SgrA$^{*}$ spin and mass estimates through the detection of an extremely large mass-ratio inspiral

TL;DR

Detecting gravitational waves from extreme mass-ratio inspirals around SgrA* can precisely determine its mass and spin, offering new insights into our galaxy's center.

Contribution

This work demonstrates that space-based gravitational wave detectors can accurately measure the mass and spin of SgrA* using signals from inspiraling brown dwarfs.

Findings

Multiple XMRIs are expected to be detectable in the galactic center.

Eccentric orbits increase the number of detectable XMRIs.

Mass and spin of SgrA* can be measured with high precision.

Abstract

Estimating the spin of ${\rm SgrA^\ast}$ is one of the current challenges we face in understanding the center of our Galaxy. In the present work, we show that detecting the gravitational waves (GWs) emitted by a brown dwarf inspiraling around ${\rm SgrA^\ast}$ will allow us to measure the mass and the spin of ${\rm SgrA^\ast}$ with unprecedented accuracy. Such systems are known as extremely large mass-ratio inspirals (XMRIs) and are expected to be abundant and loud sources in our galactic center. We consider XMRIs with a fixed orbital inclination and different spins of ${\rm SgrA^\ast}$ ($s$) between 0.1 and 0.9. For both cases, we obtain the number of circular and eccentric XMRIs expected to be detected by space-borne GW detectors like LISA and TianQin. We find that if the orbit is eccentric, then we expect to always have several XMRIs in band while for almost circular XMRIs, we only expect to have one source in band if ${\rm SgrA^\ast}$ is highly spinning. We later perform a Fisher matrix analysis to show that by detecting a single XMRI the mass of ${\rm SgrA^\ast}$ can be determined with an accuracy of the order $10^{-2}\,\text{M}_{\odot}$, while the spin can be measured with an accuracy between $10^{-7}$ and $10^{-4}$ depending on the orbital parameters of the XMRI.