Limiting Magnitudes of the Wide Field Survey Telescope (WFST)

Abstract: Expected to be of the highest survey power telescope in the northern hemisphere, the Wide Field Survey Telescope (WFST) will begin its routine observations of the northern sky since 2023. WFST will produce a lot of scientific data to support the researches of time-domain astronomy, asteroids and the solar system, galaxy formation and cosmology and so on. We estimated that the 5 $\sigma$ limiting magnitudes of WFST with 30 second exposure are $u=22.31$ mag, $g=23.42$ mag, $r=22.95$ mag, $i=22.43$ mag, $z=21.50$ mag, $w=23.61$ mag. The above values are calculated for the conditions of $airmass=1.2$, seeing = 0.75 arcsec, precipitable water vapour (PWV) = 2.5 mm and Moon-object separation = $45<sup>{\circ}$ at the darkest New Moon night of the Lenghu site (V=22.30 mag, Moon phase $\theta=0<sup>{\circ}$). The limiting magnitudes in different Moon phase conditions are also calculated. The calculations are based on the empirical transmittance data of WFST optics, the vendor provided CCD quantum efficiency, the atmospherical model transmittance and spectrum of the site. In the absence of measurement data such as sky transmittance and spectrum, we use model data.