RR Lyrae Variables in Messier 53: Near-infrared Period-Luminosity Relations and the Calibration Using Gaia Early Data Release 3

We present new near-infrared, JHK(s), period-luminosity relations (PLRs) for RR Lyrae variables in the Messier 53 (M53 or NGC 5024) globular cluster. Multi-epoch JHK(s) observations, obtained with the WIRCam instrument on the 3.6 m Canada-France-Hawaii Telescope, are used for the first time to estimate precise mean magnitudes for 63 RR Lyrae stars in M53 including 29 fundamental-mode (RRab) and 34 first-overtone mode (RRc) variables. The JHK(s)-band PLRs for RR Lyrae stars are best constrained for RRab types with a minimal scatter of 22, 23, and 19 mmag, respectively. The combined sample of RR Lyrae is used to derive the K-s-band PLR,K-s = -23.3(0.063)logP + 15.212(0.016), exhibiting a 1 sigma dispersion of only 0.027 mag. Theoretical period-luminosity-metallicity (PLZ) relations are used to predict parallaxes for 400 Galactic RR Lyrae, resulting in a median parallax zero-point offset of -7 +/- 3 mu as in Gaia Early Data Release 3 (EDR3), which increases to 22 +/- 2 mu as if the parallax corrections are applied. We also estimate a robust distance modulus, mu(M53) = 16.403 +/- 0.024 (statistical) 0.033 (systematic) mag, to M53 based on theoretical calibrations. Homogeneous and precise mean magnitudes for RR Lyrae in M53 together with similar literature data for M3, M4, M5, and omega Cen are used to empirically calibrate a new RR Lyrae PLZ(Ks), relation, Ks= -0.848(0.007) - 2.320(0.006)log P + 0.166(0.011)[Fe/H], anchored with Gaia EDR3 distances and theoretically predicted relations, and to simultaneously estimate precise RR Lyrae-based distances to these globular clusters.