The correlations among variability, optical peak time and spectral time lag of long gamma-ray bursts

Abstract

Statistical relations are useful tools to comprehend the intrinsic physics processes of gamma-ray bursts (GRBs). In this work we collect spectral lag (τ), variability (V) and optical peak time (t p,o). We find that there is a correlation between variabilities and spectral lags, reading as V = −0.0075 (±0.0007) × log10 τ + 0.0351 (±0.0024). There may also exist a relatively weak positive tendency between GRBs optical band peak times and their spectral time lags. Its Pearson coefficient is 0.398, which indicates a weak linear correlation. If we contain some “negative spectral lag” samples, then the latter relation would be worse due to two outlying points. The τ-V relation is consistent with previous studies, and the positive trend between τ and t p,o indicates the spectral lag of GRB might be caused by the curvature effect, but this conclusion is not significant.