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X-ray afterglow light curves have been collected for over 400 Swift gamma-raybursts with nearly half of them having X-ray flares superimposed on the regularafterglow decay. Evidence suggests that gamma-ray prompt emission and X-rayflares share a common origin and that at least some flares can only beexplained by long-lasting central engine activity. We have developed a shellmodel code to address the question of how X-ray flares are produced within theframework of the internal shock model. The shell model creates randomized GRBexplosions from a central engine with multiple shells and follows those shellsas they collide, merge and spread, producing prompt emission and X-ray flares.We pay special attention to the time history of central engine activity,internal shocks, and observed flares, but do not calculate the shock dynamicsand radiation processes in detail. Using the empirical E_p - E_iso (Amati)relation with an assumed Band function spectrum for each collision and anempirical flare temporal profile, we calculate the gamma-ray (Swift/BAT band)and X-ray (Swift/XRT band) lightcurves for arbitrary central engine activityand compare the model results with the observational data. We show that theobserved X-ray flare phenomenology can be explained within the internal shockmodel. The number, width and occurring time of flares are then used to diagnosethe central engine activity, putting constraints on the energy, ejection time,width and number of ejected shells. We find that the observed X-ray flare timehistory generally reflects the time history of the central engine, whichreactivates multiple times after the prompt emission phase with progressivelyreduced energy...

Modeling Gamma-Ray Burst X-Ray Flares within the Internal Shock Model