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

## TL;DR

This paper introduces new tools and a data analysis method to evaluate and reconstruct the spectral shape of a stochastic gravitational wave background using LISA, demonstrating LISA's capability to accurately recover various spectral profiles.

## Contribution

The paper presents a novel adaptive data analysis technique and the SGWBinner code for reconstructing arbitrary spectral shapes of SGWBs with LISA, based on updated sensitivity curves.

## Key findings

- LISA can effectively reconstruct the spectral shape of diverse SGWB signals.
- The proposed method accurately fits the spectral profile within frequency bins.
- The tools are adaptable to other gravitational wave observatories.

## 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.