We present a Bayesian analysis of the distances to 15,040 Large Magellanic Cloud (LMC) RR Lyrae stars using $V$- and $I$-band light curves from the Optical Gravitational Lensing Experiment, in combination with new $z$-band observations from the Dark Energy Camera. Our median individual RR Lyrae distance statistical error is 1.89 kpc (fractional distance error of 3.76 per cent). We present three-dimensional contour plots of the number density of LMC RR Lyrae stars and measure a distance to the core LMC RR Lyrae centre of ${ 50.2482\pm0.0546 { \rm(statistical)} \pm0.4628 { \rm(systematic)} { \rm kpc}}$, equivalently ${ \mu_{ \rm LMC}=18.5056\pm0.0024 { \rm(statistical)} \pm0.02 { \rm(systematic)}}$. This finding is statistically consistent with and four times more precise than the canonical value determined by a recent meta-analysis of 233 separate LMC distance determinations. We also measure a maximum tilt angle of $11.84^{ \circ}\pm0.80^{ \circ}$ at a position angle of $62^\circ$, and report highly precise constraints on the $V$, $I$, and $z$ RR Lyrae period--magnitude relations. The full dataset of observed mean-flux magnitudes, derived colour excess ${ E(V-I)}$ values, and fitted distances for the 15,040 RR Lyrae stars produced through this work is made available through the publication's associated online data.
Categories: astro-ph.IM astro-ph.GA astro-ph.SR