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

TL;DR

Problem: pre-merger detection of MBHBs in LISA must be fast to enable real-time alerts and coordinated follow-ups. Approach: a time-frequency excess-power search on STFT spectrograms with chirp tracks, Gamma background modeling, and region-tracking to produce preliminary $M_c$ and $t_c$ during data chunks. Key results: all 15 Sangria MBHBs are detected, with 14 pre-merger detections; high-SNR sources have $M_c$ errors $<3\%$ and $t_c$ errors of a few hours; end-to-end chunk processing times are $\lesssim 1$ s on a single core. Significance: the method provides rapid, informative priors for Bayesian estimation and enables near-real-time alerts and protected observational windows.

Abstract

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.

Figures (13)

• Figure 1: Summary of STFT scheme and free parameters. In our default configuration we consider a sliding chunk of 10 days sampled with cadence $T_s=5$ s. Each chunk is uniquely associated to a spectrogram, as defined in Eqs. \ref{['eq:discreteSTFT']} and \ref{['eq:stftpower']}: segments of length $\tau$, overlapping by $95\%$ are Hann-windowed according to Eq. \ref{['eq:hannwindow']} and Fourier transformed, yielding a frequency array associated to the time $p\Delta t$. We further filter the STFT to mask pixels obtained by zero-padded segments, whose window crosses the chunk borders (teal-bordered boxes), and pixels above $10^{-3} {\rm Hz}$ and below $10^{-4} {\rm Hz}$ (white, black-bordered boxes).
• Figure 2: Array of PSDs used for whitening the spectrograms at each update time $t_{\rm u}$. The Galactic confusion noise modulation is visible as a periodic brightening particularly clear at above $0.5 {\rm mHz}$. The brightness-modulated narrow horizontal line at $f=5.6e-4$ Hz is the signal emitted by a loud DWD source, at a distance of $0.1 {\rm kpc}$, far from the Galactic center, which is successfully suppressed in the whitened spectrograms.
• Figure 3: The top panel shows the default setup described in \ref{['subsec:tf_representation']}, while the bottom panel illustrates the configuration optimized for the detection of MBHB-2, discussed in \ref{['sec:results']}. This source has a chirp mass of $1.2 \times 10^6 M_\odot$: it is therefore characterized by a fainter inspiral and a big portion of the total power is emitted at higher frequencies. Both spectrograms correspond to chunk identified by $t^\star=130.5$ days, but with duration of 10 (top) and 5 (bottom) days, respectively. Dashed lines denote boundaries of a chirp slice, as defined in \ref{['subsec:detection_strategy']}: in particular, we show the slice matching the MBHB-3 signal as an outlier in our detection statistics. In the default configuration, the chirping tracks of MBHB-3 and MBHB-4 are clearly visible, whereas MBHB-2 is only marginally. By contrast, the former is clearly visible in the dedicated high-frequency configuration (bottom).
• Figure 4: Example of background distributions relative to two spectrogram slices, in orange and teal, respectively. The distribution shape is affected by number of time-frequency points selected by each slice. Supported by the derivation in \ref{['app:background_distro_derivation']}, we find a Gamma distribution to be an adequate parametric family to fit for the observed distribution, obtained as described in \ref{['subsec:detection_strategy']}. Shaded histograms and solid curve denote the synthetic realizations and the best fit obtained following the model in \ref{['eq:gamma_model']}, respectively.
• Figure 5: FAP maps at different chunk times $t^\star$, following the default search configuration described in \ref{['subsec:detection_strategy']}. The white regions in the top-right corners correspond to $(\mathcal{M}_{\mathrm{c}}, t_{\mathrm{c}}^\star)$ values associated with slices of the time–frequency plane that contain no spectrogram points because they fall outside its boundaries. We also remove the thin region corresponding to slices containing fewer than 10 points. The markers show the true chirp mass and coalescence time from the Sangria dataset metadata. As the chunk timestamp approaches the coalescences, two regions in the $(\mathcal{M}_{\mathrm{c}}, t^{\star}_{\mathrm{c}})$ space emerge and gradually concentrate around the true values. As discussed in \ref{['sec:results']} in the default configuration, MBHB-2 is not detected by our algorithm.