A new technique for detecting solar oscillations in the visible to near infrared continuum has been developed and tested at the Santa Catalina Laboratory for Experimental Relativity by Astrometry (SCLERA). In 1985, measurements of the solar radiation intensity near disk center were made by Oglesby (1986, 1987). The results of these observations have been compared to the reported detections and classifications by Hill (1984, 1985) and Rabaey and Hill (1987) of the low-order, low-degree acoustic modes; the intermediate degree f-modes; and the low-order g-modes. For the low-order, low-degree, acoustic modes and the intermediate degree f-modes, a total of 40 multiplets were used in the analysis. The coincidence rates between the peaks in the power spectrum of the 1985 observations and the classified frequency spectrum for multiplets taken in subgroups of ≈5 (same n and contiguous in ℓ) are typically 4-5 σ above the accidental coincidence rate. The maximum coincidence rates for these same subgroups of multiplets were found to occur for frequency shifts of the classified spectrum ranging from -0.27 μHz for modes that are sensitive to the internal properties near the bottom of the convection zone to 0.06 μHz for modes that are sensitive to internal properties near the top of the convection zone. Also included in this work is a comparison of diameter measurements obtained at SCLERA in 1978 (Caudell 1980) with the classified modes mentioned above. Agreement in this case is at the 3.1 σ level for both the f-mode (n = 0) multiplets with 21 ≤ ℓ ≤ 36 and the n = 1, 6 ≤ ℓ ≤ 12 acoustic modes. The confirmation of the detection and classification of the low-order g-modes of oscillation was found to be at the 3.3 σ level. Additionally, the m dependence of the 1985 power spectrum was found to behave in the manner expected for the proper classifications in m for the g-modes.

This thesis describes the 1983 solar shape investigation performed at the Santa Catalina Laboratory for Experimental Relativity by Astrometry (SCLERA). Solar diameter measurements, with the North Solar Pole defined as θ = 0° polar angle, have been made between the following polar coordinates: from θ = 0° to θ = 180° (the polar diameter), from θ = 90° to θ = -90° (the equatorial diameter), from θ = -45° to θ = 135° and from θ = 45° to θ = -135°. Expressing the Sun's apparent shape in terms of a Legendre series, these diameters have enabled the calculation of the P₂ (quadrupole) and P₄ (hexadecapole) shape coefficients. The theoretical framework used to provide a relationship between the observed shape of the Sun and the multipole moments of the solar gravitational potential field has been improved to include, in general, the effect of differential rotation in both latitude and radius. Using the shape coefficients and the theoretical framework, the gravitational potential multipole moments, expressed as the P₂ and P₄ coefficients of a Legendre series, have been found to be J₂ = (3.4 ± 1.3)E-6 and J₄ = (1.7 ± 1.1)E-6, respectively. It has been found that the contribution to the perihelion precession of Mercury's orbit, caused by the combined effects from the gravitational quadrupole term and general relativity, was approximately 1σ different from the observed amount after all other known Newtonian contributions had been removed from the observed precession. The total apparent oblateness ΔR (equator-polar radii) found from SCLERA observations is ΔR = 13.8 ± 1.3 milliarcseconds. The surface rotation contribution ΔR' to the apparent solar shape is ΔR' = 7.9 milliarcseconds. The quoted uncertainties represent formal statistical 1σ errors only. Also, it has been shown that large changes in the apparent limb darkening functions were occurring near the equatorial regions of the Sun during the time of the observations. Evidence for periodic shape distortions near the equator have also been found.

A new instrument has been developed for making unimaged whole-disk observations of low-degree solar normal-mode oscillations. The apparatus, referred to as the sky monitor, does not track the solar disk, but instead measures the radiant flux scattered by the Earth's atmosphere at 1.6 and 0.5 μ. The expected diurnal flux variation was obtained from a detailed radiative transfer calculation. Data were acquired for 15.5 months during 1991-92. Seventy-two days of data were analyzed for evidence of solar p modes in the frequency range 1800-4776 μHz. Noise generated by the Earth's atmosphere was reduced by scaling the Fourier amplitude computed from the infrared signal and subtracting it from the Fourier amplitude computed from the visible signal. A superimposed frequency analysis was then performed which revealed ∼ 2 σ peaks within 0.3 μHz of symmetry-allowed locations, while no excess power was detected at the symmetry-forbidden frequencies. The probability of obtaining by chance the observed excess power density at symmetry-allowed frequencies and deficit of power density at symmetry-forbidden frequencies was computed to be 6.9 x 10⁻³. Correcting the frequencies for solar-cycle variations, the probability was reduced to 2.9 x 10⁻⁴. These results indicate that it is quite unlikely that the observed symmetry properties have occurred by chance, and support the hypothesis that solar normal-mode signals are manifested in the data. The amplitudes I'/Iₒ averaged over radial order n of the ℓ = 0 and ℓ = 2, m = 0 modes were found to be (7.54 ± 0.54) x 10⁻⁷ and (7.68 ± 0.56) x 10⁻⁷, respectively. These results are about a factor of two smaller than the amplitude of total irradiance oscillations measured from space. While the rotational splitting of the ℓ = 2 multiplet appears to be consistent with that reported by Hill (1985a), results for ℓ = 1 and ℓ = 3 are inconclusive.

Solar seismology is a relatively new field in solar astrophysics. It provides us a way of "looking" into the deep interior of the Sun. The goal of solar seismology is to derive information about the internal structure of the Sun from the observed properties of solar oscillations. This is called the inverse problem of solar seismology. This project is to explore a new set of methods and algorithms to solve the inverse problem. The continuous orthonormalization (CON) method and the adjoint method adapted by Rosenwald can be used to compute the eigenfrequency sensitivities to the solar structure parameters in a very efficient way. In this work, the computational algorithm for using these methods has been modified and improved. Continuous parametrization for the internal structure of the Sun is introduced. The solar interior is subdivided into sections, and polynomial fits are applied to the solar structure parameters in each section. The eigenfrequency sensitivities to these polynomial coefficients--the continuous parameters--are computed. These sensitivities can be used to predict the change in solar eigenfrequencies when the structure parameters are perturbed (with the necessary physical constraints satisfied). The inverse problem for the solar internal structure is formulated by using these sensitivities. The generalized inverse technique is used to solve the nonlinear inverse problem in an iterative process. Observed data of low-degree g-modes have been used for a preliminary inversion. The nonlinearity of the solar seismic inverse problem is demonstrated. A nonlinear inversion process has been successfully performed and the results analysed. The inversion results indicate that the standard solar model is a good approximation of the real Sun. Only relatively small perturbations to the model are needed to explain the frequency deviations between observation and theory.

Two new analysis methods for solar seismology are developed. Called the continuous orthonormalization (CON) and adjoint methods, their use enables both solar eigenfrequencies and eigenfrequency sensitivities (partial derivatives with respect to solar model parameters) to be computed more accurately and efficiently than with existing methods. The CON method integrates an eighth-order nonlinear system of ordinary differential equations (ODEs) which defines the linear adiabatic nonradial oscillation modes of the Sun. (The Cowling approximation is not used.) All normal modes of oscillation are treated identically, regardless of their type (pressure, gravity or fundamental) or their predominant location inside the Sun. The adjoint method integrates a related eighth-order linear inhomogeneous system of ODEs. From the resultant solution, an eigenfrequency's partial derivatives with respect to an extensive set of solar model parameters may be computed simultaneously. Extensive numerical tests confirm the validity of the two new methods. Eigenfrequencies obtained via the CON method have seven significant digits and match within 1% the eigenfrequencies obtained via finite difference or mesh approaches. (Exact agreement is neither expected nor attainable because differently defined solar models are analyzed. The CON method analyzes models which are functionally specified on a continuum of radial points; the other methods analyze models defined on discrete sets of radial points.) Eigenfrequency sensitivities obtained via the adjoint method match within 2% the results obtained by explicitly perturbing the solar model parameters and recomputing the eigenfrequencies. The usefulness and power of the two new methods are demonstrated by applying them to the solution of an elementary solar inversion problem. A sample solar model's f-mode frequencies (obtained via the CON method) are iteratively driven into agreement with an observed set of f-mode frequencies. Adjoint sensitivity results are used to alter solar model parameters within hundreds of radial bins. The frequency movement is large, comparable to the frequency separation between adjacent degree f-modes. Model changes are also large; the density near the base of the convection zone is roughly doubled, while slightly further out it is halved.

Abstract not available

Thesis (Ph.D.)--University of Wollongong, 2003. / Typescript. Bibliographical references: leaf 287-305.

The Sun, by the virtue of its proximity to Earth, serves as an excellent astrophysical laboratory for testing our theoretical ideas. The Sun displays a plethora of visually awe-inspiring phenomena including flares, prominences, sunspots, corona, CMEs and uncountable others. It is now known that it is the magnetic field of the Sun which governs all these and also the geomagnetic storms at the Earth, which owes its presence to the interaction between the geomagnetic field and the all-pervading Solar magnetic field in the interplanetary medium. Since the solar magnetic field affects the interplanetary space around the Earth in a profound manner, it is absolutely essential that we develop a comprehensive understanding of the generation and manifestation of magnetic fields of the Sun. This thesis aims at developing a state-of-the-art dynamo code SURYA1taking into account important results from helioseismology and magnetohydrodynamics. This dynamo code is then used to study various phenomenon associated with solar activity including evolution of solar parity, response to stochastic fluctuations, helicity of active regions and prediction of future solar cycles. Within last few years dynamo theorists seem to have reached a consensus on the basic characteristics of a solar dynamo model. The solar dynamo is now believed to be comprised of three basic processes: (i)The toroidal field is produced by stretching of poloidal field lines primarily inside the tachocline – the region of strong radial shear at the bottom of the convection zone. (ii) The toroidal field so formed rises to the surface due to magnetic buoyancy to form active regions. (iii) Poloidal field is generated at the surface due to decay of tilted active regions – an idea attributed to Babcock (1961) & Leighton (1969). The meridional circulation then carries the poloidal field produced near the surface to the tachocline. The profile of the solar differential rotation has now been mapped by helioseismology and so has been the poleward branch of meridional circulation near the surface. The model I describe in this thesis is a two-dimensional kinematic solar dynamo model in a full sphere. Our dynamo model Surya was developed over the years in stages by Prof. Arnab Rai Choudhuri, Dr. Mausumi Dikpati, Dr. Dibyendu Nandy and myself. We provide all the technical details of our model in Chap. 2 of this thesis. In this model we assume the equatorward branch of the meridional circulation (which hasn’t been observed yet), to penetrate slightly below the tachocline (Nandy & Choudhuri 2002, Science, 296, 1671). Such a meridional circulation plays an important role in suppressing the magnetic flux eruptions at high latitudes. The only non-linearity included in the model is the prescription of magnetic buoyancy. Our model is shown to reproduce various aspects of observational data, including the phase relation between sunspots and the weak, efficient. An important characteristic of our code is that it displays solar-like dipolar parity (anti-symmetric toroidal fields across equator) when certain reasonable conditions are satisfied, the most important condition being the requirement that the poloidal field should diffuse efficiently to get coupled across the equator. When the magnetic coupling between the hemispheres is enhanced by either increasing the diffusion or introducing an α ff distributed throughout the convection zone, we find that the solutions in the two hemispheres evolve together with a single period even when we make the meridional circulation or the α effect different in the two hemispheres. The effect of diffusive coupling in our model is investigated in Chap. 3. After having explored the regular behaviour of the solar cycle using the dynamo code we proceed to study the irregularities of the Solar cycle.We introduce stochastic fluctuations in the poloidal source term at the solar surface keeping the meridional circulation steady for all the numerical experiments. The dynamo displays oscillatory behaviour with variable cycle amplitudes in presence of fluctuations with amplitudes as large as 200%. We also find a statistically significant correlation between the strength of polar fields at the endofone cycle and the sunspot number of the next cycle. In contrast to this there exist a very poor correlation between the sunspot number of a cycle and the polar field formed at its end. This suggests that during the declining phase of the sunspot cycle poloidal field generation from decaying spots takes place via the Babcock-Leighton mechanism which involves randomness and destroys the correlation between sunspot number of a cycle and the polar at its end. In addition to this we also see that the time series of asymmetries in the sunspot activity follows the time series of asymmetries in the polar field strength with a lag of 5 years. We also compare our finding with available observational data. Although systematic measurements of the Sun’s polar magnetic field exist only from mid-1970s, other proxies can be used to infer the polar field at earlier times. The observational data indicate a strong correlation between the polar field at a sunspot minimum and the strength of the next cycle, although the strength of the cycle is not correlated well with the polar field produced at its end. We use these findings about the correlation of polar fields with sunspots to develop an elegant method for predicting future solar cycles. We feed observational data for polar fields during the minima of cycle n into our dynamo model and run the code till the next minima in order to simulate the sunspot number curve for cycle n+1. Our results fit the observed sunspot numbers of cycles 21-23 reasonably well and predict that cycle 24 will be about 30–35% weaker than cycle 23. We fit that the magnetic diffusivity in the model plays an important role in determining the magnetic memory of the Solar dynamo. For low diffusivity, the amplitude of a sunspot cycle appears to be a complex function of the history of the polar field of earlier cycles. Only if the magnetic diffusivity within the convection zone is assumed to be high (of order 1012cms−1), we are able to explain the correlation between the polar fiat a minimum and the next cycle. We give several independent arguments that the diffusivity must be of this order. In a dynamo model with diffusivity like this, the poloidal field generated at the mid-latitudes is advected toward the poles by the meridional circulation and simultaneously diffuses towards the tachocline, where the toroidal field for the next cycle is produced. The above ideas are put forward in Chap. 6. We next come to an important product of the dynamo process namely the magnetic helicity. It has been shown independently by many research groups that the mean value of the normalized current helicity αp= B (Δ×B)/B2in solar active regions is of the order of 10−8m−1, predominantly negative in the northern hemisphere, positive in the southern hemisphere. Choudhuri (2003, Sol. Phys., 215, 31)developed a model for production of the helicity of the required sign in a Babcock-Leighton Dynamo by wrapping of poloidal field lines around a fluxtube rising through the convection zone. In Chap. 7 we calculate helicities of solar active regions based on this idea. Rough estimates based on this idea compare favourably with the observed magnitude of helicity. We use our solar dynamo model to study how helicity varies with latitude and time. At the time of solar maximum, our theoretical model gives negative helicity in the northern hemisphere and positive helicity in the south, in accordance with observed hemispheric trends. However, we fit that during a short interval at the beginning of a cycle, helicities tend to be opposite of the preferred hemispheric trends. After calculating the sign and magnitude of helicity of the sunspots we worry about the distribution of helicity inside a sunspot. In Chap. 8 we model the penetration of a wrapped up background poloidal field into a toroidal magnetic flux tube rising through the solar convective zone. The rise of the straight, cylindrical flux tube is followed by numerically solving the induction equation in a comoving Lagrangian frame, while an external poloidal magnetic field is assumed to be radially advected onto the tube with a speed corresponding to the rise velocity. One prediction of our model is the existence of a ring of reverse current helicity on the periphery of active regions. On the other hand, the amplitude of the resulting twist depends sensitively on the assumed structure (ffvs. concentrated/intermittent) of the active region magnetic field right before its emergence, and on the assumed vertical profile of the poloidal field. Nevertheless, in the model with the most plausible choice of assumptions a mean twist comparable to the observational results. Our results indicate that the contribution of this mechanism to the twist can be quite find under favourable circumstances it can potentially account for most of the current helicity observed in active regions.