Extracting the orbital axis from gravitational waves of precessing binary systems

We present a new method for extracting the instantaneous orbital axis only from gravitational wave strains of precessing binary systems observed from a particular observer direction. This method enables us to reconstruct the co-precessing frame waveforms only from observed quantities for the ideal case that the signal-to-noise ratio is high enough to analyze the waveforms directly. Specifically, we do not assume knowledge of the time evolution of the instantaneous orbital axis and the co-precessing waveforms before analyzing the data in our method. We test and measure the accuracy of our method using the numerical relativity simulation data of precessing binary black holes taken from the SXS Catalog. We show that the direction of the orbital axis is extracted within $\approx0.02~{\rm rad}$ error from gravitational waves emitted during the inspiral phase. The co-precessing waveforms are also reconstructed with high accuracy; the mismatch (assuming white noise) between them and the original co-precessing waveforms is typically a few times $10^{-3}$ including the merger-ringdown phase, and can be improved by an order of magnitude focusing only on the inspiral waveform. In this method, the co-precessing frame waveforms are not only the purely technical tools for understanding the complex nature of precessing waveforms but also direct observables.