Title: Discovery of RR Lyrae in the Ultra-Faint Dwarf Galaxy Virgo III

Abstract: Virgo III is a newly discovered ultra-faint dwarf (UFD) candidate, and finding RR Lyrae associated with this galaxy is important to constrain its distance. In this work, we present a search of RR Lyrae in the vicinity of Virgo III based on the time-series $r$-band images taken from the Lulin One-meter Telescope (LOT). We have identified three RR Lyrae from our LOT data, including two fundamental mode (ab-type) and a first-overtone (c-type) RR Lyrae. Assuming these three RR Lyrae are members of Virgo III, we derived the distance to this UFD as $154\pm25$ kpc, fully consistent with the independent measurements given in the literature. We have also revisited the relation between absolute $V$-band magnitude ($M_V$) and the number of RR Lyrae (of all types, $N_{RRL}$) found in local galaxies, demonstrating that the $M_V$-$N_{RRL}$ relation is better described with the specific RR Lyrae frequency.