Ab uno disce omnes: Single-harmonic search for extreme mass-ratio inspirals

TL;DR

This work tackles the challenge of detecting extreme mass-ratio inspirals (EMRIs) in LISA-like data by developing a semi-coherent, time-frequency search for a single EMRI harmonic. It models the EMRI frequency evolution with a data-driven Singular Value Decomposition (SVD) basis, enabling fast, differentiable generation of frequency tracks and efficient optimization on GPUs. Through injections in stationary Gaussian noise, the method achieves high detection probability (e.g., ~94% at SNR 30 for p_FA = 0.01) and recovers the dominant harmonic with ~1% relative frequency accuracy, subsequently enabling sub-percent EMRI-parameter constraints via simulation-based inference and follow-up MCMC. The approach offers a computationally scalable pathway to produce EMRI proposals for the LISA global fit, with potential extensions to multiple harmonics and more realistic noise scenarios, thereby improving EMRI identification and parameter estimation in future space-based GW data analysis.

Abstract

Extreme mass-ratio inspirals (EMRIs) are one of the key sources of gravitational waves for space-based detectors such as LISA. However, their detection remains a major data analysis challenge due to the signals' complexity and length. We present a semi-coherent, time-frequency search strategy for detecting EMRI harmonics without relying on full waveform templates. We perform an injection and search campaign of single mildly-eccentric equatorial EMRIs in stationary Gaussian noise. The detection statistic is constructed solely from the EMRI frequency evolution, which is modeled phenomenologically using a Singular Value Decomposition basis. The pipeline and the detection statistic are implemented in time-frequency, enabling efficient searches over one year of data in approximately one hour on a single GPU. The search pipeline achieves 94% detection probability at $\mathrm{SNR} = 30$ for a false-alarm probability of $10^{-2}$, recovering the frequency evolution of the dominant harmonic to 1% relative error. By mapping the EMRI parameters consistent with the recovered frequency evolution, we show that the semi-coherent detection statistic enables a sub-percent precision estimation of the EMRI intrinsic parameters. These results establish a computationally efficient framework for constructing EMRI proposals for the LISA global fit.

Figures (8)

• Figure 1: Frequency $f$ and frequency derivative $\dot{f}$ distributions for galactic binaries (GBs; pink, solid histogram), EMRIs (green, dashed-dotted histogram), and EMRI phenomenological frequency evolution constructed using the SVD basis (yellow, dashed histograms). The galactic-binary sample is taken from one of the LISA Data Challenges Baghi:2022ucj. EMRI samples represent the full frequency evolution of the dominant azimuthal mode $m=2, n=0$ across the searched parameter space of Table \ref{['tab:emri_priors']}. The SVD tracks are obtained by uniformly sampling the SVD coefficient space $\xi_p$ and reconstructing the frequency tracks. These two different priors (EMRIs and SVD) lead to two different frequency and frequency derivative densities. Contours mark 68% and 95% credible regions.
• Figure 2: Recovered frequency evolution of the search of an EMRI injection with primary mass $m_1 = 1.3379 \times 10^6\,M_\odot$, secondary mass $m_2 = 27.091\,M_\odot$, primary spin $a = 0.8636$, time to plunge $T_{\rm pl} = 0.902\ \mathrm{yr}$, and final eccentricity $e_f = 0.007086$, and $\mathrm{SNR} = 30$. Top panel: Best fit frequency evolution as a function of different observed data durations, color coded by the normalized detection statistic. The dashed lines show the best frequency evolutions obtained per each observed data duration. The dashed-dotted green line represents the true injected frequency track from the dominant $m=2, n=0$ harmonic, whereas the solid yellow line represents the best frequency evolution obtained by the search strategy across all observed data durations. The search of the entire one year dataset takes 1.1 hours and evaluates $\approx 10^7$ detection statistics. Bottom panel: The relative difference $|\Delta f/f|$ between the recovered and true frequency tracks as a function of time.
• Figure 3: Distribution of normalized detection statistic $\mathcal{S}$ under the noise-only hypothesis (pink) and signal+noise hypotheses at different SNRs. Each histogram is constructed from 100 data realizations (Sec. \ref{['subsec:data_generation']}). The pink noise-only histogram establishes the detection threshold at three different false-alarm probabilities $p_{\rm FA}=0.5$ (solid grey), $p_{\rm FA}=0.01$ (dashed grey), and $p_{\rm FA}=10^{-4}$ (dotted grey). A fit to the noise distribution is shown as solid line. The overlaid empty histograms show results from EMRI signal injections with SNR = 20 (solid green), SNR = 30 (dashed blue), and SNR = 40 (dashed-dotted yellow).
• Figure 4: Detection probability and frequency reconstruction accuracy as functions of the signal-to-noise ratio (SNR). Top panel: Detection probability curves for false alarm rate thresholds $p_{\rm FA}$: $0.5$ (pink circles), $10^{-2}$ (green squares) and $10^{-4}$ (blue diamonds). Each curve is computed from 100 independent EMRI injections with parameters uniformly sampled across the full-search prior space of Table \ref{['tab:emri_priors']}. Bottom panel: Median relative frequency error $|\delta f/f|$ of recovered frequency tracks from the search pipeline and 1$\sigma$ error bars representing the standard deviation across injections.
• Figure 5: Parameter-space dependence of detection performance for 100 EMRI injections at SNR = 25 with false alarm rate $10^{-4}$. Each panel shows stacked histograms where pink filled histograms represent successfully detected signals and the green empty histograms represent missed detections. The detection ratio is shown as black dots and obtained by dividing the counts of the detected and not detected histograms. From top to bottom and from left to right, we show distributions of (log) detector-frame primary mass $m_1$, secondary mass $m_2$, primary dimensionless spin parameter $a$, final eccentricity $e_f$, plunge time $T_{\rm pl}$, luminosity distance $d_L$, initial frequency $f_0$, initial frequency derivatives $\dot f_0$, initial semi-latus rectum $p_0$, and initial eccentricity $e_0$. The total detection probability for these sources at SNR = 25 with false alarm rate $10^{-4}$ is $\approx 50\%$ as shown in Fig. \ref{['fig:det_prob']}.