Gravitational waves from bodies orbiting the Galactic center black hole and their detectability by LISA

¹ Laboratoire Univers et Théories, Observatoire de Paris, Université PSL, CNRS, Université Paris Diderot, Sorbonne Paris Cité, 5 Place Jules Janssen, 92190 Meudon, France
e-mail: eric.gourgoulhon@obspm.fr
² Laboratoire d’Études Spatiales et d’Instrumentation en Astrophysique, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Diderot, Sorbonne Paris Cité, 5 Place Jules Janssen, 92190 Meudon, France
³ School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland

Received: 5 March 2019
Accepted: 29 May 2019

Abstract

Aims. We present the first fully relativistic study of gravitational radiation from bodies in circular equatorial orbits around the massive black hole at the Galactic center, Sgr A* and we assess the detectability of various kinds of objects by the gravitational wave detector LISA.

Methods. Our computations are based on the theory of perturbations of the Kerr spacetime and take into account the Roche limit induced by tidal forces in the Kerr metric. The signal-to-noise ratio in the LISA detector, as well as the time spent in LISA band, are evaluated. We have implemented all the computational tools in an open-source SageMath package, within the Black Hole Perturbation Toolkit framework.

Results. We find that white dwarfs, neutrons stars, stellar black holes, primordial black holes of mass larger than 10⁻⁴ M_⊙, main-sequence stars of mass lower than ∼2.5 M_⊙, and brown dwarfs orbiting Sgr A* are all detectable in one year of LISA data with a signal-to-noise ratio above 10 for at least 10⁵ years in the slow inspiral towards either the innermost stable circular orbit (compact objects) or the Roche limit (main-sequence stars and brown dwarfs). The longest times in-band, of the order of 10⁶ years, are achieved for primordial black holes of mass ∼10⁻³ M_⊙ down to 10⁻⁵ M_⊙, depending on the spin of Sgr A*, as well as for brown dwarfs, just followed by white dwarfs and low mass main-sequence stars. The long time in-band of these objects makes Sgr A* a valuable target for LISA. We also consider bodies on close circular orbits around the massive black hole in the nucleus of the nearby galaxy M 32 and find that, among them, compact objects and brown dwarfs stay for 10³–10⁴ years in LISA band with a one-year signal-to-noise ratio above ten.