We outline an approach yielding proper motions with higher precision than
exists in present catalogs for a sample of stars in the Kepler field. To
increase proper motion precision we combine first moment centroids of Kepler
pixel data from a single Season with existing catalog positions and proper
motions. We use this astrometry to produce improved reduced proper motion
diagrams, analogous to a Hertzsprung-Russell diagram, for stars identified as
Kepler Objects of Interest. The more precise the relative proper motions, the
better the discrimination between stellar luminosity classes. With UCAC4 and
PPMXL epoch 2000 positions (and proper motions from those catalogs as
quasi-bayesian priors) astrometry for a single test Channel (21) and Season (0)
spanning two years yields proper motions with an average per-coordinate proper
motion error of 1.0 millisecond of arc per year, over a factor of three better
than existing catalogs. We apply a mapping between a reduced proper motion
diagram and an HR diagram, both constructed using HST parallaxes and proper
motions, to estimate Kepler Object of Interest K-band absolute magnitudes. The
techniques discussed apply to any future small-field astrometry as well as the
rest of the Kepler field.Comment: Accepted to The Astronomical Journal 15 August 201