Dying stars’ pulses may explain unexpectedly wide white dwarf binaries

Gaia has revealed white dwarf–main-sequence binaries with orbital periods of roughly 100–1,000 days. Each pairs a compact stellar remnant with a companion still burning hydrogen in its core. Their separation poses a puzzle: many appear close enough that their stars should have interacted during the giant phase, yet wider than the usual products of a shared-envelope encounter.

In a new arXiv preprint, Yanxu Shi and colleagues investigate whether resolving a dying giant’s individual thermal pulses can help explain these systems. Their calculations identify a possible formation route, not a demonstration that every observed wide binary followed it.

Why timing matters

Common-envelope evolution begins when unstable mass transfer surrounds both stellar cores with the giant’s outer gas. As the companion moves through that envelope, the orbit contracts, releasing energy that can help expel the gas. The surviving pair is therefore usually expected to have a short orbital period.

But the energy needed to remove the envelope changes throughout the giant’s life. During the thermally pulsing asymptotic giant branch, a late evolutionary stage, repeated helium-shell flashes drive changes in the star’s radius and internal structure. Meanwhile, strong stellar winds progressively strip away its envelope.

A companion encountering the star late in this process may face much less tightly bound gas. Ejecting it can then require less orbital contraction, leaving a wider binary.

The pulses also affect whether the encounter happens at all. Expansion can push the giant beyond its Roche lobe—the region within which matter remains gravitationally associated with that star. Near this boundary, tides can transfer angular momentum from the orbit into the giant’s rotation, shrinking the orbit and further encouraging contact.

Detailed stars, millions of binaries

The researchers combined 51 detailed MESA stellar-evolution tracks, spanning initial masses of one to six times the Sun’s mass, with a population calculation sampling five million initial binaries. The tracks use a fixed initial metallicity of Z = 0.02, describing the mass fraction in elements heavier than helium.

Rather than calculating every star from scratch, the framework assigns primary stars to the precomputed mass grid. It follows changes in radius, winds, stellar spin and orbital separation, including individual thermal pulses. At the onset of mass transfer, it calculates envelope binding energy directly from the donor’s stellar structure.

This matters because a pulse can simultaneously make interaction more likely and make the envelope easier to remove. Averaging over pulses risks missing that combination.

One illustrative simulated binary begins with a 2.4-solar-mass primary and a companion just below one solar mass. After 25 thermal pulses, the giant initiates a common-envelope episode. Under the standard assumptions, it leaves a white dwarf of about 0.65 solar masses and an orbital period of about 118 days.

What the population predicts

In the standard model, approximately 11.5% of the surviving binaries produced by common-envelope episodes beginning during this late giant phase have periods longer than 30 days. That is a fraction of this modeled formation channel—not of all white dwarf binaries or Gaia detections.

The standard calculation assumes that 30% of the released orbital energy helps eject the envelope and that half of its internal energy contributes. Across 16 combinations of these uncertain efficiencies, the long-period fraction ranges from 0.77% to 42.89%. With fully efficient use of orbital energy, periods of several hundred days remain possible even without an internal-energy contribution.

The long-period remnants cluster near 0.6 solar masses. More massive progenitors generally retain more tightly bound envelopes, making wide survivors harder to produce. Massive companions can supply more orbital energy, but their shorter hydrogen-burning lifetimes limit how long those systems remain observable as white dwarf–main-sequence pairs.

A viable route, with unresolved physics

The largest caveat concerns the onset of the shared envelope. The standard model assumes that all mass transfer beginning during the thermally pulsing phase immediately becomes common-envelope evolution. A stricter mass-ratio condition substantially reduces the surviving population, although long-period systems still form.

The stellar tracks also use numerical treatments to suppress late-stage instabilities. Real stars might instead undergo violent pulsations or rapid mass ejection. The calculation does not include stable mass transfer as a competing channel or subsequent post-envelope orbital evolution.

One testable prediction survives these qualifications: wide remnants should have masses close to those expected from isolated stars with the same initial masses, because interaction occurs after most core growth. Star clusters could test this relationship by independently constraining progenitor masses. For now, orbital period alone cannot reliably reveal how a binary formed.