Describing The Black Hole At The Center Of The Milky Way

A new paper describes how the black hole at the center of the Milky Way galaxy, Sagittarius A* (SgrA*), could have both its mass and spin measures with great precision with planned Earth orbit based gravitational wave detectors.

The a precise new mass measurement (at roughly part per million precision), while interesting in its own right, it wouldn't represent much of a scientific advance, and has already been made much more crudely (approximately 4,000,000 times the mass of the Sun). 

But, even measurement of the spin of SgrA* with one significant digit precision, would be a major scientific advancement. This proposed observation method would provide an exquisitely precise measurement of both the mass and the spin of SgrA* as soon as the opportunity presented itself when a brown dwarf falls into this black hole, which probably isn't all that rare of an event.

While the properties of a spinning black hole have been worked out analytically from first principles in General Relativity, with and without black hole electromagnetic charge, there is almost no solid observational evidence regarding whether black holes actually do have spin, and if so, what the magnitude of that spin of supermassive black holes at the center of galaxies like this one is likely to be.

The paper and its abstract are as follows:

Estimating the spin of SgrA∗ 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 SgrA∗ will allow us to measure the mass and the spin of SgrA∗ 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 two scenarios for SgrA∗'s spin (s): A highly spinning scenario where s=0.9 and a low spinning scenario where s=0.1. 

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 later perform a Fisher matrix analysis to show that by detecting a single XMRI the mass of SgrA∗ can be determined with an accuracy ranging from 0.06 to 3 solar masses while the spin can be measured with an accuracy between 1.5×10^−7 and 4×10^−4.

Veronica Vazquez-Aceves, Yiren Lin, Alejandro Torres-Orjuela, "SgrA∗ spin and mass estimates through the detection of an extremely large mass-ratio inspiral" arXiv:2206.14399 (June 29, 2022).

The introduction of the paper explains that:

SgrA∗ , the super-massive black hole (SMBH) at our galactic center, was recently observed by the Event Horizon Telescope obtaining an estimated mass of 4 × 10^6 M, which is in good agreement with previous estimates; in contrast, measuring its spin remains a major challenge. 

In this work we show that detecting a single extremely large mass ratio inspiral (XMRI), i.e., a brown dwarf (BD) inspiraling towards SgrA∗ due to energy loss by gravitational waves (GWs), is enough to determine the spin and mass of SgrA∗ with very good accuracy. When an XMRI forms in our galactic center, its GW emission can be detected by space-borne detectors such as the Laser Interferometer Space Antenna (LISA) and TianQin. Furthermore, its large mass-ratio 𝑞 = 𝑚BD/𝑀SgrA∗ ≈ 10^−8 , allows the BD to spend a large amount of time inspiraling around the SMBH, and the slow evolution of the orbit simplifies the analysis of its gravitational radiation. Understanding its formation channels and evolution is a key part of the description that will lead to accurate templates to identify and extract the information encoded within its gravitational radiation. In a dense stellar system, such as our galactic center, two-body relaxation processes slowly change the orbits of the orbiting objects by diffusion in energy and angular momentum (𝐽). However, as diffusion in 𝐽 is more efficient than diffusion in energy, the eccentricity (𝑒) of the orbits changes faster than the semimajor axis (𝑎). As a consequence, the pericentre (𝑅p) of the orbit is perturbed, allowing objects to reach very close distances to the central black hole. An inspiraling system is formed when a compact object is diffused into an orbit with a small Rp such that after just one pericentre passage the orbit evolves only due to the energy lost by gravitational radiation. 

Recent estimates show that at the time the LISA and TianQin missions will be in space, there could be about 15 eccentric and five circular XMRIs in our galactic center emitting GWs in a detectable range.