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