Predicting the Number of Radio Sources Seen by Both VLASS and LSST

Abstract: Radio surveys typically sample extragalactic sources in higher redshift regimes than is typical for optical surveys, resulting in many radio sources not having a detected optical counterpart. Over the next decade the Legacy Survey of Space and Time (LSST) will be performing the deepest ($i < 26.4\,$mag) wide-area optical survey to date increasing the fraction of radio sources for which we have optical data. In this Research Note we use the Hyper Suprime-Cam survey to analyse how the fraction of radio sources in the Very Large Array Sky Survey (VLASS) with optical detections varies as a function of $i$-band magnitude and extrapolate to predict the number of optical counterparts we expect LSST to detect. Assuming a final VLASS point source depth of $S_{3\,\text{GHz}}\lesssim350\,\mu$Jy, we expect LSST to identify optical counterparts to $\sim 10^6$ radio sources in VLASS.