Reconstructing the spectral shape of a stochastic gravitational wave background with LISA

TL;DR

The paper tackles the challenge of detecting and reconstructing a stochastic gravitational wave background with LISA when the spectral shape may be complex. It introduces a bin-by-bin reconstruction approach implemented in the SGWBinner code, combining per-bin power-law fits with an Akaike Information Criterion-based bin merging to recover arbitrary spectra. By applying this method to a suite of mock SGWB shapes (including simple, broken, single/double-peaked, and wiggly spectra), the authors demonstrate that LISA can recover spectral features beyond simple power laws and distinguish potential sources, given sufficient SNR. They also quantify a practical SNR threshold (≈10) for detectability and outline how their framework can be extended to other detectors and refined noise models, offering a robust first-pass tool for SGWB characterization.

Abstract

We present a set of tools to assess the capabilities of LISA to detect and reconstruct the spectral shape and amplitude of a stochastic gravitational wave background (SGWB). We first provide the LISA power-law sensitivity curve and binned power-law sensitivity curves, based on the latest updates on the LISA design. These curves are useful to make a qualitative assessment of the detection and reconstruction prospects of a SGWB. For a quantitative reconstruction of a SGWB with arbitrary power spectrum shape, we propose a novel data analysis technique: by means of an automatized adaptive procedure, we conveniently split the LISA sensitivity band into frequency bins, and fit the data inside each bin with a power law signal plus a model of the instrumental noise. We apply the procedure to SGWB signals with a variety of representative frequency profiles, and prove that LISA can reconstruct their spectral shape. Our procedure, implemented in the code SGWBinner, is suitable for homogeneous and isotropic SGWBs detectable at LISA, and it is also expected to work for other gravitational wave observatories.

Figures (14)

• Figure 1: LISA strain sensitivity curve for the TDI-X channel: Green, the output from the LISA simulator; Black, the analytical evaluation given in eq. \ref{['eq:Sn']}. The orange band shows the allowed margin on the noise parameters $P=15\pm 20\%$ and $A=3\pm 20\%$.
• Figure 2: Blue, dotted: $h^2\Omega_s(f)$ evaluated with the strain sensitivity $S_n(f)$ output from the LISA simulator (c.f. fig. \ref{['fig:sens_curve']}). Red, solid: the LISA PLS for ${\rm SNR}_{\rm thr}=10$ and $T=3$ year, corresponding to $\sim 75\%$ of the nominal 4-year mission duration, which is the data taking efficiency of LISA.
• Figure 3: Red curve: LISA PLS with ${\rm SNR}_{\rm thr}=10$ and $T=3$ years. Black curve: the binned LISA PLS, from left to right and top to bottom, with $N=3$, $N=5$, $N=10$, $N=20$.
• Figure 4: Simulated data, sensitivity curves, input signal (not visible as it is covered by the error band of the reconstructed signal), and reconstructed signal and sensitivity by means of the SGWBinner code. See the main text for a detailed explanation.
• Figure 5: Best fit and $1$ and $2 \sigma$ contour lines for the amplitude and slope of the reconstructed signal in the central bin visible in fig. \ref{['fig:example1']}. The blue mark shows the input signal parameters.