# On a new theoretical framework for RR Lyrae stars II: Mid--Infrared Period--Luminosity--Metallicity Relations

## TL;DR

This paper develops new theoretical period-luminosity-metallicity relations for RR Lyrae stars at mid-infrared wavelengths, improving distance measurements and reducing metallicity-related dispersion.

## Contribution

It introduces comprehensive theoretical PLZ relations for RR Lyrae stars at Spitzer and WISE wavelengths, validated against empirical data and Gaia parallaxes.

## Key findings

- Theoretical PLZ relations match Gaia parallaxes.
- Distance to M4 cluster is accurately determined.
- Metallicity reduces dispersion in MIR PL relations.

## Abstract

We present new theoretical period-luminosity-metallicity (PLZ) relations for RR Lyrae stars (RRL) at Spitzer and WISE wavelengths. The PLZ relations were derived using nonlinear, time-dependent convective hydrodynamical models for a broad range in metal abundances (Z=0.0001 to 0.0198). In deriving the light curves, we tested two sets of atmospheric models (Brott & Hauschildt 2005, Castelli & Kurucz 2003) and found no significant difference between the resulting mean magnitudes. We also compare our theoretical relations to empirical relations derived from RRL in both the field and in the globular cluster M4. Our theoretical PLZ relations were combined with multi-wavelength observations to simultaneously fit the distance modulus, mu_0, and extinction, Av, of both the individual Galactic RRL and of the cluster M4. The results for the Galactic RRL are consistent with trigonometric parallax measurements from Gaia's first data release. For M4, we find a distance modulus of $\mu_0=11.257 \pm 0.035$ mag with $A_V = 1.45 \pm 0.12$ mag, which is consistent with measurements from other distance indicators. This analysis has shown that when considering a sample covering a range of iron abundances, the metallicity spread introduces a dispersion in the PL relation on the order of 0.13 mag. However, if this metallicity component is accounted for in a PLZ relation, the dispersion is reduced to ~0.02 mag at MIR wavelengths.