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

Devesh Giri, Bhooshan Gadre

TL;DR

The paper tackles the detectability and waveform-systematics of sub-solar mass intermediate mass-ratio inspirals (SSM-IMRIs) by benchmarking a perturbation-theory–based surrogate, BHPTNRSur1dq1e4, against the IMRPhenomX family. It demonstrates that higher-order GW modes are crucial for achieving usable SNRs and detection volumes in both current and next-generation detectors, and it quantifies substantial systematic biases when extrapolating phenomenological models to extreme mass ratios. Through matching, fitting-factor analyses, and Bayesian parameter estimation, the authors reveal that current fast IMRPhenomX models can severely misrepresent intrinsic parameters (e.g., $M$, $q$) and source geometry, especially for edge-on orientations, with biases exceeding statistical uncertainties by many standard deviations. The work argues for waveform models that couple perturbation-theory accuracy with mode-rich coverage across $q>100$ and for search strategies that leverage multi-mode templates, ultimately enabling SSM-IMRIs as precision probes of primordial black holes and early-universe physics.

Abstract

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.

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

TL;DR

The paper tackles the detectability and waveform-systematics of sub-solar mass intermediate mass-ratio inspirals (SSM-IMRIs) by benchmarking a perturbation-theory–based surrogate, BHPTNRSur1dq1e4, against the IMRPhenomX family. It demonstrates that higher-order GW modes are crucial for achieving usable SNRs and detection volumes in both current and next-generation detectors, and it quantifies substantial systematic biases when extrapolating phenomenological models to extreme mass ratios. Through matching, fitting-factor analyses, and Bayesian parameter estimation, the authors reveal that current fast IMRPhenomX models can severely misrepresent intrinsic parameters (e.g., , ) and source geometry, especially for edge-on orientations, with biases exceeding statistical uncertainties by many standard deviations. The work argues for waveform models that couple perturbation-theory accuracy with mode-rich coverage across and for search strategies that leverage multi-mode templates, ultimately enabling SSM-IMRIs as precision probes of primordial black holes and early-universe physics.

Abstract

We investigate the detectability and waveform systematics of sub-solar mass intermediate mass-ratio inspirals (SSM-IMRIs), characterized by mass ratios . 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 relative to quadrupole-only templates. With optimal mode inclusion, SSM-IMRIs are observable out to luminosity distances of Mpc () with Advanced LIGO and Gpc () 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.

Paper Structure

This paper contains 12 sections, 8 equations, 12 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. Waveforms
  3. BHPTNRSur1dq1e4
  4. IMRPhenomX Family Models
  5. Waveform model selection
  6. Detectability
  7. Waveform systematics
  8. Match
  9. Fitting Factors
  10. Parameter Estimation
  11. Conclusion
  12. Acknowledgments

Figures (12)

  • Figure 1: Low-frequency cutoff, $f_\text{low}$, for different cases in the $q\text{-}M$ plane for computations done for the case of aLIGO sensitivity. The maximum between $10$Hz and the starting frequency of the BHPTNRSur1dq1e4 waveform (for both all calibrated modes and only $(2,\pm 2)$ calibrated modes) is chosen as $f_\text{low}$. $f_\text{ISCO}$ is $10$Hz for $M=439.72\text{M}_\odot$ and $5$Hz for $M=879.43\text{M}_\odot$.
  • Figure 2: SNR as color-code in the $q-M$ plane calculated using BHPTNRSur1dq1e4 (all calibrated modes, i.e., till $l_\text{max}=5$) for aLIGO and ET sensitivities. \ref{['fig:snrSur_q_M_aLIGO_all_calib_modes']} and \ref{['fig:snrSur_q_M_ET_all_calib_modes']} show the SNR for aLIGO and ET, respectively. $d_L=100$ Mpc for all the cases.
  • Figure 3: Ratio of SNRs using all the calibrated modes and only the $(2,\pm2)$ modes of BHPTNRSur1dq1e4 shown in the $q-M$ plane. \ref{['fig:higher_mode_q_M_aLIGO_all_calib']} and \ref{['fig:higher_mode_q_M_ET_all_calib']} show the ratio of SNRs for aLIGO and ET, respectively, for the same parameter space.
  • Figure 4: Dependence of the higher modes on the inclination angle. Each case is same as that in Fig. \ref{['fig:higher_mode_qm_plot']}
  • Figure 5: Dependence of SNR on the inclination angle $\iota$. SNR is calculated using all the calibrated modes of BHPTNRSur1dq1e4 for aLIGO sensitivity.
  • ...and 7 more figures