51�������

Abstract:

In multi-component dark matter models, a fraction f pbh of the dark matter could be in the form of primordial black holes (PBHs) with (sub)solar masses. Some would have formed binaries that presently trace the Milky Way halo of particle dark matter. We explore the gravitational wave (GW) signal produced by such a hypothetical population of Galactic PBH binaries and assess its detectability by the LISA experiment. For this purpose, we model the formation and evolution of early-type PBH binaries accounting for GW hardening and binary disruption in the Milky Way. Our analysis reveals that the present-day Galactic population of PBH binaries is characterized by very high orbital eccentricities |1-e| ≪ 1. For a PBH mass M pbh ∼ 0.1 - 1M ⊙, this yields a GW background that peaks in the millihertz frequency range where the LISA instrumental noise is minimum. While this signal remains below the LISA detection threshold for viable f pbh ≲ 0.01, future GW observatories such as DECIGO and BBO could detect it if 0.01 ≲ M pbh ≲ 0.1M ⊙. Furthermore, we anticipate that, after 5 years of observations, LISA should be able to detect 𝒪(100) (resp. 𝒪(1)) loud Galactic PBH binaries of mass M pbh ≲ 0.1 - 1M ⊙ with a SNR ≥ 5 if f pbh = 0.01 (resp. f pbh = 0.001). Nonlinear effects not considered here such as mass accretion and dynamical capture could alter these predictions.

Abstract:

We derive an analytical model for the so-called phenomenon of resonant dynamical friction, where a disc of stars around a supermassive black hole interacts with a massive perturber, so as to align its inclination with the disc’s orientation. We show that it stems from a singular behaviour of the orbit-averaged equations of motion, which leads to a rapid alignment of the argument of the ascending node of each of the disc stars, with that of the perturber, p, with a phase difference of 90◦. This phenomenon occurs for all stars whose maximum possible ˙ (maximized over all values of for all the disc stars) is greater than ˙ p; this corresponds approximately to all stars whose semi-major axes are less than twice that of the perturber. The rate at which the perturber’s inclination decreases with time is proportional to its mass and is shown to be much faster than Chandrasekhar’s dynamical friction. We find that the total alignment time is inversely proportional to the root of the perturber’s mass. This persists until the perturber enters the disc. The predictions of this model agree with a suite of numerical N-body simulations, which we perform to explore this phenomenon, for a wide range of initial conditions, masses, etc., and are an instance of a general phenomenon. Similar effects could occur in the context of planetary systems, too.