Where has all the $r$-process gone? Timescales for GRB-Kilonovae to Enrich their Host Galaxies

Abstract: Neutron star (NS) mergers are currently the only observed source of $r$-process production in the Universe. Yet, it is unclear how much $r$-process mass from these mergers is incorporated into star-forming gas to enrich stars. This is crucial to consider as all other $r$-process mass estimates in the Universe beyond Earth are based on stellar $r$-process abundances. Here, we explore the extent to which merger location and host galaxy properties affect the incorporation of $r$-process elements into star-forming gas, and quantify an enrichment" timescale to account for this process. To put this timescale in context, we analyze a population of 12 gamma-ray bursts (GRBs) with probable associations to $r$-process kilonovae (GRB-KNe) and 74 short GRBs without claimed KNe, including new non-parametric star formation histories for the GRB-KN hosts. We find enrichment timescales for this sample are between $\approx7$ Myr$-1.6$ Gyr, suggesting that environmental enrichment is delayed from NS merger occurrence. Moreover, we find a correlation between the amount of environmental enrichment from a single event and increasing host specific star formation rate (sSFR), and little correlation with stellar mass and GRB galactocentric offset. Environments with low sSFRs ($\<10^{-10.5}$ yr$^{-1}$), which comprise 18% of short GRB hosts and the host of GW170817, will have little to no capacity for stellar enrichment. Our results indicate that not all $r$-process from NS mergers is incorporated into newly-forming stars, and instead some remainslost" to the CGM or IGM. Future studies should consider these losses to understand the total contribution from NS mergers to the Universe's $r$-process budget.