A 15.7-Minute AM CVn Binary Discovered in K2

We present the discovery of SDSS J135154.46-064309.0, a short-period variable observed using 30-minute cadence photometry in K2 Campaign 6. Follow-up spectroscopy and high-speed photometry support a classification as a new member of the rare class of ultracompact accreting binaries known as AM CVn stars. The spectroscopic orbital period of $15.65 \pm 0.12$\,minutes makes this system the fourth-shortest period AM CVn known, and the second system of this type to be discovered by the Kepler spacecraft. The K2 data show photometric periods at $15.7306 \pm 0.0003$\,minutes, $16.1121 \pm 0.0004$\,minutes and $664.82 \pm 0.06$\,minutes, which we identify as the orbital period, superhump period, and disc precession period, respectively. From the superhump and orbital periods we estimate the binary mass ratio $q = M_2/M_1 = 0.111 \pm 0.005$, though this method of mass ratio determination may not be well calibrated for helium-dominated binaries. This system is likely to be a bright foreground source of gravitational waves in the frequency range detectable by LISA, and may be of use as a calibration source if future studies are able to constrain the masses of its stellar components.