PTA-Compatible Domain Walls at LISA and Taiji: Bayesian Reconstruction and Multiband Inference

Abstract

Domain walls provide an excellent fit to Pulsar Timing Array (PTA) data. A distinctive feature of the associated gravitational-wave (GW) spectrum is its ultraviolet (UV) tail, which can extend into the mHz band and thereby make cross-detection with space-based interferometers such as LISA and Taiji possible. In this work, we explore the PTA-compatible parameter space of domain-wall models and study both the reconstruction prospects at LISA and Taiji and the information gain achievable through joint PTA--LISA and PTA--Taiji analyses. We find that LISA and Taiji can probe an extended region of parameter space yielding an ultraviolet tail in the milli-Hz band, even in the presence of astrophysical foregrounds. Within the PTA-supported region, however, the genuinely informative regime is more restricted and concentrated toward the high-signal edge. In the space-based-detector-only analysis, the posterior is strongly degenerate in the underlying model parameters, although one principal parameter combination can be reconstructed with high precision where the signal is sufficiently strong. When PTA-informed priors are incorporated, the additional information gain is localized to the same high-signal region: there the space-based data produce a non-negligible posterior update and strongly suppress the catastrophic LISA(Taiji)-only degeneracy, while the final posterior often retains an axis ratio comparable to that of PTA alone. Our analysis is based on a 10-dimensional Bayesian inference with two domain-wall signal parameters and eight nuisance parameters describing instrumental noise and astrophysical foregrounds. We use 49 grid injections for the LISA-only and Taiji-only analyses and 65 injections from the PTA-supported region for the joint analyses, with Clough--Tocher interpolation used to construct posterior heat maps.