Thesis (Ph.D.) - University of St Andrews, March 2007.

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Intermediate-degree g-modes (those with angular order ℓ ≈ 30) were first observed in the late 1970's by Hill and Caudell (1979). However, it wasn't until 1986 that a preliminary survey was made of the 1979 differential radius observations (see Bos 1982) and a set of 4 multiplets exhibiting mode-locking was classified by Hill (1986). These multiplets with angular order ℓ ≈ 30 and eigenfrequencies of ≈350 μHz were used as a starting point for the comprehensive analysis discussed in this work. This comprehensive study culminated in the classification of a set of 20 intermediate-degree g-mode multiplets containing over 600 normal modes of oscillation. Each of these multiplets was found to contain mode-coupled sections. Of more importance, however, are the internal properties of the Sun that can be inferred from this large body of classified modes. In this work two significant consequences will be discussed. Because these modes of oscillation are localized within the inner 50% of the Sun by radius and because of their large temperature eigenfunctions implied by the observed phase-locking, these modes of oscillation provide a modification of the effective temperature profile defined for a given process in the Sun. One of these processes is the ⁸B neutrino production. The second consequence of these observations is a predicted periodic modulation of the neutrino production rates. The existence of a large set of mode-coupled gravity modes will lead to a low-frequency modulation of neutrino production rates which may account for the observed periodicity in the ⁸B neutrino production (see Haubold and Gerth 1985). The prediction of this periodicity in the neutrino production rates is unique among all the competing theories that resolve the solar neutrino paradox and is testable by the new generation of solar neutrino detectors.

This work analyzes data taken in 1979 using a modification of the solar detector at SCLERA (Santa Catalina Laboratory for Experimental Relativity) designed to enhance spatial properties of the previously observed solar oscillations. Unlike previous solar observations taken at SCLERA, where the data consisted of single solar diameter measurements, the 1979 data consisted of six recorded limb profiles. This has important ramifications for the amount of signal present in the data which was generated by the terrestrial atmosphere, for the origin of the observed solar oscillations in fluctuations of the solar limb darkening function, and, most importantly, for the spatial symmetry properties of the observed solar eigenfunctions. The data consisted of 18 days of observations averaging ten hours per day and covering a total of 41 days. A linked Fourier transform of all 18 days was done for signal generated from each limb profile, and combinations of these six Fourier transforms made to increase sensitivity to symmetric or antisymmetric properties of the observed solar eigenmodes. The following results were found: 1. The observed oscillations are manifestations of fluctuations in the solar limb darkening function. 2. Terrestrial atmospheric contributions to the observed signal are negligible; thus, the sun constitutes the only possible source of the signal. 3. Given a resolution element of 1/(41 days) or 0.28 μHz, the solar oscillations observed represent individual solar eigenstates. 4. The spatial properties of the eigenstates are consistent with their interpretation in terms of spherical harmonics defined with respect to the observed solar rotational axis. 5. The eigenstates are temporally coherent for > 2 days and, in selected samples, for > 41 days. 6. The observed spacing of groups of eigenmodes is shown to be indicative of solar rotational effects; this spacing implies that the core of the sun is rotating approximately six times faster than the observed surface rotational velocity.

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Yes / A workshop was recently held at Nagoya University (31 October – 02 November 2017), sponsored by the Center for International Collaborative Research, at the Institute for Space-Earth Environmental Research, Nagoya University, Japan, to quantitatively compare the performance of today’s operational solar flare forecasting facilities. Building upon Paper I of this series (Barnes et al. 2016), in Paper II (Leka et al. 2019) we described the participating methods for this latest comparison effort, the evaluation methodology, and presented quantitative comparisons. In this paper we focus on the behavior and performance of the methods when evaluated in the context of broad implementation differences. Acknowledging the short testing interval available and the small number of methods available, we do find that forecast performance: 1) appears to improve by including persistence or prior flare activity, region evolution, and a human “forecaster in the loop”; 2) is hurt by restricting data to disk-center observations; 3) may benefit from long-term statistics, but mostly when then combined with modern data sources and statistical approaches. These trends are arguably weak and must be viewed with numerous caveats, as discussed both here and in Paper II. Following this present work, we present in Paper IV a novel analysis method to evaluate temporal patterns of forecasting errors of both types (i.e., misses and false alarms; Park et al. 2019). Hence, most importantly, with this series of papers we demonstrate the techniques for facilitating comparisons in the interest of establishing performance-positive methodologies.

Yes / Solar flares produce radiation which can have an almost immediate effect on the near-Earth environ- ment, making it crucial to forecast flares in order to mitigate their negative effects. The number of published approaches to flare forecasting using photospheric magnetic field observations has prolifer- ated, with varying claims about how well each works. Because of the different analysis techniques and data sets used, it is essentially impossible to compare the results from the literature. This problem is exacerbated by the low event rates of large solar flares. The challenges of forecasting rare events have long been recognized in the meteorology community, but have yet to be fully acknowledged by the space weather community. During the interagency workshop on “all clear” forecasts held in Boulder, CO in 2009, the performance of a number of existing algorithms was compared on common data sets, specifically line-of-sight magnetic field and continuum intensity images from MDI, with consistent definitions of what constitutes an event. We demonstrate the importance of making such systematic comparisons, and of using standard verification statistics to determine what constitutes a good prediction scheme. When a comparison was made in this fashion, no one method clearly outperformed all others, which may in part be due to the strong correlations among the parameters used by different methods to characterize an active region. For M-class flares and above, the set of methods tends towards a weakly positive skill score (as measured with several distinct metrics), with no participating method proving substantially better than climatological forecasts. / This work is the outcome of many collaborative and cooperative efforts. The 2009 “Forecasting the All-Clear” Workshop in Boulder, CO was sponsored by NASA/Johnson Space Flight Center’s Space Radiation Analysis Group, the National Center for Atmospheric Research, and the NOAA/Space Weather Prediction Center, with additional travel support for participating scientists from NASA LWS TRT NNH09CE72C to NWRA. The authors thank the participants of that workshop, in particular Drs. Neal Zapp, Dan Fry, Doug Biesecker, for the informative discussions during those three crazy days, and NCAR’s Susan Baltuch and NWRA’s Janet Biggs for organizational prowess. Workshop preparation and analysis support was provided for GB, KDL by NASA LWS TRT NNH09CE72C, and NASA Heliophysics GI NNH12CG10C. PAH and DSB received funding from the European Space Agency PRODEX Programme, while DSB and MKG also received funding from the European Union’s Horizon 2020 research and in- novation programme under grant agreement No. 640216 (FLARECAST project). MKG also acknowledges research performed under the A-EFFort project and subsequent service implementation, supported under ESA Contract number 4000111994/14/D/MPR. YY was supported by the National Science Foundation under grants ATM 09-36665, ATM 07-16950, ATM-0745744 and by NASA under grants NNX0-7AH78G, NNXO-8AQ90G. YY owes his deepest gratitude to his advisers Prof. Frank Y. Shih, Prof. Haimin Wang and Prof. Ju Jing for long discussions, for reading previous drafts of his work and providing many valuable comments that improved the presentation and contents of this work. JMA was supported by NSF Career Grant AGS-1255024 and by a NMSU Vice President for Research Interdisciplinary Research Grant.

No / The acceleration of electrons and protons caused by a super-Dreicer electric field directed along the longitudinal component By of the magnetic field is investigated. The three-component magnetic field in a nonneutral current sheet occurring at the top of the reconnecting flaring loops on the charged particle trajectories and energies is considered. Particle trajectories in the reconnecting current sheet (RCS) and their energy spectra at the point of ejection from the RCS are simulated from the motion equation for different sheet thicknesses. A super-Dreicer electric field of the current sheet is found to accelerate particles to coherent energy spectra in a range of 10-100 keV for electrons and 100-400 keV for protons with energy slightly increasing with the sheet thickness. A longitudinal By component was found to define the gyration directions of particles with opposite charges toward the RCS midplane, i.e., the trajectory symmetry. For the ratio By/Bz < 10-6 the trajectories are fully symmetric, which results in particle ejection from an RCS as neutral beams. For the ratio By/Bz > 10-2 the trajectories completely lose their symmetry toward the RCS midplane, leading to the separation of particles with opposite charges into the opposite halves from an RCS midplane and the following ejection into different legs of the reconnecting loops. For the intermediate values of By/Bz the trajectories are partially symmetric toward the midplane, leading to electrons prevailing in one leg and protons in the other.

Yes / Solar flares are extremely energetic phenomena in our Solar System. Their impulsive, often drastic radiative increases, in particular at short wavelengths, bring immediate impacts that motivate solar physics and space weather research to understand solar flares to the point of being able to forecast them. As data and algorithms improve dramatically, questions must be asked concerning how well the forecasting performs; crucially, we must ask how to rigorously measure performance in order to critically gauge any improvements. Building upon earlier-developed methodology (Barnes et al. 2016, Paper I), international representatives of regional warning centers and research facilities assembled in 2017 at the Institute for Space-Earth Environmental Research, Nagoya University, Japan to – for the first time – directly compare the performance of operational solar flare forecasting methods. Multiple quantitative evaluation metrics are employed, with focus and discussion on evaluation methodologies given the restrictions of operational forecasting. Numerous methods performed consistently above the “no skill” level, although which method scored top marks is decisively a function of flare event definition and the metric used; there was no single winner. Following in this paper series we ask why the performances differ by examining implementation details (Leka et al. 2019, Paper III), and then we present a novel analysis method to evaluate temporal patterns of forecasting errors in (Park et al. 2019, Paper IV). With these works, this team presents a well-defined and robust methodology for evaluating solar flare forecasting methods in both research and operational frameworks, and today’s performance benchmarks against which improvements and new methods may be compared.

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