The Detailed Forms of the LMC Cepheid PL and PLC Relations

TL;DR

This study investigates the linearity of the LMC Cepheid Period-Luminosity and Period-Luminosity-Color relations using OGLE and MACHO datasets, revealing nonlinearity and complex interactions, especially in the MACHO data.

Contribution

It demonstrates that the LMC Cepheid PL and PLC relations are non-linear, with significant color dependence and interactions, challenging the assumption of linearity in these relations.

Findings

Neither PL relation is linear according to nonparametric tests.

Color dependence in the relations is nonlinear, especially in MACHO data.

Interaction between period and color functions is significant in MACHO data.

Abstract

Possible deviations from linearity of the LMC Cepheid PL and PLC relations are investigated. Two datasets are studied, respectively from the OGLE and MACHO projects. A nonparametric test, based on linear regression residuals, suggests that neither PL relation is linear. If colour dependence is allowed for then the MACHO PL relation is found to deviate more significantly from the linear, while the OGLE PL relation is consistent with linearity. These finding are confirmed by fitting "Generalised Additive Models" (nonparametric regression functions) to the two datasets. Colour dependence is shown to be nonlinear in both datasets, distinctly so in the case of the MACHO Cepheids. It is also shown that there is interaction between the period and colour functions in the MACHO data.