Zwicky Transient Facility and Globular Clusters: The Period-Luminosity and Period-Wesenheit Relations for Type II Cepheids

We present the first gri-band period-luminosity (PL) and period-Wesenheit (PW) relations for 37 Type II Cepheids (hereafter TIIC) located in 18 globular clusters based on photometric data from the Zwicky Transient Facility. We also updated BV IJHK-band absolute magnitudes for 58 TIIC in 24 globular clusters using the latest homogeneous distances to the globular clusters. The slopes of g/r/i and B/V/I band PL relations are found to be statistically consistent when using the same sample of distance and reddening. We employed the calibration of ri-band PL/PW relations in globular clusters to estimate a distance to M31 based on a sample of ~270 TIIC from the PAndromeda project. The distance modulus to M31, obtained using calibrated ri-band PW relation, agrees well with the recent determination based on classical Cepheids. However, distance moduli derived using the calibrated r- and i-band PL relations are systematically smaller by ~0.2 mag, suggesting there are possible additional systematic error on the PL relations. Finally, we also derive the period-color (PC) relations and for the first time the period-Q-index (PQ) relations, where the Q-index is reddening-free, for our sample of TIIC. The PC relations based on (r-i) and near-infrared colors and the PQ relations are found to be relatively independent of the pulsation periods.