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

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.

💡 Research Summary

This paper investigates the origin and evolution of magnetic fields observed on the surfaces of white dwarfs (WDs) by tracing them back to deep‑seated dynamo fields generated in the convective cores of their main‑sequence (MS) progenitors. The authors combine stellar evolution calculations, white‑dwarf cooling models, and magnetic diffusion theory to test whether a magnetic field generated during the MS can survive the subsequent evolutionary phases and emerge at the WD surface with strengths and timing that match observations.

First, the study estimates the magnetic field strength that can be produced by convective‑core dynamos in MS stars of 1.5–5 M⊙. Using the LPCODE stellar‑evolution code, the authors compute the density and convective velocity profiles of these stars and apply an equipartition relation (B≈√(4π ρ v_c²)) to obtain field strengths ranging from ~6 × 10⁴ G for a 2 M⊙ star up to ~10⁶ G for a 5 M⊙ star. These values are consistent with three‑dimensional magnetohydrodynamic (MHD) simulations of core convection reported in the literature.

Next, a suite of WD models with carbon‑oxygen cores and masses of 0.6, 0.7, 0.8, 0.9, and 1.0 M⊙ is generated with MESA, incorporating phase‑separation physics and realistic equations of state. Electrical conductivities σ are calculated at each radius and time using the Potekhin et al. (1999, 2015) transport coefficients, which yield the Ohmic diffusivity η_ohm = c²/(4πσ). Because crystallization induces compositional convection, a turbulent diffusivity term η_turb = f_Rm η_ohm is added, where f_Rm is a free parameter proportional to the magnetic Reynolds number. The total diffusivity is η = η_ohm + η_turb.

The magnetic field is assumed to be axisymmetric and poloidal, expressed through a vector potential A_φ = Σ_l