A white dwarf in a binary system acts like a vacuum cleaner: it siphons gas from its companion star. If it has a magnetic field, the gas doesn't spread evenly over the surface but flows toward the poles, where it gathers into piles. But why doesn't the pile spread out? It is held by magnetic field lines that pass through it like invisible ropes.
The authors built a computer model in which plasma and magnetic field are tightly coupled: plasma cannot cross magnetic field lines, just as a thread cannot pass through fabric without tearing it. They found that on a typical white dwarf, a pile could grow to a kilometer in height and have the mass of a small planet. Meanwhile, the star's magnetic field weakens by only a tenth. This means that even after accumulating a large pile, the white dwarf remains a strong magnet.
These calculations could help explain why some white dwarfs undergo micronovae: small thermonuclear explosions near the poles. And if the pile is unevenly distributed, the rotating star might emit gravitational waves that future detectors could possibly catch.
White dwarfs can have magnetic fields from $10^3$ to $10^9$ G, which is a range spanning a factor of a million. At a field of $10^8$ G, the maximum supported mass reaches 0.067 solar masses, comparable to the mass of an entire giant planet.