Localizing Dynamically-Formed Black Hole Binaries in Milky Way Globular Clusters with LISA

The dynamical formation of binary black holes (BBHs) in globular clusters (GCs) may contribute significantly to the observed gravitational wave (GW) merger rate. Furthermore, LISA may detect many BBH sources from GCs at mHz frequencies, enabling the characterization of such systems within the Milky Way and nearby Universe. In this work, we use Monte Carlo N-body simulations to construct a realistic sample of Galactic clusters, thus estimating the population, detectability, and parameter measurement accuracy of BBHs hosted within them. In particular, we show that the GW signal from $0.7\pm 0.7$, $2.0\pm 1.7$, $3.6\pm 2.3$, $13.4\pm 4.7$ BBHs in Milky Way GCs can exceed the signal-to-noise ratio threshold of $\rm SNR =30$, 5, 3, and 1 for a 10-year LISA observation, with $\sim 50\%$ of detectable sources exhibiting high eccentricities ($e\gtrsim0.9$). Moreover, the Fisher matrix and Bayesian analyses of the GW signals indicate these systems typically feature highly-resolved orbital frequencies ($\delta f_{\rm orb}/ f_{\rm orb} \sim 10^{-7}-10^{-5}$) and eccentricities ($\delta e/ e \sim 10^{-3}-0.1$), as well as a measurable total mass when SNR exceeds $\sim20$. Notably, we show that high-SNR BBHs can be confidently localized to specific Milky Way GCs with a sky localization accuracy of $\delta \Omega \sim 1$~deg$^2$, and address the large uncertainties in their distance measurement ($\delta R \sim 0.3 - 20$~kpc). The detection and localization of even a single BBH in a Galactic GC would allow accurate tracking of its long-term orbital evolution, enable a direct test of the role of GCs in BBH formation, and provide a unique probe into the evolutionary history of Galactic clusters.