Solar differential rotation and meridional flow: The role of a subadiabatic tachocline for the Taylor-Proudman balance

We present a simple model for the solar differential rotation and meridional circulation based on a mean field parameterization of the Reynolds stresses that drive the differential rotation. We include the subadiabatic part of the tachocline and show that this, in conjunction with turbulent heat conductivity within the convection zone and overshoot region, provides the key physics to break the Taylor-Proudman constraint, which dictates differential rotation with contour lines parallel to the axis of rotation in case of an isentropic stratification. We show that differential rotation with contour lines inclined by 10 - 30 degrees with respect to the axis of rotation is a robust result of the model, which does not depend on the details of the Reynolds stress and the assumed viscosity, as long as the Reynolds stress transports angular momentum toward the equator. The meridional flow is more sensitive with respect to the details of the assumed Reynolds stress, but a flow cell, equatorward at the base of the convection zone and poleward in the upper half of the convection zone, is the preferred flow pattern.Comment: 15 pages, 7 figure

Observation and Modeling of the Solar-Cycle Variation of the Meridional Flow

We present independent observations of the solar-cycle variation of flows near the solar surface and at a depth of about 60 Mm, in the latitude range $\pm45^\circ$. We show that the time-varying components of the meridional flow at these two depths have opposite sign, while the time-varying components of the zonal flow are in phase. This is in agreement with previous results. We then investigate whether the observations are consistent with a theoretical model of solar-cycle dependent meridional circulation based on a flux-transport dynamo combined with a geostrophic flow caused by increased radiative loss in the active region belt (the only existing quantitative model). We find that the model and the data are in qualitative agreement, although the amplitude of the solar-cycle variation of the meridional flow at 60 Mm is underestimated by the model.Comment: To be published in Solar Physcis Topical Issue "Helioseismology, Asteroseismology, and MHD Connections

Origin of solar torsional oscillations

Helioseismology has revealed many details of solar differential rotation and also its time variation, known as torsional oscillations. So far there is no generally accepted theoretical explanation for torsional oscillations, even though a close relation to the solar activity cycle is evident. On the theoretical side non-kinematic dynamo models (including the Lorentz force feedback on differential rotation) have been used to explain torsional oscillations. In this paper we use a slightly different approach by forcing torsional oscillations in a mean field differential rotation model. Our aim is not a fully self-consistent model but rather to point out a few general properties of torsional oscillations and their possible origin that are independent from a particular dynamo model. We find that the poleward propagating high latitude branch of the torsional oscillations can be explained as a response of the coupled differential rotation / meridional flow system to periodic forcing in mid-latitudes, of either mechanical (Lorentz force) or thermal nature. The speed of the poleward propagation sets constraints on the value of the turbulent viscosity in the solar convection zone to be less than 3x10^8 m^2/s. We also show that the equatorward propagating low latitude branch is very unlikely a consequence of mechanical forcing (Lorentz force) alone, but rather of thermal origin due to the Taylor-Proudman theorem.Comment: 11 pages, 7 figures. accepted by Astrophys.

Flux-transport dynamos with Lorentz force feedback on differential rotation and meridional flow: Saturation mechanism and torsional oscillations

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 saturation takes place when the toroidal field at the base of the convection zone reaches between 1.2 an 1.5 T, the energy converted intomagnetic energy corresponds to about 0.1 to 0.2% of the solar luminosity. The torsional oscillations produced through Lorentz force feedback on differential rotation show a dominant poleward propagating branch with the correct phase relation to the magnetic cycle. We show that incorporating enhanced surface cooling of the active region belt (as proposed by Spruit) leads to an equatorward propagating branch in good agreement with observations.Comment: 15 pages, 12 figures, Accepted for publication in ApJ August 10 issue; corrected typos, corrected referenc

Chaotic saddles in nonlinear modulational interactions in a plasma

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.Comment: Physics of Plasmas, in pres

Lagrangian chaos in an ABC--forced nonlinear dynamo

The Lagrangian properties of the velocity field in a magnetized fluid are studied using three-dimensional simulations of a helical magnetohydrodynamic dynamo. We compute the attracting and repelling Lagrangian coherent structures, which are dynamic lines and surfaces in the velocity field that delineate particle transport in flows with chaotic streamlines and act as transport barriers. Two dynamo regimes are explored, one with a robust coherent mean magnetic field and one with intermittent bursts of magnetic energy. The Lagrangian coherent structures and the statistics of finite--time Lyapunov exponents indicate that the stirring/mixing properties of the velocity field decay as a linear function of the magnetic energy. The relevance of this study for the solar dynamo problem is discussed

Hybrid nanoparticles based on sulfides, oxides, and carbides

The methods for synthesis of hybrid nanoparticles based on sulfides, oxides, and carbides of heavy and transition metals were considered. The problem of the influence of the method of synthesis of the hybrid nanoparticles on their atomic structure, morphology of the nanomaterials, and functional properties was analyzed. The areas of practical use of the hybrid nanoparticles were proposed. © 2013 Springer Science+Business Media New York

Local helioseismology of sunspot regions: comparison of ring-diagram and time-distance results

Local helioseismology provides unique information about the subsurface structure and dynamics of sunspots and active regions. However, because of complexity of sunspot regions local helioseismology diagnostics require careful analysis of systematic uncertainties and physical interpretation of the inversion results. We present new results of comparison of the ring-diagram analysis and time-distance helioseismology for active region NOAA 9787, for which a previous comparison showed significant differences in the subsurface sound-speed structure, and discuss systematic uncertainties of the measurements and inversions. Our results show that both the ring-diagram and time-distance techniques give qualitatively similar results, revealing a characteristic two-layer seismic sound-speed structure consistent with the results for other active regions. However, a quantitative comparison of the inversion results is not straightforward. It must take into account differences in the sensitivity, spatial resolution and the averaging kernels. In particular, because of the acoustic power suppression, the contribution of the sunspot seismic structure to the ring-diagram signal can be substantially reduced. We show that taking into account this effect reduces the difference in the depth of transition between the negative and positive sound-speed variations inferred by these methods. Further detailed analysis of the sensitivity, resolution and averaging properties of the local helioseismology methods is necessary for consolidation of the inversion results. It seems to be important that both methods indicate that the seismic structure of sunspots is rather deep and extends to at least 20 Mm below the surface, putting constraints on theoretical models of sunspots.Comment: 10 pages, 10 figures, submitted to Journal of Physics: Conference Series (JPCS) GONG 2010 - SoHO 24 "A new era of seismology of the Sun and solar-like stars", June 27 - July 2, 2010 Aix-en-Provence, Franc

Newly identified properties of surface acoustic power

The cause of enhanced acoustic power surrounding active regions, the acoustic halo, is not as yet understood. We explore the properties of the enhanced acoustic power observed near disk center from 21 to 27 January 2002, including AR 9787. We find that (i) there exists a strong correlation of the enhanced high frequency power with magnetic-field inclination, with greater power in more horizontal fields, (ii) the frequency of the maximum enhancement increases along with magnetic field strength, and (iii) the oscillations contributing to the halos show modal ridges which are shifted to higher wavenumber at constant frequency in comparison to the ridges of modes in the quiet-Sun.Comment: 16 pages, 10 figures, submitted to solar physic

Validated helioseismic inversions for 3-D vector flows

According to time-distance helioseismology, information about internal fluid motions is encoded in the travel times of solar waves. The inverse problem consists of inferring 3-D vector flows from a set of travel-time measurements. Here we investigate the potential of time-distance helioseismology to infer 3-D convective velocities in the near-surface layers of the Sun. We developed a new Subtractive Optimally Localised Averaging (SOLA) code suitable for pipeline pseudo-automatic processing. Compared to its predecessor, the code was improved by accounting for additional constraints in order to get the right answer within a given noise level. The main aim of this study is to validate results obtained by our inversion code. We simulate travel-time maps using a snapshot from a numerical simulation of solar convective flows, realistic Born travel-time sensitivity kernels, and a realistic model of travel-time noise. These synthetic travel times are inverted for flows and the results compared with the known input flow field. Additional constraints are implemented in the inversion: cross-talk minimization between flow components and spatial localization of inversion coefficients. Using modes f, p1 through p4, we show that horizontal convective flow velocities can be inferred without bias, at a signal-to-noise ratio greater than one in the top 3.5 Mm, provided that observations span at least four days. The vertical component of velocity (v_z), if it were to be weak, is more difficult to infer and is seriously affected by cross-talk from horizontal velocity components. We emphasise that this cross-talk must be explicitly minimised in order to retrieve v_z in the top 1 Mm. We also show that statistical averaging over many different areas of the Sun allows for reliably measuring of average properties of all three flow components in the top 5.5 Mm of the convection zone.Comment: 14 pages main paper, 9 pages electronic supplement, 28 figures. Accepted for publication in Astronomy & Astrophysic