Using Type-II Cepheids as Extragalactic Standard Candles: Distances to M31

Several standard candles have been tested and used to measure accurate extragalactic distances over the past decades. There have been discussions regarding the possibility of using Type-II Cepheids (T2Cs) as an alternative tool, but rarely was this ever implemented. The aim of this project is to assert the use of T2Cs as a new avenue for calibrating the extragalactic distance scale, by using M31 as a benchmark galaxy. Since Ordinary Least Squares regression methods are not immune to outliers and offer an incomplete treatment of the uncertainties, we favor a Bayesian robust regression model to compute new Period--Luminosity (PL) and Period--Wesenheit (PW) relations calibrated using $\sim$100 T2Cs, $\sim$1000 fundamental-mode and $\sim$750 first-overtone classical Cepheids (CCs) in the LMC. Using these relations, we employ a classification routine based on Bhattacharyya distances to filter out any contaminants from the M31 sample. We validate our method by verifying that we retrieve an accurate distance for the LMC. We find a distance to M31 of $24.487\pm0.001$ (statistical) $\pm0.052$ (systematic) mag using CCs and of $24.409\pm0.025$ (statistical) $\pm0.156$ (systematic) mag using T2Cs. Both values are in excellent agreement with literature values derived from meta-analyses, from Hubble Space Telescope (HST) observations of CCs, from the Tip of the Red Giant Branch method, and from HST observations of RR Lyrae. In almost all cases, we reach a relative accuracy better than 98\%, although the archival ground-based data we use cannot compare with HST photometry. We demonstrate that T2Cs can also be used as accurate tracers for determining extragalactic distances, thereby making them excellent candidates for JWST, LSST, and ELT observations. These stars allow us to probe galaxies deprived of young populations and are beyond the reach of the fainter RR Lyrae.