Sub-Solar Mass Intermediate Mass Ratio Inspirals: Waveform Systematics and Detection Prospects with Gravitational Waves

We investigate the detectability and waveform systematics of sub-solar mass intermediate mass-ratio inspirals (SSM-IMRIs), characterized by mass ratios $q \sim 10^2-10^4$. Using the black hole perturbation theory surrogate model \textsc{BHPTNRSur1dq1e4} as a reference, we assess the performance of the \textsc{IMRPhenomX} phenomenological family in the high-mass-ratio regime. We find that the inclusion of higher-order gravitational wave modes is critical; their exclusion may degrade the signal-to-noise ratio by factors of $\sim3-5$ relative to quadrupole-only templates. With optimal mode inclusion, SSM-IMRIs are observable out to luminosity distances of $\sim575$ Mpc ($z\sim0.12$) with Advanced LIGO and $\sim10.5$ Gpc ($z\sim1.4$) with the Einstein Telescope. However, we identify substantial systematic uncertainties in current phenomenological approximants. Matches between \textsc{IMRPhenomX} and the reference surrogate model \textsc{BHPTNRSur1dq1e4} degrade to values as low as 0.2 for edge-on inclinations, and fitting factors consistently fall below 0.9, indicating a significant loss of effectualness in template-bank searches. Bayesian parameter estimation reveals that these modeling discrepancies induce systematic biases that exceed statistical errors by multiple standard deviations, underscoring the necessity for waveform models calibrated to perturbation theory in the intermediate mass-ratio regime for robust detection and inference.