| dc.description.abstract | The intriguing variety of activities displayed by the Sun naturally awakens human curiosity. Also, by virtue of its physical proximity, the Sun serves as an excellent astrophysical laboratory for testing our theoretical ideas. It is widely believed that solar variability influences global climatic changes on Earth. Flares, coronal mass ejections and magnetic storms originating in the Sun influence near-Earth space weather and pose a serious hazard to satellites and telecommunication facilities. The source of solar variability and explosive solar phenomena can be traced back to the presence of magnetic fields in the Sun. It is not surprising then that understanding the origin and evolution of solar magnetic fields remains an active and much promising area of astrophysical research. This thesis aims at developing a phenomenological model for the solar dynamo, which incorporates the recent (relevant) results from flux tube dynamics and helioseismology.
We construct a hybrid model of the solar dynamo, in which, on the one hand, we follow the Babcock-Leighton approach to include surface processes like the production of poloidal field from the decay of active regions (through a phenomenological ?-effect concentrated in a thin layer near the solar surface), and, on the other hand, we attempt to develop a mean-field theory that can be studied in quantitative detail. In this model, meridional circulation plays an important role in bringing the poloidal field generated near the solar surface down to the bottom of the solar convection zone, where the toroidal field is generated.
We introduce the subject of solar magnetic fields in Chapter 1, where we describe the relevant observations and trace the development of theoretical ideas over time. In order to concentrate on the basic physics of the problem, we work with a simplified model of the solar dynamo in the next three chapters. This simplified model considers only the radial shear in the rotation (that matches the helioseismically deduced low-latitude radial shear at the base of the solar convection zone) and neglects the latitudinal shear. In the last chapter we present results with the full rotation profile as deduced from helioseismology.
One of the uncertainties in developing such hybrid models lies in the treatment of magnetic buoyancy within a mean-field framework—a subject that has rarely been explored in the past. Since it is not a priori obvious which is the best method of implementing buoyancy, we explore some alternative buoyancy algorithms in detail in Chapter 2 and present a study in contrast. We find that all these different procedures give certain generic results, although the results also depend on the details of how magnetic buoyancy is treated. Following our findings, we discuss the best ways of treating magnetic buoyancy within the framework of a mean-field dynamo theory.
Recently, Durney formulated a more direct approach to the Babcock-Leighton type solar dynamo. He did away with the ?-effect altogether and instead handled the poloidal field generation mechanism through double ring eruptions (akin to sunspot or active region formation). This erupted double ring flux directly contributes to the poloidal field (through diffusive decay), thus bypassing the need for an ?-effect concentrated near the solar surface. One important question is how our approach (buoyancy algorithm coupled with a concentrated ?-effect) compares with Durney’s double ring formulation—an issue that should be of interest to other dynamo modelers. We explore this issue in Chapter 3, where we handle the generation of the poloidal field near the solar surface by Durney’s method of double ring eruption (by incorporating Durney’s ideas in our model) and compare the results to those of our original model (buoyancy algorithm with a concentrated ?-effect). The two methods are found to give qualitatively similar results and we conclude with a discussion on the relative merits of these two different procedures.
We now return to our original model in which magnetic buoyancy is handled with a realistic recipe—wherein toroidal flux is made to erupt from the overshoot layer wherever it exceeds a specified critical field. In Chapter 4, we present a parameter space study of this model to bring out similarities and differences between it and other well-studied models of the past. We also show that the mechanism of buoyant eruptions and the subsequent depletion of the toroidal field inside the overshoot layer is capable of constraining the magnitude of the dynamo-generated magnetic field there, although a global quenching mechanism is still required to ensure that the magnetic fields do not diverge. We believe that a critical study of this mechanism may give us new information regarding the solar interior and end with an example, where we show that a reduced diffusivity within the generating layer for the toroidal field may be of crucial importance for ensuring buoyant eruptions at low latitudes.
To concentrate on the intricacies of buoyancy inclusion, we had worked with a simplified dynamo model up to this point that included only the radial shear in the rotation. These studies have established the important role that magnetic buoyancy plays in the dynamo process.
We now carry forward the study of this hybrid (buoyancy-driven) dynamo model to its logical conclusion, by incorporating a solar-like differential rotation pattern as deduced from helioseismology. The inclusion of a solar-like rotation pattern complicates the situation to a great extent. So much so, that non-solar-like solutions are found more often than solar-like solutions. Whenever we do find solar-like oscillations, these solutions are plagued by stronger toroidal field and buoyant eruptions at high latitudes, contrary to the observation of sunspots at low latitudes. Such complicated behaviour and the difficulty of producing solar-like solutions are known to exist in many solar dynamo models published till date (which incorporate the helioseismically deduced internal rotation of the Sun). We explore various alternative scenarios through numerical experiments in our quest for solar-like solutions. We demonstrate that the (as yet) unobserved profile of the equatorward meridional counterflow is crucially important for explaining the observations of sunspots at low latitudes and the lack of eruptions at high latitudes. Our conventional wisdom of the solar cycle came mainly from mean-field dynamo models that were worked out in pre-helioseismology days. The inclusion of a solar-like rotation profile seems to indicate that there is a need to re-work some of our classical ideas about the generation of the strong “sunspot-forming” magnetic fields in the solar interior.
The ultimate aim of this thesis was to develop a realistic model of the solar cycle that can, on the one hand, explain features observed on the solar surface, and on the other hand, constrain some of the unknown physical processes in the solar interior.
• “Coefficient versus Durney's double ring approach”, Nandy, D. and Choudhuri, A.R. 2001, Astrophysical Journal, Volume 551, Page 576
• “Constraints on the solar internal magnetic field from a buoyancy-driven solar dynamo”, Nandy, D. 2002, Astrophysics & Space Science, in press
• “Explaining the latitudinal distribution of sunspots with deep meridional flow”, Nandy, D. and Choudhuri, A.R. 2002, Science, in press
• “The solar dynamo with the helioseismically deduced solar rotation”, Nandy, D. and Choudhuri, A.R. 2002, manuscript in preparation | |
