Octupolar invariants for compact binaries on quasicircular orbits

Abstract

We extend the gravitational self-force methodology to identify and compute new $\mathcal{O}(\ensuremath{\mu})$ tidal invariants for a compact body of mass $\ensuremath{\mu}$ on a quasicircular orbit about a black hole of mass $M\ensuremath{\gg}\ensuremath{\mu}$. In the octupolar sector we find seven new degrees of freedom, made up of $3+3$ conservative/dissipative `electric' invariants and $3+1$ `magnetic' invariants, satisfying $1+1$ and $1+0$ trace conditions. We express the new invariants for equatorial circular orbits on Kerr spacetime in terms of the regularized metric perturbation and its derivatives; and we evaluate the expressions in the Schwarzschild case. We employ both Lorenz gauge and Regge-Wheeler gauge numerical codes, and the functional series method of Mano, Suzuki and Takasugi. We present (i) highly-accurate numerical data and (ii) high-order analytical post-Newtonian expansions. We demonstrate consistency between numerical and analytical results, and prior work. We explore the application of these invariants in effective one-body models and binary black hole initial-data formulations.