Probing Globular Clusters using Gravitational Waves from Inspiraling Stellar-mass Binary Black Holes in Space-based Detector

Abstract Globular clusters (GCs) serve as key environments for studying stellar dynamics and galactic structure, yet precise measurements of their distances and masses are often limited by uncertainties in electromagnetic (EM) observations. We present a method that uses gravitational waves (GWs) from inspiralling stellar-mass binary black holes (BBHs) orbiting within GCs to improve the precision of GC parameter measurements. The BBH’s circular motion around the GC produces a moving-source effect, including Doppler shifts and relativistic corrections, which leaves measurable imprints on the GW signal. We model these signals using post-Newtonian waveforms and apply Lorentz transformations to compute the waveform from the moving BBHs. The information encoded in the modulated waveform is quantified with the Fisher information matrix, allowing us to extract GC parameters and combine them with EM measurements. Our results show that incorporating GW observations can substantially improve distance constraints for nearby Milky Way GCs, while the improvement in mass constraints depends strongly on the BBH outer-orbit modulation. These findings demonstrate the value of BBHs as dynamical probes and highlight the role of GWs as complementary probes of GC properties, especially for nearby and strongly modulated systems.