  DQ Tau is a young low-mass spectroscopic binary, consisting of two almost
equal-mass stars on a 15.8 d period surrounded by a circumbinary disk. Here, we
analyze DQ Tau's light curves obtained by Kepler K2, the Spitzer Space
Telescope, and ground-based facilities. We observed variability phenomena,
including rotational modulation by stellar spots, brief brightening events due
to stellar flares, long brightening events around periastron due to increased
accretion, and short dips due to brief circumstellar obscuration. The
rotational modulation appears as sinusoidal variation with a period of 3.017 d.
In our model this is caused by extended stellar spots 400 K colder than the
stellar effective temperature. During our 80-day-long monitoring we detected 40
stellar flares with energies up to 1.2$\times$10$^{35}$ erg and duration of a
few hours. The flare profiles closely resemble those in older late-type stars,
and their occurrence does not correlate with either the rotational or the
orbital period. We observe elevated accretion rate up to 5$\times$10$^{-8}
M_{\odot}$ yr$^{-1}$ around each periastron. Our Spitzer data suggests that the
increased accretion luminosity heats up the inner part of the circumbinary disk
temporarily by about 100 K. We found an inner disk radius of 0.13 au,
significantly smaller than expected from dynamical modeling of circumbinary
disks. Interestingly, the inner edge of the disk is in corotation with the
binary's orbit. DQ Tau also shows short dips of < 0.1 mag in its light curve,
reminiscent of the well-known "dipper phenomenon" observed in many low-mass
young stars.
