Blind-search constraints on the sub-kiloparsec population of continuous gravitational-wave sources

We use the latest all-sky continuous gravitational-wave (CW) searches to estimate constraints on the sub-kiloparsec population of unknown neutron stars (NS). We then extend this analysis to the forthcoming LIGO-Virgo-KAGRA observing runs and the third generation (3G) of ground-based interferometric detectors (Einstein Telescope and Cosmic Explorer). We find that sources with ellipticities greater than $\epsilon \gtrsim {10}^{-7}$ can be well-constrained by current and future detectors regardless of their frequency. 3G detectors will extend these constraints down to $\epsilon \gtrsim {10}^{-8}$ across the whole sensitive band and $\epsilon \gtrsim {10}^{-9}$ above $1\text{kHz}$. We do not expect $\epsilon \lesssim {10}^{-8}$ sources to be constrained below $1\text{kHz}$. Finally, we discuss the potential impact of using astronomical priors on all-sky searches in terms of sensitivity and computing cost. The populations here described can be used as a guide to set up future all-sky CW searches.