A complete sample of bright Swift short Gamma-Ray Bursts

We present a carefully selected sample of short gamma-ray bursts (SGRBs) observed by the Swift satellite up to June 2013. Inspired by the criteria we used to build a similar sample of bright long GRBs (the BAT6 sample), we selected SGRBs with favorable observing conditions for the redshift determination on ground, ending up with a sample of 36 events, almost half of which with a redshift measure. The redshift completeness increases up to about 70% (with an average redshift value of z = 0.85) by restricting to those events that are bright in the 15-150 keV Swift Burst Alert Telescope energy band. Such flux-limited sample minimizes any redshift-related selection effects, and can provide a robust base for the study of the energetics, redshift distribution and environment of the Swift bright population of SGRBs. For all the events of the sample we derived the prompt and afterglow emission in both the observer and (when possible) rest frame and tested the consistency with the correlations valid for long GRBs. The redshift and intrinsic X-ray absorbing column density distributions we obtain are consistent with the scenario of SGRBs originated by the coalescence of compact objects in primordial binaries, with a possible minor contribution (~10%-25%) of binaries formed by dynamical capture (or experiencing large natal kicks). This sample is expected to significantly increase with further years of Swift activity.