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 $\sim$ 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 OGLE (Optical Gravitational Lensing Experiment) 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 ~7,000 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=$22\pm4^{\circ }$ relative to the plane of the sky and position angle of the line of nodes $\theta=167\pm7^{\circ }$ (measured from north to east). The north-eastern part of the ellipsoid is closer to us and no particular associated substructures are detected as well as any metallicity gradient.