Octupolar invariants for compact binaries on quasicircular orbits

Abstract

We extend the gravitational self-force methodology to identify and compute new O(μ) tidal invariants for a compact body of mass μ on a quasicircular orbit about a black hole of mass M≫μ. 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.