Helicity Observation of Weak and Strong Fields

We report in this letter our analysis of a large sample of photospheric vector magnetic field measurements. Our sample consists of 17200 vector magnetograms obtained from January 1997 to August 2004 by Huairou Solar Observing Station of the Chinese National Astronomical Observatory. Two physical quantities, $\alpha$ and current helicity, are calculated and their signs and amplitudes are studied in a search for solar cycle variations. Different from other studies of the same type, we calculate these quantities for weak ($100G1000G$) fields separately. For weak fields, we find that the signs of both $\alpha$ and current helicity are consistent with the established hemispheric rule during most years of the solar cycle and their magnitudes show a rough tendency of decreasing with the development of solar cycle. Analysis of strong fields gives an interesting result: Both $\alpha$ and current helicity present a sign opposite to that of weak fields. Implications of these observations on dynamo theory and helicity production are also briefly discussed.Comment: accepted for publication in ApJ Lette

The Nonlinear Evolution of Instabilities Driven by Magnetic Buoyancy: A New Mechanism for the Formation of Coherent Magnetic Structures

Motivated by the problem of the formation of active regions from a deep-seated solar magnetic field, we consider the nonlinear three-dimensional evolution of magnetic buoyancy instabilities resulting from a smoothly stratified horizontal magnetic field. By exploring the case for which the instability is continuously driven we have identified a new mechanism for the formation of concentrations of magnetic flux.Comment: Published in ApJL. Version with colour figure

On Predicting the Solar Cycle using Mean-Field Models

We discuss the difficulties of predicting the solar cycle using mean-field models. Here we argue that these difficulties arise owing to the significant modulation of the solar activity cycle, and that this modulation arises owing to either stochastic or deterministic processes. We analyse the implications for predictability in both of these situations by considering two separate solar dynamo models. The first model represents a stochastically-perturbed flux transport dynamo. Here even very weak stochastic perturbations can give rise to significant modulation in the activity cycle. This modulation leads to a loss of predictability. In the second model, we neglect stochastic effects and assume that generation of magnetic field in the Sun can be described by a fully deterministic nonlinear mean-field model -- this is a best case scenario for prediction. We designate the output from this deterministic model (with parameters chosen to produce chaotically modulated cycles) as a target timeseries that subsequent deterministic mean-field models are required to predict. Long-term prediction is impossible even if a model that is correct in all details is utilised in the prediction. Furthermore, we show that even short-term prediction is impossible if there is a small discrepancy in the input parameters from the fiducial model. This is the case even if the predicting model has been tuned to reproduce the output of previous cycles. Given the inherent uncertainties in determining the transport coefficients and nonlinear responses for mean-field models, we argue that this makes predicting the solar cycle using the output from such models impossible.Comment: 22 Pages, 5 Figures, Preprint accepted for publication in Ap

Does the butterfly diagram indicate asolar flux-transport dynamo?

We address the question whether the properties of the observed latitude-time diagram of sunspot occurence (the butterfly diagram) provide evidence for the operation of a flux-transport dynamo, which explains the migration of the sunspot zones and the period of the solar cycle in terms of a deep equatorward meridional flow. We show that the properties of the butterfly diagram are equally well reproduced by a conventional dynamo model with migrating dynamo waves, but without transport of magnetic flux by a flow. These properties seem to be generic for an oscillatory and migratory field of dipole parity and thus do not permit an observational distinction between different dynamo approaches.Comment: 4 pages, 1 figur

Dynamo Action in the Solar Convection Zone and Tachocline: Pumping and Organization of Toroidal Fields

We present the first results from three-dimensional spherical shell simulations of magnetic dynamo action realized by turbulent convection penetrating downward into a tachocline of rotational shear. This permits us to assess several dynamical elements believed to be crucial to the operation of the solar global dynamo, variously involving differential rotation resulting from convection, magnetic pumping, and amplification of fields by stretching within the tachocline. The simulations reveal that strong axisymmetric toroidal magnetic fields (about 3000 G in strength) are realized within the lower stable layer, unlike in the convection zone where fluctuating fields are predominant. The toroidal fields in the stable layer possess a striking persistent antisymmetric parity, with fields in the northern hemisphere largely of opposite polarity to those in the southern hemisphere. The associated mean poloidal magnetic fields there have a clear dipolar geometry, but we have not yet observed any distinctive reversals or latitudinal propagation. The presence of these deep magnetic fields appears to stabilize the sense of mean fields produced by vigorous dynamo action in the bulk of the convection zone.Comment: 4 pages, 3 color figures (compressed), in press at ApJ

The cross helicity at the solar surface by simulations and observations

The quasilinear mean-field theory for driven MHD turbulence leads to the result that the observed cross helicity may directly yield the magnetic eddy diffusivity \eta_{T} of the quiet Sun. In order to model the cross helicity at the solar surface, magnetoconvection under the presence of a vertical large-scale magnetic field is simulated with the nonlinear MHD code NIRVANA. The very robust result of the calculations is that \simeq 2 independent of the applied magnetic field amplitude. The correlation coefficient for the cross helicity is about 10%. Of similar robustness is the finding that the rms value of the magnetic perturbations exceeds the mean-field amplitude (only) by a factor of five. The characteristic helicity speed u_{\eta} as the ratio of the eddy diffusivity and the density scale height for an isothermal sound velocity of 6.6 km/s proves to be 1 km/s for weak fields. This value well coincides with empirical results obtained from the data of the HINODE satellite and the Swedish 1-m Solar Telescope (SST) providing the cross helicity component . Both simulations and observations thus lead to a numerical value of \eta_{T} \simeq 10^12 cm^2 /s as characteristic for the surface of the quiet Sun.Comment: 6 pages, 6 figure

A Low-Order Solar Dynamo Model: Inferred Meridional Circulation Variations Since 1750

In this work we present the possible variations that the meridional circulation of the Sun might have undergone during the last 250 years. In order to do this, we reduce an α-Ω dynamo to a low-order system that focuses on the time evolution of one of the solar magnetic field components. Afterward we used a method based on the analysis of phase space of the superficial toroidal magnetic field to infer changes in the superficial meridional circulation. We used sunspot numbers to build a time series that approximately represents the magnetic field behavior. After reconstructing the time series' phase space we assume equilibrium solutions for each solar cycle and we fit them to our model. The resulting fit parameters are shown to depend on background quantities of the theoretical model, such as magnetic diffusivity, differential rotation, meridional circulation, etc. The methodology presented here allows one to extract information about the meridional circulation average behavior, and possibly other parameters, from more that 250 years of sunspot number observations

Simulations of dynamo action in fully convective stars

We present three-dimensional nonlinear magnetohydrodynamic simulations of the interiors of fully convective M-dwarfs. Our models consider 0.3 solar-mass stars using the Anelastic Spherical Harmonic code, with the spherical computational domain extending from 0.08-0.96 times the overall stellar radius. Like previous authors, we find that fully convective stars can generate kG-strength magnetic fields (in rough equipartition with the convective flows) without the aid of a tachocline of shear. Although our model stars are everywhere unstably stratified, the amplitudes and typical pattern sizes of the convective flows vary strongly with radius, with the outer regions of the stars hosting vigorous convection and field amplification while the deep interiors are more quiescent. Modest differential rotation is established in hydrodynamic calculations, but -- unlike in some prior work --strongly quenched in MHD simulations because of the Maxwell stresses exerted by the dynamo-generated magnetic fields. Despite the lack of strong differential rotation, the magnetic fields realized in the simulations possess significant mean (axisymmetric) components, which we attribute partly to the strong influence of rotation upon the slowly overturning flows.Comment: Accepted to the ApJ. 20 pages (emulateapj), 4 color figures compressed to low-resolution; higher-resolution equivalents are available at http://lcd-www.colorado.edu/~brownim/browning_2007_mstars.pd

Local models of stellar convection: Reynolds stresses and turbulent heat transport

We study stellar convection using a local three-dimensional MHD model, with which we investigate the influence of rotation and large-scale magnetic fields on the turbulent momentum and heat transport. The former is studied by computing the Reynolds stresses, the latter by calculating the correlation of velocity and temperature fluctuations, both as functions of rotation and latitude. We find that the horisontal correlation, Q_(theta phi), capable of generating horisontal differential rotation, is mostly negative in the southern hemisphere for Coriolis numbers exceeding unity, corresponding to equatorward flux of angular momentum in accordance with solar observations. The radial component Q_(r phi) is negative for slow and intermediate rotation indicating inward transport of angular momentum, while for rapid rotation, the transport occurs outwards. Parametrisation in terms of the mean-field Lambda-effect shows qualitative agreement with the turbulence model of Kichatinov & R\"udiger (1993) for the horisontal part H \propto Q_(theta phi)/cos(theta), whereas for the vertical part, V \propto Q_(r phi)/sin(theta), agreement only for intermediate rotation exists. The Lambda-coefficients become suppressed in the limit of rapid rotation, this rotational quenching being stronger for the V component than for H. We find that the stresses are enhanced by the presence of the magnetic field for field strengths up to and above the equipartition value, without significant quenching. Concerning the turbulent heat transport, our calculations show that the transport in the radial direction is most efficient at the equatorial regions, obtains a minimum at midlatitudes, and shows a slight increase towards the poles. The latitudinal heat transport does not show a systematic trend as function of latitude or rotation.Comment: 26 pages, 20 figures, final published version. For a version with higher resolution figures, see http://cc.oulu.fi/~pkapyla/publ.htm

Magnetoconvection and dynamo coefficients III: alpha-effect and magnetic pumping in the rapid rotation regime

Aims. The alpha- and gamma-effects, which are responsible for the generation and turbulent pumping of large scale magnetic fields, respectively, due to passive advection by convection are determined in the rapid rotation regime corresponding to the deep layers of the solar convection zone. Methods. A 3D rectangular local model is used for solving the full set of MHD equations in order to compute the electromotive force (emf), E = , generated by the interaction of imposed weak gradient-free magnetic fields and turbulent convection with varying rotational influence and latitude. By expanding the emf in terms of the mean magnetic field, E_i = a_ij , all nine components of a_ij are computed. The diagonal elements of a_ij describe the alpha-effect, whereas the off-diagonals represent magnetic pumping. The latter is essentially the advection of magnetic fields by means other than the underlying large-scale velocity field. Comparisons are made to analytical expressions of the coefficients derived under the first-order smoothing approximation (FOSA). Results. In the rapid rotation regime the latitudinal dependence of the alpha-components responsible for the generation of the azimuthal and radial fields does not exhibit a peak at the poles, as is the case for slow rotation, but at a latitude of about 30 degrees. The magnetic pumping is predominantly radially down- and latitudinally equatorward as in earlier studies. The numerical results compare surprisingly well with analytical expressions derived under first-order smoothing, although the present calculations are expected to lie near the limits of the validity range of FOSA.Comment: 14 pages, 12 figures, accepted for publication in Astronomy & Astrophysic