Direct Distances to Cepheids in the Large Magellanic Cloud: Evidence for a Universal Slope of the Period-Luminosity Relation up to Solar Abundance

We have applied the infrared surface brightness (ISB) technique to derive distances to 13 Cepheid variables in the LMC that span a period range from 3 to 42 days. From the absolute magnitudes of the variables calculated from these distances, we find that the LMC Cepheids define tight period-luminosity (PL) relations in the V, I, W, J, and K bands that agree exceedingly well with the corresponding Galactic PL relations derived from the same technique and are significantly steeper than the LMC PL relations in these bands observed by the OGLE-II Project in V, I, and W and by Persson and coworkers in J and K. We find that the LMC Cepheid distance moduli we derive, after correcting them for the tilt of the LMC bar, depend significantly on the period of the stars, in the sense that the shortest period Cepheids have distance moduli near 18.3, whereas the longest period Cepheids are found to lie near 18.6. Since such a period dependence of the tilt-corrected LMC distance moduli should not exist, there must be a systematic, period-dependent error in the ISB technique not discovered in previous work. We identify as the most likely culprit the p-factor, which is used to convert the observed Cepheid radial velocities into their pulsational velocities. By demanding (1) a zero slope on the distance modulus versus period diagram and (2) a zero mean difference between the ISB and ZAMS fitting distance moduli of a sample of well-established Galactic cluster Cepheids, we find that p = 1.58(±0.02) - 0.15(±0.05) log P, with the p-factor depending more strongly on Cepheid period (and thus luminosity) than indicated by past theoretical calculations. When we recalculate the distances of the LMC Cepheids with the revised p-factor law suggested by our data, we not only obtain consistent distance moduli for all stars but also decrease the slopes in the various LMC PL relations (and particularly in the reddening-independent K and W bands) to values that are consistent with the values observed by OGLE-II and Persson and coworkers. From our 13 Cepheids, we determine the LMC distance modulus to be 18.56 ± 0.04 mag, with an additional estimated systematic uncertainty of ~0.1 mag. Using the same corrected p-factor law to redetermine the distances of the Galactic Cepheids, the new Galactic PL relations are also found consistent with the observed optical and near-infrared PL relations in the LMC. Our main conclusion from the ISB analysis of the LMC Cepheid sample is that, within current uncertainties, there seems to be no significant difference between the slopes of the PL relations in the Milky Way and LMC. With literature data on more metal-poor systems, it seems now possible to conclude that the slope of the Cepheid PL relation is independent of metallicity in the broad range in [Fe/H] from -1.0 dex to solar abundance, within a small uncertainty. The new evidence from the first ISB analysis of a sizable sample of LMC Cepheids suggests that the previous, steeper Galactic PL relations obtained from this technique were caused by an underestimation of the period dependence in the model-based p-factor law used in the previous work. We emphasize, however, that our current results must be substantiated by new theoretical models capable of explaining the steeper period dependence of the p-factor law, and we will also need data on more LMC field Cepheids to rule out remaining concerns about the validity of our current interpretation.