Probing the structure of gamma-ray burst jets with the steep decay phase of their early X-ray afterglows

We show that the jet structure of gamma-ray bursts (GRBs) can be investigated with the tail emission of the prompt GRB. The tail emission that we consider is identified as a steep decay component of the early X-ray afterglow observed by the X-Ray Telescope on board Swift. Using a Monte Carlo method, we derive for the first time the distribution of the decay index of the GRB tail emission for various jet models. The new definitions of the zero of time and the time interval of a fitting region are proposed. These definitions for fitting the light curve lead us to a unique definition of the decay index, which is useful to investigate the structure of the GRB jet. We find that if the GRB jet has a core-envelope structure, the predicted distribution of the decay index of the tail has a wide scatter and multiple peaks, which cannot be seen for the case of the uniform and the Gaussian jet. Therefore, the decay index distribution gives us information about the jet structure. Especially if we observe events whose decay index is less than about 2, both the uniform and the Gaussian jet models will be disfavored, according to our simulation study.