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 105years 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 106years, 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 103–104years in LISA band with a one-year signal-to-noise ratio above ten.
Highlights
The future space-based Laser Interferometer Space Antenna (LISA; Amaro-Seoane et al 2017), selected as the L3 mission of ESA, will detect gravitational radiation from various phenomena involving massive black holes (MBHs), the masses of which range from 105 to 107 M
In the present study, we limit ourselves to circular orbits, mostly for simplicity, and because some of the scenarii discussed in Sect. 5 lead naturally to low eccentricity orbits; this involves inspiralling compact objects that result from the tidal disruption of a binary, stars formed in an accretion disk, black holes resulting from the most massive of such stars and a significant proportion (∼1/4) of the population of brown dwarfs that might be in LISA band
This is specially important for brown dwarfs, since their Roche limit occurs in the strong field region
Summary
The future space-based Laser Interferometer Space Antenna (LISA; Amaro-Seoane et al 2017), selected as the L3 mission of ESA, will detect gravitational radiation from various phenomena involving massive black holes (MBHs), the masses of which range from 105 to 107 M (see e.g. Amaro-Seoane 2018; Babak et al 2017, and references therein). This study was refined by Barack & Cutler (2004), who estimated that the signal-to-noise ratio (S/N) of a μ = 0.06 M main-sequence star observed 106 yr before plunge is of the order eleven in two years of LISA observations They have shown that the detection of such an event could lead to the spin measurement of Sgr A* with an accuracy of ∼0.5%. Linial & Sari (2017) have computed at the quadrupole order the gravitational wave emission from orbiting main-sequence stars undergoing Roche lobe overflow, treated at the Newtonian level These authors stressed the detectability by LISA and have showed the possibility of a reverse chirp signal, the reaction of the accreting system to the angular momentum loss by gravitational radiation being a widening of the orbit (outspiral) (Dai & Blandford 2013).
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