This paper introduces pyEFPEHM, a new model that predicts the gravitational-wave signal from compact binaries during their inspiral. The model is built within the post-Newtonian (PN) approximation, a controlled expansion that is valid when the two objects move slowly compared with the speed of light and are not yet merged. pyEFPEHM extends an earlier model (pyEFPE) to include orbital eccentricity, spin precession (when the objects’ spins tilt the orbit), many higher-order radiation modes, and matter effects such as adiabatic tides that are important for neutron stars.

To build the model the authors combined several technical ingredients. They incorporated all currently available high-order quasi-circular PN corrections to the orbital phase, noting that above 2.5PN order the quasi-circular pieces dominate each PN order. Concretely, the model includes non-spinning corrections up to 4.5PN order, spin-orbit and spin-spin corrections up to 4PN (with some partial results at 3.5PN), cubic-in-spin effects at 3.5PN, adiabatic tidal effects up to 7.5PN and spin-tidal effects to 6.5PN. They also extended the multiple-scale analysis (MSA) solution of the spin-precession equations to higher PN orders and added eccentric corrections to the waveform amplitudes up to 1PN order.

The waveform contains many multipoles of the emitted radiation rather than just the leading one. In particular pyEFPEHM includes the gravitational-wave multipoles with (l,|m|) = (2,2),(2,1),(2,0),(3,3),(3,2),(3,1),(3,0),(4,4),(4,2),(4,0). In practice the model uses the EFPE framework, which separates the problem into different time scales: the fast orbital motion, slower periastron advance, slower spin precession, and the slowest radiation-reaction driven inspiral. The MSA handles the coupling between these scales in an efficient, perturbative way, which helps keep the model computationally fast.