The structure of Gamma-Ray Burst (GRB) jets impacts on their prompt and afterglow emission properties. Insights into the still unknown structure of GRBs can be achieved by studying how different structures impact on the luminosity function (LF): i) we show that low ($10^{46} < L_{rm iso} < 10^{48}$ erg/s) and high (i.e. with $L_{rm iso} > 10^{50}$ erg/s) luminosity GRBs can be described by a unique LF; ii) we find that a uniform jet (seen on- and off-axis) as well as a very steep structured jet (i.e. $epsilon(theta) propto theta^{-s}$ with $s > 4$) can reproduce the current LF data; iii) taking into account the emission from the whole jet (i.e. including contributions from mildly relativistic, off-axis jet elements) we find that $E_{rm iso}(theta_{rm v})$ (we dub this quantity apparent structure) can be very different from the intrinsic structure $epsilon(theta)$: in particular, a jet with a Gaussian intrinsic structure has an apparent structure which is more similar to a power law. This opens a new viewpoint on the quasi-universal structured jet hypothesis.
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