  The sub-Chandrasekhar mass double-detonation (DDet) scenario is a
contemporary model for SNe Ia. The donor star in the DDet scenario is expected
to survive the explosion and to be ejected at the high orbital velocity of a
compact binary system. For the first time, we consistently perform 3D
hydrodynamical simulations of the interaction of SN ejecta with a helium (He)
star companion within the DDet scenario. We map the outcomes of 3D impact
simulations into 1D stellar evolution codes and follow the long-term evolution
of the surviving He-star companions. Our main goal is to provide the
post-impact observable signatures of surviving He-star companions of DDet SNe
Ia, which will support the search for such companions in future observations.
We find that our surviving He-star companions become significantly overluminous
for about 1e6 yr during the thermal re-equilibration phase. After the star
re-establishes thermal equilibrium, its observational properties are not
sensitive to the details of the ejecta-donor interaction. We apply our results
to hypervelocity star US 708, which is the fastest unbound star in our Galaxy,
travelling with a velocity of about 1200 km/s, making it natural candidate for
an ejected donor remnant of a DDet SN Ia. We find that a He-star donor with an
initial mass of >0.5 Msun is needed to explain the observed properties of US
708. Based on our detailed binary evolution calculations, however, the
progenitor system with such a massive He-star donor cannot get close enough at
the moment of SN explosion to explain the high velocity of US 708. Instead, if
US 708 is indeed the surviving He-star donor of a DDet SN~Ia, it would require
the entire pre-SN progenitor binary to travel at a velocity of about 400 km/s.
It could, for example, have been ejected from a globular cluster in the
direction of the current motion of the surviving donor star.
