The linearity of the Wesenheit function for the Large Magellanic Cloud Cepheids

There is strong evidence that the period–luminosity (PL) relation for the Large Magellanic Cloud (LMC) Cepheids shows a break at a period around 10 d. Because the LMC PL relation is extensively used in distance scale studies, the non-linearity of the LMC PL relation may affect the results based on this LMC calibrated relation. In this paper we show that this problem can be remedied by using the Wesenheit function in obtaining Cepheid distances. This is because the Wesenheit function is linear, although recent data suggest that the PL and the period–colour (PC) relations that make up the Wesenheit function are not. We test the linearity of the Wesenheit function and find strong evidence that the LMC Wesenheit function is indeed linear. This is because the non-linearity of the PL and PC relations cancel out when the Wesenheit function is constructed. We discuss this result in the context of distance scale applications. We also compare the distance moduli obtained from  μ₀=μ _V ? R (μ _V ?μ _I )  (equivalent to Wesenheit functions) constructed with the linear and the broken LMC PL relations, and we find that the typical difference in distance moduli is  ～ ±0.03 mag  . Hence, the broken LMC PL relation does not seriously affect current distance scale applications. We also discuss the random error calculated with equation  μ₀=μ _V ? R (μ _V ?μ _I )  , and show that there is a correlation term that exists from the calculation of the random error. The calculated random error will be larger if this correlation term is ignored.