The Cepheid Distance Scale: A Novel Method for Obtaining Mean Magnitudes from Single-epoch Observations

We present a novel technique for mapping single-phase observations of Cepheids in any given band into their time-averaged values, using strong priors on the known interrelations of the multiwavelength widths of Cepheid period-luminosity (PL) relations, combined with the physical ordering of individual Cepheids within and across the instability strip, as a function of temperature (or radius). The method is empirically calibrated and tested using high-precision published multiwavelength observations of Cepheids in the LMC. The example, given herein, takes a single-epoch B-band PL relation and transforms those random-phase observations to within +/- 0.05-0.06 mag of their time-averaged values. For high-precision single-phase data points, this method can transform single-phase magnitudes into mean magnitudes (without additional observations), bringing the statistical error budget for the PL relation at that wavelength down to the systematic floor. This technique is of particular importance for use with space-based facilities (e.g., Hubble Space Telescope or JWST) where limits on the availability of telescope time preclude dense phase coverage, often resulting in only single-epoch observations being available.