  SN 1572 (Tycho Brahe's supernova) clearly belongs to the Ia (thermonuclear)
type. It was produced by the explosion of a white dwarf in a binary system. Its
remnant has been the first of this type to be explored in search of a possible
surviving companion, the mass donor that brought the white dwarf to the point
of explosion. A high peculiar motion with respect to the stars at the same
location in the Galaxy, mainly due to the orbital velocity at the time of the
explosion, is a basic criterion for the detection of such companions. Radial
velocities from the spectra of the stars close to the geometrical center of
Tycho's supernova remnant, plus proper motions of the same stars, obtained by
astrometry with the {\it Hubble Space Telescope}, have been used so far. In
addition, a detailed chemical analysis of the atmospheres of a sample of
candidate stars had been made. However, the distances to the stars, remained
uncertain. Now, the Second {\it Gaia} Data Release (DR2) provides unprecedent
accurate distances and new proper motions for the stars can be compared with
those made from the {\it HST}. We consider the Galactic orbits that the
candidate stars to SN companion would have in the future. We do this to explore
kinematic peculiarity. We also locate a representative sample of candidate
stars in the Toomre diagram. Using the new data, we reevaluate here the status
of the candidates suggested thus far, as well as the larger sample of the stars
seen in the central region of the remnant.
