Physics & Astronomy ETDs

Publication Date



In this thesis, analysis tools for understanding the observed spectrum and arrival directions of ultra high energy cosmic rays are developed and applied to both simulated and observed data. Two separate statistical tests are applied to the AGASA and preliminary Auger Cosmic Ray Energy spectra in an attempt to find deviation from a pure power-law. The first test is constructed from the probability distribution for the maximum event of a sample drawn from a power-law. The second employs the TP-statistic, a function defined to deviate from zero when the sample deviates from the power-law form, regardless of the value of the power index. Un-binned versions of these and other estimators are developed and applied to simulated cosmic ray spectra. The energy spectrum of Auger events arriving in different regions of the sky is also studied. The two-point angular correlation function is a traditional method used to search for deviations from expectations of isotropy. Here, a statistically descriptive three-point method is developed and explored, with the intended application being the search for deviations from isotropy in the highest energy cosmic rays. The sensitivity of this so-called "shape-strength" method is compared to that of a two-point method for a variety of Monte-Carlo simulated anisotropic signals, and studies with anisotropic source signals diluted by an isotropic background are performed. Type I and II errors for rejecting the hypothesis of isotropic cosmic ray arrival directions are evaluated for four different event sample sizes: 27, 40, 60 and 80 events, consistent with near-term data expectations from the Pierre Auger Observatory. In all cases, the ability to reject the isotropic hypothesis improves with event size and with the fraction of anisotropic signal. But while data sets with ~ 40 events should be sufficient for reliable identification of anisotropy in cases of rather extreme (highly anisotropic) data, much larger data sets are suggested for reliable identification of more subtle anisotropies. Overall, the shape-strength method, which can be easily adapted to an arbitrary experimental exposure on the celestial sphere, consistently performs better than the two point method.

Degree Name


Level of Degree


Department Name

Physics & Astronomy

First Advisor

Matthews, John A. J.

First Committee Member (Chair)

Matthews, John A. J.

Second Committee Member

Gold, Michael

Third Committee Member

Prasad, Sudhakar

Fourth Committee Member

Roy, Mousumi




Cosmic rays--Data processing, Cosmic ray showers, Auger effect, Anisotropy.

Document Type