Joshua Ingram

Date of Award

2022

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Klingenberg, Bernhard

Area of Concentration

Statistics and Applied Mathematics with Economics

Abstract

Solar flares are impulsive releases of energy that tend to occur in active regions located in the solar corona, occurring as a results of the reconnection of the sun’s magnetic field lines. The number of solar flares occurring in the corona is strongly correlated with the phase of the solar cycle. It is common practice to describe the distribution of the number of flares occurring in a given year or over a solar cycle with a Poisson distribution. We find that the observed distributions are overdispersed relative to that expected from Poisson, and thus conclude that a Poisson generative model is not appropriate to fit to flare data aggregated in this manner. We propose that only those flares that occur within a given active region should be modeled as a Poisson process, finding that this is only the case for about 50% of them. The accumulation of flares from several concurrent active regions explains the observed properties of the flare counts. This result also has an impact on the process of analyzing the distribution of flare energies, which are known to be distributed as power-laws. The scaling parameter α of power-laws that characterize flare energy distribu- tions are usually estimated using maximum likelihood methods or linear regression in log-log space. However, flare detection efficiency decreases with flare energy, and power-law estimates become biased if the turnover in the distribution is not properly accounted for. We have devised a flexible probability-discounted power-law model built on the assumption of a Poisson process for flare occurrences. The model can describe the lower energy shape of this distribution, as well as the power-law shape at higher flare energies, and we apply it to solar flare data compiled in the GOES database over Cycles 23 and 24. We fit the model to aggregated, cycle, yearly, and active region total energy distri- butions. We report that the power-law indexes α for aggregate and cycle total energy distributions range from 1.88 to 2.01. For yearly fitted values, we observe no definitive trend in the power-law index, but do observe considerable variation throughout each year.

Download

Share

COinS