TGAS Error Renormalization from the RR Lyrae Period-Luminosity Relation

The Gaia team has applied a renormalization to their internally-derived parallax errors $\sigma_{\rm int}(\pi)$ $$ \sigma_{tgas}(\pi) = \sqrt{[A\sigma_{int}(\pi)]^2 + \sigma_0^2}; \ \ \ \ (A,\sigma_0) = (1.4,0.20\ \rm mas) $$ 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 $$ (A,\sigma_0) = (1.1,0.12\ \rm mas) \ \ \ \ (this\ paper). $$ 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: $$ \sigma_{true}(\pi) = \sqrt{(0.79\sigma_{tgas}(\pi))^2 - (0.10\ \rm mas)^2}. $$