  RR Lyrae (RR Lyr) stars are a well-known and useful distance indicator for
old stellar populations such as globular clusters and dwarf galaxies.
Fundamental-mode RR Lyr (RRab) stars are commonly used to measure distances,
and the accuracy of the determined distance is strongly constrained by
metallicity. Here, we investigate the metallicity dependence in the
period-luminosity (PL) relation of double-mode RR Lyr (RRd) stars. We find and
establish a linear relation between metallicity and period or period ratio for
RRd stars. This relation can predict the metallicity as accurately as the
low-resolution spectra. Based on this relation, we establish a
metallicity-independent PL relation for RRd stars. Combining the distance of
the Large Magellanic Cloud and Gaia parallaxes, we calibrate the zero point of
the derived PL relation to an error of 0.022 mag. Using RRd stars, we measure
the distances of globular clusters and dwarf galaxies with an accuracy of 2-3%
and 1-2%, respectively. In the future, RRd stars could anchor galaxy distances
to an accuracy of 1.0% and become an independent distance ladder in the Local
Group.

Solar and Stellar Astrophysics;Astrophysics of Galaxies