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Stochastic gravitational-wave background searches and constraints on neutron-star ellipticity

Rotating neutron stars (NSs) are promising sources of gravitational waves (GWs) in the frequency band of ground-based detectors. They are expected to emit quasi-monochromatic, long-duration GW signals, called continuous waves (CWs), due to their deviations from spherical symmetry. The degree of such deformations, and hence the information about the internal structure of a NS, is encoded in a dimensionless parameter $\varepsilon$ called ellipticity. Searches for CW signals from isolated Galactic NSs have shown to be sensitive to ellipticities as low as $\varepsilon \sim \mathcal{O}(10^{-9})$. These searches are optimal for detecting and characterising GWs from individual NSs, but they are not designed to measure the properties of NSs as population, such as the average ellipticity $\varepsilon_{\mathrm{av}}$. These ensemble properties can be determined by the measurement of the stochastic gravitational-wave background (SGWB) arising from the superposition of GW signals from individually-undetectable NSs. In this work, we perform a cross-correlation search for such a SGWB using the data from the first three observation runs of Advanced LIGO and Virgo. Finding no evidence for a SGWB signal, we set upper limits on the dimensionless energy density parameter $Ω_{\mathrm{gw}}(f)$. Using these results, we also constrain the average ellipticity of Galactic NSs and five NS ``hotspots'', as a function of the number of NSs emitting GWs within the frequency band of the search $N_{\mathrm{band}}$. We find $\varepsilon_{\mathrm{av}} \lesssim 1.8 \times 10^{-8}$, with $N_{\mathrm{band}}=1.6 \times 10^7$, for Galactic NSs, and $\varepsilon_{\mathrm{av}} \lesssim [3.5-11.8]\times 10^{-7}$, with $N_{\mathrm{band}}=1.6 \times 10^{10}$, for NS hotspots.