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

Abstract

Primordial black holes, allegedly formed in the very early Universe, have been proposed as a possible viable dark matter candidate. In this work we characterize the expected gravitational wave signal detectable by the planned space-borne interferometer LISA and the proposed next generation spaceborne interferometer µAres 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 orbits of stars in the Galactic center ( < ∼ 4 × 10 3 M within a radius of 10 −3 pc from Sgr A ), 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 10% of detecting one single 1 M 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, µAres, with a 3 orders-of-magnitude better sensitivity at 10 −5 Hz, would be able to resolve 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 100. Allowing the typical PBH mass to be in the range 0.01-10 M would increase LISA chance of detection to 40% towards the lower limit of the mass spectrum. In the case of µAres, instead, we find a "sweet spot" just about 1 M , a mass for which the number of resolvable events is indeed maximized.

Gravitational waves from an eccentric population of primordial black holes orbiting Sgr A$^{\star}$

“…where ρ is the density distribution of the PBH population, in our case the very same spiked Navarro-Frenk-White (NFW, [32]) profile [33] adopted in [13,14], and σ is the Keplerian velocity, both functions of the semimajor axis a; the mass of the supermassive black hole, in our case Sgr A , is M MBH = 4.3 × 10 6 M [19]. From Eq.…”

“…As in [13,14] we assume a population of PBHs characterized by a monochromatic mass function, m PBH = 1 M [30]. PBHs are radially distributed such as, at large distances, far from the GW-dominated regime, the density profile (referred to as unperturbed ) is driven by two-body relaxation.…”

“…The actual number of PBHs evolving because of GWs emission is obtained by first modelling the process of twobody relaxation acting at larger scales from the central supermassive BH, hence providing the infall rate of objects. To this goal we need to assume an underlying density profile which, as in [14], follows a spiked NFW [33]. We then impose the Cohn-Kalsrud condition [35,36] to estimate the inward flux.…”

“…The search for a solution to the dark matter problem [1][2][3][4] has led primordial black holes (PBHs) [5][6][7][8][9] to be considered as a serious candidate for several years now [10], especially in light of the as-of-today inconclusive results of the many experiments aimed at a direct detection of a dark matter particle [11,12]. If PBHs do exist and indeed constitute a fraction of the dark matter in the Universe, it is argued that they should clump at the center of galaxies, and supposedly orbit the supermassive black hole at their centers [13][14][15][16][17], with a mass function and abundance given by, e.g., [18]. Given the PBHs compact nature, their motion around the central supermassive black hole should be accompanied by loud gravitational wave (GWs) emission, whose detection, or lack thereof, could put constraints on the very existence of PBHs and on their relevance as a dark matter candidate.…”

“…We characterized in [14] the GW signal in the LISA and µAres interferometers expected in the most relevant case of Sgr A , the supermassive black hole at the center of the Milky Way, by allowing for a total possible diffuse mass of 4 × 10 3 M inside a 10 −3 pc (i.e., within the pericenter of star S2, see [19]), entirely comprised of PBHs, and assuming monochromatic mass functions for the resident PBH population on circular orbits. In particular, for the most physically relevant case of 1 M PBHs, a 10-years long LISA mission was found to have a 10% chance of detection of one single PBH, while µAres was expected to be able to resolve more than 140 of them.…”