Effect of double spin-precession and higher harmonics on spin-induced quadrupole moment measurements

We investigate the prospect of performing a null test of binary black hole (BBH) nature using spin-induced quadrupole moment (SIQM) measurements. This is achieved by constraining a deviation parameter ($\delta\kappa$) related to the parameter ($\kappa$) that quantifies the degree of deformation due to the spin of individual binary components on leading (quadrupolar) spin-induced moment. Throughout the paper, we refer to $\kappa$ as the SIQM parameter and $\delta\kappa$ as the SIQM-deviation parameter. The test presented here extends the earlier SIQM-based null tests for BBH nature by employing waveform models that account for double spin-precession and higher modes. We find that waveform with double spin-precession gives better constraints for $\delta\kappa$, compared to waveform with single spin-precession. We also revisit earlier constraints on the SIQM-deviation parameter for selected GW events observed through the first three observing runs (O1-O3) of LIGO-Virgo detectors. Additionally, the effects of higher-order modes on the test are also explored for a variety of mass-ratio and spin combinations by injecting simulated signals in zero-noise. Our analyses indicate that binaries with mass-ratio greater than 3 and significant spin precession may require waveforms that account for spin-precession and higher modes to perform the parameter estimation reliably.