A VLBA Trigonometric Parallax for RR Aql and the Mira PL Relation

We report VLBA observations of 22 GHz H$_{2}$O and 43 GHz SiO masers toward the Mira variable RR Aql. By fitting the SiO maser emission to a circular ring, we estimate the absolute stellar position of RR Aql and find agreement with Gaia astrometry to within the joint uncertainty of $\approx1$ mas. Using the maser astrometry we measure a stellar parallax of 2.44 $\pm$ 0.07 mas, corresponding to a distance of 410$^{+12}_{-11}$ pc. The maser parallax deviates significantly from the Gaia EDR3 parallax of 1.95 $\pm$ 0.11 mas, indicating a $3.8\sigma$ tension between radio and optical measurements. This tension is most likely caused by optical photo-center variations limiting the Gaia astrometric accuracy for this Mira variable. Combining infrared magnitudes with parallaxes for RR Aql and other Miras, we fit a period-luminosity relation using a Bayesian approach with MCMC sampling and a strong prior for the slope of -3.60 $\pm$ 0.30 from the LMC. We find a $K$-band zero-point (defined at logP(days) = 2.30) of -6.79 $\pm$ 0.15 mag using VLBI parallaxes and -7.08 $\pm$ 0.29 mag using Gaia parallaxes. The Gaia zero-point is statistically consistent with the more accurate VLBI value.