Search for Precessing Binary Black Holes in Advanced LIGO's Third Observing Run using Harmonic Decomposition

Abstract

Binary black holes (BBHs) exhibiting spin-induced orbital precession offer unique insight into compact-binary formation channels, cosmology, and tests of general relativity. We conduct a dedicated search for precessing BBHs in Advanced LIGO's third observing run (O3) using the harmonic decomposition method of precessing waveforms. We introduce a novel scheme to reduce the number of filters in a harmonic search. With our new approach, our template bank requires $5\times$ fewer filters compared to another proposed precessing search in the same region. We do not find any new significant events. Our new search method achieves up to $\sim 28\%$ improvement in sensitivity and up to $5\times$ lower computational costs compared to existing precessing search pipelines. Our method enables scalable, sensitive searches for precessing BBHs in future gravitational-wave observing runs.

Figures (11)

• Figure 1: Search region of the previous precessing searches in the O3 data of the Advanced LIGO detectors for compact binary mergers to-date. Shown is the search region as the two dimensional space of detector frame component masses $(m_{1}^{\text{det}}, m_{2}^{\text{det}})$. The green area denotes the parameter space explored in the recent NSBH precessing search that employed the same harmonic decomposition technique Fairhurst:2019vutMcIsaac:2023ijd. The orange area corresponds to the region used in the highly precessing BBH search of Schmidt:2024hac. We have chosen the exact same parameter region as the previous precessing BBH search (marked as black dotted lines).
• Figure 2: Whitened precessing waveform and the orthonormalized harmonic decomposition of the same waveform in the time-domain. On the top is the full whitened precessing waveform for a binary with $(m_1^{det}, m_2^{det} ) = (57.5, 5.7) M_{\odot}$, inclination $\sim 74^{o}$ and $b = 0.93$ generated using IMRPhenomXP . The second to sixth rows correspond to the orthonormalized harmonics, with the first being the dominant harmonic, followed by second then third and so on.
• Figure 3: The number of harmonics required by every template in our bank as represented by the $(q, b)$ parameter space, where $q=m_1/m_2$. We show the number of harmonics obtained using the original harmonic order [$h_0,h_1,h_2,h_3,h_4$] (left), and using the new harmonic order (reversed order for $b\geq 1$) (right). The color of each point represents the number of required harmonics: darker templates require more harmonics and lighter the fewer (see legend). Notice the significant reduction in the number of harmonics in the upper region $(b \gtrsim 1 )$ from left to right plot: a total of 35461 templates have fewer harmonics on the with the new harmonic scheme. By incorporating the new harmonic order, the total number of harmonics for the entire bank is reduced by 65355, and the number of templates requiring 5 harmonics reduces from 29580 to only 3. Comparing the total number of filters to the previous precessing BBH search Schmidt:2024jbpSchmidt:2024hac, we have five times fewer filters.
• Figure 4: Pie chart of the templates grouped according to their required number of harmonics (denoted by the numbers inside the pie). On the left is the distribution with the original harmonics, and on the right is the distribution with the new harmonic order where we apply the reverse harmonic order for $b \geq1$ templates. Improving to the new scheme, 35461 templates have fewer harmonics. Summing up the numbers in each pie, we find there are in total 65355 additional number of harmonics (filters) with the original harmonic order. With the new scheme the number of templates requiring five harmonics reduces from 29580 to 3.
• Figure 5: Cumulative distribution of fitting factors for the highly precessing injection set (as described in Table \ref{['Table:Injection_set']}) obtained by the previous precessing BBH search bank (blue circles) Schmidt:2024jbp, by our harmonic bank with original harmonics order (orange dotted line) and the same bank including the new harmonic order(red bold line). The previous precessing search bank contains $\sim 2.3 \times 10^6$ and our bank contains $\sim 2 \times 10^5$ templates. Our bank achieves much better fitting factors with $5 \times$ fewer filters compared to the previous search, after accounting for the extra harmonics for each template (up to three). The black-dotted line corresponds to the minimum match of the bank = 0.97.