# Gravitational waveforms for compact binaries from second-order self-force theory

Over the holidays we released our letter with the first post-adiabatic waveform from self-force theory. The comparison with numerical relativity (NR) is particularly exciting as at a mass ratio of $$q=10$$ the agreement is excellent up until close to merger — see the figure below from the letter.

There has been growing evidence that self-force results, once extended to second-order in the mass ratio, will provide accurate models of intermediate mass-ratio inspirals (IMRIs). This is the first time we have confirmed this via direct calculation. This is particular exciting as the LIGO-Virgo Collaboration are already seeing binaries with IMRI mass ratios, but currently the models they use for search and parameter estimation (PE) are not calibrated for mass ratios greater than 10:1.

The calculation of the second-order self-force needed to compute the above waveform takes many days on a computer with 40 cores (we could write more efficient code to speed this up but it will also be slow). This is an offline step though, and once the self-force is computed for a range of orbital radii this can be efficiently interpolated and then the above waveform is computed in milliseconds. That means it is almost ready-to-go for use in data analysis. The only caveat using it for IMRI search and PE is that we don’t have the transition to plunge, which contributes a very significant portion of the signal in ground-based detectors. One of our next goals is to add that piece of the waveform.

The waveform letter is in collaboration with Barry Wardell, Adam Pound, Jeremy Miller, Leanne Durkan, and Alexandre Le Tiec. It builds upon two papers published in Physical Review Letters that calculate the binding energy, and gravitational wave flux, at second-order in the mass ratio.