Searches for Post-Merger Gravitational Waves with CoCoA: Sensitivity Projections Across Large Template Banks for Current and Next-Generation Detectors

TL;DR

The paper tackles the challenge of efficiently detecting intermediate-duration post-merger GWs from NS-NS mergers using CoCoA across large template banks. It introduces a Python framework to analytically estimate CoCoA distance horizons for various detector networks and waveform grids, enabling rapid identification of promising parameter-space regions and grid resolutions. Results show that next-generation networks (e.g., CE) significantly extend reach, with horizons up to several thousand megaparsecs, while current upgrades (O4) approach distances comparable to GW170817 for secular bar-mode magnetars. The work validates the approach by reproducing established results and discusses limitations, emphasizing CoCoA as a targeted complementary method to all-sky unmodeled searches and outlining future extensions to broader post-merger scenarios and longer-duration signals.

Abstract

The multi-messenger detection of the binary neutron star (NS) merger GW170817 has revolutionized the field of gravitational wave (GW) astronomy. However, several important questions remain to be answered. One of these is the nature of the compact remnant leftover by GW170817 (short- or long-lived NS versus black hole). A key goal going forward is to understand the diversity of NS-NS merger remnants, and how such diversity maps onto their viability as gamma-ray burst (GRB) central engines. Here, we present a study aimed at assessing the sensitivity of triggered searches for intermediate-duration, post-merger GWs powered by long-lived GRB remnants using networks of current and future ground-based GW detectors and the Cross-Correlation Algorithm (CoCoA). We develop a Python-based framework to efficiently estimate CoCoA distance horizons for a broad range of post merger secular bar-mode waveforms and for different GW detector networks. This framework can be used to identify the most promising regions of parameter space in which to concentrate search efforts, helping design future search strategies to optimally balance search sensitivity and related parameter space gridding schema against computational cost.

Figures (5)

• Figure 1: The parameter space in dipolar magnetic field strength ($B$) and magnetar radius ($R$), of a GW170817-like post-merger search for secular bar-mode GW signals. This parameter space can be broadly divided into different observation times ($T_{\text{obs}}$), ranging from the fastest evolving waveforms (green) to the slowest (blue).
• Figure 2: Strain noise sensitivity curves of ground-based GW detectors. The O2 sensitivity curves are derived from real data, the other are expected sensitivities. See the caption of Table \ref{['tab:detector-network']} for details.
• Figure 3: Distance horizon estimates for current and future detector networks listed in Table \ref{['tab:detector-network']} using secular bar-mode time-frequency templates grouped in three different observation times ($T_{\rm obs} = 165$; $T_{\rm obs} = 256$ s; and $T_{\rm obs} = 512$ s). The horizon distances are shown for the three different regimes of CoCoA: stochastic (left), semi-coherent searches (center), and matched filter (right). In all panels, we color code the distance horizons (in Mpc) reached for the specific values of the magnetic field $B$ (in units of $10^{14}$ G, vertical axis) and magnetar radius $R$ (in km, horizontal axis), and we report within each $B$-$R$ pixel the corresponding waveform duration (observing time, in seconds). Note that color wedges refer to different distance ranges in the various panels. For reference, GW170817 was located at a distance of 40 Mpc. See Section \ref{['s4']} for discussion.
• Figure 4: Comparison of the match filter (blue) and semi-coherent (green; $N_{coh}$=4) limits of CoCoA. We show the detection efficiency versus distance (in Mpc) for a CoCoA single-waveform search that adopts the "correct" time-frequency track (solid) versus a search that adopts a template time-frequency track that is four steps in $\Delta R$ away from the "correct" track (dashed). The horizontal dash-dotted line marks the 50% detection efficiency. The change in horizon distance (the distance at which one reaches 50% detection efficiency at a fixed false alarm rate of 0.1%) when the "incorrect" (dashed) time-frequency track is used for the search is larger in the matched filter case (blue) than in the semi-coherent case (green). This highlights the fact that, as expected, a matched filter search is more sensitive but less robust (against signal uncertainties) than a semi-coherent search.
• Figure 5: We reproduce Figure 5 in Coyne2016, showing the smallest detectable GW amplitude for a CoCoA single-waveform search as a function of false alarm probability $\alpha$ and for a fixed false dismissal probability. See Section \ref{['s4C']} for discussion.