Relation between the intrinsic and observed central engine activity time: Implications for ultra-long GRBs

Abstract

The gamma-ray burst (GRB) central engine intrinsic activity time Tce is usually described through either the γ-ray duration T90 or through a generalized burst duration tburst that includes both the γ-ray emission and (when present) an extended flaring X-ray plateau. Here, we define a more specific operational description of Tce, and within the framework of the internal-external shock model, we develop a numerical code to study the relationship between T90 and Tce, as well as between tburst and Tce, for different initial conditions. We find that when Tce ≲ 104 s, late internal collisions or refreshed external collisions result in values of T90 and tburst larger than Tce, usually by factors of 2-3. For Tce ≳ 104 s, the tburst is always a good estimator for Tce, while T90 can underpredict Tce when the late central engine activity is moderate. We find a clear bimodal distribution for Tce, based on our simulations as well as on the observational data for T90 and tburst. We suggest that tburst is a reliable measure for defining "ultra-long" GRBs. Bursts with T90 of order 103 s need not belong to a special population, while bursts with tburst > 104 s, where the late central engine activity is more moderate and shows up in X-rays, may represent a new population. These conclusions are insensitive to the initial conditions assumed in the models.