Dust extinction curves and Lyα forest flux deficits for use in modeling gamma-ray burst afterglows and all other extragalactic point sources

Since gamma-ray burst afterglows were first detected in 1997, the relativistic fireball model has emerged as the leading theoretical explanation of the afterglows. In this paper, we present a very general, Bayesian inference formalism with which this, or any other, afterglow model can be tested, and with which the parameter values of acceptable models can be constrained, given the available photometry. However, before model comparison or parameter estimation can be attempted, one must also consider the physical processes that affect the afterglow as it propagates along the line of sight from the burst source to the observer. Namely, how does extinction by dust, both in the host galaxy and in our galaxy, and absorption by the Ly alpha forest and by H I in the host galaxy, change the intrinsic spectrum of the afterglow? Consequently, we also present in this paper a very general, eight-parameter dust extinction curve model and a two-parameter model of the Ly alpha forest flux deficit versus redshift distribution. Using fitted extinction curves from Milky Way and Magellanic Cloud lines of sight, and measurements of Ly alpha forest flux deficits from quasar absorption line systems, we construct a Bayesian prior probability distribution that weights this additional, but necessary, parameter space such that the volume of the solution space is reduced significantly, a priori. Finally, we discuss the broad applicability of these results to the modeling of light from all other extragalactic point sources, such as Type Ia supernovae.