An Intrinsic Smoothing Mechanism For Gamma-Ray Burst Spectra in the Fireball Model

It is shown that differential Doppler shift of different patches of the blastwave front in the fireball model at varying angles to the line of sight could provide an intrinsic smoothing mechanism for the spectra of gamma-ray bursts (GRBs) and the associated afterglows at lower energy bands. For the model parameters of interest, it is illustrated that a monochromatic spectrum at $\nu$ in blastwave comoving frame is smoothed and observed to have a half-width-half-maximum (HWHM) of $\sim (0.6-2.0)\nu$. Some other implications of this smoothing process are discussed. In particular, observed local spectral slope of GRBs or afterglows in the fireball model cannot be steeper than $\nu^{-\alpha}$ with $\alpha=0.75-1.25$, regardless of the intrinsic spectra in the comoving shock frame; i.e., a very steep electron distribution function (with $p>3$) could produce an observed spectrum with $\alpha\sim 1$. In addition, a generic fast-rise-slow-decay type of GRB temporal profile is expected.