  The importance of studying the Gaia DR2 parallax zero-point by external means
was underlined by Lindegren et al. (2018), and initiated by several works
making use of Cepheids, eclipsing binaries, and asteroseismology. Despite a
very efficient elimination of basic-angle variations, a small fluctuation
remains and shows up as a small offset in the Gaia DR2 parallaxes. By combining
astrometric, asteroseismic, spectroscopic, and photometric constraints, we
undertake a new analysis of the Gaia parallax offset for nearly 3000 red-giant
branch (RGB) and 2200 red clump (RC) stars observed by Kepler, as well as about
500 and 700 red giants (both RGB and RC) selected by the K2 Galactic
Archaeology Program in campaigns 3 and 6. Engaging into a thorough comparison
of the astrometric and asteroseismic parallaxes, we are able to highlight the
influence of the asteroseismic method, and measure parallax offsets in the
Kepler field that are compatible with independent estimates from literature and
open clusters. Moreover, adding the K2 fields to our investigation allows us to
retrieve a clear illustration of the positional dependence of the zero-point,
in general agreement with the information provided by quasars. Lastly, we
initiate a two-step methodology to make progress in the simultaneous
calibration of the asteroseismic scaling relations and of the Gaia DR2 parallax
offset, which will greatly benefit from the gain in precision with the third
Data Release of Gaia.
