LIGO Document T2200281-v1
- The gravitational waveform from a compact inspiraling binary, such as a BBH, can indicate the presence of a nearby massive body, such as an SMBH. The waveform is modulated by de Sitter precession of the BBH’s inner angular momentum and by the time-dependent Doppler phase shift of the BBH in its orbit. The future generation of space-based GW observatories, focused on the millihertz and decihertz band, is uniquely poised to observe these waveform modulations, as the GW frequency from stellar-mass BBHs remains in this band for the months or years over which these modulation effects accumulate. In this work, we apply the Fisher information matrix to estimate how well a decihertz detector can measure properties of BBH+SMBH hierarchical triples. We consider an eccentric orbit of the BBH about the SMBH, extending previous studies which were limited to circular orbits. We find that the uncertainties in measurements of the SMBH mass and semimajor axis can be improved by a factor of a few when the BBH takes a non-circular orbit, but improvement is not universally guaranteed. Furthermore, the eccentricity and argument of periapsis are very well measured.
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