  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 star's 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.
