2025ApJ...987..208V

We analyze the parameter estimation accuracy that can be achieved for the mass and spin of Sgr A*, the supermassive black hole in our Galactic center, by detecting multiple extremely large mass ratio inspirals (XMRIs). XMRIs are formed by brown dwarfs inspiraling into a supermassive black hole, thus emitting gravitational waves (GWs) inside the detection band of future space-based detectors such as LISA and TianQin. Theoretical estimates suggest the presence of approximately 10 XMRIs emitting detectable GWs, making them some of the most promising candidates for space-based GW detectors. Our analysis indicates that even if individual sources have low signal-to-noise ratios (SNRs; ≈10), high-precision parameter estimates can still be achieved by detecting multiple sources. In this case, the accuracy of the parameter estimates increases by approximately 1-2 orders of magnitude at least. Moreover, by analyzing a small sample of 400 initial conditions for XMRIs formed in the Galactic center, we estimate that almost 80% of the detectable XMRIs orbiting Sgr A* will have eccentricities between 0.43 and 0.95 and an SNR ∈ [10, 100]. The remaining ∼20% of the sources have an SNR ∈ [100, 1000] and eccentricities ranging from 0.25 to 0.92. Additionally, some XMRIs with high SNRs are far from being circular. These loud sources with SNR ≈ 1000 can have eccentricities as high as e ≈ 0.7; although their detection chances are low, representing ≲2% of the detectable sources, their presence is not ruled out.