A test of the planet–star unipolar inductor for magnetic white dwarfs

Abstract

Despite thousands of spectroscopic detections, only four isolated white dwarfs exhibit Balmer emission lines. The temperature inversion mechanism is a puzzle over 30 years old that has defied conventional explanations. One hypothesis is a unipolar inductor that achieves surface heating via ohmic dissipation of a current loop between a conducting planet and a magnetic white dwarf. To investigate this model, new time-resolved spectroscopy, spectropolarimetry, and photometry of the prototype GD 356 are studied. The emission features vary in strength on the rotational period, but in anti-phase with the light curve, consistent with a cool surface spot beneath an optically thin chromosphere. Possible changes in the line profiles are observed at the same photometric phase, potentially suggesting modest evolution of the emission region, while the magnetic field varies by 10 per cent over a full rotation. These comprehensive data reveal neither changes to the photometric period, nor additional signals such as might be expected from an orbiting body. A closer examination of the unipolar inductor model finds points of potential failure: the observed rapid stellar rotation will inhibit current carriers due to the centrifugal force, there may be no supply of magnetospheric ions, and no anti-phase flux changes are expected from ohmic surface heating. Together with the highly similar properties of the four cool, emission-line white dwarfs, these facts indicate that the chromospheric emission is intrinsic. A tantalizing possibility is that intrinsic chromospheres may manifest in (magnetic) white dwarfs, and in distinct parts of the HR diagram based on structure and composition.

Slow convection and fast rotation in crystallization-driven white dwarf dynamos

“…About a third of the sample is consistent with a crystallization-driven dynamo, with the other white dwarfs being either too hot to be crystallizing or having magnetic fields well above our maximum, requiring a different explanation. Interestingly, the recently discovered class of single white dwarfs with Zeemansplit Balmer emission lines (Gänsicke et al 2020;Walters et al 2021) exhibits fields that are fairly close to our maximum, potentially explaining the clustering of these white dwarfs at 𝑇 eff ≈ 7500 K, where 𝐵(𝑇 eff ) peaks for 0.6−0.8 M white dwarfs (see also Schreiber et al 2021b).…”

“…More specifically, our Fig. 2 suggests that the clustering of Balmer-emitting white dwarfs (which have masses of 0.6 − 0.8 M according to the HR diagram; see Gänsicke et al 2020;Walters et al 2021) at 𝑇 eff ≈ 7500 K may be linked to the maximum 𝐵 surf (𝑇 eff ) attained by crystallization driven dynamos as they cool. This maximum is reached shortly after the onset of crystallization, potentially explaining why both hotter and cooler white dwarfs lack Balmer emission lines.…”

“…Recently, a small class of magnetic white dwarfs that exhibit Zeeman-split Balmer emission lines has been identified (Greenstein & McCarthy 1985;Gänsicke et al 2020;Reding et al 2020;Walters et al 2021). It is not clear what mechanism heats the outer layers of these white dwarfs to high temperatures, stimulating the emission.…”

“…Interestingly, the currently known Balmer-emitting white dwarfs occupy a narrow region in the Hertzsprung-Russell (HR) diagram, clustering at temperatures 𝑇 eff ≈ 7500 K (Gänsicke et al 2020;Walters et al 2021). 1 Schreiber et al (2021b) speculated that this clustering might be related to the generation of magnetic fields by crystallization at such temperatures.…”

“…The black circle indicates a white dwarf without a measured mass. The blue star markers indicate single white dwarfs that exhibit Zeeman-split Balmer emission lines(Gänsicke et al 2020;Walters et al 2021). Intermediate polars (magenta diamonds) are fromFerrario et al (2015).…”