Measuring properties of primordial black hole mergers at cosmological distances: effect of higher order modes in gravitational waves

Primordial black holes (PBHs) may form from the collapse of matter overdensities shortly after the Big Bang. One may identify their existence by observing gravitational wave (GW) emissions from merging PBH binaries at high redshifts $z\gtrsim 30$, where astrophysical binary black holes (BBHs) are unlikely to merge. The next-generation ground-based GW detectors, Cosmic Explorer and Einstein Telescope, will be able to observe BBHs with total masses of $\mathcal{O}(10-100)~M_{\odot}$ at such redshifts. This paper serves as a companion paper of arXiv:2108.07276, focusing on the effect of higher-order modes (HoMs) in the waveform modeling, which may be detectable for these high redshift BBHs, on the estimation of source parameters. We perform Bayesian parameter estimation to obtain the measurement uncertainties with and without HoM modeling in the waveform for sources with different total masses, mass ratios, orbital inclinations and redshifts observed by a network of next-generation GW detectors. We show that including HoMs in the waveform model reduces the uncertainties of redshifts and masses by up to a factor of two, depending on the exact source parameters. We then discuss the implications for identifying PBHs with the improved single-event measurements, and expand the investigation of the model dependence of the relative abundance between the BBH mergers originating from the first stars and the primordial BBH mergers as shown in arXiv:2108.07276.