Recurring sets of recurring starspot occultations on exoplanet-host Qatar-2

We announce the detection of recurring sets of recurring starspot occultation events in the short-cadence K2 lightcurve of Qatar-2, a K dwarf star transited every 1.34 d by a hot Jupiter. In total we detect 34 individual starspot occultation events, caused by five different starspots, occulted in up to five consecutive transits or after a full stellar rotation. The longest recurring set of recurring starspot occultations spans over three stellar rotations, setting a lower limit for the longest starspot lifetime of 58 d. Starspot analysis provided a robust stellar rotational period measurement of $18.0\pm0.2$ d and indicates that the system is aligned, having a sky-projected obliquity of $0\pm8^{\circ}$. A pronounced rotational modulation in the lightcurve has a period of $18.2\pm1.6$ d, in agreement with the rotational period derived from the starspot occultations. We tentatively detect an ellipsoidal modulation in the phase-curve, with a semi-amplitude of 18 ppm, but cannot exclude the possibility that this is the result of red noise or imperfect removal of the rotational modulation. We detect no transit-timing and transit-duration variations with upper limits of 15 s and 1 min, respectively. We also reject any additional transiting planets with transit depths above 280 ppm in the orbital period region 0.5-30 d.