Paper: Signal-to-noise in gravitational-wave detection

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Common-spectrum process versus cross-correlation for gravitational-wave searches using pulsar timing arrays, by Joseph D. Romano, Jeffrey S. Hazboun, Xavier Siemens, and Anne M. Archibald

Pulsar timing arrays are trying to detect gravitational waves with periods of years by sensing their effect on the arrival time of pulses from pulsars all over the sky. A gravitational wave passing over the Earth compresses space in some directions and expands it in others, and this should produce a correlated pattern of delays between multiple pulsars. At these frequencies, the signal we expect to detect is a mixture of gravitational waves from all the supermassive black hole binaries in the Universe; this should look like random noise with a power-law spectrum, strongest at the lowest frequencies. Recently, NANOGrav detected hints of such a spectrum. It detected these hints not in the cross-correlations between pulsars, but as a common spectrum of noise in the autocorrelations of individual pulsars. By contrast, LIGO’s attempt to detect a stochastic gravitational-wave background is expected to find evidence in the cross-correlations first. (And of course we will find cross-correlations much more convincing evidence for a gravitational-wave origin than auto-correlations – there are many fewer alternative sources of cross-correlated noise.) So why did NANOGrav find evidence first in the autocorrelations? This paper uses a simple toy model to explain why.

The gravitational-wave signal, with a “red” spectrum where the lowest frequencies dominate, must be distinguished from pulsar intrinsic noise, which is largely the same at all frequencies. If the non-gravitational noise dominated even at low frequencies, as it does for LIGO, then the cross-correlations provide greater averaging and a detection will happen first in the cross-correlations. If the gravitational-wave signal is stronger than the noise at low frequencies, as it is for current pulsar timing arrays, then what limits our ability to characterize it is the fact that it is itself a noise process – its own intrinsic variance limits our ability to measure it well enough to believe it is real. In this case the cross-correlations no longer have independent noise, and averaging them provides much less benefit. In this situation, the paper shows, autocorrelations have a higher signal-to-noise.