Shallow Decay of Early X-ray Afterglows from Inhomogeneous Gamma-ray Burst Jets

Almost all the X-ray afterglows of gamma-ray bursts (GRBs) observed by the Swift satellite have a shallow decay phase in the first thousands of seconds. We show that in an inhomogeneous jet (multiple-subjet or patchy-shell) model the superposition of the afterglows of off-axis subjets (patchy shells) can have the shallow decay phase. The necessary condition for obtaining the shallow decay phase is that γ-ray bright subjets (patchy shells) should have γ-ray efficiency higher than previously estimated, and should be surrounded by γ-ray dim subjets (patchy shells) with low γ-ray efficiency. Our model predicts that events with dim prompt emission have the conventional afterglow light curve without the shallow decay phase like GRB 050416A. Subject headings: gamma rays: bursts — gamma rays: theory