Inpainting over the cracks: challenges of applying pre-merger searches for massive black hole binaries to realistic LISA datasets

Author(s)

Cabourn Davies, Gareth, Harry, Ian

Abstract

A key science target of the Large Interferometer Space Antenna (LISA) is to carry out multi-messenger observations of massive black hole binaries, observing the merger simultaneously in gravitational waves and with electromagnetic observatories. Identifying that a merger is happening and providing an updating estimate of the sky location in the hours, days and weeks before the merger is critical to enable electromagnetic observations of the merger event. In this work we demonstrate and compare two methods for premerger identification of massive black hole binaries; a zero-latency filter approach and, for the first time, an approach using an ``inpainting'' technique. We apply these methods to the LISA Data Challenge dataset 2a--Sangria-HM--and demonstrate the successful recovery of the 14 signals in the dataset that we expected to be identifiable at least half a day before merger. We show that the inpainting method can identify premerger signals even when gaps are present in the data, demonstrating the recovery of a signal even when 3 day-long data gaps are added to the 14 days preceding merger. Finally, we explore the challenge of overlapping signals, using a region of overlapping signals in the Sangria-HM dataset, all of which merge within a 10-day window, and show how removing signals that have been confidently identified from the data allows us to identify quieter signals in the same period.

Figures

Caption

Comparison of power spectral densities used in this work. The power spectral density is estimated from the Sangria-HM dataset using the Welch method with a segment duration of 18.25 days. The model shown is the noise model used to produce the Sangria-HM dataset, and is shown with and without unresolvable Galactic binary sources. We show the power spectral density model and estimate smoothed using the method described in Section~\ref{subsec:smoothing}. We also show the characteristic strain for a representative \ac{MBHB} signal from Sangria-HM (Signal 2), which shows that at 14, 7 and 4 days-before-merger, the \ac{MBHB} does not overlap the Galactic binary confusion noise in frequency, but when the signal reaches around one day before merger (blue line), the Galactic binary confusion noise starts to overlap with the signal.

Caption

The method used to smooth over the dip in the power-spectral density at 60 mHz. We draw a straight line between the two peaks either side of this point, and smoothly transition between the estimated power-spectral density and the straight line using a Hann window. This ensures that there are no immediate jumps in the power-spectral density to cause spectral leakage. This is applied to both the estimated and modeled power-spectral density used in later analysis.

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Template bank sizes assuming different power-spectral densities. Inclusion of unresolvable Galactic binary foreground in the model increases bank size by a factor between 2.1 and 2.6. Using the estimated rather than modeled power-spectral density increases bank size by a factor between 1.0 and 1.9.

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Optimal signal-to-noise ratio (SNR) build-up and signal-to-noise ratio of premerger-truncated signals matched filtered against the full signal for Signal 10. We see that the premerger-truncated signals' signal-to-noise ratios are a product of the optimal signal-to-noise and the match between the full and truncated signals. Equivalent plots for all signals are included in the data release.

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Signal 10 results, showing results with and without the secondary peaks, for the removed results, the signal is removed from the data two hours before merger. We also see peaks in the data before merger, these are the post-signal peaks for Signal 9, which is 21 days before Signal 10. Equivalent plots for all signals are included in the data release.

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Search results for the zero-latency filter search

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Signal-to-noise ratio (SNR) as a function of the forecast merger time and the time before merger. Produced using the inpainting technique to analyze the Sangria-HM dataset. Signals have been removed from the data once they reach 2 hours before merger.

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Timeline of results for Signal Zero, demonstrating the inclusion of gaps in the data in the days before merger. Timeline plots for all signals are included in the data release.

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: No removal of signals

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: Signals are removed 2 hours before merger

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Timeline of results in the congested period of days 110-140 of the Sangria-HM dataset. These are inpainting results filtered to be at the 0, 5, 1, 4, 7 and 14 days-before-merger that were used in the zero latency search. We see that Signal 4 - the loudest signal - dominates the SNR, and can actually be found before Signals 2 and 3. We remove Signal 4 14 days before merger. Signal 3 can be detected almost immediately after Signal 4 is removed from the data, and is therefore removed 11 days before merger. Signal 2 can then be found around a day before merger. Peaks remain for the 1 and 0.5 days-before-merger results for Signals 3 and 4 - this is due to imperfect removal of the signal from the data.