Sensitivity curves for searches for gravitational-wave backgrounds

Understand

We propose a graphical representation of detector sensitivity curves for stochastic gravitational-wave backgrounds that takes into account the increase in sensitivity that comes from integrating over frequency in addition to integrating over time.

• This method is valid for backgrounds that have a power-law spectrum in the analysis band.
• We call these graphs "power-law integrated curves." For simplicity, we consider cross-correlation searches for unpolarized and isotropic stochastic backgrounds using two or more detectors.
• We apply our method to construct power-law integrated sensitivity curves for second-generation ground-based detectors such as Advanced LIGO, space-based detectors such as LISA and the Big Bang Observer, and timing residuals from a pulsar timing array.