Eccentricity constraints disfavor single-single capture in nuclear star clusters as the origin of all LIGO-Virgo-KAGRA binary black holes

Abstract

Multiple formation pathways have been proposed for the origin of binary black holes (BBHs). These include isolated binary evolution and dynamical assembly in dense stellar environments such as nuclear or globular star clusters. Yet, the fraction of BBHs originating from each channel still remains uncertain. One way to constrain this fraction is by investigating the distribution of the orbital eccentricities of the BH coalescences detected by the LIGO-Virgo-KAGRA (LVK) Collaboration. In this work, we analyze 85 BBHs from the first part of the fourth LVK observing run (O4a) using a multipolar, eccentric, aligned-spin effective-one-body waveform model. We perform parameter inference with neural posterior estimation and nested sampling. After incorporating astrophysical prior odds and comparing to the quasicircular precessing-spin hypothesis, we find that no candidates reach a high enough statistical significance to claim a confident detection of eccentricity. We use these upper limits to explore a particular model, in which all O4a BBHs originate from single-single gravitational wave (GW) captures. We perform hierarchical inference on the velocity dispersion of the host environment and find $σ< 24.3\,\mathrm{km/s}$ (95% credible upper bound). This disfavors single-single capture in nuclear star clusters (~20-200 km/s) as the dominant source of all observed BBH mergers. We verify that this dispersion bound does not increase by repeating the inference on a synthetic catalog augmented with eccentric events motivated by analyses of the third observing run of the LVK (O3). Our results place improved constraints on the number of eccentric BBHs and highlight the importance of eccentricity measurements in disentangling compact-binary formation channels in current and future GW detectors.

Figures (4)

• Figure 1: Left$\log_{10} \mathcal{B}_{\text{EAS/QCAS}}$ and the $e_{\text{10Hz}}$ 90% highest-density intervals for the 85 events analyzed from O4a. Right is a histogram counting the distribution of $\log_{10} \mathcal{B}_{\text{EAS/QCAS}}$. A few of these events exclude $e_{\text{10 Hz}} = 0$ at the 90% level and have a $\log_{10} \mathcal{B}_{\text{EAS/QCAS}} > 0.2$. We also highlight GW231114_043211 which has a significant reduction in eccentricity when marginalizing over the glitch. We use different colors for these events to guide the eye. Despite a few positive Bayes factors, when taking into account the prior odds, none of these events can be considered confidently eccentric.
• Figure 2: Posterior distributions on $e_{10\text{Hz}}$ for GW190701, GW231114_043211, and GW231221_135041 when either subtracting the glitch (orange) or marginalizing over 100 glitch realizations (blue). For GW190701, when marginalizing over the glitch instead of taking one fair draw from the glitch distribution, two modes for eccentricity appear, but the distribution has support around zero $e_{10\text{Hz}} \sim 0$. When using the glitch marginalized posterior, the Bayes factors for GW190701 drop from $\log_{10} \mathcal{B}_{\text{EAS/QCAS}} = 3.68$ to $\log_{10} \mathcal{B}_{\text{EAS/QCAS}} = 0.42$. For GW231114_043211, the Bayes factors change from $\log_{10} \mathcal{B}_{\text{EAS/QCAS}} = 0.36$ to $\log_{10} \mathcal{B}_{\text{EAS/QCAS}} = 0.06$ while the change for GW231221_135041 is within the statistical error for the Bayes factor.
• Figure 3: Left: Eccentricity distributions $p(\log_{10} e_{10\,\mathrm{Hz}} | \sigma)$ for different velocity dispersions, computed using the single-single GW capture model with fiducial masses $M_1 = 30\,M_\odot$ and $M_2 = 10\,M_\odot$. Higher velocity dispersions produce systematically higher eccentricities at fixed reference frequency. Right: Posterior distributions on the velocity dispersion $\sigma$ assuming all 85 O4a BBH mergers originate from single-single captures. The dark purple curve shows the global $\sigma$ model posterior with median $9.6^{+14.7}_{-6.7}\,\mathrm{km/s}$ (90% credible interval). The thick green curve shows the mean posterior predictive distribution (PPD) on $\sigma$ from the hyper model, which mixes GC and NSC populations with mixing fraction $\beta$. Thin green lines show individual PPD draws sampled from the $\beta$ posterior. Blue and red histograms show the observed velocity dispersions of Milky Way globular clusters and NSCs, respectively; log-normal fits to these histograms define the $p_{\rm GC}(\sigma)$ and $p_{\rm NSC}(\sigma)$ components used in Equation (6). Vertical dashed and dotted lines indicate the median and 90% credible interval for the global $\sigma$ model. Both models favor low velocity dispersions consistent with GC environments and disfavor the hypothesis that single-single captures in NSCs produce all observed BBH mergers in O4a.
• Figure 4: Posterior distributions of the eccentricity, $e_{\text{10 Hz}}$ and relativistic anomaly $\zeta_{\text{10Hz}}$ of the 9 events reported in Table \ref{['tab:interesting_table']}. Note $\zeta_{\text{10Hz}} = 0$ corresponds to periastron and $\zeta_{\text{10Hz}} = \pi$ corresponds to apastron. Each posterior is colored by the density of samples with orange indicating a high density and blue a low density. In the top and side panels for each event we show the 1D marginal distributions for the eccentricity and relativistic anomaly. Colored in an orange band is the prior boundary in $e_{\text{10Hz}}$ and $\zeta_{\text{10Hz}}$. This is a function of the total mass, which is why the boundary is different for each event and a band as opposed to a line. Several events such as GW230709_122727, GW230820_212515, GW231001_140220 exhibit railing against the prior boundary.