Love number can be hard to measure

The waveform phase for a neutron star binary can be split into point-particle terms and finite-size terms (characterized by the Love number) that account for equation-of-state effects. The latter first enter at fifth post-Newtonian (5PN) order (i.e., proportional to the tenth power of the orbital velocity), but the former are only known completely to 3.5PN order, with higher-order terms only known to leading order in the mass ratio. We here find that not including point-particle terms at 4PN order to leading and first order in the mass ratio in the template model can severely deteriorate our ability to measure the equation of state. This problem can be solved if one uses numerical waveforms once their own systematic errors are under control.