SgrA* spin and mass estimates through the detection of multiple extremely large mass-ratio inspirals

Abstract: We analyze the parameter estimation accuracy that can be achieved for the mass and spin of SgrA$^\ast$, the SMBH in our Galactic Center, by detecting multiple extremely large mass-ratio inspirals (XMRIs). XMRIs are formed by brown dwarfs (BD) inspiraling into a supermassive black hole (SMBH), 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 SNRs ($\approx10$), high-precision parameter estimates can still be achieved by detecting multiple sources. In this case, the accuracy of the parameter estimates increases by approximately one to two 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 SgrA$^\ast$ will have eccentricities between 0.43 to 0.95 and an $\mathrm{SNR}\in [10,100]$. The remaining $\sim$20\,\% of the sources have an $\mathrm{SNR}\in [100,1000]$ and eccentricities ranging from 0.25 to 0.92. Additionally, some XMRIs with high SNR are far from being circular. These loud sources with $\mathrm{SNR}\approx 1000$ can have eccentricities as high as $e\approx0.7$; although their detection chances are low, representing $\lesssim$2\,\% of the detectable sources, their presence is not ruled out.