The effect of near-core mixing on rejuvenation and the asteroseismic properties of massive accretors

Abstract: The relatively recent revelation of the high occurrence rate of binary interactions, especially in intermediate- and high-mass systems, has prompted multiple investigations into their asteroseismic imprints. The near-core region just outside the convective cores of mass-accreting early-type main-sequence stars in binaries has been theorised to be sensitive to assumptions about mixing (notably semiconvection) and accretion physics. In turn, the predicted asteroseismic properties depend strongly on the physical properties of this near-core region. We explore how robust the previously identified asteroseismic imprints of mass accretion are to changes in semiconvective mixing. Using one-dimensional stellar structure and evolution models, this parameter study shows the dominant effect of convective boundary mixing on rejuvenation and the post-accretion asteroseismic properties. The recovered seismic imprint, largely robust to variations in semiconvective mixing efficiency, changes drastically when convective boundary mixing is not included in the models. We find that the post-accretion thermal relaxation is key in determining the final near-core structure and the asteroseismic imprint of accretion. We reaffirm the potential of Fourier transforms of period spacing patterns to quantify the effects of different near-core mixing and accretion-rate assumptions on asteroseismic signals. Overall, this work highlights the sensitivity of the asteroseismic imprint of accretion not only on stellar structure and evolution modelling assumptions, but also on the accretion physics. The logical next step is to arrive at a more general picture of the asteroseismic imprint of mass transfer by exploring its properties in a multi-dimensional parameter study including single- and binary-star assumptions.

• The paper finds that convective boundary mixing, rather than semiconvection, primarily drives rejuvenation, raising the central hydrogen abundance from 0.48 to as much as 0.56 in modeled accretors.
• Post-accretion thermal relaxation—not mass transfer alone—creates the double-peaked Brunt–Väisälä frequency profile by briefly expanding the convective core and later driving its recession.
• Fourier transforms of gravity-mode period-spacing patterns distinguish mixing pathways: CBM models produce multiple dominant peaks, while models without CBM generally show one, offering a potential seismic test of rejuvenation physics.

This paper by Henneco and Bowman presents a parameter study of how semiconvective mixing efficiency affects the rejuvenation and asteroseismic properties of mass-accreting early-type main-sequence stars. Building on the intermediate-mass binary configuration of Wagg et al. (2024) — an initially $3.0\,M_\odot$ accretor in a 5-day orbit that accretes $0.5\,M_\odot$ via thermal-timescale Roche-lobe overflow — the authors recompute MESA stellar evolution models with semiconvective efficiencies $\alpha_{\mathrm{sc}}$ spanning $0$ to $10^3$, plus a model using the Schwarzschild criterion (effectively infinite semiconvection). Two model sets are computed: one with exponential overshooting ($f_{\mathrm{CBM}}=0.005$) and one without convective boundary mixing (CBM). Gravity-mode period spacing patterns (PSPs) are then predicted with GYRE for zonal dipole modes and compared against equivalent single-star models. The central finding is that CBM, not semiconvection, dominates rejuvenation in accretors, and that the post-accretion thermal relaxation — rather than accretion itself — shapes the characteristic double-peaked Brunt–Väisälä frequency profile that underlies the asteroseismic imprint of accretion (2606.13567).

The models use MESA r23.05.1 with the binary module, the Kolb mass-transfer scheme, a mass-transfer efficiency of 0.5, no rotation, and no wind mass loss. Convection uses MLT with $\alpha_{\mathrm{MLT}}=2.0$ and the Ledoux criterion, with semiconvection treated via the Langer (1985) diffusion scheme. The authors deliberately use substantially higher temporal and spatial resolution than Wagg et al. (2024) (10× temporal resolution; mesh_delta_coeff of 0.075), verified by convergence tests, which means their models are similar but not identical to the original case study. Pulsations are computed with GYRE v7.1 in the adiabatic regime for $\ell=1$, $m=0$ modes, with radial orders $n = 1$–$0.5\,M_\odot$0; the authors demonstrate that this sampling choice does not alter the results. Single-star comparison models span $0.5\,M_\odot$1–$0.5\,M_\odot$2 to match the accretors' HR-diagram positions, since the degree of rejuvenation shifts accretors away from a nominal $0.5\,M_\odot$3 single-star track.

A key result contradicts the classical picture of Braun and Langer (1995), in which the semiconvective efficiency controls whether and how much an accretor rejuvenates. In the models with overshooting, all accretors rejuvenate — including the model with $0.5\,M_\odot$4 — because the exponential CBM prescription extends mixing into the chemically stratified near-core region independently of the mean molecular weight gradient. The convective core grows in mass even before semiconvection appears. Quantitatively, models with $0.5\,M_\odot$5 rejuvenate from $0.5\,M_\odot$6 at the onset of mass transfer to $0.5\,M_\odot$7–$0.5\,M_\odot$8, while the highest-efficiency models reach $0.5\,M_\odot$9, $\alpha_{\mathrm{sc}}$0, and $\alpha_{\mathrm{sc}}$1 for $\alpha_{\mathrm{sc}}$2, $\alpha_{\mathrm{sc}}$3, and the Schwarzschild model, respectively. Helium core masses at the TAMS vary only from $\alpha_{\mathrm{sc}}$4 to $\alpha_{\mathrm{sc}}$5 across the full range of $\alpha_{\mathrm{sc}}$6 with CBM included — nearly identical to single-star values — confirming that semiconvection has a minor effect when CBM is present. The implication is that any evolution code using the standard step or exponential overshooting prescriptions will predict at least some rejuvenation in accretors, regardless of semiconvection assumptions.

All models with $\alpha_{\mathrm{sc}}$7 develop one or more short-lived convective shells (off-centre convection zones) above the pre-mass-transfer convective core extent ($\alpha_{\mathrm{sc}}$8–$\alpha_{\mathrm{sc}}$9), with lifetimes of order $0$0 yr. These shells homogenise part of the pp-chain-induced $0$1 profile and contribute marginally to rejuvenation, but most of their chemical impact is washed out by the growing core and CBM region.

At high efficiencies ($0$2 and the Schwarzschild model), the behaviour changes qualitatively: the accretors undergo two large and several smaller burst-like rejuvenation episodes driven by extended, short-lived convective shells. The proposed mechanism is a secular analogue of the $0$3-mechanism: efficient semiconvection creates step-like discontinuities in the $0$4 profile, which produce opacity jumps that block the radiative flux, build up the temperature gradient, and trigger extended convection zones. The authors explicitly caution that this heat-engine-like behaviour may be an artifact of the sharp transition between efficient mixing and the imposed minimum envelope diffusion coefficient ($0$5) in MESA; they verified the bursts are not numerical by recomputing at 4× higher and lower temporal resolution, but replication in other codes or with smoothed diffusion coefficients remains an open test.

The double-peaked Brunt–Väisälä ($0$6) profile previously identified by Wagg et al. (2024) and Miszuda et al. (2025, the $0$7 $0$8 Cep case) is shown here to be a consequence of post-mass-transfer thermal relaxation rather than accretion per se. After the abrupt end of mass transfer, the accretor contracts by $0$9, releasing gravitational energy that transiently grows the convective core to $10^3$0 before it recedes. The contraction pushes the sharp chemical gradient responsible for the outer $10^3$1 peak outward, and the subsequent core recession creates the inner peak, leaving a thin plateau in the hydrogen profile between them. A control experiment with progressively decreasing accretion rate near the end of mass transfer reproduces the same final core mass, confirming this is not an artifact of the artificially abrupt mass-transfer termination.

This interpretation reconciles apparently divergent results in the literature. A companion model with a 1.5-day initial period — Case A, nuclear-timescale mass transfer — shows that accretors remaining in thermal equilibrium barely contract ($10^3$2), do not grow their cores post-transfer, and produce a $10^3$3 profile in which the two peaks merge, matching the morphology seen in Wu et al. (2026). The authors derive a simple criterion: with $10^3$4 and thermal-timescale transfer, accretors fall out of thermal equilibrium for initial mass ratios $10^3$5, giving $10^3$6 for $10^3$7. They also address a potential objection regarding mass-dependent thermal timescales: although the $10^3$8 accretor of Miszuda et al. has a thermal timescale only ~3.6× shorter than a $10^3$9 accretor, its mass-transfer rate is $f_{\mathrm{CBM}}=0.005$0 times larger, so the thermal-equilibrium argument holds.

For accretors with CBM, the PSPs show quasi-periodic deviations from the asymptotic period spacing $f_{\mathrm{CBM}}=0.005$1 with higher amplitude and a phase shift relative to equivalent single stars, plus a second variability component — consistent across all semiconvective efficiencies. The absolute differences in $f_{\mathrm{CBM}}=0.005$2 between accretors and single stars are at most ~100 s (e.g. $f_{\mathrm{CBM}}=0.005$3 s at $f_{\mathrm{CBM}}=0.005$4), which the authors note is generally insufficient to flag a star as anomalous in population studies. Qualitatively, the PSP morphology is robust to $f_{\mathrm{CBM}}=0.005$5, implying that the seismic imprints reported in earlier accretor seismology studies are not sensitive artifacts of a particular semiconvection assumption — though the authors note this conclusion should be verified with dedicated parameter studies at different masses.

The more discriminating diagnostic is the Fourier transform of the normalised PSP in radial-order space, following Guo (2026) and Wu et al. (2026). FT peaks map onto sharp variations in $f_{\mathrm{CBM}}=0.005$6 via $f_{\mathrm{CBM}}=0.005$7, where $f_{\mathrm{CBM}}=0.005$8 is the buoyancy coordinate. Accretors with CBM show multiple FT peaks corresponding to the double-peaked $f_{\mathrm{CBM}}=0.005$9 structure, whereas single stars show a single dominant peak. The relative heights and locations of these peaks vary quantitatively with $\alpha_{\mathrm{MLT}}=2.0$0 even when the PSPs themselves look nearly identical, establishing the FT as the practical means of distinguishing mixing assumptions.

When overshooting is removed, the classical Braun and Langer picture re-emerges. Models with $\alpha_{\mathrm{MLT}}=2.0$1 show no rejuvenation at all: $\alpha_{\mathrm{MLT}}=2.0$2 stays essentially constant, and their helium cores at TAMS ($\alpha_{\mathrm{MLT}}=2.0$3–$\alpha_{\mathrm{MLT}}=2.0$4) are undermassive relative to single stars. Rejuvenation begins at $\alpha_{\mathrm{MLT}}=2.0$5 and increases monotonically with efficiency, producing overmassive cores for $\alpha_{\mathrm{MLT}}=2.0$6. Notably, a considerable fraction of the rejuvenation still occurs after mass transfer ends, with the pace set by semiconvection and convective shells persisting for more than two thermal timescales.

Seismically, these models lack the double-peaked $\alpha_{\mathrm{MLT}}=2.0$7 structure entirely. Each low-efficiency model has a single dominant mode-trapping location, fixed by the bottom of the accretion-induced convective shell at the pre-transfer core extent, and consequently a single dominant FT peak. This yields a direct observational test: if real accretors rejuvenate via the CBM-free pathway, their PSP Fourier transforms should show only one dominant peak, and the multi-peak signature used to identify post-accretion stars loses its diagnostic power. The presence of multiple dominant FT peaks in an observed SPB star would therefore constitute evidence that CBM enabled core growth during accretion. The authors also flag that the sharp $\alpha_{\mathrm{MLT}}=2.0$8 features at the bottom of convective shells — responsible for mode trapping in these models — might be amplified by the absence of CBM at shell boundaries in their setup.

The paper is candid about several dependencies. The CBM-driven rejuvenation result rests on overshooting prescriptions that are, by construction, insensitive to the near-core chemical stratification — an assumption the authors consider physically unlikely, since stratification should presumably damp penetrating convective material. Whether CBM is sufficient to drive core growth in real accretors must ultimately be settled by 3D simulations. The secular heat-engine mechanism at high $\alpha_{\mathrm{MLT}}=2.0$9 may be an implementation artifact of sharp mixing-coefficient transitions in 1D codes, and its physical reality is unconfirmed. The study fixes the accreted-to-initial mass ratio at ~0.17, a single initial mass ratio $\ell=1$0, and a single binary configuration; rotation-induced mixing is excluded, though prior work suggests it can flatten the outer $\ell=1$1 peak in some systems but not others. Whether the PSP robustness conclusions extend to different stellar masses remains to be demonstrated.

This parameter study establishes that convective boundary mixing, rather than semiconvection, is the dominant enabler of rejuvenation in mass-accreting intermediate-mass stars, revising the classical semiconvection-controlled picture. The double-peaked Brunt–Väisälä profile underlying the asteroseismic imprint of accretion is shown to originate from post-transfer thermal relaxation, with accretion rate (via thermal disequilibrium) determining whether that profile is double-peaked or merged. The asteroseismic imprint of accretion is robust to semiconvective efficiency when CBM is present, but its diagnostic character changes fundamentally without CBM, making the number of dominant peaks in the Fourier transform of a period spacing pattern a direct test of the rejuvenation mechanism. The work underscores that accretor seismology predictions are sensitive both to stellar physics assumptions and to mass-transfer physics, and that a unified picture requires systematic multi-dimensional exploration across binary configurations.