Concerning the Slope of the Cepheid Period-Luminosity Relation

TL;DR

This paper examines how variations in the slope of the Cepheid Period-Luminosity relation affect distance measurements, demonstrating that the Wesenheit function W remains largely insensitive to such changes, ensuring reliable extragalactic distances.

Contribution

The study shows that the Wesenheit function W is highly insensitive to slope variations in the Cepheid PL relation, supporting its robustness for distance measurements.

Findings

Wesenheit function W is insensitive to slope changes in PL relations.

Reddening trajectories are parallel to lines of constant period.

W-based PL relations have low residual dispersion.

Abstract

We discuss the impact of possible differences in the slope of the Cepheid Period-Luminosity relation on the determination of extragalactic distances in the context of recent studies that suggest changes in this slope. We show that the Wesenheit function W = V - R x ((V-I), widely used for the determination of Cepheid distances, is expected to be highly insensitive to changes in the slope of the underlying (monochromatic) Period-Luminosity (PL) relations. This occurs because the reddening trajectories in the color-magnitude plane are closely parallel to lines of constant period. As a result W-based Period-Luminosity relations have extremely low residual dispersion, which is because differential (and total line-of-sight) reddening is eliminated in the definition of W and the residual scatter due to a star's intrinsic color/position within the Cepheid is also largely insensitive to W. Basic equations are presented and graphically illustrated, showing the insensitivity of W to changes in the monochromatic PL relations.