A test of the power-law relationship between gamma-ray burst pulse-width ratio and energy expected in fireballs and uniform jets

Abstract

A power-law relationship between the pulse width and energy of gamma-ray bursts (GRBs) has been found by many authors. Recently, under the assumption that the Doppler effect of the relativistically expanding fireball surface (or, in some papers, the curvature effect) is important, Qin et al. showed that, in most cases, this power-law relationship would exist in a certain energy range, and, within a similar range, a power-law relationship of an opposite trend between the ratio of the rising width to the decaying width and energy would be expected for the same burst. We check this prediction with two GRB samples that contain well-identified pulses. A power-law anticorrelation between the full pulse width and energy and a power-law correlation between the pulse-width ratio and energy are seen in the light curves of the majority (around 65 per cent) of bursts of the two samples within the energy range of BATSE, suggesting that these bursts probably arise from the emission associated with the shocks occurring on a relativistically expanding fireball surface. For the rest of the bursts, the relationships between these quantities had not been predicted previously. We propose considering other spectral evolutionary patterns or other radiation mechanisms such as a varying synchrotron or Comptonized spectrum to check whether the observed relationships for these bursts can also be accounted for by the Doppler model. In addition, we find that the upper limits of the width ratio for the two samples do not exceed 0.9, in agreement with what has previously been predicted by the Doppler model. The plateau/power law/plateau and the peaked features predicted and detected previously by Qin et al. are generally observed, with exceptions noticed only in a few cases. According to the distinct values of two power-law indices, alpha(FWHM) and alpha(ratio), we divide the bursts into three subsets that are located in different areas of the alpha(FWHM)-alpha(ratio) plane. We suspect that different locations of (alpha(FWHM), alpha(ratio)) might correspond to different mechanisms.