Peaks of optical and X-ray afterglow light-curves
Abstract
The peaks of 30 optical afterglows and 14 X-ray light-curves display a good anticorrelation of the peak flux with the peak epoch: Fp ~ tp-2.0 in the optical, Fp ~ tp-1.6 in the X-ray, the distributions of the peak epochs being consistent with each other. We investigate the ability of two forward-shock models for afterglow light-curve peaks -- an observer location outside the initial jet aperture and the onset of the forward-shock deceleration -- to account for those peak correlations. For both models, the slope of the Fp - tp relation depends only on the slope of the afterglow spectrum. We find that only a conical jet seen off-aperture and interacting with a wind-like medium can account for both the X-ray peak relation, given the average X-ray spectral slope betax = 1.0, and for the larger slope of the optical peak relation. However, any conclusion about the origin of the peak flux - peak epoch correlation is, at best, tentative, because the current sample of X-ray peaks is too small to allow a reliable measurement of the Fp - tp relation slope and because more than one mechanism and/or one afterglow parameter may be driving that correlation.