Aims. We present the rest-frame light curves in the optical and X-ray bands of an unbiased and complete sample of the Swift long gamma-ray bursts (GRBs), namely, the BAT6 sample. Methods. The unbiased BAT6 sample (consisting of 58 events) has the highest level of completeness in redshift (~95%), allowing us to compute the rest-frame X-ray and optical light curves for 55 and 47 objects, respectively. We compute the X-ray and optical luminosities, which accounte for any possible source of absorption (Galactic and intrinsic) that could affect the observed fluxes in these two bands. Results. We compare the behaviour observed in the X-ray to that in the optical bands to assess the relative contribution of the emission during the prompt and afterglow phases. We unarguably demonstrate that rest-frame optical luminosity distribution of the GRBs is not bimodal and is clustered around the mean value Log(LR) = 29.9 ± 0.8 when estimated at a rest-frame time of 12 h. This is in contrast to what is found in previous works and confirms that the GRB population has an intrinsic unimodal luminosity distribution. For more than 70% of the events, the rest-frame light curves in the X-ray and optical bands have a different evolution, indicating distinct emitting regions and/or mechanisms. The X-ray light curves, which are normalised to the GRB isotropic energy (Eiso), provide evidence for X-ray emission that is still powered by the prompt emission until late times (~hours after the burst event). On the other hand, the same test performed for the Eiso-normalised optical light curves shows that the optical emission is a better proxy of the afterglow emission from early to late times.
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