Uninterrupted optical light curves of main-belt asteroids from the K2 mission

Context. Because the second reaction wheel failed, a new mission was conceived for the otherwise healthy Kepler space telescope. In the course of the K2 mission, the telescope is staring at the plane of the Ecliptic. Thousands of solar system bodies therefore cross the K2 fields and usually cause additional noise in the highly accurate photometric data. Aims. We here follow the principle that some person's noise is another person's signal and investigate the possibility of deriving continuous asteroid light curves. This is the first such endeavor. In general, we are interested in the photometric precision that the K2 mission can deliver on moving solar system bodies. In particular, we investigate space photometric optical light curves of main-belt asteroids. Methods. We studied the K2 superstamps that cover the fields of M35, and Neptune together with Nereid, which were observed in the long-cadence mode (29.4 min sampling). Asteroid light curves were generated by applying elongated apertures. We used the Lomb-Scargle method to determine periodicities that are due to rotation. Results. We derived K2 light curves of 924 main-belt asteroids in the M35 field and 96 in the path of Neptune and Nereid. The light curves are quasi-continuous and several days long. K2 observations are sensitive to longer rotational periods than typical ground-based surveys. Rotational periods are derived for 26 main-belt asteroids for the first time. The asteroid sample is dominated by faint objects (>20 mag). Owing to the faintness of the asteroids and the high density of stars in the M35 field, only 4.0% of the asteroids with at least 12 data points show clear periodicities or trends that signal a long rotational period, as opposed to 15.9% in the less crowded Neptune field. We found that the duty cycle of the observations had to reach similar to 60% to successfully recover rotational periods.