  We use Gaia Data Release 2 to search for possible surviving binary companions
to three of the best studied historical Milky Way core-collapse supernovae.
Consistent with previous work, we find there to be no plausible binary
companion to either the Crab or Cas A supernovae. For the first time, we
present a systematic search for a former companion to the Vela supernova, and
rule out essentially any surviving luminous ($>L_\odot$) companion. Based on
parallax and proper motion, we identify a faint source (Star A; Gaia Source ID
5521955992667891584) which is kinematically consistent with being a former
binary companion to the Vela SN progenitor. However, the inferred absolute
magnitude of this source is extremely faint, raising the possibility that it
may in fact be a background interloper. In addition, we derive a new distance
($3.37^{+4.04}_{-0.97}$ kpc) to the Crab SN based on the Gaia parallax
measurements, which is significantly further than the 2 kpc distance typically
adopted. Finally, we demonstrate that Gaia can be used to measure the secular
decline in the luminosity of the Crab pulsar, and provide a new test of pulsar
models.

Solar and Stellar Astrophysics;High Energy Astrophysical Phenomena