The Physical Nature and Orbital Behavior of the Eclipsing System DK Cygni

New CCD photometry is presented for the hot overcontact binary DK Cyg, together with reasonable explanations for the light and period variations. Historical light and velocity curves from 1962 to 2012 were simultaneously analyzed with the Wilson-Devinney (W-D) synthesis code. The brightness disturbances were satisfactorily modeled by applying a magnetic cool spot on the primary star. Based on 261 times of minimum light including 116 new timings and spanning more than 87 yrs, a period study reveals that the orbital period has varied due to a periodic oscillation superposed on an upward parabola. The period and semi-amplitude of the modulation are about 78.1 yrs and 0.0037 d, respectively. This detail is interpreted as a light-travel-time effect due to a circumbinary companion with a minimum mass of $M_3$=0.065 $M_\odot$, within the theoretical limit of $\sim$0.07 M$_\odot$ for a brown dwarf star. The observed period increase at a fractional rate of $+$2.74 $\times$10$^{-10}$ is in excellent agreement with that calculated from our W-D synthesis. Mass transfer from the secondary to the primary component is mainly responsible for the secular period change. We examined the evolutionary status of the DK Cyg system from the absolute dimensions.