Going beyond χ_eff in spin-precessing binary neutron stars

The effective spin parameter χ_eff  is currently the best-constrained spin-related quantity measurable from gravitational-wave observations. This parameter remains constant under the orbit-averaged spin-precession equations up to 2PN order, but only for binary black holes. When non–black-hole objects such as neutron stars are involved, χ_eff  ceases to be conserved: it evolves on the precession timescale and thus varies throughout the inspiral, possibly losing its primate of best-measurable spin realted paraemter. We revisit the generic spin-precession equations, including spin-induced quadrupole moments relevant for non–black-hole compact objects, and show that they still admit a conserved quantity up to 2PN order. We identify this new parameter and investigate whether it can take the place of χ_eff as the best-constrained spin parameter in binaries containing at least one neutron star. We assess its measurability using both existing gravitational-wave events and simulated ones, in the context of current and next-generation ground-based detectors.