Background information: A study on the sensitivity of astrophysical gravitational-wave background searches

The vast majority of gravitational-wave signals from stellar-mass compact binary mergers are too weak to be individually detected with present-day instruments and instead contribute to a faint, persistent background. This astrophysical background is targeted by searches that model the gravitational-wave ensemble collectively with a small set of parameters. The traditional search models the background as a stochastic field and estimates its amplitude by cross-correlating data from multiple interferometers. A different search uses gravitational-wave templates to marginalize over all individual event parameters and measure the duty cycle and population properties of binary mergers. Both searches ultimately estimate the total merger rate of compact binaries and are expected to yield a detection in the coming years. Given the conceptual and methodological differences between them, though, it is not well understood how their results should be mutually interpreted. In particular, when a detection of an astrophysical compact binary background is claimed by either approach, which portion of the population is in fact contributing to this detection? In this paper, we use the Fisher information to study the implications of a background detection in terms of which region of the Universe each approach probes. Specifically, we quantify how information about the compact binary merger rate is accumulated by each search as a function of the event redshift. For the LIGO design sensitivity and a uniform-in-comoving-volume distribution of equal-mass 30⁢𝑀⊙ binaries, the traditional cross-correlation search obtains 99% of its information from binaries up to redshift 2.5 (average signal-to-noise ratio <8), and the template-based search from binaries up to redshift 1.0 (average signal-to-noise ratio ∼8). While we do not calculate the total information accumulated by each search, our analysis emphasizes the need to pair any claimed detection of the stochastic background with an assessment of which binaries contribute to said detection. In the process, we also clarify the astrophysical assumptions imposed by each search.