Large Magellanic Cloud Near-Infrared Synoptic Survey. III. A Statistical Study of Non-Linearity in the Leavitt Laws

TL;DR

This study investigates non-linearities in Cepheid variable relations in the LMC across optical and near-infrared wavelengths, revealing period-dependent breaks and their implications for distance measurements.

Contribution

It provides a comprehensive statistical analysis of non-linearities in Cepheid P-L, P-W, and P-C relations, highlighting wavelength-dependent period breaks and their impact on calibrations.

Findings

Optical P-L, P-W, P-C relations are non-linear at 10 days.

Near-infrared P-L and P-W relations are non-linear around 18 days.

A global slope of -3.212±0.013 is determined for the W^H_{V,I} relation.

Abstract

We present a detailed statistical analysis of possible non-linearities in the Period-Luminosity (P-L), Period-Wesenheit (P-W) and Period-Color (P-C) relations for Cepheid variables in the LMC at optical ($VI$) and near-infrared ($JHK_{s}$) wavelengths. We test for the presence of possible non-linearities and determine their statistical significance by applying a variety of robust statistical tests ($F$-test, Random-Walk, Testimator and the Davies test) to optical data from OGLE III and near-infrared data from LMCNISS. For fundamental-mode Cepheids, we find that the optical P-L, P-W and P-C relations are non-linear at 10 days. The near-infrared P-L and the $W^H_{V,I}$ relations are non-linear around 18 days; this break is attributed to a distinct variation in mean Fourier amplitude parameters near this period for longer wavelengths as compared to optical bands. The near-infrared P-W relations are also non-linear except for the $W_{H,K_s}$ relation. For first-overtone mode Cepheids, a significant change in the slope of P-L, P-W and P-C relations is found around 2.5 days only at optical wavelengths. We determine a global slope of $\textrm{-}3.212\pm0.013$ for the $W^H_{V,I}$ relation by combining our LMC data with observations of Cepheids in Supernovae host galaxies \citep{riess11}. We find this slope to be consistent with the corresponding LMC relation at short periods, and significantly different to the long-period value. We do not find any significant difference in the slope of the global-fit solution using a linear or non-linear LMC P-L relation as calibrator, but the linear version provides a $2\times$ better constraint on the slope and metallicity coefficient.