A theoretical model of the variation of the meridional circulation with the solar cycle

Observations of the meridional circulation of the Sun, which plays a key role in the operation of the solar dynamo, indicate that its speed varies with the solar cycle, becoming faster during the solar minima and slower during the solar maxima. To explain this variation of the meridional circulation with the solar cycle, we construct a theoretical model by coupling the equation of the meridional circulation (the $\phi$ component of the vorticity equation within the solar convection zone) with the equations of the flux transport dynamo model. We consider the back reaction due to the Lorentz force of the dynamo-generated magnetic fields and study the perturbations produced in the meridional circulation due to it. This enables us to model the variations of the meridional circulation without developing a full theory of the meridional circulation itself. We obtain results which reproduce the observational data of solar cycle variations of the meridional circulation reasonably well. We get the best results on assuming the turbulent viscosity acting on the velocity field to be comparable to the magnetic diffusivity (i.e. on assuming the magnetic Prandtl number to be close to unity). We have to assume an appropriate bottom boundary condition to ensure that the Lorentz force cannot drive a flow in the subadiabatic layers below the bottom of the tachocline. Our results are sensitive to this bottom boundary condition. We also suggest a hypothesis how the observed inward flow towards the active regions may be produced.Comment: 15 pages, 11 figures, accepted for publication in MNRA

A New Formula for Predicting Solar Cycles

A new formula for predicting solar cycles based on the current theoretical understanding of the solar cycle from flux transport dynamo is presented. Two important processes---fluctuations in the Babcock-Leighton mechanism and variations in the meridional circulation, which are believed to be responsible for irregularities of the solar cycle---are constrained by using observational data. We take the polar field near minima of the cycle as a measure of the randomness in the Babcock-Leighton process, and the decay rate near the minima as a consequence of the change in meridional circulation. We couple these two observationally derived quantities into a single formula to predict the amplitude of the future solar cycle. Our new formula suggests that the cycle 25 would be a moderate cycle. Whether this formula for predicting the future solar cycle can be justified theoretically is also discussed using simulations from the flux transport dynamo model.Comment: 12 pages, 6 figures, Accepted for publication in Ap

Is a deep one-cell meridional circulation essential for the flux transport Solar Dynamo?

The solar activity cycle is successfully modeled by the flux transport dynamo, in which the meridional circulation of the Sun plays an important role. Most of the kinematic dynamo simulations assume a one-cell structure of the meridional circulation within the convection zone, with the equatorward return flow at its bottom. In view of the recent claims that the return flow occurs at a much shallower depth, we explore whether a meridional circulation with such a shallow return flow can still retain the attractive features of the flux transport dynamo (such as a proper butterfly diagram, the proper phase relation between the toroidal and poloidal fields). We consider additional cells of the meridional circulation below the shallow return flow---both the case of multiple cells radially stacked above one another and the case of more complicated cell patterns. As long as there is an equatorward flow in low latitudes at the bottom of the convection zone, we find that the solar behavior is approximately reproduced. However, if there is either no flow or a poleward flow at the bottom of the convection zone, then we cannot reproduce solar behavior. On making the turbulent diffusivity low, we still find periodic behavior, although the period of the cycle becomes unrealistically large. Also, with a low diffusivity, we do not get the observed correlation between the polar field at the sunspot minimum and the strength of the next cycle, which is reproduced when diffusivity is high. On introducing radially downward pumping, we get a more reasonable period and more solar-like behavior even with low diffusivity.Comment: 12 pages, 13 figure

A theoretical study of the build-up of the Sun's polar magnetic field by using a 3D kinematic dynamo model

We develop a three-dimensional kinematic self-sustaining model of the solar dynamo in which the poloidal field generation is from tilted bipolar sunspot pairs placed on the solar surface above regions of strong toroidal field by using the SpotMaker algorithm, and then the transport of this poloidal field to the tachocline is primarily caused by turbulent diffusion. We obtain a dipolar solution within a certain range of parameters. We use this model to study the build-up of the polar magnetic field and show that some insights obtained from surface flux transport (SFT) models have to be revised. We present results obtained by putting a single bipolar sunspot pair in a hemisphere and two symmetrical sunspot pairs in two hemispheres.We find that the polar fields produced by them disappear due to the upward advection of poloidal flux at low latitudes, which emerges as oppositely-signed radial flux and which is then advected poleward by the meridional flow. We also study the effect that a large sunspot pair, violating Hale's polarity law would have on the polar field. We find that there would be some effect---especially if the anti-Hale pair appears at high latitudes in the mid-phase of the cycle---though the effect is not very dramatic.Comment: 18 pages, 18 figures, published in Ap

Set Partition and Trace Based Verification of Web Service Composition

AbstractDe*signing and running Web services compositions are error-prone as it is difficult to determine the behavior of web services during execution and their conformance to functional requirements. Interaction among composite Web services may cause concurrency related issues. In this paper, we present a formal model for reasoning and verifying Web services composition at design level. We partition the candidate services being considered for composition into several subsets on the basis of their service invocation order. We arrange these subsets to form a Web services set partition graph and transform to a set of interacting traces. Then, we propose a novel methodology for service interaction verification that uses service description (from WSDL file) to extract the necessary information and facilitates the process of modeling, analyzing, and reasoning the composite services. As a part of verification technique, we use two levels of modeling. This includes abstract modeling that further leads to detailed modeling if required, thereby reducing the computation time and modeling complexity

Deliberative democracy and the politics of redistribution: the case of the Indian Panchayats

By examining evidence from India, where quotas for women in local government were introduced in 1993, this article argues that institutional reform can disturb hegemonic discourses sufficiently to open a window of opportunity where deliberative democratic norms take root and where, in addition to the politics of recognition, the politics of redistribution also operates

Mean field models of flux transport dynamo and meridional circulation in the Sun and stars

The most widely accepted model of the solar cycle is the flux transport dynamo model. This model evolved out of the traditional $\alpha \Omega$ dynamo model which was first developed at a time when the existence of the Sun's meridional circulation was not known. In these models, the toroidal magnetic field (which gives rise to sunspots) is generated by the stretching of the poloidal field by solar differential rotation. The primary source of the poloidal field in the flux transport models is attributed to the Babcock--Leighton mechanism, in contrast to the mean-field $\alpha$-effect used in earlier models. With the realization that the Sun has a meridional circulation, which is poleward at the surface and is expected to be equatorward at the bottom of the convection zone, its importance for transporting the magnetic fields in the dynamo process was recognized. Much of our understanding about the physics of both the meridional circulation and the flux transport dynamo has come from the mean field theory obtained by averaging the equations of MHD over turbulent fluctuations. The mean field theory of meridional circulation makes clear how it arises out of an interplay between the centrifugal and thermal wind terms. We provide a broad review of mean field theories for solar magnetic fields and flows, the flux transport dynamo modeling paradigm and highlight some of their applications to solar and stellar magnetic cycles. We also discuss how the dynamo-generated magnetic field acts on the meridional circulation of the Sun and how the fluctuations in the meridional circulation, in turn, affect the solar dynamo. We conclude with some remarks on how the synergy of mean field theories, flux transport dynamo models, and direct numerical simulations can inspire the future of this field.Comment: 43 pages, 8 figures, submitted to Space Science Review

Correlation between Decay Rate and Amplitude of Solar Cycles as Revealed from Observations and Dynamo Theory

Using different proxies of solar activity, we have studied the following features of solar cycle. (i) A linear correlation between the amplitude of cycle and its decay rate, (ii) a linear correlation between the amplitude of cycle $n$ and the decay rate of cycle $(n - 1)$ and (iii) an anti-correlation between the amplitude of cycle $n$ and the period of cycle $(n - 1)$. Features (ii) and (iii) are very useful because they provide precursors for future cycles. We have reproduced these features using a flux transport dynamo model with stochastic fluctuations in the Babcock-Leighton $\alpha$ effect and in the meridional circulation. Only when we introduce fluctuations in meridional circulation, we are able to reproduce different observed features of solar cycle. We discuss the possible reasons for these correlations.Comment: 22 pages, 10 figures and 2 tables, accepted in Solar Physic