Template bank for compact binary mergers in the fourth observing run of Advanced LIGO, Advanced Virgo, and KAGRA

Matched-filtering gravitational-wave search pipelines identify gravitational-wave signals by computing correlations, i.e., signal-to-noise ratios, between gravitational-wave detector data and gravitational-wave template waveforms. Intrinsic parameters, the component masses and spins, of the gravitational-wave waveforms are often stored in “template banks,” and the construction of a densely populated template bank is essential for some gravitational-wave search pipelines. This paper presents a template bank that is currently being used by the GstLAL-based compact binary search pipeline in the fourth observing run of the LIGO, Virgo, and KAGRA collaboration, and was generated with a new binary tree approach of placing templates, manifold. The template bank contains $1.8\times {10}^6$ sets of template parameters covering plausible neutron star and black hole systems up to a total mass of $400M_{\odot }$ with component masses between $1–200M_{\odot }$ and mass ratios between 1 and 20 under the assumption that each component object’s angular momentum is aligned with the orbital angular momentum. We validate the template bank generated with our new method, manifold, by comparing it with a template bank generated with the previously used stochastic template placement method. We show that both template banks have similar effectualness. The GstLAL search pipeline performs singular value decomposition (SVD) on the template banks to reduce the number of filters used. We describe a new grouping of waveforms that improves the computational efficiency of SVD by nearly 5 times as compared to previously reported SVD sorting schemes.

Figure 1

PSD is the power distribution in frequency space that provides a measure for the detectors’ sensitivity and dictates the number of templates in a template bank. As the PSD has been updated since the O2/O3 template bank was generated, the LIGO PSD for “O4 simulation purposes” [77] of 190 Mpc was used to construct and test the O4 template bank. The Virgo PSD was obtained from [78] and the KAGRA PSD was obtained from [79]. Among the PSDs listed in [62], the high-sensitivity noise curves were chosen to be plotted here.

Figure 2

Template placement of the O4 template bank.

Figure 3

The plot shows the two (“+” and “x”) checkerboarded template banks overlapping one another in the ${\log }_{10}(m_1)$ vs ${\log }_{10}(m_2)$ space. The two checkerboarded template banks contain half of the O4 template bank, and the templates in the two checkerboarded template banks are nearly identical sets as a result of manifold’s binary tree approach of template placement. The two checkerboarded template banks are deployed on analyses running on two separate computing clusters. Each checkerboarded template bank consists of $\sim 1\times {10}^6$ templates.

Figure 4

An illustration of how the template bank is bundled into split banks by the sorting parameters ${\mu }^1$ and ${\mu }^2$. Each split bank contains $X_2$ templates and each background bin contains $X_3$ split banks. SVD is performed on the individual split banks. The overlapping regions of the split banks mitigate the boundary effects.

Figure 5

Comparison of SVD efficiency of $\overrightarrow{\mu }$ sorting and previously used $\mathcal{M}$ sorting. The $x$ axis is the number of SVD filters divided by the number of templates in the background bin where the numerator and denominator are weighted by the sampling rate, which gives the SVD efficiency. Lower values correspond to higher efficiencies. The $y$ axis is the number of background bins with a certain efficiency. $\overrightarrow{\mu }$ sorting has less variation and higher SVD efficiency as compared to $\mathcal{M}$ sorting.

Figure 6

Cumulative histogram of the injections’ mismatches for the O4 template bank and the sbank template bank. The $y$ axis is the fraction of injections above a given mismatch value. Here, the results of the BNS, NSBH, and BBH injections for each template bank are combined to present the summary. The plot has been truncated at a mismatch of ${10}^{-4}$ to visually present the results.

Figure 7

Plots for the BNS injections. Panels (a) and (b) show the total masses of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. To visually present the mismatch of the entire BNS parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. 90% of the BNS injections have fitting factors of 98.62% or higher for the O4 template bank, and 98.22% or higher for the sbank template bank.

Figure 8

Plots for the NSBH injections. Panels (a) and (b) show the total masses of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. To visually present the mismatch of the entire NSBH parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. 90% of the NSBH injections have fitting factors of 98.17% or higher for the O4 template bank, and 98.15% or higher for the sbank template bank.

Figure 9

Plots for the BBH injections. Panels (a) and (b) show the total masses of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. To visually present the mismatch of the entire BBH parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. 90% of the BBH injections have fitting factors of 98.60% or higher for the O4 template bank, and 98.95% or higher for the sbank template bank.

Figure 10

Plots for the BNS injections for the checkerboarded template banks. Panels (a) and (b) show the total masses of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. Lower masses have larger mismatches. To visually present the mismatch of the entire BNS parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. 90% of the BNS injections have fitting factors of 97.60% or higher for the left half of the O4 template bank and 97.58% or higher for the right side of the O4 template bank.

Figure 11

Plots for the NSBH injections for the checkerboarded template banks. Panels (a) and (b) show the total masses of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. Lower masses have higher mismatches. To visually present the mismatch of the entire NSBH parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. 90% of the NSBH injections have fitting factors of 97.07% or higher for the left half of the O4 template bank and 97.10% or higher for the right side of the O4 template bank.

Figure 12

Plots for the BBH injections for the checkerboarded template banks. Panels (a) and (b) show the total masses of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. Lower masses have larger mismatches. To visually present the mismatch of the entire BBH parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. 90% of the BBH injections have fitting factors of 97.82% or higher for the left half of the O4 template bank and 97.83% or higher for the right side of the O4 template bank.

Figure 13

Plots for the BNS region injections with large NS spins. Panels (a) and (b) show the total masses of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. To visually present the mismatch of the entire BNS parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. 90% of the BNS injections with large NS spins have fitting factors of 16.28% or higher for the O4 template bank, and 15.55% or higher for the sbank template bank.

Figure 14

Plots for the NSBH injections with large NS spins. Panels (a) and (b) show the total masses of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. To visually present the mismatch of the entire NSBH parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. The mismatches are larger as the injection ${\chi }_{\mathrm{eff}}$ values approach the upper (lower) limits. 90% of the NSBH injections with large NS spins have fitting factors of 98.13% or higher for the O4 template bank, and 98.12% or higher for the sbank template bank.

Figure 15

Plots for the NSBH injections with mass ratios up to $q=50$. Panels (a) and (b) show the mass ratio of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. The figures show that large mismatches occur for large positive (negative values) of ${\chi }_{\mathrm{eff}}$ and for mass ratios above 20. To visually present the mismatch of the entire NSBH parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. 90% of the NSBH injections with mass ratio up to 50 have fitting factors of 80.53% or higher for the O4 template bank, and 78.44% or higher for the sbank template bank.

Figure 16

Plots for the BBH injections with mass ratio up to $q=50$. Panels (a) and (b) show the mass ratio of the injections on the $x$ axis, ${\chi }_{\mathrm{eff}}$ on the $y$ axis, and the mismatch [$=1-(\text{fitting factor})$] on the color bar. The figures show that large mismatches occur for large mass ratio injections. To visually present the mismatch of the entire BBH parameter space, mismatches smaller than ${10}^{-2}$ are mapped to ${10}^{-2}$. 90% of the BBH injections with mass ratio up to 50 have fitting factors of 98.34% or higher for the O4 template bank, and 98.39% or higher for the sbank template bank.