Date of Award
Master of Science
Physics and Astronomy
Steven D. Kawaler
We evaluate techniques presently used to match slates of stellar evolution models to asteroseismic observations by using numeric simulations of the model fits with randomly generated numbers. Measuring the quality of the fit between a simulated model and the star by a raw χ2 shows how well a reported model fit to a given star compares to a distribution of random model fits to the same star. The distribution of χ2 between “models” and simulated pulsations exhibits the behavior of a log–normal distribution, which suggests a link between the distribution and an analytic solution. Since the shape of the distribution strongly depends on the peculiar distribution of modes within the simulations, there appears to be no universal analytic quality–of–fit criterion, so evaluating seismic model fits must be done on a case–by–case basis.
We also perform numeric simulations to determine the validity of spacings between pulsations by comparing the spacing between the observed modes of a given star to those between 106 sets of random numbers using the Q parameter of the Kolmogorov–Smirnov test. The observed periods in GD 358 and PG 1159—035 outperform these numeric simulations and validate their perceived spacings, while there is little support for spacings in PG 1219+534 or PG 0014+067. The best period spacing in BPM 37098 is marginally significant. The observed frequencies of η Boötis outstrip random sets with an equal number of modes, but the modes are selectively chosen by the investigators from over 70 detected periodicities. When choosing the random data from sets of 70 values, the observed modes’ spacings are reproducible by at least 2% of the random sets. Comparing asteroseismic data to random numbers statistically gauge the prominence of any possible spacing which removes another element of bias from asteroseismic analysis.
Erik Stewart Johnson
Johnson, Erik Stewart, "Statistics in asteroseismology: evaluating confidence in stellar model fits" (2011). Graduate Theses and Dissertations. 12213.