Improving Semi-Analytic Spin Precession with NITs

          @misc{ pirsa_PIRSA:21060011,
            doi = {10.48660/21060011},
            url = {https://pirsa.org/21060011},
            author = {LaHaye, Michael},
            keywords = {Other},
            language = {en},
            title = {Improving Semi-Analytic Spin Precession with NITs},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {jun},
            note = {PIRSA:21060011 see, \url{https://pirsa.org}}
          }
          

Abstract

Semi-analytic solutions are useful because they are much faster than full numerical evolutions by virtue of the fact that they do not have to use as many points to achieve similar levels of accuracy. Currently there exists a semi-analytic solution for spin precessing binaries, which is implemented in LIGO and used to generate waveforms for comparison with gravitational waves. This solution comes with a caveat: it was calculated using precession averaged equations and thus has an oscillating error associated with the unaccounted for precession. This error is large enough that it can’t be overlooked for second and third generation detectors. By using near identity transforms (NITs) to reintroduce the effects of precession to the evolution, we can lower the error significantly. When implementing the NIT we found that the phase of oscillations we introduce (which coincides with the precession phase) does not line up with the precession in the numerical evolution, this causes the NIT to be less effective at reducing the error than it could be. To fix this issue we also introduce corrections to the evolution of the precession phase that were previously overlooked.