  We present a study of the membership of the Hyades open cluster, derive
kinematically-modelled parallaxes of its members, and study the colour-absolute
magnitude diagram of the cluster. We use Gaia DR1 Tycho-Gaia Astrometric
Solution (TGAS) data complemented by Hipparcos-2 data for bright stars not
contained in TGAS. We supplement the astrometric data with radial velocities
collected from a dozen literature sources. By assuming that all cluster members
move with the mean cluster velocity to within the velocity dispersion, we use
the observed and the expected motions of the stars to determine individual
cluster membership probabilities. We subsequently derive improved parallaxes
through maximum-likelihood kinematic modelling of the cluster. This method has
an iterative component to deal with 'outliers', caused for instance by double
stars or escaping members. Our method extends an existing method and supports
the mixed presence of stars with and without radial velocities. We find 251
candidate members, 200 of which have a literature radial velocity, and 70 of
which are new candidate members with TGAS astrometry. The cluster is roughly
spherical in its centre but significantly flattened at larger radii. The
observed colour-absolute magnitude diagram shows a clear binary sequence. The
kinematically-modelled parallaxes that we derive are a factor ~1.7 / 2.9 more
precise than the TGAS / Hipparcos-2 values and allow to derive an extremely
sharp main sequence. This sequence shows evidence for fine-detailed structure
which is elegantly explained by the full spectrum turbulence model of
convection.

Astrophysics of Galaxies