Gravitational waves carry information beyond effective spin parameters but it is hard to extract

Gravitational wave observations of binary black hole mergers probe their astrophysical origins via the binary spin, namely the spin magnitudes and directions of each component black hole, together described by six degrees of freedom. However, the emitted signals primarily depend on two effective spin parameters that condense the spin degrees of freedom to those parallel and those perpendicular to the orbital plane. Given this reduction in dimensionality between the physically relevant problem and what is typically measurable, we revisit the question of whether information about the component spin magnitudes and directions can successfully be recovered via gravitational-wave observations, or if we simply extrapolate information about the distributions of effective spin parameters. To this end, we simulate three astrophysical populations with the same underlying effective-spin distribution but different spin magnitude and tilt distributions, on which we conduct full individual-event and population-level parameter estimation. We find that parameterized population models can indeed qualitatively distinguish between populations with different spin magnitude and tilt distributions at current sensitivity. However, it remains challenging to either accurately recover the true distribution or to diagnose biases due to model misspecification. We attribute the former to practical challenges of dealing with high-dimensional posterior distributions, and the latter to the fact that each individual event carries very little information about the full six spin degrees of freedom.