Curvature Effect of a Non-Power-Law Spectrum and Spectral Evolution of   GRB X-Ray Tails
  The apparent spectral evolution observed in the steep decay phase of many GRB early afterglows raises a great concern of the high-latitude "curvature effect" interpretation of this phase. However, previous curvature effect models only invoked a simple power law spectrum upon the cessation of the prompt internal emission. We investigate a model that invokes the "curvature effect" of a more general non-power-law spectrum and test this model with the Swift/XRT data of some GRBs. We show that one can reproduce both the observed lightcurve and the apparent spectral evolution of several GRBs using a model invoking a power-law spectrum with an exponential cut off. GRB 050814 is presented as an example. 
Bin-Bin Zhang, Bing Zhang, En-Wei Liang, Xiang-Yu Wang