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The missing multipole problem: investigating biases from model starting frequency in gravitational-wave analyses
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DOI：10.1093/mnras/stag398.png)
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Abstract
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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.
Keywords:
gravitational waves
black hole binaries
waveform models
multipole moments
parameter estimation biases
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4.8
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