The main astronomical source of r-process elements has not yet been identified .
One plausible site is neutron star mergers ( NSMs ) , but from perspective of the Galactic chemical evolution , it has been pointed out that NSMs can not reproduce the observed r-process abundance distribution of metal-poor stars at [ { Fe } / { H } ] < -3 .
Recently , Tsujimoto & Shigeyama ( 2014 ) pointed out that NSM ejecta can spread into much larger volume than ejecta from a supernova .
We re-examine the enrichment of r-process elements by NSMs considering this difference in propagation using the chemical evolution model under the hierarchical galaxy formation .
The observed r-process enhanced stars around [ { Fe } / { H } ] \sim - 3 are reproduced if the star formation efficiency is lower for low-mass galaxies under a realistic delay time distribution for NSMs .
We show that a significant fraction of NSM ejecta escape from its host proto-galaxy to pollute intergalactic matter and other proto-galaxies .
The propagation of r-process elements over proto-galaxies changes the abundance distribution at [ { Fe } / { H } ] < -3 and obtains distribution compatible with observations of the Milky Way halo stars .
In particular , the pre-enrichment of intergalactic medium explains the observed scarcity of EMP stars without Ba and abundance distribution of r-process elements at [ { Fe } / { H } ] \lesssim - 3.5 .