  The Kepler Mission has recently announced the discovery of Kepler-10 b, the
smallest exoplanet discovered to date and the first rocky planet found by the
spacecraft. A second, 45-day period transit-like signal present in the
photometry from the first eight months of data could not be confirmed as being
caused by a planet at the time of that announcement. Here we apply the
light-curve modeling technique known as BLENDER to explore the possibility that
the signal might be due to an astrophysical false positive (blend). To aid in
this analysis we report the observation of two transits with the Spitzer Space
Telescope at 4.5 {\mu}m. When combined they yield a transit depth of 344 \pm 85
ppm that is consistent with the depth in the Kepler passband (376 \pm 9 ppm,
ignoring limb darkening), which rules out blends with an eclipsing binary of a
significantly different color than the target. Using these observations along
with other constraints from high resolution imaging and spectroscopy we are
able to exclude the vast majority of possible false positives. We assess the
likelihood of the remaining blends, and arrive conservatively at a false alarm
rate of 1.6 \times 10-5 that is small enough to validate the candidate as a
planet (designated Kepler-10 c) with a very high level of confidence. The
radius of this object is measured to be Rp = 2.227+0.052 -0.057 Earth radii.
Kepler-10 c represents another example (with Kepler-9 d and Kepler-11 g) of
statistical "validation" of a transiting exoplanet, as opposed to the usual
"confirmation" that can take place when the Doppler signal is detected or
transit timing variations are measured. It is anticipated that many of Kepler's
smaller candidates will receive a similar treatment since dynamical
confirmation may be difficult or impractical with the sensitivity of current
instrumentation.
