Statistical Tests for the Metallicity Dependency of the Synthetic Cepheid Period-Luminosity Relations in IRAC Bands

The mid-infrared (MIR) period-luminosity (P-L) relations for Cepheids will be important in the JWST era, as it holds the promise of deriving the Hubble constant within 2% accuracy. It is expected that the MIR P-L to be insensitive to metallicity. In this work, we test this assumption of metallicity independent of the IRAC band P-L relation by applying well-known statistical methods to the synthetic P-L slopes from a series of pulsating models with known metallicity. The statistical tests suggest that the P-L slopes in MIR are linearly depending on metallicity.