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We present new period–luminosity and period–luminosity–metallicity relations for Galactic RR Lyrae stars based on a sample of 28 pulsators located at distances of up to 1.5 kpc from the Sun. Near-infrared photometry was obtained at the Cerro Armazones Observatory, and parallaxes were taken from the Gaia Early Data Release 3. Relations were determined for the 2MASS JHK _s bands and the W _JK Wesenheit index. We compare our results with other calibrations available in the literature and obtain very good agreement with the photometry of RR Lyraes from the Large Magellanic Cloud (LMC) anchored using the distance to the Cloud, which is based on detached eclipsing binaries. We find that the dependence of absolute magnitudes on metallicity of 0.070 ± 0.042 ( J band) to 0.087 ± 0.031 ( W _JK index) mag dex ^−1 for the population of fundamental pulsators (RRab) is in agreement with previously published phenomenological works. We perform a refined determination of distance to the LMC based on our new calibration and photometry from Szewczyk et al. We study the dependence of the fitted parameters of the fiducial relations and the LMC distance on the systematic parallax offset.

Because of their period–luminosity relation (PLR), classical Cepheids play a key role in the calibration of the extragalactic distance scale and the determination of the Hubble–Lemaître constant H _0 . Recent findings show that the majority of classical Cepheids should be in binary or multiple systems, which might undermine their accuracy, as the extra—and unaccounted for—light from the companions of Cepheids causes a shift in the PLR. We quantify this shift using synthetic populations of binary Cepheids that we developed for this purpose, as described in Paper I of this series. We find that while all PLRs are shifted toward brighter values due to the excess light from the companions, the bias in the relative distance modulus between two galaxies hosting binary Cepheids can be either positive or negative, depending on the percentage of binary Cepheids in them. If the binarity percentage in the two galaxies is similar, the effect of binarity is canceled. Otherwise, it introduces a shift in the distance modulus of the order of millimagnitudes in the near-infrared passbands and Wesenheit indices, and tens of millimagnitudes in the visual domain; its exact value depends on the variant of the synthetic population (a unique combination of metallicity, star formation history, shape and location of the instability strip, and initial parameter distributions). Such shifts in the distance moduli to Type Ia supernova host galaxies introduce an additional statistical error on H _0 , which however does not prevent measuring H _0 with a precision of 1%.

We present the first period–luminosity (PL) and period–Wesenheit (PW) relations in the Sloan–Pan-STARRS g _P _1 r _P _1 i _P _1 bands for classical fundamental-mode Cepheids in the Milky Way. We used a relatively modest number of 76 stars for the PL and 84−85 stars for the PW relations calibration. The data for the project were collected with the network of 40 cm telescopes of the Las Cumbres Observatory, and Gaia Data Release 3 parallaxes were used for the calculations. These gri -band PL and PW relations calibrations will be a useful tool for distance determinations in the era of large sky surveys using the Sloan photometric system, especially with the near-future start of the Large Synoptic Survey of Space and Time.