Spectral lags caused by the curvature effect of fireballs

Abstract

ABSTRACT Recently, Shen et al. have studied the contributions of the curvature effect of fireballs to the spectral lag and have shown that the observed lags can be accounted for by the effect. Here, we check their results by performing a more precise calculation with both formulae presented by Shen et al. and Qin et al. Several other aspects which were not considered by Shen et al. are investigated. We find that in the case of ultrarelativistic motions, both formulae are identical as long as the whole fireball surface is concerned. In our analysis, the previous conclusion that the detected spectral lags can be accounted for by the curvature effect is confirmed, while the conclusion that the lag has no dependence on the radius of fireballs is not true. We find that introducing extreme physical parameters is not the only outlet to explain these observed large lags. Even for the larger lags (∼5 s), a wider local pulse (Δtθ,FWHM= 107 s) can account for it. Some conclusions not presented in Shen et al. or those modified in our analysis are listed below: (i) lag ∝Γ-ε with ε > 2; (ii) lag is proportional to the local pulse width and the full width at half-maximum of the observed light curves; (iii) a large lag requires a large α0 and a small β0 as well as a large E0,p; (iv) when the rest-frame spectrum varies with time, the lag would become larger; (v) lag decreases with the increase of Rc; (vi) lag ∝E within the certain energy range for a given Lorentz factor; (vii) lag is proportional to the opening angle of uniform jets when θj < 0.6Γ-1. © 2006 RAS.