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 an NS, is encoded in a dimension-less parameter s called ellipticity. Searches for CW signals from isolated Galactic NSs have shown to be sensitive to ellipticities as low as epsilon similar to O(10(-9)). These searches are optimal for detecting and characterizing GWs from individual NSs, but they are not designed to measure the properties of NSs as population, such as the average ellipticity epsilon(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 an SGWB signal, we set upper limits on the dimension-less energy density parameter Omega(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-band. We find epsilon(av) less than or similar to 1.8 x 10(-8), with N-band = 1.6 x 10(7), for Galactic NSs, and epsilon(av) less than or similar to [3.5 - 11.8] x 10(-7) , with N-band = 1.6 x 10(10), for NS hotspots.