Evolution of a Long-Lived Deep-Seated Main-Sequence Magnetic Field During White Dwarf Cooling

TL;DR

This work investigates whether magnetic fields generated by core-convective dynamos during the main sequence can survive to the white dwarf phase and account for observed WD magnetism. It combines main-sequence dynamo boundary estimates, carbon-oxygen WD models from MESA, and a diffusion-based evolution of an axisymmetric poloidal field (including ohmic and turbulent diffusion) to predict surface field strengths across WD masses and cooling ages. The study finds that surface fields can match observations if the main-sequence dynamo produces fields of order $10^3$–$10^5$ G, with dipole and dipole+quadrupole geometries yielding a 2–4× range in surface strength, and that crystallization-driven diffusion can modify the evolution. These results support a unified origin for many magnetic WDs via survival of a main-sequence dynamo field, while highlighting uncertainties in magnetic boundary placement and initial-to-final mass relations that warrant case-by-case analyses.

Abstract

We study the evolution of white dwarf (WD) magnetic fields that originate from core-convective dynamos during the main-sequence. Using stellar evolution and WD cooling models combined with magnetic field diffusion calculations, we demonstrate that a surviving field from the main-sequence can account for various features observed in magnetic WDs. In particular, the earlier emergence of stronger magnetic fields in more massive WDs, compared to older, less massive, and less magnetic ones, can be explained by this framework. This is because the magnetic boundary at the onset of WD cooling lies deeper in less massive WDs, resulting in a slower and weaker evolution of the surface magnetic field due to increasing electrical conductivity over time. We further show that many of the magnetic field strengths observed across different WD samples can be reproduced if the deep-seated field generated during the main sequence is comparable to predictions from magnetohydrodynamic simulations of core-convective dynamos, or if equipartition provides a valid scaling for the main-sequence dynamo. Additionally, our predictions for surface magnetic fields vary by a factor of 2 to 4 when higher-order modes of poloidal magnetic field expansion and turbulent diffusion driven by crystallization-induced convection are included. These effects should therefore be considered when investigating the origin of magnetic fields in individual WDs.

Figures (7)

• Figure 1: Magnetic field strength of the main sequence dynamo assuming equipartition for main sequence stars of 1.5, 3, 4, and 5 M$_\odot$. The solid vertical lines indicate the final white dwarf masses, assuming the initial-to-final-mass relation of 2008MNRAS.387.1693C. The dashed vertical lines indicate the location of the magnetic boundaries below which we expect the magnetic field to be buried at the beginning of the white dwarf phase, assuming the cubic fit prescription from 2024AA...691L..21C. Note that in the x-axis $\mathrm{M_{r}}=m/M_{\odot}$, where $m$ is the total mass contained at the location from the center in solar masses.
• Figure 2: Two-dimensional visualization of the evolution of the magnetic field lines for our 0.7 M$_\odot$ model, assuming an axisymmetric dipole field (left panels), a quadrupole field (middle-left panels), a dipole plus quadrupole field (middle-right panels), and an off-centered dipole field (right panels). The lines in each panel are the magnetic field lines with equal magnetic flux, and the color scaling indicates increasing magnetic field strength for brighter colors.
• Figure 3: Evolution of the magnetic field strength (top panel) and the magnetic diffusivity (bottom) as a function of the normalized white dwarf radius for our 0.6 M$_\odot$ model, assuming an initial axisymmetric dipole field. In this case, we included turbulent diffusivity inside the compositionally-driven convection zone with $\mathrm{f_{RM}}=10$.
• Figure 4: Left panel: Surface magnetic field as a function of the cooling age for our dipole (solid lines) and dipole plus quadrupole (dashed lines) initial configurations. Right panel: Same as left panel, but simulating turbulent diffusion in the crystallization induced by Rayleigh-Taylor unstable regions (see text for details). Maximum values are indicated using filled circles, and the dotted vertical lines on the right panel indicate the crystallization onset in each white dwarf sequence.
• Figure 5: Color map indicating the logarithmic prediction of the magnetic field at the WD surface as a function of the WD mass and cooling time. For this, we assumed dipole geometry, a $B_{0}$ scaled to equipartition from the main-sequence dynamo, and considered magnetic flux conservation. For comparison, the non-MWDs and MWDs from the local 20-40pc sample of 2022ApJ...935L..12B are shown with the same color scale as the background for their measured field. The crystallization onset and the moment when the magnetic field models reach their maximum as a function of the WD mass are plotted using black and cyan lines, respectively (the dashed part of the cyan line takes the same age as the maximum of the $1\ M_{\odot}$ model for the more massive WDs).