Abstract

Estimating the spin of SgrA* is one of the current challenges we face in understanding the centerof our Galaxy. We show that detecting the gravitational waves (GWs) emitted by a brown dwarfinspiraling around SgrA* will allow us to measure the mass and the spin of SgrA* withunprecedented accuracy. Such systems are known as extremely large mass-ratio inspirals (XMRls)and are expected to be abundant and loud sources in our galactic center. We consider XMRls witha fixed orbital inclination and diferent spins of SgrA*(s) between 0.1 and 0.9. For both cases, weobtain the number of circular and eccentric XMRls expected to be detected by space-borne GWdetectors like LlSA and TianQin. We find that if the orbit is eccentric, then we expect to always haveseveral XMRls in band while for almost circular XMRls, we only expect to have one source in bandif SgrA* is highly spinning. We later perform a Fisher matrix analysis to show that by detecting asingle XMRl the mass of SarA can be determined with an accuracy of the order 10" solar masses.while the spin can be measured with an accuracy between 10' and 104 depending on the orbitalparameters of the XMRI.