In a binary star system, a white dwarf acts like a vacuum cleaner, pulling gas from its companion star. If the dwarf has a magnetic field, the gas does not fall anywhere but flows toward the poles, like iron filings to a magnet. There it accumulates into a pile. But what keeps this pile from spreading out? The magnetic field lines that thread through it like invisible ropes.
The authors of the new work transferred the calculation method from neutron stars to white dwarfs. They solved the equilibrium equation that describes how plasma and magnetic field reach a compromise. The key idea is that plasma cannot cross magnetic field lines: they are frozen into each other, like fibers in a piece of fabric. Therefore, a pile growing at the pole does not just press on the field but stretches and deforms it.
The most interesting part is how much matter the field can hold in principle. It turns out that the maximum mass grows as the square of the magnetic field and falls as the square of the temperature. If the field is strong and the temperature is low, the pile can reach the mass of a giant planet. Meanwhile, the magnetic field under the pile weakens, but not catastrophically: its dipole component decreases by no more than 10 percent. This means that the white dwarf does not lose its magnetic identity, even after accumulating a substantial pile.
Such a tool will be useful for astronomers observing polars and intermediate polars, which are binary systems with strong magnetic fields. If a critical mass accumulates at the pole of such a dwarf, a micronova may occur, a localized thermonuclear explosion similar to the flare of a sparkler. Furthermore, if the pile is asymmetric, the rotating white dwarf may emit gravitational waves. Future space detectors might just hear this whisper of magnetic mountains.
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.