A flexible, GPU-accelerated approach for the joint characterization of LISA instrumental noise and Stochastic Gravitational Wave Backgrounds

TL;DR

The paper tackles the challenge of jointly inferring LISA instrumental noise and stochastic gravitational-wave backgrounds when exact spectral shapes are uncertain. It proposes a data-driven framework that represents arbitrary perturbations to both noise and signal spectra with Akima splines and performs Bayesian inference via Reversible Jump MCMC on the AET TDI channels, enabling adaptive model complexity. A two-step procedure first fits baseline templates and then allows spline deviations, improving convergence while quantifying the impact of spectral flexibility on SGWB detectability. Validation on simulations including a cosmic-string SGWB shows that splines can absorb spectral power and reduce detection strength (e.g., from a Bayes factor of about 6515.65 for templates to 6.54 with splines), while still recovering the injected spectra; the approach is GPU-accelerated for feasible global fits and sets the stage for more realistic LISA data challenges.

Abstract

LISA data analysis represents one of the most challenging tasks ahead for the future of gravitational-wave (GW) astronomy. Characterizing the instrument's noise properties while fitting for all the other detectable sources is a key requirement of any robust inference pipeline. Noise estimation will also play a crucial role in searches and parameter estimation of cosmological and astrophysical stochastic signals. Previous studies have tackled this topic by assuming perfect knowledge of the spectral shape of the instrumental noise and of different possible types of GW Stochastic Backgrounds (SGWBs), usually resorting to parametrized templates. Recently, various works that employ template-agnostic methods have been presented. In this work, we take an additional step further, introducing flexible spectral shapes in both the instrumental noise and the stochastic signals. We account for the lack of knowledge of the exact shape of the individual contributions to the overall power spectral density by using splines to represent arbitrary perturbations of the noise and signal spectral densities. We implement a data-driven Reversible Jump MCMC algorithm to fit different components simultaneously and to infer the level of flexibility required under different scenarios. We test this approach on simulated LISA data produced under different assumptions. We investigate the impact of this increased flexibility on the reconstruction of both the injected signal and the noise level, and we discuss the prospects for claiming a successful SGWB detection.

Figures (6)

• Figure 1: Reconstructed posterior distribution of the different contributions to the total PSD in the $A$ channel. The black dashed (dash-dotted) line represents the PSD used to generate the noise (SGWB from cosmic strings) dataset. The averaged data periodogram is shown as a grey line. Blue (orange) lines and filled contours represent medians and $90\, \%$ credible regions for the reconstructed noise (signal) PSD when both contributions are present in the model. Red lines and contours refer to the case where only the noise has been used to fit the totality of the data. Insets show a zoom-in on the region $f \in [2.5, \, 4]\, \rm mHz$. Left panel: Result of the analysis performed using only the baseline templates Right panel: Result of the analysis performed introducing splines in the model.
• Figure 2: Posteriors on the number of in-between spline knots for the datastream containing noise and an SGWB due to cosmic strings. Blue (orange) bars refer to the noise in the $A$ channel (signal) contribution. Red bars refer to the analysis performed only with the noise component.
• Figure 3: Posterior distribution of reconstructed total PSD in the three TDI channels at a reference frequency of $\bar{f}=10^{-3} \, \rm Hz$, for the datastream containing noise and an SGWB due to cosmic strings. Black solid lines represent the values evaluated at the injected parameters. 2D contours represent the $1-\sigma$ and $2-\sigma$ regions, while the 1D shaded areas represent $95\%$ credible regions.
• Figure 4: Reconstructed posterior distribution of the reconstruction of the total PSD in the $A$ channel. The black dashed (dash-dotted) line represents the "perturbed" PSD used to generate the noise dataset (the base noise PSD before applying the spline perturbation). The averaged data periodogram is shown as a grey line. Blue lines and filled contours represent the median and $90\%$ credible interval for the reconstructed noise PSD. The inset shows a zoom-in on the region $f \in [3.1,\,4]\, \rm mHz$.
• Figure 5: Posteriors on the number of in-between spline knots for the datastream containing only noise generated from the "perturbed" PSD.