# LISA Constraints on an Intermediate-Mass Black Hole in the Galactic Centre

## TL;DR

This paper proposes using LISA gravitational wave observations of binaries near the Galactic Centre to constrain the presence and properties of intermediate-mass black holes, filling a gap in current detection methods.

## Contribution

It introduces a novel method to detect IMBHs via Doppler shifts in gravitational wave signals from binaries orbiting Sgr A*.

## Key findings

- LISA can effectively constrain IMBHs with masses between 10^3 and 10^5 solar masses.
- Doppler shift measurements are most feasible for binaries within 0.1 to 2 milliparsecs of the SMBH.
- Gravitational-wave captures are identified as the most efficient formation channel for such binaries.

## Abstract

Galactic nuclei are potential hosts for intermediate-mass black holes (IMBHs), whose gravitational field can affect the motion of stars and compact objects. The absence of observable perturbations in our own Galactic Centre has resulted in a few constraints on the mass and orbit of a putative IMBH. Here, we show that the Laser Interferometer Space Antenna (LISA) can further constrain these parameters if the IMBH forms a binary with a compact remnant (a white dwarf, a neutron star, or a stellar-mass black hole), as the gravitational-wave signal from the binary will exhibit Doppler-shift variations as it orbits around Sgr A$^\star$. We argue that this method is the most effective for IMBHs with masses $10^3\,M_\odot\lesssim M_{\rm IMBH}\lesssim 10^5\,M_\odot$ and distances of $0.1$ mpc to $2$ mpc with respect to the supermassive black hole, a region of the parameter space partially unconstrained by other methods. We show that in this region the Doppler shift is most likely measurable whenever the binary is detected in the LISA band, and it can help constrain the mass and orbit of a putative IMBH in the centre of our Galaxy. We also discuss possible ways for an IMBH to form a binary in the Galactic Centre, showing that gravitational-wave captures of stellar-mass black holes and neutron stars are the most efficient channel.