On a New Theoretical Framework for RR Lyrae Stars. II. Mid-infrared Period–Luminosity–Metallicity Relations

Abstract

We present new theoretical period-luminosity-metallicity (PLZ) relations for RR Lyrae stars (RRLs) at Spitzer and WISE wavelengths. The PLZ relations were derived using nonlinear, time-dependent convective hydrodynamical models for a broad range of metal abundances (Z=0.0001-0.0198). In deriving the light curves, we tested two sets of atmospheric models and found no significant difference between the resulting mean magnitudes. We also compare our theoretical relations to empirical relations derived from RRLs 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, μ 0 , and extinction, A V , 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 μ 0 =11.257±0.035 mag with A V =1.45±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 mid-infrared wavelengths.

Observations of field and cluster RR Lyræ with Spitzer. Towards high precision distances with Population II stellar tracers

“…The right panel shows the PLZ for first overtone and fundamental mode RR Lyrae, derived for IRAC 3.6 and 4.5 μm bands. The period slope we measured in the NIR ( [3]) and MIR ( [12]) are shown in Figure 1, and are in good agreement with their theoretical values. Repeating this measurement for the other single-metallicity clusters observed as part of the CRRP program will allow us to refine the fitted values of b λ , and check that this term is indeed independent from [Fe/H].…”

“…Period slope of RR Lyrae PLZ relations in optical and infrared bands. Different symbols indicate slope observational values from cluster and field RR Lyrae, compared with the theoretical prediction presented in [11] and [12] (black circles). Note that the slope is very shallow in the visible, and then increases in the NIR up to the H band.…”

“…Right -PL relations for first overtone (RRc, blue empty circles) and fundamental mode (RRab, red filled circles) M4 RR Lyrae at 3.6 and 4.5 μm (fundamentalized relations on the right). Both figures are adapted from [12].…”

“…The advantage of using GCs is of course that the distance of the cluster from Earth is much larger than the relative spatial distribution of the individual stars within the GC, and variable extinction in front of the cluster only contributes to a small unbiased scatter around the overall RR Lyrae PL: for RR Lyrae in a GC the period slope b λ can be accurately fit as the slope of the PL relation constructed with the reddened apparent magnitudes. Figure 2 (adapted from [12]) presents an example based on our observations of M4 (NGC 6121). The right panel shows the PLZ for first overtone and fundamental mode RR Lyrae, derived for IRAC 3.6 and 4.5 μm bands.…”

“…The two panels on the right show how the scatter is much reduced when the metallicity term is subtracted by the stars' absolute magnitude, especially in the MIR band, where it becomes less than 0.02 magnitudes. Adapted from [12].…”