A distinct peak-flux distribution of the third class of gamma-ray bursts: A possible signature of X-ray flashes?

Gamma-ray bursts are the most luminous events in the Universe. Going beyond the short-long classification scheme we work in the context of three burst populations with the third group of intermediate duration and softest spectrum. We are looking for physical properties which discriminate the intermediate duration bursts from the other two classes. We use maximum likelihood fits to establish group memberships in the duration-hardness plane. To confirm these results we also use k-means and hierarchical clustering. We use Monte-Carlo simulations to test the significance of the existence of the intermediate group and we find it with 99.8% probability. The intermediate duration population has a significantly lower peak-flux (with 99.94% significance). Also, long bursts with measured redshift have higher peak-fluxes (with 98.6% significance) than long bursts without measured redshifts. As the third group is the softest, we argue that we have {related} them with X-ray flashes among the gamma-ray bursts. We give a new, probabilistic definition for this class of events.