The independence of the mid-infrared RR Lyrae Period-Luminosity relation from metallicity from a study of three globular clusters in the Large Magellanic Cloud

RR Lyrae are pulsating variable stars tracing old (>10 Gyr) stellar populations, and exhibit a strong mid-infrared Period-Luminosity (PL) relation that can be calibrated with known parallaxes to infer distances. Here we present Period-Luminosity relations and distance moduli for three isolated globular clusters in the Large Magellanic Cloud: Reticulum, NGC 1841, and NGC 1466. Our analysis uses legacy Spitzer Space Telescope images obtained by the Carnegie RR Lyrae Program, and an internally self-consistent sample restricted to RRab stars, with cluster membership confirmed using Gaia DR3 proper motions and photometry. In the Spitzer 3.6 μm band, we simultaneously fit a PL for these clusters using a slope derived from Galactic Globular Clusters, yielding extinction-corrected distance moduli of 18.47 ± 0.09 mag for Reticulum, 18.29 ± 0.09 mag for NGC 1841, and 18.61 ± 0.09 mag for NGC 1466. The latter two are the first RR Lyrae PL-based distance moduli for these clusters, and all three are consistent with literature values from other techniques. Additionally we fit a PL with slope as a free parameter, and find that this LMC-derived PL is consistent with that derived from Galactic GCs. Simultaneously fitting a PLZ for the three clusters yields a metallicity coefficient c = −0.03 ± 0.05 mag dex−1 which can be considered a negligible dependence of the PL on metallicity (|c| < 0.1 mag dex−1). Modelling an intrinsic width, W, to the PL/ PLZ yields a consistent value W ≈ 0.1 ± 0.02 mag, suggesting intrinsic width is not driven by metallicity.