Wesenheit function for Galactic Cepheids: Application to the projection factors

Galactic Cepheids are necessary tools for calibrating the period-luminosity relation, but distances to individual Galactic Cepheids are difficult to measure precisely and their application is limited to a small number of techniques, such as direct parallax measurements, main-sequence fitting to open clusters that host Cepheids, and Baade-Wesselink (BW)-type methods. Here, we re-examine the application of Wesenheit functions in determining distances to more than 300 Galactic Cepheids by taking advantage of the fact that the Wesenheit function is extinction-free by definition. Wesenheit distances are used to calibrate the projection (p) factor for Galactic Cepheids that also have BW distances. Based on ~ 70 Cepheids, we find that the period-p-factor relation may exhibit a nonlinear trend with a considerable scatter. We found discrepant p factors for δ Cephei in the literature. This may be due to inconsistent measurements of its angular diameter using different empirical techniques. We discuss the reason for the inconsistency in angular-diameter measurements and offer a possible remedy.