A 0.3 per cent calibration of the W UMa-type contact binary luminosity based on <i>Gaia</i> DR3

ABSTRACT W Ursa Majoris-type contact binary systems (CBs) with period–luminosity (PL) relations are valuable distance indicators. The PL relations of CBs are affected by metallicity. Here, we establish PL relations and period–luminosity–metallicity (PLZ) relations in nine bands from optical to mid-infrared ($BP$, G, $RP$, J, H, $K_S$, $W1$, $W2$, and $W3$) and in five Wesenheit bands based on Gaia Data Release 3 parallaxes. The dispersion of PLZ relations gradually decreases from the optical to mid-infrared bands, with the minimum dispersion of 0.138 mag. We fit the best PL relations for three bands ($W1$, $W_{G,BP,RP}$, and $W_{W1,BP,RP}$) under different parallax uncertainty criteria and determine a parallax (after correction) zero-point of ${\rm zp}_\varpi =24\pm 4$ $\mu$as. After fixing the parallax zero-point, we find that the total zero errors of the PL and PLZ relations are smallest when the parallax uncertainty is less than 2 per cent, resulting in a calibrated CB luminosity with an accuracy of 0.33 per cent, which is more accurate than the classical Cepheids. Furthermore, by examining the absolute magnitude residuals in different metallicity intervals, we find that the use of a linear metallicity effect is appropriate for CBs with different metallicities. These results indicate that CBs are excellent standard candles.