TGAS Error Renormalization from the RR Lyrae Period-Luminosity Relation

The Gaia team has applied a renormalization to their internally-derived parallax errors $σ_{\rm int}(π)$ $σ_{tgas}(π) = \sqrt{[Aσ_{int}(π)]^2 + σ_0^2}; \ \ \ \ (A,σ_0) = (1.4,0.20\ \rm mas)$ 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 $(A,σ_0) = (1.1,0.12\ \rm mas) \ \ \ \ (this\ paper).$ 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: $σ_{true}(π) = \sqrt{(0.79σ_{tgas}(π))^2 - (0.10\ \rm mas)^2}.$

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