[Paper Review] Origin of the rotation rates of single white dwarfs

H. C. Spruit|arXiv (Cornell University)|Feb 11, 1998

Stellar, planetary, and galactic studies1 references3 citations

TL;DR

This paper proposes that the rotation of single white dwarfs originates not from their main-sequence progenitors but from angular momentum transfer during mass loss on the asymptotic giant branch (AGB), driven by weak, non-axisymmetric asymmetries in the AGB superwind. Simulations show that small random non-axisymmetries (~10⁻³) in mass loss can produce white dwarf rotation periods of about one day, consistent with observations.

ABSTRACT

I argue that the rotation of white dwarfs is not a remnant of the angular momentum of their main sequence progenitors but a result of the mass loss process on the AGB. Weak magnetic fields, if present in stellar interiors, are likely to maintain approximately uniform rotation in stars, both on the main sequence and on the giant branches. The nearly uniform rotation of the core of the Sun is evidence for the existence of such fields. Exactly axisymmetric mass loss on the AGB from uniformly rotating stars would lead lead to white dwarfs with very long rotation periods ($>$ 10 yr). Small random non-axisymmetries ($\sim 10^{-3}$) in the mass loss process, on the other hand, add sufficient angular momentum to explain the observed rotation periods around one day. The process illustrated with a computation of the probability distribution of the rotation periods under the combined influence of random forcing by weak nonaxisymmetries and angular momentum loss in the AGB superwind. Such asymmetries can in principle be observed by proper motion studies of the clumps in interferometric images of SiO maser emission.

Motivation & Objective

• To resolve the discrepancy between observed white dwarf rotation periods (~1 day) and theoretical expectations from uniform main-sequence angular momentum.
• To investigate whether angular momentum in white dwarfs is inherited from progenitor stars or generated during the AGB phase.
• To determine the role of weak magnetic fields and non-axisymmetric mass loss in shaping white dwarf rotation rates.
• To model the probability distribution of rotation periods under the influence of random asymmetries in the AGB superwind.
• To link observable features in maser emission clumps to the underlying asymmetries driving rotation.

Proposed method

• Modeling the AGB mass loss process as a combination of nearly axisymmetric wind with small random non-axisymmetric perturbations (~10⁻³ amplitude).
• Using a dynamical model to compute the angular momentum transfer from the star to the outflowing wind under these asymmetric conditions.
• Simulating the probability distribution of resulting white dwarf rotation periods based on the stochastic nature of the asymmetries.
• Incorporating the effect of weak internal magnetic fields that maintain near-uniform rotation in stellar interiors, as supported by solar core rotation.
• Predicting observable signatures in SiO maser emission clumps via proper motion studies to detect asymmetries in the mass loss.
• Applying conservation of angular momentum in the wind to derive the final spin period of the white dwarf remnant.

Experimental results

Research questions

• RQ1 Why do single white dwarfs exhibit rotation periods of approximately one day, despite low angular momentum in their main-sequence progenitors?
• RQ2 To what extent can non-axisymmetric mass loss on the AGB account for the observed rotation rates of white dwarfs?
• RQ3 What level of asymmetry in the AGB superwind is required to produce the observed white dwarf rotation periods?
• RQ4 Can weak internal magnetic fields explain the uniform core rotation observed in stars like the Sun, and how does this affect white dwarf spin?
• RQ5 Are the non-axisymmetric features in the AGB mass loss process observable through proper motion studies of maser clumps?

Key findings

• Non-axisymmetric mass loss with amplitude ~10⁻³ in the AGB superwind can transfer sufficient angular momentum to produce white dwarf rotation periods of about one day.
• Axisymmetric mass loss alone would result in white dwarf rotation periods exceeding 10 years, inconsistent with observations.
• The observed distribution of white dwarf rotation periods is well explained by stochastic, small-amplitude asymmetries in the mass loss process.
• Weak magnetic fields in stellar interiors are likely responsible for maintaining nearly uniform rotation in stars, including the Sun’s core.
• The asymmetries driving white dwarf rotation could, in principle, be detected via proper motion measurements of clumps in interferometric images of SiO maser emission.
• The model predicts a probability distribution of rotation periods that matches the observed range, supporting the AGB mass loss origin of white dwarf spin.