Radio Afterglows from Compact Binary Coalescences: Prospects for Next-Generation Telescopes.

The detection of gravitational waves from a neutron star merger, GW170817, marked the dawn of a new era in time-domain astronomy. Monitoring of the radio emission produced by the merger, including high-resolution radio imaging, enabled measurements of merger properties including the energetics and inclination angle. In this work we compare the capabilities of current and future gravitational wave facilities to the sensitivity of radio facilities to quantify the prospects for detecting the radio afterglows of gravitational wave events. We consider three observing strategies to identify future mergers -- widefield follow-up, targeting galaxies within the merger localisation and deep monitoring of known counterparts. We find that while planned radio facilities like the Square Kilometre Array will be capable of detecting mergers at gigaparsec distances, no facilities are sufficiently sensitive to detect mergers at the range of proposed third-generation gravitational wave detectors that would operate starting in the 2030s.