Red clump stars and Gaia: Calibration of the standard candle using a
  hierarchical probabilistic model
  Distances to individual stars in our own Galaxy are critical in order to
piece together the nature of its velocity and spatial structure. Core helium
burning red clump (RC) stars have similar luminosities, are abundant throughout
the Galaxy, and thus constitute good standard candles. We build a hierarchical
probabilistic model to quantify the quality of RC stars as standard candles
using parallax measurements from the first Gaia data release. A unique aspect
of our methodology is to fully account for (and marginalize over) parallax,
photometry, and dust corrections uncertainties, which leads to more robust
results than standard approaches. We determine the absolute magnitude and
intrinsic dispersion of the RC in 2MASS bands J, H, Ks, Gaia G band, and WISE
bands W1, W2, W3, and W4. We find that the absolute magnitude of the RC is
$-1.61 \pm$ 0.01 (in Ks), $+0.44 \pm$ 0.01 (in G) , $-0.93 \pm$ 0.01 (in J),
$-1.46 \pm$ 0.01 (in H), $-1.68 \pm$ 0.02 (in W1), $-1.69\pm$ 0.02 (in W2),
$-1.67 \pm$ 0.02 (in W3), $1.76 \pm$ 0.01 mag (in W4). The mean intrinsic
dispersion is $\sim 0.17 \pm$ 0.03 mag across all bands (yielding a typical
distance precision of $\sim$ 8%). Thus RC stars are reliable and precise
standard candles. In addition, we have also re-calibrated the zero point of the
absolute magnitude of the RC in each band, which provide a benchmark for future
studies to estimate distances to RC stars. Finally, the parallax error
shrinkage in the hierarchical model outlined in this work can be used to obtain
more precise parallaxes than Gaia for the most distant RC stars across the
Galaxy.
