Gravitational waves from binary black hole mergers have allowed us to
    directly observe stellar-mass black hole binaries for the first time, and
    therefore explore their formation channels. One of the ways to infer how a
    binary system is assembled is by measuring the system’s orbital eccentricity.
    Current methods of parameter estimation do not include all physical effects of
    eccentric systems such as spin-induced precession, higher-order modes, and the
    initial argument of periapsis: an angle describing the orientation of the
    orbital ellipse. We explore how varying the argument of periapsis changes
    gravitational waveforms and study its effect on the inference of astrophysical
    parameters. We use the eccentric spin-aligned waveforms TEOBResumS and SEOBNRE
    to measure the change in the waveforms as the argument of periapsis is changed.
    We find that the argument of periapsis could already be impacting analyses
    performed with TEOBResumS. However, it is likely to be well-resolvable in the
    foreseeable future only for the loudest events observed by LIGO–Virgo–KAGRA.
    The systematic error in previous, low-eccentricity analyses that have not
    considered the argument of periapsis is likely to be small.

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