Transits and Lensing by Compact Objects in the Kepler Field: Disrupted
  Stars Orbiting Blue Stragglers
  Kepler's first major discoveries are two hot objects orbiting stars in its
field. These may be the cores of stars that have each been eroded or disrupted
by a companion star. The companion, which is the star monitored today, is
likely to have gained mass from its now-defunct partner, and can be considered
to be a blue straggler. KOI-81 is almost certainly the product of stable mass
transfer; KOI-74 may be as well, or it may be the first clear example of a blue
straggler created throughthree-body interactions.
  We show that mass transfer binaries are common enough that Kepler should
discover ~1000 white dwarfs orbiting main sequence stars. Most, like KOI-74 and
KOI-81, will be discovered through transits, but many will be discovered
through a combination of gravitational lensing and transits, while lensing will
dominate for a subset. In fact, some events caused by white dwarfs will have
the appearance of "anti-transits" --i.e., short-lived enhancements in the
amount of light received from the monitored star. Lensing and other mass
measurements methods provide a way to distinguish white dwarf binaries from
planetary systems. This is important for the success of Kepler's primary
mission, in light of the fact that white dwarf radii are similar to the radii
of terrestrial planets, and that some white dwarfs will have orbital periods
that place them in the habitable zones of their stellar companions. By
identifying transiting and/or lensing white dwarfs, Kepler will conduct
pioneering studies of white dwarfs and of the end states of mass transfer. It
may also identify orbiting neutron stars or black holes. The calculations
inspired by the discovery of KOI-74 and KOI-81 have implications for
ground-based wide-field surveys as well as for future space-based surveys.
