The missing multipole problem: investigating biases from model starting frequency in gravitational-wave analyses

ABSTRACT Our ability to infer the true source properties of colliding black holes from gravitational-wave observations requires not only accurate waveform models but also their correct use. A key property when evaluating time-domain models is when to start the waveform: choosing a time that is too late can omit low-frequency power from higher order multipoles. By focusing on binary systems with total mass $\ge 200 \, {\rm M}_{\odot }$, we show that current detectors are sensitive to this missing power and biased source properties can be obtained. We show that for systems with total mass $\lesssim 300 \, {\rm M}_{\odot }$, mass ratio $\gtrsim 0.33$, and signal-to-noise ratio $\rho \gtrsim 20$, templates starting at $20 \, \mathrm{Hz}$ recover biased source properties. As the total mass increases, and the component masses become more asymmetric, templates starting from $13 \, \mathrm{Hz}$ recover biased properties. If the gravitational-wave signal is observed at signal-to-noise ratio $\rho \lt 20$, time-domain models can start from $20\, \mathrm{Hz}$ as statistical uncertainties dominate.