  KIC 8462852 is a superficially ordinary main sequence F star for which Kepler
detected an unusual series of brief dimming events. We obtain accurate relative
photometry of KIC 8462852 from the Kepler full frame images, finding that the
brightness of KIC 8462852 monotonically decreased over the four years it was
observed by Kepler. Over the first ~1000 days, KIC 8462852 faded approximately
linearly at a rate of 0.341 +/- 0.041%/yr, for a total decline of 0.9%. KIC
8462852 then dimmed much more rapidly in the next ~200 days, with its flux
dropping by more than 2%. For the final ~200 days of Kepler photometry the
magnitude remained approximately constant, although the data are also
consistent with the decline rate measured for the first 2.7 yr. Of a sample of
193 nearby comparison stars and 355 stars with similar stellar parameters, none
exhibit the rapid decline by 2% or the cumulative fading by 3% of KIC 8462852.
Moreover, of these comparison stars, only one changes brightness as quickly as
the 0.341%/yr measured for KIC 8462852 during the first three years of the
Kepler mission. We examine whether the rapid decline could be caused by a cloud
of transiting circumstellar material, finding while such a cloud could evade
detection in sub-mm observations, the transit ingress and duration cannot be
explained by a simple cloud model. Moreover, this model cannot account for the
observed longer-term dimming. No known or proposed stellar phenomena can fully
explain all aspects of the observed light curve.
