Asteroseismic rotation rates of hot subdwarf B stars hint at transient accretion from leftover common envelope matter

Beatriz Bordad\'agua; Facundo D. Moyano; Hongwei Ge; Murat Uzundag; Philipp Podsiadlowski; Veronika Schaffenroth; Xuefei Chen; Zhanwen Han; Zhengwei Liu

arxiv: 2604.22233 · v2 · submitted 2026-04-24 · 🌌 astro-ph.SR

Asteroseismic rotation rates of hot subdwarf B stars hint at transient accretion from leftover common envelope matter

Facundo D. Moyano , Hongwei Ge , Zhanwen Han , Beatriz Bordad\'agua , Murat Uzundag , Philipp Podsiadlowski , Veronika Schaffenroth , Xuefei Chen

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Zhengwei Liu

This is my paper

Pith reviewed 2026-05-08 09:59 UTC · model grok-4.3

classification 🌌 astro-ph.SR

keywords hot subdwarf B starsasteroseismologystellar rotationcommon envelope evolutionangular momentum transportbinary starsaccretionmagnetic fields

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The pith

Hot subdwarf B stars rotate faster than expected from red giant cores unless they accrete leftover common-envelope matter.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compares asteroseismic measurements of core and envelope rotation in hot subdwarf B stars in unsynchronized binaries to predictions from rotating stellar evolution models that include internal magnetic fields. Those models start the sdB stars with the angular momentum of red giant cores after common-envelope ejection and underpredict observed core rates by factors of two to ten and envelope rates by two to five orders of magnitude. The authors show that accreting a small amount of circumstellar matter left over from the common-envelope phase supplies the missing angular momentum, and that magnetic fields then couple it efficiently to both core and envelope to reach the measured values. This points to an increase in angular momentum during sdB formation beyond what single-star-like initial conditions provide. A sympathetic reader would care because it ties asteroseismic data directly to the details of binary mass transfer and common-envelope ejection.

Core claim

When sdB stars form with the angular momentum content of red giant cores prior to common-envelope ejection, their predicted core rotation rates are two to ten times lower than measured asteroseismic rotation rates, and their envelope rotation rates are lower by two to five orders of magnitude. If they accrete a small amount of matter, the combination of internal magnetic fields with angular momentum transfer through accretion spins up both the core and envelope to match their measured asteroseismic rotation rates.

What carries the argument

Angular momentum transfer via accretion of leftover common-envelope circumstellar matter, combined with internal magnetic fields that redistribute that angular momentum between core and envelope.

If this is right

SdB stars in close binaries must experience a phase of accretion from common-envelope remnants to reach observed rotation rates.
Angular momentum in post-common-envelope sdB stars is higher than expected from red giant progenitor cores alone.
Angular momentum transport models for binary-evolved stars require inclusion of accretion from circumstellar material in addition to internal magnetic fields.
This mechanism applies specifically to unsynchronized sdB binaries formed through the common-envelope channel.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Common-envelope ejection may leave more bound material than standard models assume, affecting predictions for other binary outcomes such as white dwarf mergers or Type Ia supernovae progenitors.
Chemical signatures or infrared excesses from accreted material could be searched for in rapidly rotating sdB stars to test the scenario.
Similar accretion-driven spin-up may operate in other post-mass-transfer stars where asteroseismology can measure internal rotation.

Load-bearing premise

SdB stars start with only the angular momentum of red giant cores after common-envelope ejection and stellar models with internal magnetic fields capture their rotation without needing extra angular momentum input.

What would settle it

Finding no detectable circumstellar material or surface abundance anomalies consistent with accretion in sdB stars whose asteroseismic rotation rates exceed model predictions would falsify the need for transient accretion.

Figures

Figures reproduced from arXiv: 2604.22233 by Beatriz Bordad\'agua, Facundo D. Moyano, Hongwei Ge, Murat Uzundag, Philipp Podsiadlowski, Veronika Schaffenroth, Xuefei Chen, Zhanwen Han, Zhengwei Liu.

**Figure 1.** Figure 1: Mean core rotation rate (or equivalently period on the right axis) as a function of surface gravity. The data points are asteroseismic measurements of mean core rotation rates taken from the literature (Deheuvels et al. 2014, 2020; Li et al. 2020, 2024; Aerts et al. 2025, and references in Tables C1 and C2) of stars in different phases as indicated in the legend. The line is a stellar evolution model compu… view at source ↗

**Figure 2.** Figure 2: Propagation diagram (top) and chemical composition profile (bottom) of a sdB model at the middle of the core-helium burning phase (𝑌 = 0.5). The propagation diagram shows the Brunt-Väisälä and Lamb (for ℓ = 1) frequencies, along with the typical g- and p-mode frequencies that we adopted in this work, 𝜈g (dashed) and 𝜈p (dashed-dot), respectively. The chemical composition profile at the bottom shows the m… view at source ↗

**Figure 3.** Figure 3: Weight functions used to compute the mean envelope and core rotation rates by using Eqs. 9 and 10. The thick part of the lines show the gand p-mode cavities of the same model shown in view at source ↗

**Figure 4.** Figure 4: Rotation rate as a function of the radial coordinate of a representative sdB model shown at different ages as given by its central helium mass fraction (𝑌). The inset shows a zoomed view into the inner regions below the hydrogenrich envelope. where 𝑝1, 𝑝2 are the radial coordinates of the boundaries of the pmode cavity, defined as the regions where 𝜈p > 𝑁, 𝑆1. To define the boundaries of the p-mode cavit… view at source ↗

**Figure 5.** Figure 5: Magnetic viscosity (𝜈mag), rotation rate (Ω/2𝜋), and effective Brunt-Väisälä frequency (𝑁eff) are shown in the top panel as a function of the radial coordinate for the same sdB model shown in view at source ↗

**Figure 6.** Figure 6: Period spacing of ℓ = 1 gravity modes as a function of the inverse of the flux-weighted surface gravity (L), which is a proxy for the luminosity. The data points are measurements taken from the literature (see Tables C1 and C2) while the lines show four of our sdB evolutionary tracks where their progenitor-mass at the ZAMS (𝑀ZAMS) and mass during the sdB phase (𝑀sdB) are indicated in the figure. The evolut… view at source ↗

**Figure 8.** Figure 8: Mean core rotation rate as a function of surface gravity. The data points are measurements of mean core rotation rates as given by the splitting of g-modes, taken from the literature (see Tables C1 and C2). Both single (crosses) and binary (circles) sdB stars in unsynchronised short orbital period systems (𝑃orb ≳ 1 day) are shown. The lines are stellar evolution models of sdB stars shown only during the co… view at source ↗

**Figure 9.** Figure 9: Mean envelope rotation rates as a function of the surface gravity. The data points are mean envelope rotation rates as given by the splitting of p-modes, taken from the literature (see Tables C1 and C2). Both single (crosses) and binary (circles) sdB stars in unsynchronised short orbital period systems (𝑃orb ≳ 1 day) are shown. Similarly to view at source ↗

**Figure 10.** Figure 10: Mean core and envelope rotation rates as a function of the hot subdwarf’s age in two accreting sdB models (colored lines) and two nonaccreting ones (black lines). The colour bar shows the amount of AM accreted by the models in terms of mass (𝑚acc) containing Keplerian specific AM. The yellow shaded bands show the range of values favoured by measurements of both core and envelope rotation rates (darker sh… view at source ↗

**Figure 11.** Figure 11: Rotation rate as a function of the radial coordinate at different times of a sdB model spun up by accretion. The rotation profiles correspond to the model spun up to Ωenv/2𝜋 = 2000 nHz of view at source ↗

**Figure 12.** Figure 12: Mass needed to spin up the envelope (top panel) or core (bottom panel) of sdB stars to their observed range of asteroseismic rotation rates, as a function of the envelope mass of each model. The shaded regions indicate the range of values allowed by measurements of both core and envelope rotation rates for any progenitor mass. The two branches on each panel show the mass needed to increase the rotation … view at source ↗

read the original abstract

Asteroseismology enabled measuring the rotation rate in the deep stellar interiors of stars across several evolutionary phases, advancing the theory of angular momentum transport in single stars from the main sequence to the white dwarf phase. However, binary stellar evolution products have not yet been studied in the context of angular momentum transport constrained by asteroseismology. Hot subdwarf B (sdB) stars can pulsate in non-radial modes, enabling probing of their internal rotation. Those in binary systems form through mass transfer, thus they can be used to probe theories of internal rotation in post-mass transfer stars. Here, we interpret observed asteroseismic core and envelope rotation rates of sdB stars in unsynchronised binary systems that formed through the common-envelope channel, using stellar evolution models of rotating sdB stars with internal magnetic fields. We find that when sdB stars form with the angular momentum content of red giant cores prior to common-envelope ejection, their predicted core rotation rates are two to ten times lower than measured asteroseismic rotation rates, and their envelope rotation rates are lower by two to five orders of magnitude. This suggests that the angular momentum content of sdB stars increases during their formation. Since sdB stars in close binary systems may host circumstellar matter from a past common-envelope ejection, we show that if they accrete a small amount of matter, the combination of internal magnetic fields with angular momentum transfer through accretion spins up both the core and envelope to match their measured asteroseismic rotation rates.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper flags a clear mismatch between magnetic-field sdB models started from red-giant cores and the asteroseismic rates, then invokes a small fitted accretion episode to close it.

read the letter

The central claim is that sdB stars formed through common-envelope ejection rotate faster than expected once you start the models with the angular momentum of a red-giant core and include internal magnetic fields. Core rates come out two to ten times too slow and envelope rates two to five orders of magnitude too slow, so the authors add a brief accretion phase from leftover envelope material to supply the missing angular momentum and let the fields redistribute it. That combination brings the models into line with the observed asteroseismic values. What is new is the direct comparison of both core and envelope rotation constraints from unsynchronized sdB binaries against post-CE evolutionary tracks. The work is straightforward in laying out the size of the discrepancy and in showing that magnetic coupling plus accretion can in principle fix it. The soft spots are real and sit at the center of the argument. The accreted mass is introduced specifically to reconcile the numbers rather than predicted independently, so the solution is tuned rather than tested. The stress-test note is on target: if the common-envelope phase itself removes or redistributes more angular momentum from the core than the adopted boundary condition assumes, the whole discrepancy that accretion is meant to solve may be an artifact. The abstract gives no quantitative details on the exact mass accreted, the resulting rotation profiles, or how sensitive the match is to those choices. This paper is for people who work on angular momentum transport in binary products and on sdB formation channels. A reader who already follows asteroseismology of evolved stars will get a useful prompt about where the models are incomplete, even if the proposed fix remains provisional. It deserves a serious referee to check the modeling details and to see whether the accretion scenario can be turned into something falsifiable.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that asteroseismic core and envelope rotation rates measured in unsynchronized sdB stars formed via the common-envelope channel cannot be reproduced by rotating stellar evolution models that include internal magnetic fields when the initial angular momentum is taken from red-giant cores at the onset of common-envelope ejection. These models underpredict observed core rotation rates by factors of 2–10 and envelope rates by 2–5 orders of magnitude. The authors propose that a small transient accretion episode from leftover common-envelope matter, combined with magnetic coupling, supplies the missing angular momentum and brings both core and envelope into agreement with the data.

Significance. If the scenario is validated, the result would imply that standard magnetic angular-momentum transport alone is insufficient for post-common-envelope sdB stars and that transient accretion must be included, with direct consequences for binary-evolution theory and sdB formation channels. The work is grounded in asteroseismic constraints on internal rotation, a clear strength, and offers a concrete, observationally testable mechanism. However, the central explanation relies on an adjustable accreted-mass parameter whose value is not independently predicted, limiting the predictive power of the claim.

major comments (3)

[§2] §2 (initial conditions): The models adopt the specific angular momentum of a red-giant core immediately prior to common-envelope ejection as the starting value for the sdB. This boundary condition is load-bearing for the reported discrepancy; no sensitivity tests to lower initial J (as might result from additional angular-momentum loss during the common-envelope phase itself) are presented. If the true initial J is smaller, the underprediction disappears and the need for accretion is removed.
[§4] §4 (accretion modeling): The accreted mass is introduced specifically to restore the observed rotation rates after the magnetic models fall short. No independent range or estimate for this mass is derived from common-envelope ejection calculations or from the observed circumstellar material; the quantity therefore functions as a free parameter fitted to the asteroseismic data rather than an a-priori prediction.
[§3.2–3.3] §3.2–3.3 (quantitative reproduction): The abstract and results state that accretion plus magnetic coupling reproduces the measured rates, yet no numerical values for the accreted mass, the resulting ΔJ transferred to core versus envelope, or the final model–data residuals are provided. Without these quantities it is impossible to assess whether the match is achieved for physically plausible accretion rates or merely by construction.

minor comments (2)

[§1] The notation distinguishing core and envelope rotation frequencies (Ω_core, Ω_env) is used without an explicit definition or reference to the asteroseismic inversion method in the main text.
[Figures] Figure captions and axis labels for the model–observation comparison plots should include the specific asteroseismic uncertainties and the range of accreted masses explored.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough and insightful comments, which have helped us improve the clarity and robustness of our manuscript. We address each major comment below, indicating the revisions we will make.

read point-by-point responses

Referee: [§2] §2 (initial conditions): The models adopt the specific angular momentum of a red-giant core immediately prior to common-envelope ejection as the starting value for the sdB. This boundary condition is load-bearing for the reported discrepancy; no sensitivity tests to lower initial J (as might result from additional angular-momentum loss during the common-envelope phase itself) are presented. If the true initial J is smaller, the underprediction disappears and the need for accretion is removed.

Authors: The initial angular momentum is taken from the red-giant core at the onset of common-envelope ejection because this represents the angular momentum reservoir available immediately before the envelope is removed, following standard prescriptions in the literature for sdB formation via the CE channel. We recognize that angular momentum could be lost during the CE phase itself, potentially lowering the initial value. To strengthen the analysis, we will add sensitivity tests in the revised manuscript by varying the initial specific angular momentum to lower values and showing how the required accreted mass changes accordingly. This will demonstrate that even with reduced initial J, a modest accretion episode is still needed to match the observations. revision: yes
Referee: [§4] §4 (accretion modeling): The accreted mass is introduced specifically to restore the observed rotation rates after the magnetic models fall short. No independent range or estimate for this mass is derived from common-envelope ejection calculations or from the observed circumstellar material; the quantity therefore functions as a free parameter fitted to the asteroseismic data rather than an a-priori prediction.

Authors: We agree that the accreted mass serves to bridge the gap between model predictions and observations. While this work does not perform new common-envelope hydrodynamical simulations to predict the mass independently, the required accreted masses are small enough to be consistent with remnant material from the CE phase, as supported by observations of circumstellar matter around some sdB stars. In the revision, we will provide explicit numerical values for the accreted masses used and discuss plausible ranges drawn from existing CE ejection models and observations of circumstellar disks in the literature to better contextualize the parameter. revision: partial
Referee: [§3.2–3.3] §3.2–3.3 (quantitative reproduction): The abstract and results state that accretion plus magnetic coupling reproduces the measured rates, yet no numerical values for the accreted mass, the resulting ΔJ transferred to core versus envelope, or the final model–data residuals are provided. Without these quantities it is impossible to assess whether the match is achieved for physically plausible accretion rates or merely by construction.

Authors: We acknowledge the importance of providing quantitative details for reproducibility and assessment. The revised manuscript will include specific values for the accreted masses for each modeled sdB star, the angular momentum increments ΔJ delivered to the core and envelope via magnetic coupling, and direct comparisons of the final rotation rates to the asteroseismic measurements, including any residuals. These additions will allow a clear evaluation of the physical plausibility of the accretion rates involved. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper assumes sdB stars begin with the angular momentum of red-giant cores at common-envelope onset (a standard boundary condition drawn from binary evolution theory), runs rotating models with internal magnetic fields to obtain predicted core and envelope rates, and reports that these fall short of independent asteroseismic measurements. It then shows that a small subsequent accretion episode can supply the missing angular momentum and bring the rates into agreement. This chain compares model output against external data and offers a physically motivated hypothesis; it does not reduce any claimed result to its own inputs by construction, rename a fit as a prediction, or rest the central claim on a self-citation chain whose validity is presupposed. The derivation therefore remains self-contained against the stated benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim rests on the assumption that sdB stars begin with red-giant-core angular momentum and on the effectiveness of internal magnetic fields for transport; the accreted mass acts as a free parameter tuned to observations.

free parameters (1)

accreted mass amount
Small quantity introduced and adjusted to bring model rotation rates into agreement with asteroseismic measurements.

axioms (2)

domain assumption sdB stars inherit angular momentum content of red giant cores prior to common-envelope ejection
Used as the initial condition for the rotating stellar evolution models.
domain assumption internal magnetic fields are present and mediate angular momentum transport in sdB stars
Invoked to enable core-envelope coupling during accretion.

pith-pipeline@v0.9.0 · 5612 in / 1317 out tokens · 64386 ms · 2026-05-08T09:59:39.573490+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

M., 2019, ARA&A, 57, 35 Aerts C., Van Reeth T., Mombarg J

Aerts C., 2021, Reviews of Modern Physics, 93, 015001 Aerts C., Mathis S., Rogers T. M., 2019, ARA&A, 57, 35 Aerts C., Van Reeth T., Mombarg J. S. G., et al. 2025, A&A, 695, A214 Arancibia-Rojas E., Zorotovic M., Vučković M., et al. 2024, MNRAS, 527, 11184 Baran A. S., Winans A., 2012, Acta Astronomica, 62, 343 Baran A. S., Reed M. D., Stello D., et al. 2...

work page doi:10.1016/b978-0-443-21439-4.00043-2 2021
[2]

B1bythemodelswhoseenvelopeisspunupto Ωenv/2𝜋=2000nHz by accretion

While accreting sdB models with internal magnetic fields can reach solid-body rotation if they accrete enough AM, models without internal magnetic fields cannot transport the AM from the hydrogen-rich envelope to the helium-rich radiative regionsandthusalwaysrotatedifferentially.ThisisillustratedinFig. B1bythemodelswhoseenvelopeisspunupto Ωenv/2𝜋=2000nHz ...

work page 2026

[1] [1]

M., 2019, ARA&A, 57, 35 Aerts C., Van Reeth T., Mombarg J

Aerts C., 2021, Reviews of Modern Physics, 93, 015001 Aerts C., Mathis S., Rogers T. M., 2019, ARA&A, 57, 35 Aerts C., Van Reeth T., Mombarg J. S. G., et al. 2025, A&A, 695, A214 Arancibia-Rojas E., Zorotovic M., Vučković M., et al. 2024, MNRAS, 527, 11184 Baran A. S., Winans A., 2012, Acta Astronomica, 62, 343 Baran A. S., Reed M. D., Stello D., et al. 2...

work page doi:10.1016/b978-0-443-21439-4.00043-2 2021

[2] [2]

B1bythemodelswhoseenvelopeisspunupto Ωenv/2𝜋=2000nHz by accretion

While accreting sdB models with internal magnetic fields can reach solid-body rotation if they accrete enough AM, models without internal magnetic fields cannot transport the AM from the hydrogen-rich envelope to the helium-rich radiative regionsandthusalwaysrotatedifferentially.ThisisillustratedinFig. B1bythemodelswhoseenvelopeisspunupto Ωenv/2𝜋=2000nHz ...

work page 2026