The rapid neutron-capture process (r-process) is a major process for the synthesis of elements heavier than iron-peak elements, but the astrophysical site(s) of the r-process has not yet been identified. Neutron star mergers (NSMs) are suggested to be a major r-process site according to nucleosynthesis studies. Previous chemical evolution studies, however, required unlikely short merger times of NSMs to reproduce the observed large star-to-star scatters in the abundance ratios of r-process elements to iron: the [Eu/Fe] of extremely metal-poor stars in the Milky Way (MW) halo. This problem can be solved by considering chemical evolution in dwarf spheroidal galaxies (dSphs), which would be building blocks of the MW and have lower star formation efficiencies than the MW halo. We demonstrate the enrichment of r-process elements in dSphs by NSMs using an N-body/smoothed particle hydrodynamics code. Our high-resolution model reproduces the observed [Eu/Fe] due to NSMs with a merger time of 100 Myr when the effect of metal mixing is taken into account. This is because metallicity is not correlated with time ~300 Myr from the start of the simulation due to the low star formation efficiency in dSphs. We also confirm that this model is consistent with observed properties of dSphs such as radial profiles and metallicity distribution. The merger time and the Galactic rate of NSMs are suggested to be 300 Myr and ~10?4 year?1, respectively, which are consistent with the values suggested by population synthesis and nucleosynthesis studies. This study supports the argument that NSMs are the major astrophysical site of the r-process.
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