yes / A comprehensive spectral analysis of both the solar background magnetic field (SBMF) in cycles 21-23 and the sunspot magnetic field in cycle 23 reported in our recent paper showed the presence of two principal components (PCs) of SBMF having opposite polarity, e. g., originating in the northern and southern hemispheres, respectively. Over a duration of one solar cycle, both waves are found to travel with an increasing phase shift toward the northern hemisphere in odd cycles 21 and 23 and to the southern hemisphere in even cycle 22. These waves were linked to solar dynamo waves assumed to form in different layers of the solar interior. In this paper, for the first time, the PCs of SBMF in cycles 21-23 are analyzed with the symbolic regression technique using Hamiltonian principles, allowing us to uncover the underlying mathematical laws governing these complex waves in the SBMF presented by PCs and to extrapolate these PCs to cycles 24-26. The PCs predicted for cycle 24 very closely fit (with an accuracy better than 98%) the PCs derived from the SBMF observations in this cycle. This approach also predicts a strong reduction of the SBMF in cycles 25 and 26 and, thus, a reduction of the resulting solar activity. This decrease is accompanied by an increasing phase shift between the two predicted PCs (magnetic waves) in cycle 25 leading to their full separation into the opposite hemispheres in cycle 26. The variations of the modulus summary of the two PCs in SBMF reveals a remarkable resemblance to the average number of sunspots in cycles 21-24 and to predictions of reduced sunspot numbers compared to cycle 24: 80% in cycle 25 and 40% in cycle 26.

Solar flare soft x-ray emission from 0.5 Å to 8.5 Å was observed during 1967-68 by U.S. Naval Research Laboratory Bragg crystal (LiF and EDDT) spectrometers aboard the OS0-4 satellite and also by NRL broad band ionization detectors aboard the OG0-4 satellite. In this work, instrumental parameters for the LiF crystal spectrometer based on experimental values have been determined and used in the data analysis. The source continuum spectra between 1 Å and 3.8 Å have been obtained for selected flares from OS0-4 spectrometer scans. As these spectra are each affected by time variations over 14 minutes, they are compared with the thermal continuum (free-free and free-bound) spectra predicted in the following manner. The instantaneous electron kinetic temperature and emission measure (equal to the product of the square of the electron number density and the total volume) of the flare plasma are determined from the available OG0-4 broad band data. The expected continuum flux is calculated by using these parameters. The comparison shows that there is good agreement between 2 Å and 3.8 Å. Thus it has been concluded that reliable values of the average electron temperature can be determined from the OG0-4 flare data. The earlier wavelength assigrunent and line identification list published by Meekins et al (1970, Solar Physics 13, 198) has been substantially improved in this work by separately summing a large number of OS0-4 spectrometer scans of the flaring and active sun. All identified wavelengths are found to agree with the more accurate theoretical valuesto within + 0.01 Å. Identifications of several weak lines as due to hydrogen-like and helium-like ions of chlorine and phosphorus have also been suggested. The temporal behaviour of selected ion line intensities (due to Fe, Ca, Si, S, Al, and Mg) indicates that they follow the expected temperature variations during the flare. The total continuum emission in the 0.5 to 3 Å and the 1 to 8 Å broad band segments has been determined from OG0-4 data for 21 flares. In doing this, a simple and approximate method of converting the total emission based on the gray body approximation (in which the OG0-4 data are reported) to one based on the thermal continuum spectrum has been developed. This study shows that the total energy lost in the 0.5 to 8 Å soft x-ray channel is of the order of 10²⁸ to 10³⁰ ergs depending on the Hα importance of the flare (from sub- to class 2); it is also shown that this energy is comparable with that emitted in higher wave length segments estimated by other authors. / Graduate

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Sustainable Built Environments Senior Capstone Project- Report and Final Document / The purpose of this study is to create a spatial decision support system for sustainable landscape design in an urban setting. As more and more of the worlds population concentrates in cites, the design of these spaces becomes critical to global sustainability. The built environment exhibits different environmental conditions than its rural or natural counterparts— the following study focuses on building a GIS model of unique sun exposure conditions at a site, and using this model in a spatial decision support system. The system will compare the exposure needs of just over 150 native or near native plants with the exposure availability of Tucson’s Historic Y Building, and provide tailored list for each area. This will allow for design flexibility within sustainable parameters.

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.

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The upper atmosphere of the sun, the solar corona, is approximately 1,000,000K hotter than the surface of the Sun, a property which cannot be explained by the normal processes of heat conduction and radiation. It is now commonly believed that the magnetic fields which fill the solar atmosphere, and propagate down into the interior of the Sun, are important for transferring and transforming energy from the strong plasma flows inside the Sun into the corona as heat. I have investigated an elementary flux interaction which forms a fundamental building block of the coronal heating process. This interaction involves two opposite polarity sources on the Sun's surface in the presence of an overlying magnetic field. To fully understand how this interaction transfers heat into the solar corona, the magnetic skeleton is required, which shows possible sites of heating that are due to magnetic reconnection. A magnetic field is best described by its magnetic skeleton. The most important parts of the magnetic skeleton to find are the null points, from which separatrix surfaces extend that divide magnetic flux of different topology. Part of this thesis proposes a new method of finding null points, for which the accuracy is shown and then compared with another commonly used method (which gave false results). Using these techniques for finding the magnetic skeleton in the magnetic interaction above, the evolution of the skeleton was found to head through seven distinct states, some of which were far more complicated than expected. This included a high number of separators (the intersection of two separatrix surfaces), which are a known location of magnetic reconnection. This separator reconnection was shown to be the main heating mechanism in this interaction, from which the total amount and rates of reconnection in the experiment was calculated. This led to the discovery of recursive reconnection, a process where magnetic flux is reconnected before reconnecting back to its original state, to allow for the process to repeat again. This recursive reconnection was shown to allow far more reconnection than would have been previously expected, all of which releases heat into the neighbouring areas of the atmosphere. Finally, the interaction was modelled with sources of different magnetic radii but of equal flux. This showed that when the antisymmetric nature of the previous interactions was removed, there was little change in the reconnection rates, but when the strength of the overlying magnetic field was increased, the reconnection rates were found to increase. This increase in the overlying magnetic field strength also produced a new magnetic feature called a bald-edge, which was found to replace some of the null points. These bald-edges were found to be associated with surfaces similar to separatrix surfaces that divide flux of different topology but do not extend from a null point. Also features similar to separators extend from these bald-edges.

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