Observability of eccentricity in a population of merging compact binaries

TL;DR

This work evaluates the observability of residual orbital eccentricity in merging BBHs by quantifying power in eccentric harmonics using the framework of Patterson:2024vbo within LVK O4 sensitivities. It combines an astrophysically motivated BBH population from globular-cluster simulations (CMC catalogs) with a log-uniform model and employs TEOBResumS-Dali waveforms to decompose signals into eccentric harmonics, identifying an eccentric-harmonic SNR $\rho_{\mathrm{ecc}}$ that captures measurable eccentricity when $\rho_{\mathrm{ecc}}\ge 4$ alongside a quasi-circular SNR $\rho_{\mathrm{circ}}\ge 10$. The study finds that the subset of BBHs with observable eccentricity tends to have $e_{10\mathrm{Hz}}\sim 0.3$ and $\rho_{\mathrm{tot}}\sim 20$, significantly higher than the overall detectable BBH population, and it reports consistency with some GWTC-3 eccentric claims while highlighting model-dependence. It also explores the potential of eccentric-harmonic searches (dominant $k=0$ and subleading $k=\pm1$) to improve detection efficiency over quasi-circular templates, especially for lower masses, while reducing the template-bank burden; these results motivate targeted eccentric-harmonic searches to enhance sensitivity to eccentric BBHs in current and future GW data analyses.

Abstract

We investigate the prospects of observing residual eccentricity in a population of compact binaries by calculating the power in the eccentric harmonics, following the methodology in arXiv:2411.04187. Although most observed compact binary coalescences are expected to circularize before entering the sensitivity band of the ground-based gravitational-wave (GW) detectors, dynamical interactions in dense star clusters can lead to a fraction of these binaries with non-negligible eccentricity at the time of detection. To quantify the observability of eccentricity, we simulate a population of merging compact binaries and identify those which have sufficient power in sub-dominant eccentric harmonics to be clearly distinguishable from quasi-circular systems. We consider a binary black hole (BBH) population derived from globular cluster simulations with residual eccentricity distribution obtained from Cluster Monte Carlo (CMC) catalogs as well as a fiducial log-uniform model. Assuming the LIGO-Virgo network of GW detectors with their sensitivities achieved during LIGO-Virgo-KAGRA (LVK) Observing Run (O4), we find that the BBH population with measurable eccentricity will have a significantly higher median eccentricity $e_{\mathrm{10Hz}}\sim 0.3$ (with $90\%$ range: $0.1 - 0.5$) and signal-to-noise ratio (SNR) $\sim 20$ ($90\%$ range: $13 - 57$) compared to the observable population of BBHs. We compare our predictions of the regions of parameter space where eccentricity is detectable with the claimed observations of eccentricity in GW events from third Gravitational Wave Transient Catalog (GWTC-3).

Figures (5)

• Figure 1: The distributions of residual eccentricity at orbit-averaged frequency of $10$Hz for the total population in blue, observed population in orange (assuming matched filtering SNR of best matching quasi-circular template is greater than 10), and observed eccentric population in green (assuming eccentric harmonic SNR is greater than 4), for BBH from CMC simulations (left) and the log-uniform model (right). In the O4 observing scenario of LVK, we find $\sim90\%$ of the measurable eccentricities are $\geq 0.2$ for both populations. The SNR loss due to filtering eccentric signals against quasi-circular templates affects the detection of BBH at larger eccentricities.
• Figure 2: The distribution of eccentricity as a function of full expected network SNR (assuming eccentric templates) for observed (in dark blue to yellow colormap) and measurably eccentric (in cyan to pink colormap) population of BBH using quasi-circular templates. The colormap density here corresponds to the number of binaries. The median eccentricity and SNR (denoted by '+' with median SNR and eccentricities, respectively, quoted in the brackets) for the measurably eccentric population are significantly higher with respect to the observed population of BBH. Right: Same as left plot but the log uniform eccentricity and PLP mass distributions. The conclusions are largely same as for CMC model. This highlights the model independence of the measurably eccentric population distribution of BBH.
• Figure 3: Same as Fig. \ref{['fig:ecc_scatter_plot']} but here the categorization whether the system is observable or measurable eccentric considers the effect of noise. The distribution of the measured eccentric harmonic SNR follow non-central chi-square distribution with 3 degrees of freedom and non-centrality parameter being the square of the true eccentric harmonic SNR.
• Figure 4: The detection efficiency of the quasi-circular (in green), dominant eccentric harmonic $k=0$ (in orange), and two sub-leading eccentric harmonics in adition to dominant harmonic $k=(0, 1, -1)$ (in blue) searches with respect to full eccentric template search. In all cases, we require a network SNR above 10 for detection even though, as discussed in the text, the threshold is likely to be higher for the more complex searches incorporating multiple harmonics or spanning the full space of eccentric signals. The quasi-circular approach suffers from loss of the sensitivity for BBH with $e_{\mathrm{10Hz}} > 0.1$, whereas the $k=0$ harmonic search shows significant improvement over the quasi-circular search for $e_{\mathrm{10Hz}} > 0.2$.
• Figure 5: The detection efficiency of the quasi-circular (dotted line), dominant eccentric harmonic (dashed line), and three leading eccentric harmonics (solid line) with respect to full eccentric templates in different chirp mass bins. For high masses, the detection efficiency of the dominant harmonic search is comparable to the quasi-circular search whereas three leading eccentric harmonics search is significantly better. On the other hand, for low mass BBHs, the dominant harmonic performs significantly better than quasi-circular, and inclusion of two subleading harmonics further improves the detection efficiency.