Optical and near-infrared pulsation properties of RR Lyrae and
  Population II Cepheid variables in the Messier 15 globular cluster
  Messier 15 (NGC 7078) is an old and metal-poor post core-collapse globular
cluster which hosts a rich population of variable stars. We report new optical
($gi$) and near-infrared (NIR, $JK_s$) multi-epoch observations for 129 RR
Lyrae, 4 Population II Cepheids (3 BL Herculis, 1 W Virginis), and 1 anomalous
Cepheid variable candidate in M15 obtained using the MegaCam and the WIRCam
instruments on the 3.6-m Canada-France-Hawaii Telescope. Multi-band data are
used to improve the periods and classification of variable stars, and determine
accurate mean magnitudes and pulsational amplitudes from the light curves
fitted with optical and NIR templates. We derive optical and NIR
period-luminosity relations for RR Lyrae stars which are best constrained in
the $K_s$-band, $m_{K_s} = -2.333~(0.054) \log P + 13.948~(0.015)$ with a
scatter of only $0.037$ mag. Theoretical and empirical calibrations of RR Lyrae
period-luminosity-metallicity relations are used to derive a true distance
modulus to M15: $15.196~\pm~0.026$~(statistical)~$\pm~ 0.039$~(systematic) mag.
Our precise distance moduli based on RR Lyrae stars and Population II Cepheid
variables are mutually consistent and agree with recent distance measurements
in the literature based on {\it Gaia} parallaxes and other independent methods.
