We present rotation periods for 71 single dwarf members of the open cluster
NGC6811 determined using photometry from NASA's Kepler Mission. The results are
the first from The Kepler Cluster Study which combine Kepler's photometry with
ground-based spectroscopy for cluster membership and binarity. The rotation
periods delineate a tight sequence in the NGC6811 color-period diagram from ~1
day at mid-F to ~11 days at early-K spectral type. This result extends to ~1
Gyr similar prior results in the ~600 Myr Hyades and Praesepe clusters,
suggesting that rotation periods for cool dwarf stars delineate a well-defined
surface in the 3-dimensional space of color (mass), rotation, and age. It
implies that reliable ages can be derived for field dwarf stars with measured
colors and rotation periods, and it promises to enable further understanding of
various aspects of stellar rotation and activity for cool stars.Comment: 13 pages (aastex 12pt preprint style), 4 figures, 1 table, accepted
for publication in ApJ Letter