to look for changes in the internal rotation near the base of the convection zone. The relevant data are from the 1986, 1988, 1989 and 1990 Big Bear Solar Observatory( BBSO) sets, Libbrecht and Woodard(1992, private communication). These four datasets were gathered at the same site for roughly the same number of days, reduced in the same way and span the same temporal and spatial frequency ranges—the differences between the sets should arise primarily because they were obtained in different years.

Random waves and dynamo action

1975 ◽  
Vol 69 (1) ◽  
pp. 145-177 ◽  
Author(s):  
A. M. Soward
Keyword(s):  
Magnetic Field ◽  
Wave Energy ◽  
Dynamo Model ◽  
Length Scale ◽  
Kinetic Energy Density ◽  
Random Waves ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
The Waves ◽  
Upper Boundary

The propagation of waves in an inviscid, electrically conducting fluid is considered. The fluid rotates with angular velocity Ω* and is permeated by a magnetic field b* which varies on the length scale L = Ql, where Q = Ω*l2/λ (l is the length scale of the waves, λ is the magnetic diffusivity) is assumed large (Q [Gt ] 1). A linearized theory is readily justified in the limit of zero Rossby number R0 (= U0/Ω*l, where U0 is a typical fluid velocity) and for this case it is shown that the total wave energy of a wave train is conserved and transported at the group velocity except for that which is lost by ohmic dissipation. The analysis is extended to encompass the propagation of a sea of random waves.A hydromagnetic dynamo model is considered in which the fluid is confined between two horizontal planes perpendicular to the rotation axis a distance L0(=O(L)) apart. Waves of given low frequency Ω*0 (= O(R0Q½Ω*)) and horizontal wavenumber l−1 but random orientation are excited at the lower boundary, where the kinetic energy density is 2πρU20. The waves are absorbed perfectly at the upper boundary, so that there is no reflexion. The linear wave energy equation remains valid in the double limit 1 [Gt ] R0Q½[Gt ]Q−½, for which it is shown that dynamo action is possible provided $\Delta = L_0U^2_0/l^3\omega_0^{*2} > 1 $. When dynamo action maintains a weak magnetic field (Δ −1 [Lt ] 1) which only slightly modifies the inertial waves analytic solutions are obtained. In the case of a strong magnetic field (Δ [Gt ] 1) for which Coriolis and Lorentz forces are comparable solutions are obtained numerically. The latter class includes the more realistic case (Δ → ∞) in which the upper boundary is absent.

scholarly journals An Insight into the Solar Dynamo Theory

2017 ◽  
Vol 3 (1) ◽  
pp. 27-36
Author(s):  
Babu Ram Tiwari ◽  
Mukul Kumar
Keyword(s):  
Magnetic Field ◽  
Toroidal Field ◽  
Solar Dynamo ◽  
Dynamo Model ◽  
The Sun ◽  
Poloidal Field ◽  
Dynamo Theory ◽  
Dynamo Action ◽  
Flux Transport ◽  
Alpha Omega

The Sun manifests its magnetic field in form of the solar activities, being observed on the surface of the Sun. The dynamo action is responsible for the evolution of the magnetic field in the Sun. The present article aims to present an overview of the studies have been carried on the theory and modelling of the solar dynamo. The article describes the alpha-omega dynamo model. Generally, the dynamo model involves the cyclic conversion between the poloidal field and the toroidal field. In case of alpha-omega dynamo model, the strong differential rotation generates a toroidal field near the base of the convection zone. On the other hand, the turbulent helicity leads to the generation of the poloidal field near the surface. The turbulent diffusion and the meridional circulation are considered as the two important flux transport agents in this model. The article briefly describes the theory of solar dynamo and mean field dynamo model.

A Dynamo Model for Magnetic Stars with Long Periods

1976 ◽  
Vol 32 ◽  
pp. 39-42
Author(s):  
M. Schüssler
Keyword(s):  
Magnetic Field ◽  
Main Sequence ◽  
Convection Zone ◽  
Dynamo Model ◽  
Magnetic Stars ◽  
Order Of Magnitude ◽  
Linear Effects ◽  
The Right ◽  
Right Order ◽  
The Magnetic Field

SummaryA α - effect dynamo model is presented which can be relevant for the group of magnetic stars.with observed periods between 1 y and 72 ys. The model is based on an axisymmetric α2- dynamo including non-linear effects due to the “cut off α- effect”; no differential rotation is taken into account. There are oscilliations of the magnetic field with periods in the right order of magnitude under the assumption of an outer convection zone between R ≥ r ≥.5 R ….7R. In the sense of this model therefore these stars should be young objects passing from their Hayashi track down to the main sequence.

scholarly journals Solar and Galactic Magnetic Halo Structure: Force-Free Dynamos?

Galaxies ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 53 ◽  
Author(s):  
Richard Henriksen
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Minimum Energy ◽  
Energy Condition ◽  
Galactic Halos ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Scale Invariant ◽  
Halo Structure ◽  
New Formulation

Magnetic fields may relax dissipatively to the minimum energy force-free condition whenever they are not constantly created or distorted. We review the axially symmetric solutions for force-free magnetic fields, especially for the non-linear field. A new formulation for the scale invariant state is given. Illustrative examples are shown. Applications to both stellar coronas and galactic halos are possible. Subsequently we study whether such force-free fields may be sustained by classical magnetic dynamo action. Although the answer is `not indefinitely’, there may be an evolutionary cycle wherein the magnetic field repeatedly relaxes to the minimum energy condition after a period of substantial growth and distortion. Different force-free dynamos may coexist at different locations. Helicity transfer between scales is studied briefly. A dynamo solution is given for the temporal evolution away from an initial linear force-free magnetic field due to both α 2 and ω terms. This can be used at the sub scale level to create a `delayed’ α effect.

scholarly journals A physical approach to modelling large-scale galactic magnetic fields

2019 ◽  
Vol 623 ◽  
pp. A113 ◽  
Author(s):  
Anvar Shukurov ◽  
Luiz Felippe S. Rodrigues ◽  
Paul J. Bushby ◽  
James Hollins ◽  
Jörg P. Rachen
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Large Scale ◽  
Milky Way ◽  
Mean Field ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Disc Galaxy ◽  
Large Scale Magnetic Field ◽  
Dynamo Equation

Context. A convenient representation of the structure of the large-scale galactic magnetic field is required for the interpretation of polarization data in the sub-mm and radio ranges, in both the Milky Way and external galaxies. Aims. We develop a simple and flexible approach to construct parametrised models of the large-scale magnetic field of the Milky Way and other disc galaxies, based on physically justifiable models of magnetic field structure. The resulting models are designed to be optimised against available observational data. Methods. Representations for the large-scale magnetic fields in the flared disc and spherical halo of a disc galaxy were obtained in the form of series expansions whose coefficients can be calculated from observable or theoretically known galactic properties. The functional basis for the expansions is derived as eigenfunctions of the mean-field dynamo equation or of the vectorial magnetic diffusion equation. Results. The solutions presented are axially symmetric but the approach can be extended straightforwardly to non-axisymmetric cases. The magnetic fields are solenoidal by construction, can be helical, and are parametrised in terms of observable properties of the host object, such as the rotation curve and the shape of the gaseous disc. The magnetic field in the disc can have a prescribed number of field reversals at any specified radii. Both the disc and halo magnetic fields can separately have either dipolar or quadrupolar symmetry. The model is implemented as a publicly available software package GALMAG which allows, in particular, the computation of the synchrotron emission and Faraday rotation produced by the model’s magnetic field. Conclusions. The model can be used in interpretations of observations of magnetic fields in the Milky Way and other spiral galaxies, in particular as a prior in Bayesian analyses. It can also be used for a simple simulation of a time-dependent magnetic field generated by dynamo action.

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