We perform a full nuclear-network numerical calculation of the $r$-process nuclei in binary neutron-star mergers (NSMs), with the aim of estimating $\gamma$-ray emissions from the remnants of Galactic NSMs up to $10^6$ years old. The nucleosynthesis calculation of 4,070 nuclei is adopted to provide the elemental composition ratios of nuclei with an electron fraction $Y_{ \rm e}$ between 0.10 and 0.45 . The decay processes of 3,237 unstable nuclei are simulated to extract the $\gamma$-ray spectra. As a result, the NSMs have different spectral color in $\gamma$-ray band from various other astronomical objects at less than $10^5$ years old. In addition, we propose a new line-diagnostic method for $Y_{ \rm e}$ that uses the line ratios of either $^{ 137{ \rm m}}$Ba/$^{ 85}$K or $^{ 243}$Am/$^{ 60{ \rm m}}$Co, which become larger than unity for young and old $r$-process sites, respectively, with a low $Y_{ \rm e}$ environment. From an estimation of the distance limit for $\gamma$-ray observations as a function of the age, the high sensitivity in the sub-MeV band, at approximately $10^{ -9}$ photons s$^{ -1}$ cm$^{ -2}$ or $10^{ -15}$ erg s$^{ -1}$ cm$^{ -2}$, is required to cover all the NSM remnants in our Galaxy if we assume that the population of NSMs by \citet{ 2019ApJ...880...23W}. A $\gamma$-ray survey with sensitivities of $10^{ -8}$--$10^{ -7}$ photons s$^{ -1}$ cm$^{ -2}$ or $10^{ -14}$--$10^{ -13}$ erg s$^{ -1}$ cm$^{ -2}$ in the 70--4000 keV band is expected to find emissions from at least one NSM remnant under the assumption of NSM rate of 30 Myr$^{ -1}$. The feasibility of $\gamma$-ray missions to observe Galactic NSMs are also studied.
Categories: astro-ph.HE