Theoretical astrophysics and plasma physics at RPC

Abstract:

Collisions between particles in a low density plasma are described by the Fokker–Planck collision operator. In applications, this nonlinear integro-differential operator is often approximated by linearised or ad-hoc model operators due to computational cost and complexity. In this work, we present an implementation of the nonlinear Fokker–Planck collision operator written in terms of Rosenbluth potentials in the Rosenbluth–MacDonald–Judd (RMJ) form. The Rosenbluth potentials may be obtained either by direct integration or by solving partial differential equations (PDEs) similar to Poisson's equation: we optimise for performance and scalability by using sparse matrices to solve the relevant PDEs. We represent the distribution function using a tensor-product continuous-Galerkin finite-element representation and we derive and describe the implementation of the weak form of the collision operator. We present tests demonstrating a successful implementation using an explicit time integrator and we comment on the speed and accuracy of the operator. Finally, we speculate on the potential for applications in the current and next generation of kinetic plasma models.

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.