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

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 , mainsequence 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 10 5 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 10 6 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 M32 and find that, among them, compact objects and brown dwarfs stay for 10 3 to 10 4 years in LISA band with a one-year signal-to-noise ratio above ten.

Gravitational wave echoes from strange stars

“…To make clear how extreme are these cases, consider that the central baryonic densities of these strange stars are about 25 times the nuclear saturation density. Actually, such extreme values of the baryonic densities are in agreement with the results obtained by simple models of NS collapse [38] and by numerical simulations including rotation, see for example [39,40]. In these works, polytropic EoSs are used to mimic nuclear matter.…”

A Galactic centre gravitational-wave Messenger

“…Without the supply, the Messenger will drift out of the orbit and plunge into the Sgr A* black hole. The change of the orbital frequency in time, d f /dt is diverging at the ISCO 17,22 , as indicated in Fig. 2.…”

“…Values of P GW for other values of m can be found in Table 1. The above results relies on exact computations in the Kerr metric 17 . As a check, let us note that an approximate estimate of P GW can be obtained by a 1.5-order post-Newtonian formula based on 20 :…”

“…1. Any circular orbital motion generates gravitational waves, which are periodic with a dominant mode at twice the orbital frequency 16,17 . From Eq.…”

“…Secular frequency change due to gravitational radiation loss in terms of the orbital radius r 0 , as computed in17 . The corresponding SageMath Notebook is publicly available.…”