Double Compact Binary Merger Rate Density in Open Star Clusters: Black Holes, Neutron Stars, and White Dwarfs

Studying compact-object binary mergers in star clusters is crucial for understanding stellar evolution and dynamical interactions in galaxies. Open clusters in particular are more abundant over cosmic time than globular clusters, however, previous research on low-mass clusters with $\lesssim 10^3~\textrm{M}_{\odot}$ has focused on binary black holes (BBHs) or black hole-neutron star (BH-NS) binaries. Binary mergers of other compact objects, such as white dwarfs (WDs), are also crucial as progenitors of transient phenomena such as Type Ia supernovae and Fast Radio Bursts. We present simulations of three types of open clusters with masses of $10^2$, $10^3$, and $10^4~\mathrm{M}_{\odot}$. In massive clusters with $\gtrsim 10^4~\textrm{M}_{\odot}$, BBHs are dynamically formed, however, less massive compact binaries such as WD-WD and WD-NS are perturbed inside the star clusters, causing them to evolve into other objects. We further find BH-NS mergers only in $10^3~\textrm{M}_{\odot}$ clusters. Considering star clusters with a typical open cluster mass, we observe that WD-WD merger rates slightly increase for $10^3~\textrm{M}_{\odot}$ clusters but decrease for $10^2~\textrm{M}_{\odot}$ clusters. Since the host clusters are tidally disrupted, most of them merge outside of the clusters. Our WD-WD merger results have further implications for two classes of transients. Super-Chandrasekhar WD-WD mergers are present in our simulations, demonstrating potential sources of Fast Radio Bursts at a rate of 70-780 Gpc$^{-3}$yr$^{-1}$, higher than the rate estimated for globular clusters. Additionally, we find that Carbon-Oxygen WD-WD mergers in our open clusters (34-640 $\textrm{Gpc}^{-3}$yr$^{-1}$) only account for 0.14-2.6% of the observed Type Ia supernova rate in our local Universe.