The merging rate of double neutron stars (DNS) has a great impact on many astrophysical issues, including the interpretation of gravitational waves signals, of the short gamma-ray bursts (GRBs), and of the chemical properties of stars in galaxies. Such rate depends on the distribution of the delay times (DDT) of the merging events. In this paper, we derive a theoretical DDT of merging DNS following from the characteristics of the clock controlling their evolution. We show that the shape of the DDT is governed by a few key parameters, primarily the lower limit and the slope of the distribution of the separation of the DNS systems at birth. With a parametric approach, we investigate on the observational constraints on the DDT from the cosmic rate of short GRBs and the europium-to-iron ratio in Milky Way stars, taken as tracer of the products of the explosion. We find that the local rate of DNS merging requires that ∼ per cent of neutron stars progenitors live in binary systems which end their evolution as merging DNS within a Hubble time. The redshift distribution of short GRBs does not yet provide a strong constraint on the shape of the DDT, although the best-fitting models have a shallow DDT. The chemical pattern in Milky Way stars requires an additional source of europium besides the products from merging DNS, which weakens the related requirement on the DDT. At present both constraints can be matched with the same DDT for merging DNS.
