Pith. sign in

REVIEW 3 major objections 4 minor 54 references

Testing tidal theory using Gaia binaries: the red giant branch

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Gaia red-giant binaries stay circular twice as far out as f-mode tidal theory allows, pointing to an extra circularization process in the early red giant branch.

desk verdict A genuinely new forward-model test of tidal circularization against 30,000 Gaia giants; the early-RGB discrepancy is real but its size is not yet secure because it sits on the adopted eddy-viscosity prescription. read the letter →

arxiv 2501.13929 v2 pith:46QEJGTQ submitted 2025-01-23 astro-ph.SR astro-ph.GA

Janosz W. Dewberry , Yanqin Wu This is my paper · ORCID
classification astro-ph.SRastro-ph.GA
keywords tidalcircularizationredgiantbranchGaiaDR3binarystarseddyviscositydynamicaltidesf-modeeccentricitydistribution
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper uses about 30,000 red-giant binaries from Gaia DR3 to test whether tidal dissipation theory explains where binary orbits become circular as the primary star swells along the red giant branch. The authors compute the tidal evolution of a 1.5-solar-mass primary with f-mode dynamical tides damped by an eddy viscosity in the convective envelope, then compare predicted eccentricity distributions with the observed ones in the dimensionless plane $a/R$ (semi-major axis over stellar radius). The model produces a fixed circularization limit at $a/R \approx 4$ at every red-giant stage, whereas the data show early red giants circularized out to $\beta \equiv a(1-e)/R \approx 6$, with extended cool islands of circular orbits reaching $a/R \sim 10$--$15$: roughly twice the predicted reach. The paper concludes that f-mode tides are adequate for the late red giant branch but that an additional circularization process, still unidentified, must operate during the early red giant branch. If correct, the result sharpens both where tidal theory succeeds and where binary evolution models are missing physics.

What carries the argument

The central machinery is the 'f-mode' tidal model: the tidal response of the evolving 1.5-solar-mass primary is expanded in the star's fundamental and lowest-order pressure modes, and each mode's dissipation is evaluated with a frequency-dependent eddy viscosity from convective turbulence. The resulting dissipative coefficients $\kappa_{mk}$ enter secular equations for orbital decay, eccentricity damping, and spin evolution that are integrated along the stellar evolutionary track. The organizing diagnostic is the dimensionless ratio $a/R$, with $\beta \equiv a(1-e)/R$ marking the eccentricity upper envelope; plotting eccentricity against $a/R$ makes both theory and data nearly stationary across evolutionary stages, so the gap between the predicted boundary at $a/R \approx 4$ and the observed early-RGB reach at $\beta \approx 6$ becomes the measurable quantity that drives the conclusion.

What would settle it

Compute the early-RGB population with an eddy-viscosity prescription that omits or weakens the fast-tide suppression in Equation (7); if the predicted circularization boundary shifts from $a/R \approx 4$ to $\beta \approx 6$, the claimed need for an additional circularization process would not be supported.

Watch

Extended reading notes

Core claim

On its own terms, this paper claims that f-mode tidal theory with a frequency-dependent eddy viscosity predicts a universal circularization boundary of $a/R \approx 4$ for red giants, independent of the star's position on the red giant branch. Against that prediction, Gaia binaries in the early red giant phase are observed circularized out to $\beta \approx 6$ and show an extended cool island of circular orbits out to $a/R \sim 10$--$15$, about twice the theoretical reach; in the late red giant branch the observed reach shrinks to $\beta \approx 3$ and agrees with the model. From this the authors conclude that an additional circularization process must act in the early red giant branch, and they note the same missing physics may underlie the even larger discrepancy long seen for main-sequence binaries. The calculations also produce two by-products: tides can spin giant primaries up to rotation rates that should change their mass loss, and many binaries may enter Roche-lobe overflow while still significantly eccentric.

Load-bearing premise

The predicted circularization limit rests on the assumed eddy-viscosity prescription for convective envelopes, and if the true viscosity is stronger than the fast-tide suppression allows, the theory's boundary would move outward and the early-red-giant discrepancy would shrink or vanish.

Editorial extensions

If this is right

  • If the f-mode limit is fixed at $a/R \approx 4$, every red-giant binary with dimensionless pericenter $\beta \lesssim 4$ should be effectively circular; the early-RGB binaries with $\beta \approx 6$ mark where that rule fails.
  • Tidal spin-up can bring close giant primaries near orbital synchronization, roughly $\Omega/\omega_{\rm dyn} \approx 0.3$ at Roche-lobe overflow for a 2/3 mass ratio, so mass-loss prescriptions based on slowly rotating single stars need revision for these binaries.
  • Binaries with initial periods near $10^3$ to $3\times 10^3$ days can begin Roche-lobe overflow while still substantially eccentric, contradicting older equilibrium-tide expectations of full circularization beforehand.
  • If the early-RGB excess is real, it may share a mechanism with the main-sequence cool island, turning two separate tidal-theory failures into one missing-process problem.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct test would be to rerun the population calculation with a weaker fast-tide suppression in the eddy-viscosity law; if the predicted boundary moves from $a/R \approx 4$ to $\approx 6$ in the early RGB, the claimed missing process would dissolve.
  • Because the model predicts a universal $a/R$ limit, observed circularization periods should scale linearly with primary radius; future samples with asteroseismic radii can test this scaling and separate radius errors from genuine tidal effects.
  • The early-RGB excess could come from internal gravity waves breaking in the still-substantial radiative core, so comparing same-radius giants of different masses (hence different core sizes) could discriminate among the proposed mechanisms.
  • Tidal spin-up out to periods of roughly 5000 days on the RGB and 10,000 days on the AGB should be measurable in asteroseismic rotation rates of red giants, providing an independent check of the dissipation model.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper confronts state-of-the-art tidal theory with the Gaia DR3 sample of ~31,500 red-giant binaries. The authors build a forward model: a 1.5 M⊙ primary (with a 1.0 M⊙ companion) is evolved through the RGB and AGB in MESA; linear tidal responses are computed in an f-mode/p-mode eigenmode expansion (and in a zero-frequency 'equilibrium' variant) using GYRE; dissipation is supplied by a frequency-dependent eddy-viscosity model (Eq. 7) calibrated to the local simulations of Duguid et al. (2020); and a synthetic population is generated from observationally motivated initial period and eccentricity distributions (Section 4.3). The model predicts that the eccentricity upper envelope in a/R space is pinned at β ≡ a(1−e)/R ≈ 4 at every RGB stage. The Gaia data instead show an envelope that starts at β ≈ 6 in the early RGB and declines to β ≈ 3 near the tip, plus 'cool islands' of circular orbits extending to a/R ≈ 10–15 in early stages, about twice the predicted reach. The paper concludes that f-mode tides with the adopted viscous prescription describe the late RGB well but that 'an additional circularization process' is needed during the early RGB. It also reports theory-driven predictions of strong tidal spin-up of giant primaries (with consequences for mass loss) and of binaries beginning Roche-lobe overflow while still significantly eccentric.

Significance. If substantiated, the early-RGB discrepancy is a significant result: it connects the long-standing main-sequence tidal-circularization problem to evolved stars and points to missing dissipation physics (internal gravity waves, inertial waves, mode locking, or magnetic effects) in early-RGB convective envelopes. The paper's method is a genuine strength: the predicted a/R ≈ 4 boundary is produced from first principles (a linear f-mode response plus an eddy viscosity from independent local simulations), with no parameter fitted to the Gaia circularization data, and the a/R rescaling makes the comparison clean and physically motivated. The paper also makes concrete, falsifiable predictions: spin-up to Ω/ω_dyn ≈ 0.3 at RLOF, eccentric RLOF onset, and synchronization out to ~5000-day periods on the RGB. The main weakness is identified by the authors themselves: Section 5 notes that the adopted viscosity prescription 'may be too conservative,' and the early-RGB discrepancy is concentrated precisely in the regime where the uncertain fast-tide suppression branch of Eq. (7) acts (short-period orbits, with ω/ω_c ≳ 1–5 in parts of the envelope).

major comments (3)
  1. [§3.3, Eq. (7); §5; §6] The central quantitative claim — that f-mode tides plus the adopted eddy viscosity cap tidal circularization at a/R ≈ 4 on the entire RGB, and hence that 'there needs to be an additional circularization process during the early RGB' (Section 6) — depends on the high-frequency branch of the viscosity prescription in Eq. (7). The early-RGB binaries at issue have the shortest orbital periods (Fig. 4), so their tidal frequencies place a significant fraction of the convective envelope in the frequency-dependent suppressed regimes (1 ≲ ω/ω_c ≲ 5 in the middle branch and ≳ 5 in the fast branch), including deeper zones at the largest ratios. Section 5 concedes both that the Duguid et al. (2020) scaling suppresses dissipation 'stronger in the early RGB' and that the adopted prescription 'may be too conservative.' Since the comparison in Fig. 11 is a factor-of-two mismatch in exactly this regime, the manuscript should include a sensitivity study in which the predicted β and cool-island edges are recomputed for the plausible range of viscosity scalings (e.g., Zahn (1977) without high-frequency suppression, the Goldreich & Nicholson (1977) form with varied prefactor, and the alternatives of Goodman & Oh (1997) and Terquem (2021, 2023)), and the resulting change in the predicted boundary should be reported. Absent this test, the discrepancy that motivates the paper's main conclusion is not established.
  2. [§2.2, Figs. 4 and 11] The measured quantities used for the discrepancy claim — the upper-envelope values β ≈ 6.5 → 3.0 and the cool-island edges at a/R ≈ 10–15 (Fig. 4, right panels) — are reported without uncertainties. Section 2.2 states that these uncertainties 'are hard to quantify at this moment,' but the central result is precisely a comparison of these numbers with the theoretical β ≈ 4 boundary (Fig. 11). To support a factor-of-two claim, the paper should provide at least a bootstrap estimate of the sampling uncertainty in β and the island edges (e.g., resampling the binary catalog), propagate the quoted 2–4% eccentricity errors, and test the sensitivity of the derived β values to the adopted Gaia masses in the period-to-a/R conversion. Without error bars on the observational limits, the statistical significance of the early-RGB discrepancy cannot be assessed.
  3. [§2.2 vs. §3.1; Fig. 10] The two sides of the comparison use inconsistent mass assumptions. Observed a/R values are computed with a total mass of 1.5× the Gaia primary mass (Section 2.2), while the theoretical population is evolved with M + M′ = 2.5 M⊙ for a 1.5 M⊙ primary, i.e., 1.67× (Section 3.1); this produces a ~4% systematic offset in a/R between data and model. In addition, the model uses a single 1.5 M⊙ track while the observed sample spans roughly 1–10 M⊙ (Fig. 3); the claim in Section 3.1 that radius rather than mass controls the tidal evolution is plausible but untested. Computing even one additional track (e.g., 1.0 M⊙ and 2.5 M⊙ primaries) would show whether the predicted a/R ≈ 4 boundary is robust to the primary mass. These checks are inexpensive and directly bear on the quality of the comparison in Fig. 10.
minor comments (4)
  1. [Appendix B, text after Eq. (B5)] The boundary-conditions sentence contains a duplicated phrase: 'that the normal and that the normal and tangential stresses vanish'; it should read 'that the normal and tangential stresses vanish.'
  2. [Fig. 1 caption] The label '1.5M' on the evolutionary track should read '1.5 M⊙' in both the caption and the figure legend.
  3. [§2.2, red-clump excision] The red-clump excision combines a density-peak criterion with a P < 300 day cut; a brief statement of how the derived β values and cool-island edges change when this cut is varied (e.g., 200 or 400 days) would strengthen confidence in the sample boundary.
  4. [Software and data availability] The text lists the software packages used (MESA, GYRE, scipy, numpy) but does not state where the MESA tracks, pre-computed mode properties, or the orbital-integration code can be obtained; making these available would substantially aid reproducibility of the population-level predictions in Figs. 10 and 12.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted a/R≈4 boundary is computed from an independently sourced eddy-viscosity model and a linear f-mode tidal response, not fitted to the Gaia giant binaries.

full rationale

The predicted circularization boundary a/R ≈ 4 is produced by integrating the secular tidal equations (10)-(13) with dissipation coefficients κ_mk computed from the linear f-mode response (Appendix B, Eq. B7) and the eddy-viscosity law in Eq. (7), which is adopted from Duguid et al. (2020) local simulations. No parameter in that chain is fitted to the ~30,000 Gaia giant binaries; the observed β ≡ a(1−e)/R values in Figs. 4 and 10 are an independent comparison set. The initial eccentricity distribution (Rayleigh, σ_e ≈ 0.30) is cited to the authors' own Wu et al. (2024), but it is a prior empirical measurement from wide/main-sequence Gaia binaries, not derived from the target red-giant circularization envelope, so it is not a fitted input renamed as a prediction. The paper itself flags the main sensitivity in Section 5: 'It is possible that we have adopted a prescription for turbulent viscosity that is too conservative.' That is a model-uncertainty caveat, not a circular reduction: the predicted a/R limit is contingent on a physical input sourced independently of the data being predicted. The total-mass assumption for period-to-a/R conversion is a systematic uncertainty, not a definitional shortcut. No equation in the paper reduces to its own input by construction, and the discrepancy (predicted β≈4 vs observed early-RGB β≈6) is a genuine forward-model comparison.

Assumptions & free parameters 4 free parameters · 9 assumptions · 0 invented entities

The central comparison rests on several modeling choices. The most important are the eddy viscosity prescription, the truncated mode set, the inner boundary placement, the assumed initial conditions, and the Gaia-derived masses used for the a/R conversion. No new physical entities are introduced.

free parameters (4)
  • Eddy viscosity scaling coefficients = 5, 1/2, 25*sqrt(20); thresholds |ω|/ωc = 10^-2 and 5
    Adopted from Duguid et al. (2020) local simulations. They set the magnitude and frequency suppression of turbulent viscosity and directly control the predicted circularization limit. Not fitted to Gaia data, but central to the discrepancy, especially the high-frequency suppression for early-RGB orbits.
  • Initial stellar rotation rate = Ω = 0.01 ω_dyn
    Assumed initial condition in all integrations (Section 4.4). The authors note it is quickly erased by tidal and mass-loss spin evolution, so it has little effect on final outcomes.
  • Total system mass multiplier = 1.5 × primary mass
    Used to convert orbital period to semi-major axis and hence a/R (Section 2.2). The observed β and cool island edges depend on this choice; the paper does not quantify the resulting uncertainty.
  • Initial period and eccentricity distribution parameters = log-normal mean 5, σ=2.3; Rayleigh σ_e=0.30
    Sampled for the synthetic population (Section 4.3). Adopted from Moe & Di Stefano (2017) for periods and Wu et al. (2024) for eccentricities. The synthetic cool island extent depends on these inputs, although the β≈4 envelope is mostly insensitive.
assumptions (9)
  • domain assumption The tidal response can be represented by a truncated expansion in the f-mode and ten lowest-order p-modes
    Appendix B assumes this mode set suffices to compute dissipation; internal gravity waves and higher-order modes are neglected. This is load-bearing because gravity waves are a candidate for the early-RGB discrepancy.
  • domain assumption The inner boundary of the tidal calculation is set at the outer edge of the radiative core
    Appendix B places the boundary with GYRE's ZERO_H condition, justified 'because we focus on the later stages of the RGB.' For early RGB, the radiative core is larger and this approximation may underestimate core dissipation.
  • domain assumption Primary stars rotate rigidly and uniformly
    Section 3.5 assumes a single rotation rate Ω(t) and moment of inertia; differential rotation, inertial waves, and gravito-inertial modes are ignored. The authors list rotation as a possibly important missing ingredient.
  • domain assumption Initial eccentricities follow a Rayleigh distribution with σ_e = 0.30, independent of period
    Section 4.3 adopts this distribution from Wu et al. (2024) for periods 20-1200 days and assumes it applies to giant binary progenitors. A different primordial eccentricity distribution would change the predicted population.
  • domain assumption Mass loss follows the Reimers/Blöcker prescriptions and is not modified by tidal spin-up
    Section 3.1 uses the MESA 1M_pre_ms_to_wd test suite's mass loss; Section 4.4 notes that tidal spin-up could invalidate these prescriptions, casting doubt on late evolution and spin predictions.
  • domain assumption Roche-lobe overflow does not significantly alter tidal evolution before integration is halted
    Appendix D halts integration at RLOF and assumes no tidal change during mass transfer; the authors say halting at RLOF produces similar results, but eccentric RLOF is an outcome they predict.
  • standard math The linearized tidal response equations (2)-(5) are valid
    The governing equations assume small amplitude perturbations and linear superposition of tidal components; this is standard for weak tides in binary systems.
  • domain assumption Gaia DR3 astrophysical parameters (radii, masses) are sufficiently accurate for the a/R conversion
    Sections 2.1-2.2 use Gaia radii and masses to group stars and convert period to a/R. Red-clump masses are flagged as possibly erroneous, and mass uncertainties propagate to the measured β values.
  • domain assumption A single 1.5 M_sun primary evolutionary track represents all observed RGB primaries
    Section 3.1 argues that radius, not mass, controls tidal evolution, and that similar radii give similar mean densities. However, mass affects the a/R conversion and the binary's Roche geometry, so this representative-track assumption is load-bearing for the population comparison.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Testing tidal theory using Gaia binaries: the red giant branch." pith.science (2026). https://pith.science/paper/46QEJGTQ

@misc{pith2026250113929,
  author       = {Pith},
  title        = {Pith review of: Testing tidal theory using Gaia binaries: the red giant branch},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/46QEJGTQ}},
  note         = {Machine review of arXiv:2501.13929}
}
read the original abstract

Tidal interaction is a major ingredient in the theory of binary evolution. Here, we study tidal circularization in binaries with red giant primaries. We compute the tidal evolution for binaries as their primary stars evolve along the red giant branch, under dissipation of dynamical tides in the convective envelope. We then compare this evolution with a sample of ~30,000 red giant binaries reported by Gaia DR3. These binaries clearly show the expected gradual advance of tidal circularization, as the primary expands. But some tension with theory remains. While our calculations always predict a critical separation for tidal circularization at about 3-4 times the stellar radii, binaries with less evolved giants are observed to be circularized out to about twice as far. They also exhibit an overly extended `cool island', a collection of circular orbits that reach a couple times beyond the circularization limit. These discrepancies are reminiscent of, but less severe than, the situation for main-sequence binaries. We also find that tides can spin giant stars up to rotation rates that should affect their mass-loss. Additionally, many binaries may begin mass transfer while still eccentric.

Figures

Figures reproduced from arXiv: 2501.13929 by the authors.

Figure 1
Figure 1. HR diagram for the Gaia binary sample used in this work. The gray points indicate main-sequence binaries, while the colored denote red-giant binaries (colored by different primary radii). The contours represent sample density. The two black curves show the isochrones for zero-age-main-sequence and 10 Myr old systems, for solar metallicity stars (PARSEC isochrone, Bressan et al. 2012). The evolutionary trajectory of … view at source ↗
Figure 2
Figure 2. Eccentricity-period distributions of Gaia Main￾sequence binaries, including primaries with radii from 0.3R⊙ to 3R⊙. They are not the focus of this work and are only in￾cluded here for completeness. Top panel: eccentricity-period distribution, with kernel density estimates over-plotted on the data points. Contour levels are [0.05, 0.11, 0.18...1] and remain the same throughout this paper. The teal curve indi￾cates or… view at source ↗
Figure 3
Figure 3. Radii and inferred masses for the primary stars in the giant binaries. There is a strong correlation between radius and mass. Red clump stars cause the large excess around R/R⊙ ∼ 10. Their mass determination is difficult and may be erroneous. radii into 6 divisions. Such a division is convenient. Not only do these radii reflect the stars’ evolutionary state along the RGB, they also, as we argue below, provide suitab… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Eccentricity distributions of Gaia giant binaries, represented by kernel density estimates and separated into groups by the primary radii. In the left column the x-axis shows period, while in the right column we convert period to the ratio a/R. The eccentricity distrib…
Figure 5
Figure 5. Figure 5: plots the mass, radius, and relevant frequencies for our 1.5M⊙ primary star as it evolves past the main sequence toward its final white dwarf stage. We focus on tidal evolution during the RGB and HB (red clump) phases. Compared to its main-sequence progenitor, a giant …
Figure 7
Figure 7. Figure 7: also highlights the differences between the f￾mode and equilibrium tidal models. Results from f￾mode tidal calculations asymptote toward equilibrium predictions at long periods, as is expected. But at short periods they contain more structure due to resonances with fun…
Figure 8
Figure 8. Figure 8: Orbital evolution driven by f-mode tides. From top to bottom, the panels show orbital period, stellar ro￾tation rate (relative to both the dynamical frequency and the orbital mean motion), and eccentricity for some repre￾sentative initial conditions (light/dark line co…
Figure 9
Figure 9. Figure 9: Evolution of orbital eccentricity (left panel) and primary spin (right panel, normalized by ωdyn), as functions of orbital period, for an assortment of initial conditions (green tri-stars) and integrated with f-mode tides. Line colors indicate evolutionary stages, and …
Figure 10
Figure 10. Figure 10: Kernel density estimates computed from eccentricity and distance data for Gaia giant binaries (left) and theoretical tidal calculations (right). The panels are split vertically by the radius of the primary star (our proxy for age). The bottom row singles out red clump…
Figure 11
Figure 11. Figure 11: Extents of tidal circularization, obtained from Gaia binaries (teal color, from [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: Scatterplots and kernel density estimates showing eccentricity and orbital period values, sampled from orbital evolution calculations sliced evenly in time (point colors again indicate evolutionary stage), and perturbed as described in Appendix D. The contours indicat…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

54 extracted references · 10 canonical work pages

  1. [1]

    Barker, A. J. 2022, ApJL, 927, L36, doi: 10.3847/2041-8213/ac5b63

    doi:10.3847/2041-8213/ac5b63 2022

  2. [2]

    J., & Astoul, A

    Barker, A. J., & Astoul, A. A. V. 2021, MNRAS, 506, L69, doi: 10.1093/mnrasl/slab077

    doi:10.1093/mnrasl/slab077 2021

  3. [3]

    2023, MNRAS, 522, 1184, doi: 10.1093/mnras/stad999

    Bashi, D., Mazeh, T., & Faigler, S. 2023, MNRAS, 522, 1184, doi: 10.1093/mnras/stad999

    doi:10.1093/mnras/stad999 2023

  4. [4]

    G., Mathis, S., Gallet, F., et al

    Beck, P. G., Mathis, S., Gallet, F., et al. 2018, MNRAS, 479, L123, doi: 10.1093/mnrasl/sly114

    doi:10.1093/mnrasl/sly114 2018

  5. [5]

    G., Grossmann, D

    Beck, P. G., Grossmann, D. H., Steinwender, L., et al. 2024, A&A, 682, A7, doi: 10.1051/0004-6361/202346810 Bl¨ ocker, T. 1995, A&A, 297, 727

    doi:10.1051/0004-6361/202346810 2024

  6. [6]

    J., & Ogilvie, G

    Braviner, H. J., & Ogilvie, G. I. 2015, MNRAS, 447, 1141, doi: 10.1093/mnras/stu2521

    work page doi:10.1093/mnras/stu2521 2015

  7. [7]

    2012, MNRAS, 427, 127, doi: 10.1111/j.1365-2966.2012.21948.x

    Bressan, A., Marigo, P., Girardi, L., et al. 2012, MNRAS, 427, 127, doi: 10.1111/j.1365-2966.2012.21948.x

    arXiv 2012

  8. [8]

    Townsend, R. H. D. 2024, Nature Astronomy, 8, 1387, doi: 10.1038/s41550-024-02351-3

    doi:10.1038/s41550-024-02351-3 2024

Show all 54 references
  1. [9]

    D., Barker, A

    Duguid, C. D., Barker, A. J., & Jones, C. A. 2020, MNRAS, 497, 3400, doi: 10.1093/mnras/staa2216

    2020 doi

  2. [10]

    D., de Vries, N

    Duguid, C. D., de Vries, N. B., Lecoanet, D., & Barker, A. J. 2024, ApJL, 966, L14, doi: 10.3847/2041-8213/ad3c40

    2024 doi

  3. [11]

    Eggleton, P. P. 1983, ApJ, 268, 368, doi: 10.1086/160960

    1983 doi

  4. [12]

    2024, arXiv e-prints, arXiv:2407.10573, doi: 10.48550/arXiv.2407.10573

    Esseldeurs, M., Mathis, S., & Decin, L. 2024, arXiv e-prints, arXiv:2407.10573, doi: 10.48550/arXiv.2407.10573

    2024 doi arXiv

  5. [13]

    2017, MNRAS, 472, 1538, doi: 10.1093/mnras/stx2135 Gaia Collaboration, Arenou, F., Babusiaux, C., et al

    Fuller, J. 2017, MNRAS, 472, 1538, doi: 10.1093/mnras/stx2135 Gaia Collaboration, Arenou, F., Babusiaux, C., et al. 2023, A&A, 674, A34, doi: 10.1051/0004-6361/202243782

    2017 doi

  6. [14]

    Goldreich, P., & Nicholson, P. D. 1977, Icarus, 30, 301, doi: 10.1016/0019-1035(77)90163-4

    1977 doi

  7. [15]

    Goodman, J., & Dickson, E. S. 1998, ApJ, 507, 938, doi: 10.1086/306348

    1998 doi

  8. [16]

    Goodman, J., & Oh, S. P. 1997, ApJ, 486, 403, doi: 10.1086/304505

    1997 doi

  9. [17]

    I., & Barker, A

    Guo, Z., Ogilvie, G. I., & Barker, A. J. 2023, MNRAS, 521, 1353, doi: 10.1093/mnras/stad569

    2023 doi

  10. [18]

    2020, Research in Astronomy and Astrophysics, 20, 161, doi: 10.1088/1674-4527/20/10/161

    Han, Z.-W., Ge, H.-W., Chen, X.-F., & Chen, H.-L. 2020, Research in Astronomy and Astrophysics, 20, 161, doi: 10.1088/1674-4527/20/10/161

    2020 doi

  11. [19]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

    2020 doi

  12. [20]

    Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55

    2007 doi

  13. [21]

    R., Tout, C

    Hurley, J. R., Tout, C. A., & Pols, O. R. 2002, MNRAS, 329, 897, doi: 10.1046/j.1365-8711.2002.05038.x

    2002

  14. [22]

    S., Bauer, E

    Jermyn, A. S., Bauer, E. B., Schwab, J., et al. 2023, ApJS, 265, 15, doi: 10.3847/1538-4365/acae8d

    2023 doi

  15. [23]

    2010, A&A, 516, A64, doi: 10.1051/0004-6361/201014337

    Leconte, J., Chabrier, G., Baraffe, I., & Levrard, B. 2010, A&A, 516, A64, doi: 10.1051/0004-6361/201014337

    2010 doi

  16. [24]

    Lin, Y., & Ogilvie, G. I. 2018, MNRAS, 474, 1644, doi: 10.1093/mnras/stx2764

    2018 doi

  17. [25]

    2008, in EAS Publications Series, Vol

    Mazeh, T. 2008, in EAS Publications Series, Vol. 29, Tidal Effects in Stars, Planets and Disks, ed. M. J. Goupil & J. P. Zahn, 1–65, doi: 10.1051/eas:0829001

    2008 doi

  18. [26]

    Meibom, S., & Mathieu, R. D. 2005, ApJ, 620, 970, doi: 10.1086/427082

    2005 doi

  19. [27]

    D., & Stassun, K

    Meibom, S., Mathieu, R. D., & Stassun, K. G. 2006, ApJ, 653, 621, doi: 10.1086/508252

    2006 doi

  20. [28]

    2017, ApJS, 230, 15, doi: 10.3847/1538-4365/aa6fb6

    Moe, M., & Di Stefano, R. 2017, ApJS, 230, 15, doi: 10.3847/1538-4365/aa6fb6

    2017 doi

  21. [29]

    2023, A&A, 674, A16, doi: 10.1051/0004-6361/202245330

    Mowlavi, N., Holl, B., Lecoeur-Ta ¨ ıbi, I., et al. 2023, A&A, 674, A16, doi: 10.1051/0004-6361/202245330

    2023 doi

  22. [30]

    Ogilvie, G. I. 2013, MNRAS, 429, 613, doi: 10.1093/mnras/sts362 —. 2014, ARA&A, 52, 171, doi: 10.1146/annurev-astro-081913-035941

    2013 doi

  23. [31]

    I., & Lin, D

    Ogilvie, G. I., & Lin, D. N. C. 2007, ApJ, 661, 1180, doi: 10.1086/515435

    2007 doi

  24. [32]

    2011, ApJS, 192, 3, doi: 10.1088/0067-0049/192/1/3

    Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3, doi: 10.1088/0067-0049/192/1/3

    2011 doi

  25. [33]

    2013, ApJS, 208, 4, doi: 10.1088/0067-0049/208/1/4

    Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4, doi: 10.1088/0067-0049/208/1/4

    2013 doi

  26. [34]

    2015, ApJS, 220, 15, doi: 10.1088/0067-0049/220/1/15

    Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS, 220, 15, doi: 10.1088/0067-0049/220/1/15

    2015 doi

  27. [35]

    B., et al

    Paxton, B., Schwab, J., Bauer, E. B., et al. 2018, ApJS, 234, 34, doi: 10.3847/1538-4365/aaa5a8

    2018 doi

  28. [36]

    2019, ApJS, 243, 10, doi: 10.3847/1538-4365/ab2241

    Paxton, B., Smolec, R., Schwab, J., et al. 2019, ApJS, 243, 10, doi: 10.3847/1538-4365/ab2241

    2019 doi

  29. [37]

    2007, in SF2A-2007: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics, ed

    Pichon, B. 2007, in SF2A-2007: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics, ed. J. Bouvier, A. Chalabaev, & C. Charbonnel, 549

    2007

  30. [38]

    M., & Goodman, J

    Price-Whelan, A. M., & Goodman, J. 2018, ApJ, 867, 5, doi: 10.3847/1538-4357/aae264

    2018 doi

  31. [39]

    Rafikov, R. R. 2016, ApJ, 830, 8, doi: 10.3847/0004-637X/830/1/8

    2016 doi

  32. [40]

    1975, Circumstellar Envelopes and Mass Loss of Red Giant Stars (Berlin, Heidelberg: Springer Berlin Heidelberg), 229–256, doi: 10.1007/978-3-642-80919-4 8

    Reimers, D. 1975, Circumstellar Envelopes and Mass Loss of Red Giant Stars (Berlin, Heidelberg: Springer Berlin Heidelberg), 229–256, doi: 10.1007/978-3-642-80919-4 8

    1975 doi

  33. [41]

    K., Arras, P., Flanagan, ´E

    Schenk, A. K., Arras, P., Flanagan, ´E. ´E., Teukolsky, S. A., & Wasserman, I. 2001, PhRvD, 65, 024001, doi: 10.1103/PhysRevD.65.024001

    2001 doi

  34. [42]

    2021, MNRAS, 503, 5789, doi: 10.1093/mnras/stab224 —

    Terquem, C. 2021, MNRAS, 503, 5789, doi: 10.1093/mnras/stab224 —. 2023, MNRAS, 525, 508, doi: 10.1093/mnras/stad2163 18

    2021 doi

  35. [43]

    Terquem, C., Papaloizou, J. C. B., Nelson, R. P., & Lin, D. N. C. 1998, ApJ, 502, 788, doi: 10.1086/305927

    1998 doi

  36. [44]

    Townsend, R. H. D., & Teitler, S. A. 2013, MNRAS, 435, 3406, doi: 10.1093/mnras/stt1533

    2013 doi

  37. [45]

    Verbunt, F., & Phinney, E. S. 1995, A&A, 296, 709

    1995

  38. [46]

    2020, MNRAS, 496, 3767, doi: 10.1093/mnras/staa1784

    Vick, M., & Lai, D. 2020, MNRAS, 496, 3767, doi: 10.1093/mnras/staa1784

    2020 doi

  39. [47]

    2021, MNRAS, 503, 5569, doi: 10.1093/mnras/stab850

    Vick, M., MacLeod, M., Lai, D., & Loeb, A. 2021, MNRAS, 503, 5569, doi: 10.1093/mnras/stab850

    2021 doi

  40. [48]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2

    2020 doi

  41. [49]

    N., Sun, M., Arras, P., & Essick, R

    Weinberg, N. N., Sun, M., Arras, P., & Essick, R. 2017, ApJL, 849, L11, doi: 10.3847/2041-8213/aa9113

    2017 doi

  42. [50]

    G., & Savonije, G

    Witte, M. G., & Savonije, G. J. 1999, A&A, 350, 129, doi: 10.48550/arXiv.astro-ph/9909073

    1999 doi arXiv

  43. [51]

    Matzner, C. D. 2024, arXiv e-prints, arXiv:2411.09905, doi: 10.48550/arXiv.2411.09905

    2024 doi arXiv

  44. [52]

    2017, PhRvD, 96, 083005, doi: 10.1103/PhysRevD.96.083005

    Xu, W., & Lai, D. 2017, PhRvD, 96, 083005, doi: 10.1103/PhysRevD.96.083005

    2017 doi

  45. [53]

    Zahn, J. P. 1977, A&A, 57, 383

    1977

  46. [54]

    J., & Wu, Y

    Zanazzi, J. J., & Wu, Y. 2021, AJ, 161, 263, doi: 10.3847/1538-3881/abf097

    2021 doi

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.