Mysterious, variable, and extremely hot: White dwarfs showing ultra-high excitation lines

About 10% of all stars exhibit absorption lines of ultra-high excited (UHE) metals (e.g. OVIII) in their optical spectra when entering the white dwarf cooling sequence. The recent discovery of a both spectroscopic and photometric variable UHE white dwarf led to the speculation that the UHE lines might be created in a shock-heated circumstellar magnetosphere. We investigate (multi-band) light curves from several ground- and space-based surveys of all 16 currently known UHE white dwarfs (including one newly discovered) and eight white dwarfs that show only the HeII line problem, as both phenomena are believed to be connected. We find that $75^{+8}_{-13}$% of the UHE white dwarfs, and $75^{+9}_{-19}$% of the HeII line problem white dwarfs are significantly photometrically variable, with periods ranging from 0.22d to 2.93d and amplitudes from a few tenth to a few hundredth mag. The high variability rate is in stark contrast to the variability rate amongst normal hot white dwarfs (we find $9^{+4}_{-2}$%), marking UHE and HeII line problem white dwarfs as a new class of variable stars. The period distribution of our sample agrees with both the orbital period distribution of post-common envelope binaries and the rotational period distribution of magnetic white dwarfs if we assume that the objects in our sample will spin-up as a consequence of further contraction. The lack of increasing photometric amplitudes towards longer wavelengths, as well as the non-detection of optical emission lines arising from the highly irradiated face of a hypothetical secondary in the optical spectra of our stars, makes it seem unlikely that an irradiated late type companion is the origin of the photometric variability. Instead, we believe that spots on the surfaces of these stars and/or geometrical effects of circumstellar material might be responsible. (abridged)