We determine the period-magnitude relations of RR Lyrae stars in 13 photometric bandpasses from 0.4 to 12 \mu m using timeseries observations of 134 stars with prior parallax measurements from Hipparcos and the Hubble Space Telescope ( HST ) .
The Bayesian formalism , extended from our previous work to include the effects of line-of-sight dust extinction , allows for the simultaneous inference of the posterior distribution of the mean absolute magnitude , slope of the period-magnitude power-law , and intrinsic scatter about a perfect power-law for each bandpass .
In addition , the distance modulus and line-of-sight dust extinction to each RR Lyrae star in the calibration sample is determined , yielding a sample median fractional distance error of 0.66 per cent .
The intrinsic scatter in all bands appears to be larger than the photometric errors , except in WISE W 1 ( 3.4 \mu m ) and WISE W 2 ( 4.6 \mu m ) where the photometric error ( \sigma \approx 0.05 mag ) appears to be comparable or larger than the intrinsic scatter .
This suggests that additional observations at these wavelengths could improve the inferred distances to these sources further .
With \sim 100 , 000 RR Lyrae stars expected throughout the Galaxy , the precision dust extinction measurements towards 134 lines-of-sight offer a proof of concept for using such sources to make 3D tomographic maps of dust throughout the Milky Way .
We find a small but significant increase ( 3 per cent ) in the effective extinction towards sources far from the Galactic plane relative to the expectation from recent dust maps and we suggest several explanations .
As an application of the methodology , we infer the distance to the RRc-type star RZCep at low Galactic latitude ( b = 5.5 ^ { \circ } ) to be \mu = 8.0397 \pm 0.0123 mag ( 405.4 \pm 2.3 pc ) with colour excess E ( B - V ) = 0.2461 \pm 0.0089 mag .
This distance , equivalent to a parallax of 2467 \pm 14 microarcsec , is consistent with the published HST parallax measurement but with an uncertainty that is 13 times smaller than the HST measurement .
If our measurements ( and methodology ) hold up to scrutiny , the distances to these stars have been determined to an accuracy comparable to those expected with Gaia .
As RR Lyrae are one of the primary components of the cosmic distance ladder , the achievement of sub-1 per cent distance errors within a formalism that accounts for dust extinction may be considered a strong buttressing of the path to eventual 1 per cent uncertainties in Hubble ’ s constant .