Detection of radio emission from stars via proper-motion searches

We present a method for identifying radio stellar sources using their proper-motion. We demonstrate this method using the FIRST, VLASS, RACS-low and RACS-mid radio surveys, and astrometric information from Gaia Data Release 3. We find eight stellar radio sources using this method, two of which have not previously been identified in the literature as radio stars. We determine that this method probes distances of similar to 90pc when we use FIRST and RACS-mid, and similar to 250pc when we use FIRST and VLASS. We investigate the time baselines required by current and future radio sky surveys to detect the eight sources we found, with the SKA (6.7 GHz) requiring <3 yr between observations to find all eight sources. We also identify nine previously known and 43 candidate variable radio stellar sources that are detected in FIRST (1.4 GHz) but are not detected in RACS-mid (1.37 GHz). This shows that many stellar radio sources are variable, and that surveys with multiple epochs can detect a more complete sample of stellar radio sources.