TGAS Error Renormalization from the RR Lyrae Period-Luminosity Relation

The Gaia team has applied a renormalization to their internally-derived parallax errors ${\sigma }_{\mathrm{i}\mathrm{n}\mathrm{t}}(\pi )$ $${\sigma }_{tgas}(\pi )=\sqrt{[A{\sigma }_{int}(\pi ){]}^2+{\sigma }_0^2};(A,{\sigma }_0)=(1.4,0.20\mathrm{m}\mathrm{a}\mathrm{s})$$ based on comparison to Hipparcos astrometry. We use a completely independent method based on the RR Lyrae $K$-band period-luminosity relation to derive a substantially different result, with smaller ultimate errors $$(A,{\sigma }_0)=(1.1,0.12\mathrm{m}\mathrm{a}\mathrm{s})(\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{s}\mathrm{p}\mathrm{a}\mathrm{p}\mathrm{e}\mathrm{r})\mathrm{.}$$ We argue that our estimate is likely to be more accurate and therefore that the reported TGAS parallax errors should be reduced according to the prescription: $${\sigma }_{true}(\pi )=\sqrt{(0.79{\sigma }_{tgas}(\pi ){)}^2-(0.10\mathrm{m}\mathrm{a}\mathrm{s}{)}^2}\mathrm{.}$$