Detecting the anisotropic astrophysical gravitational wave background in the presence of shot noise through cross-correlations

Abstract

The spatial and temporal discreteness of gravitational wave sources leads to shot noise that may, in some regimes, swamp any attempts at measuring the anisotropy of the gravitational wave background. Crosscorrelating a gravitational wave background map with a sufficiently dense galaxy survey can alleviate this issue, and potentially recover some of the underlying properties of the gravitational wave background. We quantify the shot noise level and we explicitly show that cross-correlating the gravitational wave background and a galaxy catalog improves the chances of a first detection of the background anisotropy with a gravitational wave observatory operating in the frequency range (10 Hz, 100 Hz), given sufficient sensitivity.

The $N_\ell$ of gravitational wave background experiments

“…As was shown in [33,34,36], in the frequency band of ground-based interferometers, the astrophysical background is dominated by a "pop-corn" component associated to the discreteness in time of binary merger events, which has a larger amplitude than the clustering component and depend on the horizon for the detectability of resolvable events (see [34,36]). Figure 13 shows these two components of the power spectrum for the astrophysical GWB for two different distance cutoffs d (i.e.…”

“…In particular, we have presented results for astrophysical GWBs arising from binary mergers, since we expect this to be the dominant signal (see e.g. [34,36,45,60,[65][66][67][68][69][70]). This means that, in our choice of E f we have chosen a power law with spectral index α I = −7/3, corresponding to a slope in energy den-sity Ω GW ∝ f α with α = 2/3 = −3 + α I .…”

“…a fixed background), Eq. ( 52) depends on different parameters: the observation time T obs , the baseline b AB For each choice we plot the contribution from clustering (∝ 1/ ) and the contribution from Poisson noise (flat off-set) [34,36].…”

“…This approach would not be able to measure the anisotropy over the whole sky, but, if successful it would provide a localised measurement of the GWB. Cross-correlated searches with large scale structure are expected to improve the SNR of auto-correlation by typically a factor 10 [36]. The potential of cross-correlation, while not sufficient to get a detection of the anisotropy for present and planned instrumental noise levels, should be kept in mind when looking at new detection strategies.…”

“…[32] for a recent review on the topic. We will not include, in the derivation of our instrumental noise model, the shot noise that arises from discrete GW sources, a topic which has been discussed elsewhere [33][34][35][36]. Nevertheless, it must be included in the noise budget if one wishes to produce accurate forecasts of the signal to noise for planned observations.…”