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 μ m 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 plus or minus0.09 mag for Reticulum, 18.29 plus or minus0.09 mag for NGC 1841, and 18.61 plus or minus0.09 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 plus or minus0.05 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 about0.1 plus or minus0.02 mag, suggesting intrinsic width is not driven by metallicity.