Archival Inference for Eccentric Stellar-Mass Binary Black Holes in Space-Based Gravitational Wave Observations

TL;DR

The paper tackles the computational challenge of detecting and characterizing eccentric stellar-mass BBHs in the space band by exploiting ground-based detections to constrain the search space for archival space-band analyses. It introduces a Bayesian framework that incorporates eccentricity and uses ground-informed priors, facilitated by a heterodyned likelihood to speed up computation. For a GW190521-like source, space-based observations with ground priors can measure the chirp mass to about $\mathcal{O}(10^{-5})\,M_\odot$ and constrain the eccentricity to about $\mathcal{O}(10^{-5})$ around $e_{0.01\mathrm{Hz}}=0.1$, while reducing the effective detection threshold to $\rho_{\rm thr} \sim 7$ in archival searches. This approach expands the multiband detection yield, improves population inferences on formation channels, and strengthens tests of gravity using space-band data; joint TianQin+LISA observations further enhance sensitivity and sky coverage.

Abstract

Space-based gravitational-wave observatories will detect the early inspiral of stellar-mass binary black holes and can track their eccentricity evolution. However, untargeted searches in the space band are computationally demanding and require relatively high detection thresholds (signal-to-noise ratio $\sim 15$). Information from ground-based detections can significantly shrink the parameter space for space-band analyses and thereby substantially reduce the detection threshold. We present a Bayesian inference pipeline for ground-triggered archival space-band analyses that includes eccentricity. Using ground-informed priors, we demonstrate that with one year of LISA or TianQin data a GW190521-like source with signal-to-noise ratio $\sim 7$ can be distinguished and tightly constrained. In this setup, space observations sharpened the redshifted chirp mass from $\mathcal{O}(10^{-3})M_\odot$ to $\mathcal{O}(10^{-5})M_\odot$, and constrain the eccentricity to $\mathcal{O}(10^{-5})$ around the injected value $e_{0.01\mathrm{Hz}}=0.1$. These results demonstrate that inference of eccentric stellar-mass binary black holes in noisy space-band data is practically feasible, supports an expanded yield of multiband detections, and strengthens prospects for future astrophysical and gravitational tests.

Figures (4)

• Figure 1: Posterior distributions for the GW190521-like joint-detection example recovered with a network of next-generation ground-based detectors, using the injection and priors in Table \ref{['prior']}. The red line marks the injected ("true") value. Two-dimensional contours enclose 50% and 90% of the posterior. In the one-dimensional marginals, blue dotted lines indicate the posterior median and the central 90% credible interval.
• Figure 2: Posterior distributions for the GW190521-like source recovered with TianQin, LISA, and the joint TianQin+LISA network, using ground-informed priors listed in Table \ref{['prior']}.
• Figure 3: Comparison between the Gaussian likelihood and the heterodyned likelihood for a LISA analysis at true value $e_{0.01\mathrm{Hz}}=0.1$. The orange (blue) curve shows the Gaussian (heterodyned) log-likelihood ratio. The red band marks the 90% credible interval of the one-dimensional posterior for $e_{0.01\mathrm{Hz}}$ from Fig. \ref{['pe']}. To better highlight differences between the likelihood models, here we assume zero-noise data.
• Figure 4: Sky maps of the network SNR for a GW190521-like source observed with TianQin (top), LISA (middle), and the joint TianQin+LISA network (bottom). The white contour on the TianQin panel marks sky locations where $\mathrm{SNR}_{\rm TQ}=\mathrm{SNR}_{\rm LISA}$ for this setup.