Differential rotation plays a crucial role in the alpha-omega dynamo, and thus also in creation of magnetic fields in stars with convective outer envelopes. Still, measuring the radial differential rotation on stars is impossible with the current techniques, and even the measurement of surface differential rotation is difficult. In this work we investigate the surface differential rotation obtained from dynamo models using similar techniques as are used on observations, and compare the results with the known radial differential rotation used when creating the Dynamo model.
Stretching solar dynamos from differential rotation in a Riemannian manifold setting is presented. The spherical model follows closely a twisted magnetic flux tube Riemannian geometrical model or flux rope in solar physics, presented previously by Ricca [Solar Physics (1997)]. The spherical model presented here present new and interesting feature concerning its connection with spherical steady solar dynamos. One of this new feature is represented by the fact that the by considering poloidal magnetic field component much weaker than its toroidal counterpart, one obtains a stretch dynamo action …
Magnetic fields can be created in stably stratified (non-convective) layers in a differentially rotating star. A magnetic instability in the toroidal field (wound up by differential rotation) replaces the role of convection in closing the field amplification loop. Tayler instability is likely to be the most relevant magnetic instability. A dynamo model is developed from these ingredients, and applied to the problem of angular momentum transport in stellar interiors. It produces a prodominantly horizontal field. This dynamo process might account for the observed pattern of rotation in the solar…
We report our first results on comparing the variations of the solar internal rotation with solar activity, as predicted by non-linear solar dynamo modelling, with helioseismic measurements using the SOHO MDI data.
We study axisymmetric mean-field dynamo models containing differential rotation, the $α$ effect and the additional turbulent induction effects. The additional effects result from the combined action of rotation and an inhomogeneity of the large-scale magnetic field. The best known of them is the $\vecΩ\times\vec{J}$ effect. We also include anisotropic diffusion and a new dynamo term which is of third order in the rotation vector $\vecΩ$ The model calculations are carried out using the rotation profile of the Sun as obtained from helioseismic measurements and radial profiles of other quantities…
The topological mapping between a torus of big radius and a sphere is applied to the Riemannian geometry of a stretched and twisted very thick magnetic flux tube, to obtain spherical dynamos solving the magnetohydrodynamics (MHD) self-induction equation for the magnetic flux tubes undergoing differential (non-uniform) rotation along the tube magnetic axis. Constraints on the shear is also computed. It is shown that when the hypothesis of the convective cyclonic dynamo is used the rotation is constant and a solid rotational body is obtained. As usual toroidal fields are obtained from poloidal m…
Dynamos in astrophysical disks are usually explained in terms of the standard alpha-omega mean field dynamo model where the local helicity generates a radial field component from an azimuthal field. The subsequent shearing of the radial field gives rise to exponentially growing dynamo modes. There are several problems with this model. The exponentiation time for the galactic dynamo is hard to calculate, but is probably uncomfortably long. Moreover, numerical simulations of magnetic fields in shearing flows indicate that the presence of a dynamo does not depend on a non-zero average helicity. H…
We present numerical simulations of a self-sustaining magnetic field in a differentially rotating non-convective stellar interior. A weak initial field is wound up by the differential rotation; the resulting azimuthal field becomes unstable and produces a new meridional field component, which is then wound up anew, thus completing the `dynamo loop'. This effect is observed both with and without a stable stratification. A self-sustained field is actually obtained more easily in the presence of a stable stratification. The results confirm the analytical expectations of the role of Tayler instabi…
The thin-disc global asymptotics are discussed for axisymmetric mean-field dynamos with vacuum boundary conditions allowing for non-local terms arising from a finite radial component of the mean magnetic field at the disc surface. This leads to an integro-differential operator in the equation for the radial distribution of the mean magnetic field strength, $Q(r)$ in the disc plane at a distance $r$ from its centre; an asymptotic form of its solution at large distances from the dynamo active region is obtained. Numerical solutions of the integro-differential equation confirm that the non-local …
We reconsider thin-disc global asymptotics for kinematic, axisymmetric mean-field dynamos with vacuum boundary conditions. Non-local terms arising from a small but finite radial field component at the disc surface are consistently taken into account for quadrupole modes. As in earlier approaches, the solution splits into a local part describing the field distribution along the vertical direction and a radial part describing the radial (global) variation of the eigenfunction. However, the radial part of the eigenfunction is now governed by an integro-differential equation whose kernel has a wea…
In this paper we discuss a dynamic flux-transport dynamo model that includes the feedback of the induced magnetic field on differential rotation and meridional flow. We consider two different approaches for the feedback: meanfield Lorentz force and quenching of transport coefficients such as turbulent viscosity and heat conductivity. We find that even strong feedback on the meridional flow does not change the character of the flux-transport dynamo significantly; however it leads to a significant reduction of differential rotation. To a large degree independent from the dynamo parameters, the s…
Many stars exhibit strong magnetic fields, some of which are thought to be of primordial origin and others a sign of magnetic dynamo processes. We briefly review the results of observational studies of solar-type stars seeking to evaluate the linkage between rotation rate and possible magnetic cycles of activity. Clearly turbulent convection and rotation within spherical shell geometries provide ingredients essential for dynamo action. However, intensive efforts over several decades in solar research have demonstrated that it is no easy matter to achieve cyclic magnetic activity that is in acc…
The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using three-dimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The rea…
We examine the effects of the magnetic field created by the Tayler--Spruit dynamo in differentially rotating stars. Magnetic fields of the order of a few $10^4$ G are present through most of the stellar envelope, with the exception of the outer layers. The diffusion coefficient for the transport of angular momentum is very large and it imposes nearly solid body rotation during the MS phase. In turn, solid body rotation drives meridional circulation currents which are much faster than usual and leads to much larger diffusion coefficients than the magnetic diffusivity for the chemical species. T…
Increasing evidence is becoming available about not only the surface differential rotation of rapidly rotating cool stars but, in a small number of cases, also about temporal variations, which possibly are analogous to the solar torsional oscillations. Given the present difficulties in resolving the precise nature of such variations, due to both the short length and poor resolution of the available data, theoretical input is vital to help assess the modes of behaviour that might be expected, and will facilitate interpretation of the observations. Here we take a first step in this direction by …
We examine the behaviour of an axisymmetric galactic dynamo model with a radial accretion flow in the disc. We also introduce a vertical magnetic flux through the galactic midplane, to simulate the presence of a large scale magnetic field trapped by the galaxy when forming. The trapped vertical flux is conserved and advected towards the disc centre by the radial flow. We confirm that accretion flows of magnitude several km/s through a significant part of the galactic disc can markedly inhibit dynamo action. Moreover, advection of the vertical flux in general results in mixed parity galactic fi…
We continue our attempt to connect observational data on current helicity in solar active regions with solar dynamo models. In addition to our previous results about temporal and latitudinal distributions of current helicity (Kleeorin et al. 2003), we argue that some information concerning the radial profile of the current helicity averaged over time and latitude can be extracted from the available observations. The main feature of this distribution can be presented as follows. Both shallow and deep active regions demonstrate a clear dominance of one sign of current helicity in a given hemisph…
We present statistically robust observational evidence which imposes new limits on dynamo saturation in young solar-type stars. These are inferred from the increasing amplitude of the V-band optical flux with rotation, caused by the filling of the disc with surface spots in a non-axisymmetric pattern. Assuming spot coverage acts as a tracer of the total magnetic surface flux we find that the magnetic activity saturates at a level at least 6 -- 10 times greater than that inferred from chromospheric and transition line indicators. We suggest that these new limits imply a minimum rotation for sat…
The plethora of asymmetric planetary nebulae and the curiously high momenta of pre-planetary nebula outflows suggest that rotational energy is extracted from the engines. Magneto-rotational outflows driven by dynamos might be operating therein. I summarize scenarios involving (a) an isolated AGB star and (b) a binary. The efficacy of (a) requires re-establishing differential rotation over the AGB star's lifetime, whereas (b) delivers the angular momentum at the end of the AGB phase when needed, and may involve turbulent disks. Both can produce fields that drive outflows of the required mechani…
Stellar dynamos are driven by complex couplings between rotation and turbulent convection, which drive global-scale flows and build and rebuild stellar magnetic fields. When stars like our sun are young, they rotate much more rapidly than the current solar rate. Observations generally indicate that more rapid rotation is correlated with stronger magnetic activity and perhaps more effective dynamo action. Here we examine the effects of more rapid rotation on dynamo action in a star like our sun. We find that vigorous dynamo action is realized, with magnetic field generated throughout the bulk o…
We further develop the Tayler--Spruit dynamo theory, based on the most efficient instability for generating magnetic fields in radiative layers of differentially rotating stars. We avoid the simplifying assumptions that either the $μ$-- or the $T$--gradient dominates, but we treat the general case and we also account for the nonadiabatic effects, which favour the growth of the magnetic field. Stars with a magnetic field rotate almost as a solid body. Several of their properties (size of the core, MS lifetimes, tracks, abundances) are closer to those of models without rotation than with rotatio…
We discuss the mean-field dynamo action in protoneutron stars that are subject to instabilities during the early evolutionary phase. The mean field is generated in the neutron-finger unstable region where the Rossby number is $\sim 1$ and mean-field dynamo is efficient. Depending on the rotation rate, the mean-field dynamo can lead to the formation of three different types of pulsars. If the initial period of the protoneutron star is short, then the generated large-scale field is very strong ($> 3 \times 10^{13}$G) and exceeds the small-scale field at the neutron star surface. If rotation is m…
An essential ingredient in kinematic dynamo models is the velocity field within the solar convection zone. In particular, the differential rotation is now well constrained by helioseismic observations. Helioseismology also gives us information about the depth-dependence of the meridional circulation in the near-surface layers. The typical velocity inputs used in solar dynamo models, however, continue to be an analytic fit to the observed differential rotation and a theoretically constructed meridional flow profile that matches only the peak flow speed at the surface. Here we take the first ste…
We present the results of 3--D nonlinear simulations of magnetic dynamo action by core convection within A-type stars of 2 solar masses, at a range of rotation rates. We consider the inner 30% by radius of such stars, with the spherical domain thereby encompassing the convective core and a portion of the surrounding radiative envelope. The compressible Navier-Stokes equations, subject to the anelastic approximation, are solved to examine highly nonlinear flows that span multiple scale heights, exhibit intricate time dependence, and admit magnetic dynamo action. Small initial seed magnetic fiel…
The generation of solar non-axisymmetric magnetic fields is studied based on a linear alpha2-Omega dynamo model in a rotating spherical frame. The model consists of a solar-like differential rotation, a magnetic diffusivity varied with depth, and three types of alpha-effects with different locations, i.e. the tachocline, the whole convective zone and the sub-surface. Some comparisons of the critical alpha-values of axisymmetric m=0 and longitude-dependent modes m=1,2,3 are presented to show the roles of the magnetic diffusivity in the problem of modes selection. With the changing of diffusivit…
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 …
In low-mass Red Giant Branch (RGB) and Asymptotic Giant Branch (AGB) stars, anomalous mixing must transport material near the hydrogen-burning shell to the convective envelope. Recently, it was suggested that buoyant magnetic flux tubes could supply the necessary transport rate (Busso et al. 2007). The fields are assumed to originate from a dynamo operating in the stellar interior. Here, we show what is required of an $α-Ω$ dynamo in the envelope of an AGB star to maintain these fields. Differential rotation and rotation drain via turbulent dissipation and Poynting flux, so if shear can be res…
The physical mechanism(s) responsible for transitioning from a spherical Asymptotic Giant Branch (AGB) star to an asymmetric post-AGB (pAGB) object is poorly understood. In particular, excess momenta in the outflows of pAGB objects suggest that a binary may be required to supply an additional source of energy and angular momentum. The extraction of rotational energy from the engine is likely fundamental and may be facilitated if a dynamo is operating in the interior. In this regard, single star magnetic outflow models have been proposed as mechanisms for producing and shaping PNe, however thes…
Flux-dominated solar dynamo models, which have demonstrated to be quite successful in reproducing most of the observed features of the large scale solar magnetic cycle, generally produce an inappropriate latitudinal distribution of the toroidal magnetic fields, showing fields of large magnitude in polar regions where the radial shear has a maximum amplitude. Employing a kinematic solar dynamo model, we here explore the contribution of both the radial and the latitudinal shear in the generation of the toroidal magnetic fields by varying the shape and the thickness of the solar tachocline. We al…
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 me…
The theory of the solar/stellar activity cycles is presented, based on the mean-field concept in magnetohydrodynamics. A new approach to the formulation of the electromotive force and the theory of differential rotation and meridional circulation is described. Dynamo cycles in the overshoot layer and distributed dynamos are compared, with the latter including the influence of meridional flow. The overshoot layer dynamo reproduces the solar cycle periods and the butterfly diagram only if alpha=0 in the convection zone (CZ). The distributed dynamo including meridional flows shows the observed bu…
Observations in polarized emission reveal the existence of large-scale coherent magnetic fields in a wide range of spiral galaxies. Radio-polarization data show that these fields are strongly inclined towards the radial direction, with pitch angles up to $35\degr$ and thus cannot be explained by differential rotation alone. Global dynamo models describe the generation of the radial magnetic field from the underlying turbulence via the so called $α$-effect. However, these global models still rely on crude assumptions about the small-scale turbulence. To overcome these restrictions we perform fu…
Core convection and dynamo activity deep within rotating A-type stars of 2 solar masses are studied with 3--D nonlinear simulations. Our modeling considers the inner 30% by radius of such stars, thus capturing within a spherical domain the convective core and a modest portion of the surrounding radiative envelope. The MHD equations are solved using the ASH code to examine turbulent flows and magnetic fields, both of which exhibit intricate time dependence. By introducing small seed magnetic fields into our progenitor hydrodynamic models rotating at one and four times the solar rate, we assess …
Recent observations indicate that fully convective stars can effectively build magnetic fields without the aid of a tachocline of shear, that those fields can possess large-scale components, and that they may sense the effects of rotation. Motivated by these puzzles, we present global three-dimensional simulations of convection and dynamo action in the interiors of fully convective M-dwarfs of 0.3 solar masses. We use the Anelastic Spherical Harmonic (ASH) code, adopting a spherical computational domain that extends from 0.08-0.96 times the overall stellar radius. We find that such fully conve…
Rapidly rotating spherical kinematic dynamos are computed using the combination of a quasi geostrophic (QG) model for the velocity field and a classical spectral 3D code for the magnetic field. On one hand, the QG flow is computed in the equatorial plane of a sphere and corresponds to Rossby wave instabilities of a geostrophic internal shear layer produced by differential rotation. On the other hand, the induction equation is computed in the full sphere after a continuation of the QG flow along the rotation axis. Differential rotation and Rossby-wave propagation are the key ingredients of the …
Differential rotation is widely supposed to be essential for the dynamo effects that sustain solar and planetary magnetic fields, but dynamo effects tend to oppose the flows that drive them, and it is uncertain what drives differential rotation. The relative sign of the differential rotation and meridional circulation is not consistent with simple convection modified by Coriolis forces. We investigate dynamo mechanisms consistent with the observed solar circulation, and discuss how reactive JxB forces would affect such flows. We formulate scaling rules that relate the magnetic field strength t…
