Top: relation between asteroseismic (left) or TGAS (right) parallaxes and de-reddened 2MASS Ks magnitudes (mKs) for our sample. The markers indicate the evolutionary state of the star, including the red giant branch (RGB or AGB), the red clump (RC), and the secondary clump (SC). We note that the uncertainties on mKs are typically smaller than the marker size. The dashed red line in both panels shows the theoretical relation used for the residuals in the bottom panels. The relation is given by Eq. (1) using the median theoretical value of from the literature (see Girardi 2016, and references therein); the gray regions around the relations indicate the span of the literature values. The filled red markers denote the six asteroseismic RC stars in the M67 cluster (Stello et al. 2016) for which TGAS parallaxes were available. The middle panel shows fractional differences between the observed and predicted mKs magnitudes from Eq. (1) at the asteroseismic (left) and TGAS (right) parallaxes of the RC stars. The bottom panel shows residuals between observed and predicted parallaxes from Eq. (1) at the asteroseismic (left) and TGAS (right) parallaxes of the RC stars. The red dash-dot lines and shaded confidence regions follow the predicted offset of −0.39 ± 0.08 mas of the TGAS parallaxes by Stassun & Torres (2016), adopting the ecliptic latitude β = 55° ± 5 of the Kepler field-of-view. The inserts in the middle and bottom panels are violin plots of the distributions of the fractional differences and residuals, with the horizontal black lines giving the median values; the colors indicate the mKs magnitudes.
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