The VMC Survey – XLII. Near-infrared period–luminosity relations for RR Lyrae stars and the structure of the Large Magellanic Cloud

We present results from an analysis of ∼29 000 RR Lyrae stars located in the Large Magellanic Cloud (LMC). For these objects, near-infrared time-series photometry from the VISTA survey of the Magellanic Clouds system (VMC) and optical data from the Optical Gravitational Lensing Experiment (OGLE) IV survey and the Gaia Data Release 2 catalogue of confirmed RR Lyrae stars were exploited. Using VMC and OGLE IV magnitudes we derived period–luminosity (PL), period–luminosity–metallicity (PLZ), period–Wesenheit (PW), and period–Wesenheit–metallicity (PWZ) relations in all available bands. More that  7000 RR Lyrae were discarded from the analysis because they appear to be overluminous with respect to the PL relations. The $PL_{K_{\mathrm{s}}}$ relation was used to derive individual distance to ${\sim}22\, 000$ RR Lyrae stars, and study the three-dimensional structure of the LMC. The distribution of the LMC RR Lyrae stars is ellipsoidal with the three axis S 1  = 6.5 kpc, S 2  = 4.6 kpc, and S 3  = 3.7 kpc, inclination i = 22 ± 4° relative to the plane of the sky and position angle of the line of nodes θ = 167 ± 7° (measured from north to east). The north-eastern part of the ellipsoid is closer to us and no particular associated substructures are detected and neither any metallicity gradient.