Starship Asterisk*

The measurement of the velocity of the star seems to imply consideration of a particular inertial frame of reference, appropriate to this context. Is it's motion assumed to be relative to the sun, the galactic center, the whole cosmos?

Couldn't Jupiter sometimes appear to display a separate, dimmer halo? Maybe that would be too dim to visualize when the moon appears in close proximity to Jupiter. Has a Jovian halo ever been photographed under darker conditions when the moon isn't visible?