Magnetic field breakout from white dwarf crystallization dynamos

Abstract: A convective dynamo operating during the crystallization of white dwarfs is one of the promising channels to produce their observed strong magnetic fields. Although the magnitude of the fields generated by crystallization dynamos is uncertain, their timing may serve as an orthogonal test of this channel's contribution. The carbon-oxygen cores of $M\approx 0.5-1.0\,{\rm M}\odot$ white dwarfs begin to crystallize at an age $t{\rm cryst}\propto M^{-5/3}$, but the magnetic field is initially trapped in the convection zone - deep inside the CO core. Only once a mass of $m_{\rm cryst}$ has crystallized, the convection zone approaches the white dwarf's helium layer, such that the magnetic diffusion time through the envelope shortens sufficiently for the field to break out to the surface, where it can be observed. This breakout time is longer than $t_{\rm cryst}$ by a few Gyr, scaling as $t_{\rm break}\propto t_{\rm cryst}f^{-1/2}$, where $f\equiv 1-m_{\rm cryst}/M$ depends on the white dwarf's initial C/O profile before crystallization. The first appearance of strong magnetic fields $B\gtrsim 1\textrm{ MG}$ in volume-limited samples approximately coincides with our numerically computed $t_{\rm break}(M)$ - potentially signalling crystallization dynamos as a dominant magnetization channel. However, some observed magnetic white dwarfs are slightly younger, challenging this scenario. The dependence of the breakout process on the white dwarf's C/O profile implies that magnetism may probe the CO phase diagram, as well as uncertainties during the core helium burning phase in the white dwarf's progenitor, such as the $^{12}{\rm C}(\alpha,\gamma)^{16}{\rm O}$ nuclear reaction.