Analytical Afterglow Light Curves of Gamma-ray Bursts: the Case of a Flat Electron Spectrum

In the standard afterglow model, the swept electrons have a single power-law energy distribution dn/dγe ∝ γ−p e (p ∼ 2.3), owing to the first order Fermi acceleration process. However, in some events people find a lot of evidence for a flat electron spectrum (i.e., p < 2). In this work, the analytical afterglow light curves in the case of a flat electron energy distribution are presented respectively for a single power-law spectrum and a broken power-law spectrum, then the results are applied to the specific burst GRB 060908. Besides, we have also speculated a possible solution of the so-called low energy spectrum crisis of Gamma-ray Bursts