Radial velocity measurements of J1529+2928 also show that there is no companion star or companion brown dwarf in orbit around it that could be responsible for the eclipse-like events. The dark spot on J1529+2928 is predicted to have a temperature of roughly 10000 K and covers ~14 percent of the surface area of the white dwarf. The presence of such a dark spot is most likely due to channelling of accreted heavy elements onto a spot on the surface of the white dwarf by a magnetic field. Because heavy elements are more opaque to shorter wavelengths of light, this can explain why the depth of the eclipse-like events is shallower when J1529+2928 is observed at longer wavelengths.
Reference:
Kilic et al. (2015), “A Dark Spot on a Massive White Dwarf”, arXiv:1511.07320 [astro-ph.SR]