Time-dependent photoionization in a dusty medium. I. Code description and general results

We present a time-dependent photoionization code that combines self-consistently metal evolution and dust destruction under an intense X-ray UV radiation field. First, we extend the mathematical formulation of the time-dependent evolution of dust grains under an intense radiation flux with the inclusion of the process of ion field emission (IFE). We determine the relative importance of IFE with respect to X-ray and UV sublimation as a function of grain size, intensity, and hardness of the incident spectrum. We then combine the processes of dust destruction with a photoionization code that follows the evolution of the ionization states of the metals and the relative radiative transitions. Our code treats, self-consistently, the gradual recycling of metals into gas as dust is sublimated away; it allows for any initial dust grain distribution and follows its evolution in space and time. In this first paper, we use our code to study the time-dependent behavior of the X-ray and optical opacities in the nearby environment of a gamma-ray burst and show how the time variability of the low- and high-energy opacities can yield powerful clues on the characteristics of the medium in which the bursts occur.