Methods for Detecting Gravitational Waves from mini-Extreme-Mass-Ratio Inspirals I: Statistics Based on Time-Frequency Signal Tracks

TL;DR

This paper tackles the challenge of detecting long-lived gravitational-wave signals from mini-EMRIs, sub-solar mass binaries that produce evolving quasi-monochromatic tracks in time-frequency space. It extends standard Hough-transform–based semi-coherent searches by introducing Track, a statistic that sums along the exact signal track and explicitly accounts for spectral leakage, enabling robust analysis of rapidly evolving signals. The authors derive a weak-signal sensitivity framework, develop a track-averaged statistic, and provide semi-analytic expressions for detection distances, while outlining a practical parameter-space grid for mini-EMRI searches. The approach demonstrates that current ground-based detectors can probe sub-solar-mass compact objects, including primordial black holes, and offers a foundation for future, more realistic searches in non-ideal noise conditions, with potential GPU acceleration to manage computational demands.

Abstract

Mini-extreme-mass-ratio inspirals (mini-EMRIs), composed of a stellar-mass compact object and a much lighter companion, are promising sources of continuous gravitational waves in the frequency band of ground-based interferometers such as LIGO-Virgo-KAGRA. Such systems, consisting of sub-solar-mass compact objects, provide a unique probe of exotic compact objects, including primordial black holes. Detecting such long-lived signals, however, remains challenging. Here, we adapt standard methods used in searches for quasi-monochromatic signals to search for mini-EMRIs, and derive a statistical framework that explicitly handles spectral leakage. In particular, we introduce a new method that sums along the tracks in the time-frequency plane carved out by possible mini-EMRI signals, which we call $Σ$Track. This refinement establishes a general basis for analyzing long-duration transient signals with rapid frequency evolutions, regardless of the underlying mechanism for gravitational-wave emission. We also compute a new semi-analytic sensitivity estimate within our new statistical framework, which is valid under the assumption that the signal is weak with respect to the noise level. We then establish a statistic that quantifies how to discretize the search parameter space for our method, which works for mini-EMRIs, as well as arbitrary signal types. Our results provide a foundation for mini-EMRI searches and demonstrate the potential of current ground-based detectors to probe the existence of sub-solar-mass compact objects.

Figures (14)

• Figure 1: Comparison of the frequency evolution of typical mini-EMRI systems with and without relativistic corrections. The horizontal axis $\tau$ denotes the time to coalescence under the Newtonian approximation. The orbits are assumed to be circular, and the spins of the objects are neglected. The mass ratio is fixed at $q \simeq 10^{-5}$. The upper and lower panels correspond to systems with a neutron star and a stellar-mass black hole as the primary object, respectively. In these two cases, the correction factor is smaller than one in the former and greater than one in the latter.
• Figure 2: Mini-EMRI signal $s(t)$ injected into Gaussian noise $n(t)$. The system consists of a primary mass of $1.5 M_\odot$ and a companion mass of $10^{-5} M_\odot$ at a distance of $8\,\mathrm{kpc}$. The noise is generated using the O3 LIGO-H1 PSD and band-pass filtered between 100 and 200 Hz. The sky location and orbital orientation are selected randomly. The binary orbit is assumed to be circular, and the spins of the objects are neglected. $x(t)$ is covered completely by $n(t)$.
• Figure 3: The scheme of CW methods based on the Hough transform, but including our new method, Track, which replaces the Hough transform.
• Figure 4: The relative power contained in different frequency bins for a monochromatic signal which has been windowed by a rectangular window a rectangular window. Different colors correspond to different offsets $o$ of the signal frequency from the frequency bin in which it should fall. The horizontal axis is bin indices, referenced to the signal frequency. This figure is adapted from Allen:2002bpRiles:2022wwz.
• Figure 5: Probability density distribution of peak counts $n$ for noise (upper panel) and signal (lower panel) tracks. The blue histograms show the simulation results, while the orange and red curves represent the distributions modeled by \ref{['eq:normal_approx', 'eq:normal_approx_modified']}, respectively.