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We present a new method for extracting the instantaneous orbital axis onlyfrom gravitational wave strains of precessing binary systems observed from aparticular observer direction. This method enables us to reconstruct theco-precessing frame waveforms only from observed quantities for the ideal casethat the signal-to-noise ratio is high enough to analyze the waveformsdirectly. Specifically, we do not assume knowledge of the time evolution of theinstantaneous orbital axis and the co-precessing waveforms before analyzing thedata in our method. We test and measure the accuracy of our method using thenumerical relativity simulation data of precessing binary black holes takenfrom the SXS Catalog. We show that the direction of the orbital axis isextracted within $\approx0.02~{\rm rad}$ error from gravitational waves emittedduring the inspiral phase. The co-precessing waveforms are also reconstructedwith high accuracy; the mismatch (assuming white noise) between them and theoriginal co-precessing waveforms is typically a few times $10^{-3}$ includingthe merger-ringdown phase, and can be improved by an order of magnitudefocusing only on the inspiral waveform. In this method, the co-precessing framewaveforms are not only the purely technical tools for understanding the complexnature of precessing waveforms but also direct observables.

Extracting the orbital axis from gravitational waves of precessing binary systems