We study the evolution of the [Eu/Fe] ratio in the Galactic halo by means of a stochastic chemical evolution model considering merging neutron stars as polluters of europium. We improved our previous stochastic chemical evolution model by adding a time delay distribution for the coalescence of the neutron stars, instead of constant delays. The stochastic chemical evolution model can reproduce the trend and the observed spread in the [Eu/Fe] data with neutron star mergers as unique producers if we assume: (i) a delay time distribution ∝t-1.5, (ii) an $M_{oldsymbol{ Eu}}= 3 imes 10^{-6} , oldsymbol{M}_{odot }$ per event, (iii) progenitors of neutron stars in the range $9!-!50, oldsymbol{M}_{odot}$, and (iv) a constant fraction of massive stars in the initial mass function (0.02) that produce neutron star mergers. Our best model is obtained by relaxing point (iv) and assuming a fraction that varies with metallicity. We confirm that the mixed scenario with both merging neutron stars and supernovae as europium producers can provide a good agreement with the data relaxing the constraints on the distribution time delays for the coalescence of neutron stars. Adopting our best model, we also reproduce the dispersion of [Eu/Fe] at a given metallicity, which depends on the fraction of massive stars that produce neutron star mergers. Future high-resolution spectroscopic surveys, such as 4MOST and WEAVE, will produce the necessary statistics to constrain at best this parameter.
