| The Gamma-Ray Burst (GRB) Afterglow Modeling Project (AMP) will model, in a statistically sound and self-consistent way, every GRB afterglow observed since the first detection in 1997, using all available radio, infrared, optical, ultraviolet and X-ray data. The result will be a catalog of fitted empirical model parameters describing the intrinsic afterglow emission, and extinction due to dust and absorption due to gas along the line of sight to the GRB. This ever-growing catalog of fitted model parameters will allow us to infer the astrophysical properties of GRBs and their environments, and to explore their variety and evolution over the history of the universe. First, I present a new, broadly applicable statistical technique, the TRF statistic, for fitting model distributions to data in two dimensions, where the data have intrinsic uncertainties in both dimensions, and extrinsic scatter in both dimensions that is greater than can be accounted for by the intrinsic uncertainties alone. I demonstrate the properties of the TRF statistic, which is invertible but not scalable, and present an algorithm for obtaining an optimum scale for fits to a given data set. I then apply the TRF statistic to observations of interstellar extinction of stars along various Milky Way and Magellanic Cloud lines of sight, and to observations of Lyalpha forest flux deficits in quasars, to construct a comprehensive empirical model for extinction due to interstellar dust in the source frame and in the Milky Way, and absorption due to gas in the source frame and in the intergalactic medium. Combined with theoretical models of synchrotron emission from GRB jets, the resulting parameterization provides a framework for modeling the observed emission from most GRB afterglows. Furthermore, the extinction and absorption models are broadly applicable, in that they may be used to model observations of any extragalactic point source of radiation. Finally, I describe the results of model fitting to NIR, optical and X-ray observations of the afterglow of GRB 090313, which exercises all aspects of the AMP modeling framework presented in this thesis. |
