Estimating the angular power spectrum of the gravitational-wave background in the presence of shot noise

Abstract

There has been much recent interest in studying anisotropies in the astrophysical gravitational-wave (GW) background, as these could provide us with interesting new information about galaxy clustering and large-scale structure. However, this information is obscured by shot noise, caused by the finite number of GW sources that contribute to the background at any given time. We develop a new method for estimating the angular spectrum of anisotropies, based on the principle of combining statistically-independent data segments. We show that this gives an unbiased estimate of the true, astrophysical spectrum, removing the offset due to shot noise power, and that in the limit of many data segments, it is the most efficient (i.e. lowest-variance) estimator possible.

Search for anisotropic gravitational-wave backgrounds using data from Advanced LIGO and Advanced Virgo’s first three observing runs

“…The background may also include signals of cosmological origin, i.e., produced in the early Universe during an inflationary epoch [19][20][21][22][23][24][25][26][27], or as a direct result of phase transitions [28][29][30], primordial black hole mergers [31][32][33][34], or other associated phenomena [35]. Different models could, in principle, be distinguished by characteristic features in the angular distribution [36][37][38][39][40][41][42][43][44][45][46][47]. For example, cosmic strings have an angular power spectrum which is sharply peaked at small multipoles [48,49], while neutron stars in our Galaxy would trace out the Galactic plane [50,51].…”

Projection effects on the observed angular spectrum of the astrophysical stochastic gravitational wave background

“…Other predictions for the GW angular power spectrum have been derived in [18,19], with both analytical and numerical results using galaxy catalogs from the Millennium Simulation. More recently, [20][21][22] have analyzed the astrophysical dependence of the angular power spectrum for different stellar models, while in [23,24] the effect of shot noise on the angular power spectrum has been considered, and a new method to extract the true astrophysical spectrum by combining statistically independent data segments has been proposed.…”

Cross-correlation of the astrophysical gravitational-wave background with galaxy clustering

“…Note in particular that the magnitude of the signal changes drastically with k max , meaning that the autocorrelation signal depends heavily on the shape of the low redshift power spectrum on nonlinear scales. This is likely one of the causes behind the discrepancy between Jenkins et al and Cusin et al and suggests that an accurate prediction of the autocorrelation signal should take into account not only the shot-noise contribution [38,44], but also the uncertainties due to baryonic effects in the matter distribution at small scales [50,51]. We point out, in particular, that the galaxy catalogue based on dark-matteronly simulations of [52] and the HaloFit model of [53] are not designed to consistently or accurately model this uncertainty.…”

“…In this section, we discuss the autocorrelation signal of the anisotropic GWB. This signal, as well as the shot-noise contamination, have been extensively studied in previous works [25,38,44]. Here, we review the main aspects of modelling these and describe some particularities.…”