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±0.0546(statistical)±0.4628(systematic)kpc,
equivalently μLMC​=18.5056±0.0024(statistical)±0.02(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∘±0.80∘ at a position angle of
62∘, 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.Comment: 7 pages, 8 figure