Non-stationary astrophysical stochastic gravitational-wave background: a new probe to the high-redshift population of binary black holes

The astrophysical stochastic gravitational-wave background (SGWB) originates from the mergers of compact binary objects that are otherwise undetected as individual events, along with other sources such as supernovae, magnetars, etc. The individual gravitational-wave (GW) signal is time-varying over a time-scale that depends on the chirp mass of the coalescing binaries. Another time-scale that plays a role is the time-scale at which the sources repeat, which depends on the merger rate. The combined effect of these two leads to a breakdown of the time translation symmetry of the observed SGWB and a correlation between different frequency modes in the signal covariance matrix of the SGWB. Using an ensemble of SGWB due to binary black hole coalescence, calculated using simulations of different black hole mass distributions and merger rates, we show how the structure of the signal covariance matrix varies. This structure in the signal covariance matrix brings additional information about the sources on top of the power spectrum. We show that there is a significant improvement in the figure of merit by using this additional information in comparison to only power spectrum estimation for the LIGO-Virgo-KAGRA (LVK) network of detectors with the design sensitivity noise with 2 yr of observation. The inclusion of the off-diagonal correlation in the covariance of the SGWB in the data analysis pipelines will be beneficial in the quest for the SGWB signal in LVK frequency bands as well as in lower frequencies and in getting an insight into its origin.