A Deep Test of Radial Differential Rotation in a Helium-atmosphere White Dwarf.I. Discovery of Pulsations in PG 0112+104

We present the detection of non-radial oscillations in a hot, helium-atmosphere white dwarf using 78.7 d of nearly uninterrupted photometry from the Kepler space telescope. With an effective temperature >30,000 K, PG 0112+104 becomes the hottest helium-atmosphere white dwarf known to pulsate. The rich oscillation spectrum of low-order g-modes includes clear patterns of rotational splittings from consecutive sequences of dipole and quadrupole modes, which can be used to probe the rotation rate with depth in this highly evolved stellar remnant. We also measure a surface rotation rate of 10.17404 hr from an apparent spot modulation in the K2 data. With two independent measures of rotation, PG 0112+104 provides a remarkable test of asteroseismic inference.