摘要：We present the first gri-band period–luminosity (PL) and period–Wesenheit (PW) relations for 37 Type II Cepheids (TIICs) located in 18 globular clusters based on photometric data from the Zwicky Transient Facility. We also updated BVIJHK-band absolute magnitudes for 58 TIICs 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 TIICs 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 errors 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 TIICs. 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.
