pith. sign in

arxiv: 2512.16225 · v2 · submitted 2025-12-18 · 🌌 astro-ph.SR

Weakened Inspirals I: High Mass Ratio Common Envelope Interactions in RGB Stars

Jack Nibbs , Orsola De Marco , Lionel Siess , Ryosuke Hirai , Daniel Price This is my paper

Pith reviewed 2026-05-16 21:55 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords common envelope evolutionhigh mass ratio binariesred giant branch starspost-CE separationcircumbinary discshydrodynamical simulationsbinary stellar evolutionmass transfer stability
0
0 comments X p. Extension

The pith

Higher mass ratios in common envelope interactions with red giants produce wider post-interaction separations up to about 40 solar radii and significantly more stable inspirals once the mass ratio reaches or exceeds 1.

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

This paper uses three-dimensional hydrodynamical simulations to test how the mass ratio between a red giant branch star and its compact companion changes the outcome of a common envelope interaction. The simulations show that larger companions extend the initial mass transfer phase and reduce the severity of the subsequent orbital decay, leaving the binary at larger separations than in lower mass ratio cases. These wider separations still fall short of the 100 to 800 solar radius systems seen in observations, yet the fallback of ejected envelope material forms circumbinary discs whose properties match those observed around post-interaction binaries. The work therefore supplies a concrete mechanism that weakens but does not eliminate the rapid inspiral expected in standard common envelope evolution.

Core claim

For mass ratios q = M2/M1 greater than or equal to 1, the common envelope inspiral of a 0.88 solar mass, 90 solar radius red giant becomes markedly more stable after a prolonged pre-inspiral mass transfer phase, yielding final separations as large as approximately 40 solar radii; higher mass ratios also increase mass loss through the L2 and L3 points while promoting circumbinary disc formation from fallback material at radii between 0.5 and 5 au on timescales of a few hundred years.

What carries the argument

Three-dimensional smoothed particle hydrodynamics simulations performed with the PHANTOM code that follow the full interaction of a red giant branch primary with companions spanning mass ratios 0.68 to 1.5, tracking orbital decay, envelope ejection, and fallback.

If this is right

  • Post-common-envelope separations increase with mass ratio, reaching a maximum near 40 solar radii for q greater than or equal to 1.
  • The pre-inspiral mass transfer phase lasts longer and is more stable when the companion is more massive.
  • Mass ejection through the outer Lagrange points rises with mass ratio, yet most circumbinary material originates from bound envelope fallback rather than direct L2/L3 outflow.
  • Fallback discs form rapidly at radii 0.5 to 5 au and spread viscously on timescales of hundreds of years, producing structures consistent with observed circumbinary discs.
  • Even the widest simulated separations remain smaller than the 100–800 solar radius post-red-giant binaries found in surveys.

Where Pith is reading between the lines

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

  • Additional angular momentum transport from the newly formed circumbinary disc may be required to reach the largest observed separations.
  • Improved numerical resolution will likely push the upper limit on stable post-interaction separations beyond the current 40 solar radius value.
  • Systems with mass ratios near unity may serve as the transition population between classical close post-common-envelope binaries and the wider observed systems.
  • The short fallback times imply that disc formation and viscous evolution occur well before the binary reaches thermal equilibrium after envelope ejection.

Load-bearing premise

The duration and stability of the pre-common-envelope mass transfer phase are treated as adequately captured at the present numerical resolution, although higher resolution is expected to lengthen that phase further.

What would settle it

A measured post-interaction separation larger than 40 solar radii in a system whose primary was clearly a red giant branch star at the time of interaction, or the absence of any circumbinary disc at 0.5–5 au around a confirmed high mass ratio post-common-envelope binary.

Figures

Figures reproduced from arXiv: 2512.16225 by Daniel Price, Jack Nibbs, Lionel Siess, Orsola De Marco, Ryosuke Hirai.

Figure 1
Figure 1. Figure 1: Illustration summarising the three evolutionary phases of post-RGB and post-AGB binaries. The interaction stage refers to a type of ’weak’ CE interaction, or a grazing envelope evolution interaction (Soker, 2015a). After the envelope ejection and the end of the central binary’s inspiral, the second phase is defined by the formation of a stable circumbinary disc. The third phase is much slower and is the on… view at source ↗
Figure 2
Figure 2. Figure 2: Cross sections of density in the orbital plane of the 68H (left), 85H (centre), and 100H (right) simulations. Each column is a time sequence starting with two moments before the inspiral (top two rows), and ending with the start (ti) and end (t f ) of the inspiral (bottom two rows). Each box is approximately 7 au in size [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Top panel: binary core separation as a function of time for the twelve simulations (see [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of bound mass (K + U < 0) throughout simulations 68H (top left), 85H (top right), 100H (bottom left), and 150H (bottom right). The pixels are binned at approximately 10 days in width, and 5 R⊙in height, where we calculate the average energy of the gas within that radial bin, at that time step. Top panel: normalised orbital separation (blue) and the bound envelope (red). The vertical lines span… view at source ↗
Figure 5
Figure 5. Figure 5: As in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Slices of energy (Etot, calculated as in Figures 4 and 5 but for both positive and negative energies) in the x-y plane (top) and the x-z plane (bottom) for the 68H simulation. The selected times reflect the early mass transfer period (top left), the start of the inspiral (top right), whereas the bottom two panels depict the unbinding that occurs shortly after the inspiral concludes (as seen after the dashe… view at source ↗
Figure 7
Figure 7. Figure 7: Numerically-derived L1 mass transfer rates as a function of time for each simulation, where the low, high and tabulated EoS simulations, are the dotted, solid, and dashed lines, respectively, in each panel. The calculation is then stopped at the point of steepest inspiral (tsteep in [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Density slices in the x-y plane of simulations 68L (left), 68H (middle), and 68MH (right) at the beginning of the dynamical inspiral (circles in [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Velocity of each SPH particle as a function of distance from the binary’s centre of mass for the 68H (left) and 68MH (right) simulations. The times shown in chronological order from top to bottom are the start of the inspiral, the end of the inspiral, and the last timestep of the simulation. For simplicity the black line is an approximate escape velocity that assumes the central mass is the primary star an… view at source ↗
Figure 10
Figure 10. Figure 10: Fall-back time as a function of distance from the centre of mass for our 68H (top), and 68MH (bottom) simulations. The colour bar indicates the amount of mass within each logarithmically sized bin (pixel), to show the distribution of bound ejecta at t = tend. To calculate the fall back time we take half the orbital period, where the semi-major axis, a, is derived from the orbital energy of the gas particl… view at source ↗
Figure 11
Figure 11. Figure 11: shows the distribution of the bound gas with respect to its fall-back radius, as given by Equation 5. The blue line is the H simulations, that unbinds only part of the gas, leading to more massive discs, while the orange line is the MH simulation that unbinds most of the gas leading to a significantly less massive disc. We find that the distribution of fall-back material depends somewhat on the mass ratio… view at source ↗
read the original abstract

The common envelope (CE) interaction between an expanding giant star and a compact companion typically leads to a rapid orbital decay, ending in either a merger or the formation of a close binary. However, the existence of post-red giant and post-asymptotic giant branch binaries with separations of 100 to 800 Rsun challenges this standard picture, as these systems appear to have experienced strong interactions without undergoing a classic CE inspiral. In this work, we investigate the effect of high mass ratio, q = M2/M1, on the CE inspiral using three-dimensional hydrodynamical simulations performed with the smoothed particle hydrodynamics code PHANTOM. The primary is a 0.88 Msun, 90 Rsun red giant branch star, while the companion masses span q = 0.68 to 1.5. Higher mass ratios lead to wider post-CE separations, with a maximum of approximately 40 Rsun. The pre-CE mass transfer phase is longer for larger companion masses, and for q greater than or equal to 1 the inspiral becomes significantly more stable, broadly consistent with analytical expectations. This phase is not fully converged with respect to numerical resolution, and higher resolution simulations are expected to further increase its duration and stability. Although higher q systems show enhanced mass loss through the L2 and L3 Lagrange points, we find that circumbinary discs are more likely to form from fallback of bound envelope material. Fallback times are short, of order a few hundred years, and fallback radii lie well outside the binary, between 0.5 and 5 au, where discs are expected to spread efficiently through viscous torques. While high mass ratio systems produce wider post-interaction separations, these remain smaller than those observed. In contrast, fallback-formed discs have properties consistent with observed circumbinary discs.

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.

Referee Report

3 major / 2 minor

Summary. This manuscript uses 3D SPH simulations with PHANTOM to study common-envelope interactions between a 0.88 Msun, 90 Rsun RGB primary and companions spanning mass ratios q = 0.68–1.5. It reports that higher q produces wider post-CE separations (maximum ~40 Rsun), longer pre-CE mass-transfer phases, and markedly more stable inspirals once q >= 1, broadly consistent with analytic expectations. Enhanced L2/L3 mass loss is noted, but circumbinary discs are argued to form primarily via fallback of bound envelope material on timescales of a few hundred years at radii 0.5–5 au. The pre-CE phase is explicitly stated to be unconverged with resolution; higher resolution is expected to increase its duration and stability. Observed wide post-CE binaries (100–800 Rsun) remain larger than the simulated separations.

Significance. If the reported trends survive resolution increases, the work supplies direct numerical evidence that mass ratio can weaken CE inspiral and produce wider final separations, addressing a key tension with observed post-RGB/post-AGB binaries. The hydrodynamical treatment avoids fitted analytic models and the fallback-disc discussion offers a concrete mechanism for observed circumbinary material. The explicit acknowledgment of non-convergence is a strength that allows readers to assess the quantitative reach of the claims.

major comments (3)
  1. [Abstract] Abstract and results on pre-CE phase: the central claim of significantly more stable inspiral for q >= 1 is extracted from the duration and outcome of the pre-CE mass-transfer phase, yet the manuscript states this phase is not converged with respect to numerical resolution and that higher resolution will increase both duration and stability. This directly scales the quantitative strength of the stability and separation results.
  2. [Abstract] Abstract, post-CE separation claim: the reported maximum separation of approximately 40 Rsun is measured from the end state after the pre-CE phase; because that phase lengthens and becomes more stable at higher resolution, the quoted separations are expected to shift, weakening the comparison to observed systems with separations of 100–800 Rsun.
  3. [Discussion] Discussion of analytic consistency: the statement that results are 'broadly consistent with analytical expectations' for q >= 1 stability lacks a specific reference to the analytic model or equation being tested, making it difficult to judge whether the simulations provide an independent check or merely reproduce the input assumptions.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'broadly consistent with analytical expectations' should cite the specific analytic work or equations invoked so readers can evaluate the degree of agreement.
  2. [Results] Notation: mass ratio q is defined as M2/M1 but the text occasionally refers to 'higher mass ratios' without repeating the definition; a single explicit reminder in the results section would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which help clarify the limitations of our current simulations. We address each major comment below and describe the revisions we will implement.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results on pre-CE phase: the central claim of significantly more stable inspiral for q >= 1 is extracted from the duration and outcome of the pre-CE mass-transfer phase, yet the manuscript states this phase is not converged with respect to numerical resolution and that higher resolution will increase both duration and stability. This directly scales the quantitative strength of the stability and separation results.

    Authors: We agree that the non-convergence of the pre-CE phase is a key limitation that affects the quantitative strength of the stability claims. The manuscript already states this caveat, but we will revise the abstract to more prominently emphasize that the reported increase in stability for q >= 1 is a qualitative trend whose magnitude will grow with resolution. This revision will better frame the results without overstating their precision. revision: partial

  2. Referee: [Abstract] Abstract, post-CE separation claim: the reported maximum separation of approximately 40 Rsun is measured from the end state after the pre-CE phase; because that phase lengthens and becomes more stable at higher resolution, the quoted separations are expected to shift, weakening the comparison to observed systems with separations of 100–800 Rsun.

    Authors: We acknowledge that the quoted maximum separation of ~40 Rsun is resolution-dependent and that longer pre-CE phases at higher resolution are likely to produce wider final separations. We will revise the abstract to note explicitly that the reported value is a lower limit from the current resolution and that the gap to observed wide binaries (100–800 Rsun) may therefore be larger than currently stated. The central trend—that higher mass ratios weaken the inspiral—remains robust and will be highlighted as such. revision: yes

  3. Referee: [Discussion] Discussion of analytic consistency: the statement that results are 'broadly consistent with analytical expectations' for q >= 1 stability lacks a specific reference to the analytic model or equation being tested, making it difficult to judge whether the simulations provide an independent check or merely reproduce the input assumptions.

    Authors: We will add a specific reference to the relevant analytic framework in the discussion section. The consistency refers to the standard expectation from binary evolution theory that companions with q >= 1 experience reduced orbital decay during envelope ejection. We will cite the appropriate model to demonstrate that the simulations provide an independent numerical test rather than simply assuming the analytic outcome. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results obtained from direct hydrodynamical simulations

full rationale

The paper reports outcomes of 3D SPH simulations performed with the PHANTOM code for a fixed RGB primary and varying companion masses. Post-CE separations, mass-loss channels, and inspiral stability are measured directly from the evolved particle distributions at simulation end states. No analytic model, fitted parameter, or self-referential equation is invoked to generate the headline quantitative results (maximum separation ~40 Rsun, enhanced stability for q >= 1). The explicit statement that the pre-CE mass-transfer phase is not fully converged is an acknowledgment of numerical uncertainty rather than a definitional loop. No self-citation is used to justify a uniqueness theorem or to smuggle an ansatz. The derivation chain is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard hydrodynamics and stellar structure assumptions rather than new postulates. No free parameters are fitted to match the target result; companion masses are chosen as a parameter scan. No new entities are invented.

axioms (2)
  • domain assumption Standard SPH hydrodynamics and self-gravity treatment in PHANTOM accurately capture the envelope response and orbital evolution.
    Invoked throughout the simulation setup and results section.
  • domain assumption The initial 0.88 Msun, 90 Rsun RGB model represents a realistic pre-CE primary.
    Used to set the primary structure.

pith-pipeline@v0.9.0 · 5653 in / 1554 out tokens · 27311 ms · 2026-05-16T21:55:44.679144+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    Artymowicz, P., & Lubow, S. H. 1994, Dynamics of Binary-Disk Interaction. I. Resonances and Disk Gap Sizes Bollen, D., Van Winckel, H., & Kamath, D. 2017, A&A, 607, A60 Dan, M., Rosswog, S., Guillochon, J., & Ramirez-Ruiz, E. 2011, ApJ, 737, 89 De Marco, O., & Izzard, R. G. 2017, PASA, 34, e001 Duchêne, G., & Kraus, A. 2013, ARA&A, 51, 269 Eggleton, P. P....

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  2. [2]

    Nibbset al

    Resolution-dependent unbinding for low res- olution simulations In Figure A1 we show the distribution of bound gas in ideal gas EoS simulations demonstrating that the low resolution sim- ulations unbind gas at the base of the envelope (the white zone that develops after the dotted vertical lines in three of the panels in Figure A1), a behaviour typical of...

    work page 2022

  3. [3]

    On the comparison of numerical and analyti- cal mass transfer rates Reichardt et al. (2019) carried out a comparison between the mass transfer rate before the CE inspiral in their simulations, versus values derived using the analytical approximation of Paczyński & Sienkiewicz (1972), using variables measured from the simulations. In that work the comparis...

    work page 2019

  4. [4]

    Numeric Analytic with R1 = 107 R Analytic with R1 = 88 R 0.0 0.5 1.0 -7 -5 -3 Figure A2.A recreation of figure 7 of Reichardt et al. (2019). The orange and blue lines are those used in that work, representing the the mass transfer rate calculated using the analytical equation for mass transfer, along with quantities measured using the simulation (orange l...

    work page 2019