Systematic Error of the Gaia DR1 TGAS Parallaxes from Data for the Red
  Giant Clump
  Based on the Gaia DR1 TGAS parallaxes and photometry from the Tycho-2, Gaia,
2MASS, and WISE catalogues, we have produced a sample of about 100 000 clump
red giants within about 800 pc of the Sun. The systematic variations of the
mode of their absolute magnitude as a function of the distance, magnitude, and
other parameters have been analyzed. We show that these variations reach 0.7
mag and cannot be explained by variations in the interstellar extinction or
intrinsic properties of stars and by selection. The only explanation seems to
be a systematic error of the Gaia DR1 TGAS parallax dependent on the square of
the observed distance in kpc: $0.18R^2$ mas. Allowance for this error reduces
significantly the systematic dependences of the absolute magnitude mode on all
parameters. This error reaches 0.1 mas within 800 pc of the Sun and allows an
upper limit for the accuracy of the TGAS parallaxes to be estimated as 0.2 mas.
A careful allowance for such errors is needed to use clump red giants as
"standard candles". This eliminates all discrepancies between the theoretical
and empirical estimates of the characteristics of these stars and allows us to
obtain the first estimates of the modes of their absolute magnitudes from the
Gaia parallaxes: $mode(M_H)=-1.49^m\pm0.04^m$,
$mode(M_{K_s})=-1.63^m\pm0.03^m$, $mode(M_{W1})=-1.67^m\pm0.05^m$,
$mode(M_{W2})=-1.67^m\pm0.05^m$, $mode(M_{W3})=-1.66^m\pm0.02^m$,
$mode(M_{W4})=-1.73^m\pm0.03^m$, as well as the corresponding estimates of
their de-reddened colors.
