We present time-series observations of Population ii 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 Gaia DR1 for VY Pyx and the 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 \mu _ { LMC } = 18.54 \pm 0.08 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 2 \sigma ) with estimates based on the M _ { V } - [ Fe / H ] relation for horizontal branch stars .