We present the first statistical analysis of 27 UVOT optical/ultra-violet lightcurves of GRB afterglows. We have found, through analysis of the lightcurves in the observers frame, that a significant fraction rise in the first 500s after the GRB trigger, that all lightcurves decay after 500s, typically as a power-law with a relatively narrow distribution of decay indices, and that the brightest optical afterglows tend to decay the quickest. We find that the rise could either be produced physically by the start of the forward shock, when the jet begins to plough into the external medium, or geometrically where an off-axis observer sees a rising lightcurve as an increasing amount of emission enters the observers line of sight, which occurs as the jet slows. We find that at 99.8% confidence, there is a correlation, in the observed frame, between the apparent magnitude of the lightcurves at 400s and the rate of decay after 500s. However, in the rest frame a Spearman Rank test shows only a weak correlation of low statistical significance between luminosity and decay rate. A correlation should be expected if the afterglows were produced by off-axis jets, suggesting that the jet is viewed from within the half-opening angle theta or within a core of uniform energy density theta_c. We also produced logarithmic luminosity distributions for three rest frame epochs. We find no evidence for bimodality in any of the distributions. Finally, we compare our sample of UVOT lightcurves with the XRT lightcurve canonical model. The range in decay indices seen in UVOT lightcurves at any epoch is most similar to the range in decay of the shallow decay segment of the XRT canonical model. However, in the XRT canonical model there is no indication of the rising behaviour observed in the UVOT lightcurves.
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