On the detectability of gravitational waves from primordial black holes orbiting Sgr A*

TL;DR

This paper evaluates the potential of future space-based gravitational wave detectors like LISA and $$Ares to detect signals from primordial black holes orbiting Sgr A*, highlighting detection probabilities and the influence of black hole mass.

Contribution

It provides the first detailed assessment of gravitational wave detectability from primordial black holes near Sgr A* for upcoming space interferometers, considering simplified orbital assumptions.

Findings

LISA has about a 10% chance to detect a 1 M$_{\u00a0}$ black hole in 10 years.

$$Ares could resolve approximately 140 solar mass black holes in the same period.

The unresolved background signal would be detectable with high significance by $$Ares.

Abstract

In this work we characterize the expected gravitational wave signal detectable by the planned space-borne interferometer LISA and the proposed next generation space-borne interferometer $\mu$Ares arising from a population of primordial black holes orbiting Sgr A*, the super-massive black hole at the Galactic center. Assuming that such objects indeed form the entire diffuse mass allowed by the observed orbit of S2 in the Galactic center, under the simplified assumption of circular orbits and monochromatic mass function, we assess the expected signal in gravitational waves, either from resolved and non-resolved sources. We estimate a small but non negligible chance of $\simeq$ 10% of detecting one single 1 M$_{\odot}$ primordial black hole with LISA in a 10-year-long data stream, while the background signal due to unresolved sources would essentially elude any reasonable chance of detection. On the contrary, $\mu$Ares, with a $\simeq$ 3 orders-of-magnitude better sensitivity at $\simeq$ 10$^{-5}$ Hz, would be able to resolve $\simeq$ 140 solar mass primordial black holes in the same amount of time, while the unresolved background should be observable with an integrated signal-to-noise ratio $\gtrsim$ 100. Allowing the typical PBH mass to be in the range 0.01-10 M$_{\odot}$ would increase LISA chance of detection to $\simeq$ 40% towards the lower limit of the mass spectrum. In the case of $\mu$Ares, instead, we find a "sweet spot" just about 1 M$_{\odot}$, a mass for which the number of resolvable events is indeed maximized.