Searches for continuous gravitational waves from textit{unknown} Galactic neutron stars provide limits on the shapes of neutron stars. A rotating neutron star will produce gravitational waves if asymmetric deformations exist in its structure that are characterized by the stars ellipticity. In this study, we use a simple model of the spatial and spin distribution of Galactic neutron stars to estimate the total number of neutron stars probed, using gravitational waves, to a given upper limit on the ellipticity. This may help optimize future searches with improved sensitivity. The improved sensitivity of third-generation gravitational wave detectors may increase the number of neutron stars probed, to a given ellipticity, by factors of 100 to 1000.
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