Global time-frequency search for stellar-mass binary black holes in LISA

Abstract

We present a complete pipeline for detecting and characterising gravitational waves (GWs) produced by the inspiral of stellar-mass binary black holes in data from the Laser Interferometer Space Antenna (LISA). The analysis framework relies on an efficient time-frequency implementation of an adaptive semi-coherent detection statistic, which we show to be robust against non-stationary noise and the presence of gaps of varying duration and cadence. The search is able to detect signals down to a coherent signal-to-noise ratio $\approx$ 11 over the full parameter space of black holes with spins aligned to the orbital angular momentum and orbital eccentricity $\leq$ 0.01 when deployed on the 2-year-long LISA Data Challenge Yorsh. The search can be run within a day using $\approx$ 40 GPUs. The techniques presented here have wider applications in GW astronomy, in particular the search for extreme-mass-ratio inspirals in LISA data.

Figures (6)

• Figure 1: Time-frequency representations of TDI channel $A$ of the Yorsh dataset, containing smBBHs. In both panels, the data are whitened according to the Sangria analytical PSD, which we use in the analysis (see text for more details). Left: The full (GW signals plus noise) Yorsh data, with data gaps at 85% duty cycle. Dark vertical lines correspond to the location of the data gaps. Other features visible by eye are described in the text. Right: The GW signal-only contribution to the data (no gaps), showing the time-frequency tracks of the 8 smBBHs present in the data set (labels correspond to the Yorsh source ID, see Supplemental Material); all signals are completely invisible in the time-frequency data on the left.
• Figure 2: The results of the search on both 100% and 85% duty cycle datasets. Top-left: Maximum detection statistic $\hat{\Upsilon}_1 \equiv \mathrm{max}_{\xi}(\Upsilon_1)$ within each search tile $(\mathcal{M}_c, f_\mathrm{in})$. A conservative threshold of $\Upsilon_1\geq 90$ distinguishes significant search triggers (green) from noise triggers (red). Vertical black dotted lines indicate tiles with injected sources. Top-right: Heat-map on the sky of $\Upsilon_{1}(\lambda, \beta)$, conditioned on the search results for each detected source. Blue crosses denote the true location of a source and lime green circles denote the sky position returned by the search. We stress that the density function $\exp(\Upsilon_{1}(\lambda, \beta)/2)$, which could serve as a proposal for estimating the posterior distribution of the source's location in the sky, is significantly more compact than the region covered by the heat-map (see Table 2 in Ref. Bandopadhyay:2025). Both top panels refer to the analysis of the 100% duty cycle dataset. Bottom: The distribution of $\hat{\Upsilon}_1$ from background analyses compared to the value of the detection statistic returned by the search for each significant tile, with solid (dashed) lines corresponding to the analysis on the $100\%$ ($85\%$) duty-cycle Yorsh data set. Associated false alarm probability estimates are provided in Table. \ref{['tab:false-alarm']} of the Supplemental Material.
• Figure 3: Wall-time per set of source parameters in the evaluation of \ref{['eq:Upsilon-seg']} as a function of batch size for $N_\mathcal{F} = 21$ (see \ref{['eq:inner-segment-tf']}), $T_\mathrm{obs}=2\,\mathrm{yr}$ and $\Delta t=5\,\mathrm{s}$. The implementation on an NVIDIA A100 GPU (solid) outperforms the one on a $2.4\,$GHz Intel Xeon Platinum single-core CPU (dashed lines) starting from a batch size $\approx 30$ (single core). Wall-times are averaged uniformly with respect to mass ratio and eccentricity within the bounds targeted by our search. The oscillations in the wall-time for batches larger than $\sim 10^4$ are due to saturation of GPU resources.
• Figure 4: Computational wall-time per evaluation of \ref{['eq:Upsilon-seg']} in the $(\mathcal{M}_c, f_\mathrm{in})$ plane, averaged over the mass ratio and eccentricity ranges probed by our pipeline. The upper-right corner of the plot (where costs are lowest) corresponds to signals that exit the LISA band during the observational window.
• Figure 5: Relative error in the recovery of $\mathcal{M}_c$ and $f_\mathrm{in}$ (with respect to injected values) for detected signals at either $100\%$ (filled circles) or $85\%$ (triangles) duty cycle. As we search with a stochastic optimiser, some variability in the maximum-statistic parameters is expected, which can cause relative error to decrease despite the loss in SNR when gaps are present.