Nonparametric estimation of the off-pulse interval(s) of a pulsar light curve

Abstract

The main objective of this thesis is the development of a non-parametric sequential estimation technique for the off-pulse interval(s) of a source function originating from a pulsar. It is important to identify the off-pulse interval of each pulsar accurately, since the properties of the off-pulse emissions are further researched by astrophysicists in an attempt to detect potential emissions from the associated pulsar wind nebula (PWN). The identification technique currently used in the literature is subjective in nature, since it is based on the visual inspection of the histogram estimate of the pulsar light curve. The developed non-parametric estimation technique is not only objective in nature, but also accurate in the estimation of the off-pulse interval of a pulsar, as evident from the simulation study and the application of the developed technique to observed pulsar data. The first two chapters of this thesis are devoted to a literature study that provides background information on the pulsar environment and -ray astronomy, together with an explanation of the on-pulse and off-pulse interval of a pulsar and the importance thereof for the present study. This is followed by a discussion on some fundamental circular statistical ideas, as well as an overview of kernel density estimation techniques. These two statistical topics are then united in order to illustrate kernel density estimation techniques applied to circular data, since this concept is the starting point of the developed non-parametric sequential estimation technique. Once the basic theoretical background of the pulsar environment and circular kernel density estimation has been established, the new sequential off-pulse interval estimator is formulated. The estimation technique will be referred to as `SOPIE'. A number of tuning parameters form part of SOPIE, and therefore the performed simulation study not only serves as an evaluation of the performance of SOPIE, but also as a mechanism to establish which tuning parameter configurations consistently perform better than some other configurations. In conclusion, the optimal parameter configurations are utilised in the application of SOPIE to pulsar data. For several pulsars, the sequential off-pulse interval estimators are compared to the off-pulse intervals published in research papers, which were identified with the subjective "eye-ball" technique. It is found that the sequential off-pulse interval estimators are closely related to the off-pulse intervals identified with subjective visual inspection, with the benefit that the estimated intervals are objectively obtained with a non-parametric estimation technique.