Accuracy Requirements: Assessing the Importance of First Post-Adiabatic Terms for Small-Mass-Ratio Binaries

TL;DR

This paper evaluates the significance of first post-adiabatic (1PA) terms in gravitational waveforms for small-mass-ratio binaries, showing their impact on parameter estimation and the importance of including these terms for accurate results.

Contribution

It is the first study to use Bayesian inference to assess systematic errors caused by neglecting 1PA terms in waveform models for small-mass-ratio inspirals.

Findings

Neglecting 1PA terms causes significant biases for mass ratios $-5$ in quasi-circular orbits.

Resummed 3PN expressions at 1PA order can mitigate these biases.

Secondary spin cannot be constrained for $
e-5$ mass ratios due to strong correlations.

Abstract

We investigate the impact of post-adiabatic (1PA) terms on parameter estimation for extreme and intermediate mass-ratio inspirals using state-of-the-art waveform models. Our analysis is the first to employ Bayesian inference to assess systematic errors for 1PA waveforms. We find that neglecting 1PA terms introduces significant biases for the (small) mass ratio $\epsilon \gtrsim 10^{-5}$ for quasi circular orbits in Schwarzschild spacetime, which can be mitigated with resummed 3PN expressions at 1PA order. Moreover, we show that the secondary spin is strongly correlated with the other intrinsic parameters, and it can not be constrained for $\epsilon \lesssim 10^{-5}$. Finally, we highlight the need for addressing eccentric waveform systematics in the small-mass-ratio regime, as they yield stronger biases than the circular limit in both intrinsic and extrinsic parameters.