Fast pre-merger detection of massive black-hole binaries in LISA based on time-frequency excess power

The Laser Interferometer Space Antenna is expected to observe gravitational waves from massive black hole binaries across cosmic time. Many are anticipated to be detectable hours to weeks before coalescence. We present a fast algorithm for the pre-merger detection and preliminary characterization of such binaries. The method performs a search for excess power with a chirping time-frequency morphology in short-time Fourier transform spectrograms. By tiling the time-frequency plane with slices defined by the quadrupole frequency evolution, we define a signal significance relative to a fitted background distribution of instrumental noise and Galactic foreground. Individual search triggers are followed by a coherence tracker, which groups over time triggers consistent with the same physical signal . Doing so, our analysis provides progressively refined estimates of the chirp mass and coalescence time. We validate our algorithm on the Sangria LISA Data Challenge dataset, successfully detecting all 15 injected MBHBs: 14 of them hours-to-weeks before merger, while one is only detected after the binary coalescence. The algorithm yields chirp mass relative errors below $3%$ for high-SNR sources and coalescence time uncertainties of up to a few hours. With a computational cost of less than a second to process a 10-day data segment on single core, our approach is suitable for generating real-time alerts, trigger protected observational periods, and provide informative priors for Bayesian parameter estimation.

💡 Research Summary

This paper presents a low‑latency pipeline designed to detect massive black‑hole binary (MBHB) inspirals in LISA data before coalescence and to provide early estimates of their physical parameters. The authors build on the successful use of excess‑power searches in short‑time Fourier transform (STFT) spectrograms for ground‑based detectors, adapting the method to the specific challenges of LISA: a signal‑dominated data stream, a cyclostationary Galactic white‑dwarf foreground, and the possibility of multiple overlapping MBHB signals lasting weeks to months.

The pipeline consists of four main stages. First, the raw TDI X, Y, Z streams are linearly combined into the orthogonal A, E, T channels and segmented into overlapping 10‑day “chunks” that slide forward every 200 minutes. For each chunk an STFT is computed using a Hann window of 10⁵ s length with 95 % overlap, yielding a spectrogram covering the 10⁻⁴–10⁻³ Hz band. Second, a background power‑spectral density (PSD) is estimated from a 5‑day window of past data (excluding any bright transients) by taking the median power over the 76 time‑segments that compose the window. This procedure captures both the instrumental noise and the slowly varying Galactic confusion noise, producing 500 reference PSDs that are updated throughout the simulated year. The spectrogram is then whitened by dividing by the appropriate PSD.

The third stage implements the core detection algorithm. The authors adopt a simple quadrupole‑only inspiral model, where the instantaneous GW frequency follows f(t; M_c, t_c) ∝ (t_c − t)⁻³⁄⁸. For any pair (M_c, t_c) a “chirp slice” – a narrow band in the time‑frequency plane following the corresponding frequency evolution – is defined. The spectrogram pixels inside each slice are summed, and the resulting excess‑power statistic is compared to an empirically fitted background distribution. When the statistic exceeds a pre‑determined threshold, a trigger is recorded, together with an initial estimate of M_c and t_c.

The fourth stage is a coherence tracker that links triggers across successive chunks. Triggers that are consistent with the same (M_c, t_c) pair are grouped into a candidate source; a least‑squares refinement updates the parameter estimates and their uncertainties each time new data become available. This iterative refinement yields progressively tighter constraints on the chirp mass and the time‑to‑coalescence, even when the initial trigger is based on a modest excess‑power signal.

The authors validate the pipeline on the Sangria LISA Data Challenge dataset, which contains 15 injected MBHBs with masses in the 10⁴–10⁷ M_⊙ range and waveforms generated with the PhenomHM model. All 15 sources are recovered; 14 are detected hours to weeks before merger, while one is only identified after coalescence. For high‑SNR sources the relative error on the chirp mass is below 3 % and the coalescence‑time uncertainty is a few hours. Even for lower‑SNR injections (SNR ≈ 10) the mass error remains within 5–10 % and the merger time is constrained to within ≈ 10 hours. The pipeline processes a 10‑day chunk in less than one second on a single CPU core, demonstrating that it can operate in real time and issue alerts within the required latency budget.

The paper discusses several limitations. The detection model uses only the dominant quadrupole mode, neglecting higher harmonics, spin‑precession, and eccentricity, which could affect parameter accuracy for certain systems. The background PSD is estimated from median power in past data, assuming the Galactic foreground evolves slowly; rapid foreground variations or bright unresolved sources could increase the false‑alarm rate. Finally, the fixed frequency band and window length are not optimal for very low‑mass or high‑frequency binaries, suggesting that adaptive settings would improve sensitivity.

Future work will extend the method to include multi‑mode waveforms, incorporate spin effects, and develop a more sophisticated, possibly Bayesian, background model that can adapt to changing foreground conditions. The authors envision integrating this low‑latency pipeline with LISA’s Distributed Data Processing Center to provide early alerts that trigger protected observational periods, guide electromagnetic follow‑up campaigns, and supply informative priors for downstream full‑Bayesian parameter‑estimation pipelines, thereby enhancing the scientific return of LISA’s multimessenger observations.