Large Magellanic Cloud Near-Infrared Synoptic Survey. IV. Leavitt Laws for Type II Cepheid Variables

We present time-series observations of Population \rom{2} Cepheids in the Large Magellanic Cloud at near-infrared ($JHK_s$) wavelengths. Our sample consists of 81 variables with accurate periods and optical ($VI$) magnitudes from the OGLE survey, covering various subtypes of pulsators (BL Herculis, W Virginis and RV Tauri). We generate light curve templates using high-quality $I$-band data in the LMC from OGLE and $K_s$-band data in the Galactic Bulge from VVV and use them to obtain robust mean magnitudes. We derive Period-Luminosity (P-L) relations in the near-infrared and Period-Wesenheit (P-W) relations by combining optical and near-infrared data. Our P-L and P-W relations are consistent with published work when excluding long-period RV Tauris. We find that Pop II Cepheids and RR Lyraes follow the same P-L relations in the LMC. Therefore, we use trigonometric parallax from the {\it Gaia DR1} for VY~Pyx and the {\it Hubble Space Telescope} parallaxes for $k$~Pav and 5 RR Lyrae variables to obtain an absolute calibration of the Galactic $K_s$-band P-L relation, resulting in a distance modulus to the LMC of $μ_{\rm LMC} = 18.54\pm0.08$~mag. We update the mean magnitudes of Pop~II Cepheids in Galactic globular clusters using our light curve templates and obtain distance estimates to those systems, anchored to a precise late-type eclipsing binary distance to the LMC. We find the distances to these globular clusters based on Pop~II Cepheids are consistent (within $2σ$) with estimates based on the $M_V-[\rm{Fe}/\rm{H}]$ relation for horizontal branch stars.