Isotropic stochastic gravitational wave background reconstruction for Taiji constellation

TL;DR

This work develops a pipeline for reconstructing an isotropic SGWB in Taiji's millihertz band, addressing the challenge of separating the stochastic signal from instrument noise in a space-based, single-detector context. It combines template-based parameter estimation with a model-agnostic spectral reconstruction using trans-dimensional MCMC (RJMCMC) to infer $Ω_ ext{gw}(f)$ from cross-correlated TDI observables, while accounting for realistic Taiji features such as unequal armlengths and time-varying detector response. Evaluations on Taiji Data Challenge II training datasets show that, with a known spectral template, the SGWB parameters can be recovered and biases from equal-arm assumptions are mitigated by segmenting data and inverting the full covariance; with a flexible RJMCMC approach, the spectrum can be reconstructed without a fixed template, recovering injected spectra in both astrophysical and cosmological scenarios within the instrument band. The framework advances model-agnostic SGWB spectroscopy for Taiji and provides a public codebase, with planned extensions to include Galactic binaries foreground and anisotropic backgrounds.

Abstract

The stochastic gravitational wave background is a broadband target from diverse astrophysical and cosmological sources. The background falls within the mHz frequency band could become a potential observable for future space-based interferometers. Taiji, a proposed space mission slated for launch in the 2030s, will enable the study of such a background. However, the unique characteristics of space missions pose distinctive challenges for separating the stochastic background from instrumental noise. To address the data analysis requirements, we develop a preliminary pipeline to search for the SGWB and evaluate its performance with Taiji simulation datasets. At present, we demonstrate that the algorithm can successfully recover the parameters of injected background with a known spectral density after setting aside the complication of galactic binaries foreground. Furthermore, by employing the trans-dimensional Markov Chain Monte Carlo method, we extend the analysis to reconstruct the background with unknown spectral morphology.

Figures (10)

• Figure 1: Schematic diagram of Taiji constellation.
• Figure 2: PSDs of various components in A channel. All spectra except for the PT SGWB are selected from 2.8_EQ dataset; the latter are derived from 2.9_EQ dataset. Spectra estimated from observational results are plotted with solid lines, while theoretically calculated spectra are shown with dashed lines. Grey shaded regions denote frequencies notched out in our analysis.
• Figure 3: Posterior distributions for the parameters of astrophysical SGWB in 2.8_EQ dataset. The red lines denote injected values while the vertical dashed lines show the median and $1\sigma$ CI. The shaded regions represent $68\%$ and $95\%$ confidence levels.
• Figure 4: Posterior distributions for ACC and OMS noise amplitudes in 2.8_EQ datasets, arranged in ascending order of SC index $i$ from top to bottom. The red lines denote injected values while the vertical dashed lines show the median and $1\sigma$ CI.
• Figure 5: Posterior distributions for the parameters of astrophysical SGWB in 2.8 dataset. The red lines denote injected values while the vertical dashed lines show the median and $1\sigma$ CI. The Shaded regions represent $68\%$ and $95\%$ confidence levels.