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arxiv: 2605.11343 · v1 · submitted 2026-05-11 · 🌌 astro-ph.SR · astro-ph.EP· astro-ph.HE

Recognition: no theorem link

Continuous mass ablation of planets engulfed in stellar envelopes

Damien Gagnier, Friedrich K. R\"opke, Giovanni Leidi, Ilya Mandel, Javier Mor\'an-Fraile, Mike Y. M. Lau, Robert Andrassy

Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:20 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.EPastro-ph.HE
keywords planetary engulfmenthydrodynamical simulationsmass ablationKelvin-Helmholtz instabilitylithium enrichmentstellar envelopesplanet dissolution
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The pith

Planets engulfed by stars dissolve through continuous mass ablation instead of sudden destruction at one depth.

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

The paper performs three-dimensional hydrodynamical simulations of a resolved gaseous Jupiter-like planet inside a stellar envelope using a wind-tunnel configuration. It shows that mass loss proceeds steadily via surface instabilities rather than occurring abruptly when ram pressure, tides, or evaporation reach a threshold at some fixed depth. The ablation rate follows the wind momentum flux closely and remains largely independent of Mach number, matching a simple Kelvin-Helmholtz model. When the measured drag and ablation efficiencies are inserted into an integrated inspiral path through a stellar structure, the planet can fully dissolve inside the convective zone, releasing its material and producing surface lithium enrichment.

Core claim

In three-dimensional hydrodynamical simulations that resolve the gaseous structure of a Jupiter-like planet in a wind-tunnel setup representing stellar envelope conditions, a continuous mass-ablation process operates throughout engulfment. The ablation rate scales nearly linearly with wind momentum flux and shows little dependence on Mach number, consistent with Kelvin-Helmholtz instability growth at the planet surface. Pressure-drag coefficients of 0.44-0.56 and ablation efficiencies of 0.054-0.11 are measured; when these are used in a numerically integrated inspiral, the planet dissolves completely within the convective envelope and enriches the stellar surface in lithium.

What carries the argument

The wind-tunnel hydrodynamical simulation that resolves the planet's gaseous body, allowing direct capture of Kelvin-Helmholtz instabilities that drive ongoing surface ablation.

If this is right

  • The measured drag and ablation coefficients supply ready prescriptions for large-scale parameter studies of engulfment.
  • Continuous ablation permits complete planetary dissolution inside the convective envelope.
  • Dissolution releases planetary material that can produce observable lithium enrichment at the stellar surface.
  • Chemical enrichment signatures may appear across a wider range of stellar masses and evolutionary stages than models assuming threshold destruction predict.

Where Pith is reading between the lines

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

  • Stellar evolution codes that treat engulfment as an instantaneous event should be revised to include gradual mass loss.
  • Enhanced lithium detections in red-giant atmospheres could trace this continuous ablation channel in more systems than previously modeled.
  • The weak Mach-number dependence implies the ablation process remains effective across varying envelope densities and velocities.

Load-bearing premise

The simplified wind-tunnel flow with a resolved gaseous planet accurately captures the three-dimensional, time-dependent interaction that occurs during actual inspiral through a realistic stellar envelope.

What would settle it

A simulation or observation in which planetary mass loss halts at a specific depth set by ram pressure or tidal forces rather than continuing steadily as the planet spirals inward.

Figures

Figures reproduced from arXiv: 2605.11343 by Damien Gagnier, Friedrich K. R\"opke, Giovanni Leidi, Ilya Mandel, Javier Mor\'an-Fraile, Mike Y. M. Lau, Robert Andrassy.

Figure 1
Figure 1. Figure 1: Illustration of the stretched grid geometry with a density [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Volume rendering showing the ablation of planetary material in the fiducial simulation at a grid resolution of 1536 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Slices of the fiducial simulation in the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Velocity divergence in the z = 0 slice of the fiducial simulation. Shock fronts appear as thin blue filaments of strongly negative velocity divergence, indicating abrupt compression. The sequence of panels shows the formation and evolution of the bow shock, the forward shock, and the recompression shock. The rightmost panel uses an extended plotting range, showing the downstream recompression of the flow. … view at source ↗
Figure 5
Figure 5. Figure 5: Top panel: Evolution in planet mass for the fiducial wind [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Quasi-steady planet ablation rate, ⟨ −M˙ p⟩, as a function of fm (Panel (a)), fe (Panel (b)), and M∞ (Panel (c)) at different grid resolutions. The error bars indicate 1σ uncertainties due to temporal fluctuations and any secular growth of −M˙ p (see Appendix D). To prevent overlapping, data markers with the same abscissa are separated in the dashed regions and a small horizontal displacement is also appli… view at source ↗
Figure 7
Figure 7. Figure 7: Terms in the integrated momentum equation (Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Quasi-steady values of the ablation and pressure-drag coe [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Variation in the quasi-steady shock stand-o [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the planet’s inspiral and mass evolution across several models. The blue line shows results from the 3D [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
read the original abstract

Most stars host short-period planets that are expected to be engulfed during post-main-sequence expansion. The dissolution of engulfed planets has been proposed as a possible mechanism for producing stars enriched in lithium and refractory elements. We perform three-dimensional hydrodynamical simulations of a Jupiter-like planet engulfed within a stellar envelope using the Seven-League Hydro code. Unlike previous studies that represent the planet as a point mass or rigid sphere, we adopt a wind-tunnel setup that resolves the planet's gaseous structure. We find that a continuous mass-ablation process operates during planetary engulfment, contrary to the common assumption that destruction occurs at a specific depth due to ram pressure, tidal forces, or thermal evaporation. The ablation rate scales nearly linearly with the wind momentum flux and is largely insensitive to the Mach number, consistent with an analytical model based on Kelvin-Helmholtz instability developing at the planetary surface. We define efficiency coefficients for drag and ablation, finding pressure-drag coefficients of 0.44-0.56 and smaller ablation efficiencies of 0.054-0.11. Applying these coefficients to a numerically integrated inspiral through a stellar profile, we find that continuous ablation could lead to complete dissolution of the planet within the convective envelope, producing observable lithium enrichment at the stellar surface. Our results provide prescriptions for drag and mass loss that enable large parameter-space studies of planetary engulfment and suggest that chemical enrichment may occur over a broader range of stellar parameters than previously thought.

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

2 major / 2 minor

Summary. The manuscript reports 3D hydrodynamical wind-tunnel simulations (using the Seven-League Hydro code) of a resolved gaseous Jupiter-like planet in uniform stellar-envelope flow. It finds continuous surface ablation driven by Kelvin-Helmholtz instability rather than abrupt destruction at a critical depth, with ablation rate scaling nearly linearly with wind momentum flux and insensitive to Mach number. Drag and ablation efficiency coefficients (0.44-0.56 and 0.054-0.11) are extracted and inserted into a separate 1D orbital-inspiral integrator through a stellar profile, yielding predictions of complete planetary dissolution and surface lithium enrichment.

Significance. If the reported linear scaling and constant efficiencies hold under realistic conditions, the work supplies practical, parameterizable prescriptions for drag and mass loss that enable population-level studies of post-main-sequence planetary engulfment. The explicit comparison to an analytic KH model and the demonstration of continuous rather than threshold destruction are concrete strengths that could broaden the predicted range of chemical-enrichment signatures.

major comments (2)
  1. [Inspiral integration and application to stellar profile] The central claim that continuous ablation leads to complete dissolution rests on efficiencies measured in fixed-planet, uniform-flow wind-tunnel runs being inserted unchanged into the inspiral integrator. No simulation is presented in which the background density and velocity evolve self-consistently on the local dynamical time while the planet ablates and its orbit decays; this extrapolation is load-bearing for the lithium-enrichment prediction.
  2. [Hydrodynamic simulation setup and results] The wind-tunnel boundary conditions impose steady uniform inflow at constant Mach and momentum flux. The manuscript does not quantify how the measured efficiencies would change under the radially varying density, velocity, and pressure gradients encountered during actual inspiral (e.g., near the convective-radiative boundary), which directly affects whether the linear scaling remains valid throughout the envelope.
minor comments (2)
  1. [Abstract] The abstract states ablation efficiencies of 0.054-0.11 but does not indicate the precise range of momentum fluxes or Mach numbers over which these values were averaged; a brief table or sentence linking the quoted range to the simulation grid would improve clarity.
  2. [Figures and captions] Figure captions and axis labels should explicitly state whether the reported drag and ablation efficiencies are time-averaged or instantaneous, and over what interval, to allow direct comparison with the analytic KH model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments correctly identify the key modeling assumptions in our work. We respond point by point below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: The central claim that continuous ablation leads to complete dissolution rests on efficiencies measured in fixed-planet, uniform-flow wind-tunnel runs being inserted unchanged into the inspiral integrator. No simulation is presented in which the background density and velocity evolve self-consistently on the local dynamical time while the planet ablates and its orbit decays; this extrapolation is load-bearing for the lithium-enrichment prediction.

    Authors: We agree that a fully self-consistent 3D simulation in which the background stellar profile evolves simultaneously with the planet's ablation and orbital decay would constitute a stronger test. Such calculations remain computationally prohibitive at the required resolution and timescale separation. Our 1D integrator is intended as a parameterization that propagates the locally measured efficiencies to estimate global outcomes. In the revised manuscript we will expand the discussion of this extrapolation, explicitly state the assumptions, and qualify the lithium-enrichment result as conditional on the efficiencies remaining approximately constant under envelope gradients. We will also add a simple timescale comparison between local KH growth and inspiral to support the separation of scales. revision: partial

  2. Referee: The wind-tunnel boundary conditions impose steady uniform inflow at constant Mach and momentum flux. The manuscript does not quantify how the measured efficiencies would change under the radially varying density, velocity, and pressure gradients encountered during actual inspiral (e.g., near the convective-radiative boundary), which directly affects whether the linear scaling remains valid throughout the envelope.

    Authors: The uniform-flow setup is chosen to isolate the local planet-wind interaction at a representative depth. Because the planet radius is much smaller than the local pressure scale height throughout most of the convective envelope, the uniform approximation is expected to be reasonable. We nevertheless accept that the manuscript does not quantify the effect of gradients. In the revision we will add an analytic estimate, based on the KH model already presented, of how a background density gradient modifies the ablation rate, together with a short discussion of possible additional effects near the convective-radiative interface. This will clarify the domain of applicability of the reported linear scaling. revision: partial

Circularity Check

0 steps flagged

No significant circularity; efficiencies measured from direct simulations and applied externally

full rationale

The paper's core result (continuous ablation during engulfment) is obtained from 3D hydrodynamical wind-tunnel simulations that resolve the planet's gaseous structure. Drag (0.44-0.56) and ablation (0.054-0.11) efficiency coefficients are direct outputs of those runs at fixed Mach and momentum flux. These measured values are then inserted into a separate inspiral integrator through a 1D stellar profile. No equation or step in the provided text reduces the central claim to a self-definition, a fitted input renamed as prediction, or a self-citation chain. The KH-based analytical model is invoked only for consistency, not as the load-bearing derivation. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on numerical extraction of two efficiency coefficients from the hydro runs and on the assumption that Kelvin-Helmholtz surface mixing governs the mass-loss rate; these are then extrapolated to a full stellar profile.

free parameters (2)
  • pressure-drag coefficient = 0.44-0.56
    Value range 0.44-0.56 extracted from the wind-tunnel simulations and used in the inspiral integration.
  • ablation efficiency coefficient = 0.054-0.11
    Value range 0.054-0.11 extracted from the same simulations and used to compute cumulative mass loss.
axioms (1)
  • domain assumption Kelvin-Helmholtz instability at the planet-wind interface sets the ablation rate scaling
    Invoked to explain why ablation is linear in momentum flux and insensitive to Mach number.

pith-pipeline@v0.9.0 · 5592 in / 1291 out tokens · 44035 ms · 2026-05-13T01:20:54.993795+00:00 · methodology

discussion (0)

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Works this paper leans on

75 extracted references · 75 canonical work pages · 1 internal anchor

  1. [1]

    H., & Carlberg, J

    Aguilera-Gómez, C., Chanamé, J., Pinsonneault, M. H., & Carlberg, J. K. 2016, ApJ, 829, 127

    work page 2016

  2. [2]

    Alexander, J. B. 1967, The Observatory, 87, 238

    work page 1967

  3. [3]

    & Wortman, A

    Ambrosio, A. & Wortman, A. 1962, ARS Journal, 32, 281

    work page 1962

  4. [4]

    2022, A&A, 659, A193

    Andrassy, R., Higl, J., Mao, H., et al. 2022, A&A, 659, A193

    work page 2022

  5. [5]

    2024, A&A, 683, A97 Andrássy, R

    Andrassy, R., Leidi, G., Higl, J., et al. 2024, A&A, 683, A97 Andrássy, R. & Spruit, H. C. 2013, A&A, 559, A122

    work page 2024

  6. [6]

    1965, ApJ, 142, 451

    Bodenheimer, P. 1965, ApJ, 142, 451

    work page 1965

  7. [7]

    1952, MNRAS, 112, 195

    Bondi, H. 1952, MNRAS, 112, 195

    work page 1952

  8. [8]

    A., Sneden, C., Lambert, D

    Brown, J. A., Sneden, C., Lambert, D. L., & Dutchover, Jr., E. 1989, ApJS, 71, 293

    work page 1989

  9. [9]

    M., Burbidge, G

    Burbidge, E. M., Burbidge, G. R., Fowler, W. A., & Hoyle, F. 1957, Reviews of Modern Physics, 29, 547 Carrillo-Santamaría, J., López-Cámara, D., De Colle, F., Moreno Méndez, E., & Sánchez-Salcedo, F. J. 2025, MNRAS, 540, 2952

    work page 1957

  10. [10]

    R., Ho, A

    Casey, A. R., Ho, A. Y . Q., Ness, M., et al. 2019, ApJ, 880, 125

    work page 2019

  11. [11]

    R., Ruchti, G., Masseron, T., et al

    Casey, A. R., Ruchti, G., Masseron, T., et al. 2016, MNRAS, 461, 3336

    work page 2016

  12. [12]

    1943, ApJ, 97, 255

    Chandrasekhar, S. 1943, ApJ, 97, 255

    work page 1943

  13. [13]

    1961, Hydrodynamic and hydromagnetic stability

    Chandrasekhar, S. 1961, Hydrodynamic and hydromagnetic stability

    work page 1961

  14. [14]

    P., Mustill, A

    Church, R. P., Mustill, A. J., & Liu, F. 2020, MNRAS, 491, 2391

    work page 2020

  15. [15]

    & Woodward, P

    Colella, P. & Woodward, P. R. 1984, Journal of Computational Physics, 54, 174

    work page 1984

  16. [16]

    1928, Mathematische Annalen, 100, 32

    Courant, R., Friedrichs, K., & Lewy, H. 1928, Mathematische Annalen, 100, 32

    work page 1928

  17. [17]

    2023, Nature, 617, 55

    De, K., MacLeod, M., Karambelkar, V ., et al. 2023, Nature, 617, 55

    work page 2023

  18. [18]

    W., et al

    De, S., MacLeod, M., Everson, R. W., et al. 2020, ApJ, 897, 130

    work page 2020

  19. [19]

    Edelmann, P. V . F. 2014, Dissertation, Technische Universität München

    work page 2014

  20. [20]

    Edelmann, P. V . F., Horst, L., Berberich, J. P., et al. 2021, A&A, 652, A53

    work page 2021

  21. [21]

    Fehlberg, E. 1969, Low-order Classical Runge-Kutta Formulas with Stepsize Control and Their Application to Some Heat Transfer Problems, Technical Report NASA TR R-315, National Aeronautics and Space Administration (NASA)

    work page 1969

  22. [22]

    2013, ApJ, 766, 81

    Fressin, F., Torres, G., Charbonneau, D., et al. 2013, ApJ, 766, 81

    work page 2013

  23. [23]

    Gagnier, D., Leidi, G., Vetter, M., Andrassy, R., & Röpke, F. K. 2026, A&A, 707, A1

    work page 2026

  24. [24]

    2019, ApJS, 245, 33

    Gao, Q., Shi, J.-R., Yan, H.-L., et al. 2019, ApJS, 245, 33

    work page 2019

  25. [25]

    S., & Udalski, A

    Gould, A., Dorsher, S., Gaudi, B. S., & Udalski, A. 2006, Acta Astron., 56, 1

    work page 2006

  26. [26]

    Gruzinov, A., Levin, Y ., & Matzner, C. D. 2020, MNRAS, 492, 2755 Article number, page 13 of 18 A&A proofs:manuscript no. planet

    work page 2020

  27. [27]

    2020, MN- RAS, 499, 1154

    Hirai, R., Sato, T., Podsiadlowski, P., Vigna-Gómez, A., & Mandel, I. 2020, MN- RAS, 499, 1154

    work page 2020

  28. [28]

    Horst, L., Edelmann, P. V . F., Andrássy, R., et al. 2020, A&A, 641, A18

    work page 2020

  29. [29]

    Horst, L., Hirschi, R., Edelmann, P. V . F., Andrassy, R., & Roepke, F. K. 2021, A&A, 653, A55

    work page 2021

  30. [30]

    W., Marcy, G

    Howard, A. W., Marcy, G. W., Bryson, S. T., et al. 2012, ApJS, 201, 15

    work page 2012

  31. [31]

    & Lyttleton, R

    Hoyle, F. & Lyttleton, R. A. 1939, Proceedings of the Cambridge Philosophical Society, 35, 405

    work page 1939

  32. [32]

    C., Ford, E

    Hsu, D. C., Ford, E. B., Ragozzine, D., & Ashby, K. 2019, AJ, 158, 109

    work page 2019

  33. [33]

    Hubbard, W. B. 1984, Planetary interiors (Van Nostrand Reinhold)

    work page 1984

  34. [34]

    1986, MNRAS, 223, 129

    Inaguchi, T., Matsuda, T., & Shima, E. 1986, MNRAS, 223, 129

    work page 1986

  35. [35]

    & Spruit, H

    Jia, S. & Spruit, H. C. 2018, ApJ, 864, 169

    work page 2018

  36. [36]

    1950, Memoirs of the College of Science, University of Kyoto, Series A, 26, 207

    Kawamura, T. 1950, Memoirs of the College of Science, University of Kyoto, Series A, 26, 207

    work page 1950

  37. [37]

    Kramer, M., Schneider, F. R. N., Ohlmann, S. T., et al. 2020, A&A, 642, A97

    work page 2020

  38. [38]

    Landau, L. D. 1944, Dokl. Akad. Nauk. SSSR, 44, 339

    work page 1944

  39. [39]

    Landau, L. D. & Lifshitz, E. M. 1959, Fluid mechanics

    work page 1959

  40. [40]

    Lebedev, V . I. & Laikov, D. N. 1999, Doklady Akademii Nauk, 366, 741

    work page 1999

  41. [41]

    Leidi, G., Andrassy, R., Higl, J., Edelmann, P. V . F., & Röpke, F. K. 2023, A&A, 679, A132

    work page 2023

  42. [42]

    2024, A&A, 686, A34

    Leidi, G., Andrassy, R., Barsukow, W., et al. 2024, A&A, 686, A34

    work page 2024

  43. [43]

    2022, A&A, 668, A143

    Leidi, G., Birke, C., Andrassy, R., et al. 2022, A&A, 668, A143

    work page 2022

  44. [44]

    Phlegethon: a fully compressible magnetohydrodynamic code for simulations in stellar astrophysics

    Leidi, G., Holas, A., Vitovsky, K., et al. 2026, arXiv e-prints, arXiv:2604.12672

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  45. [45]

    D., & Armitage, P

    Li, X., Chang, P., Levin, Y ., Matzner, C. D., & Armitage, P. J. 2020, MNRAS, 494, 2327

    work page 2020

  46. [46]

    & Soker, N

    Livio, M. & Soker, N. 1984, MNRAS, 208, 763

    work page 1984

  47. [47]

    Lobb, R. K. 1964, in The High Temperature Aspects of Hypersonic Flow, ed. W. C. Nelson (Oxford: Pergamon Press), 519–527

    work page 1964

  48. [48]

    2021, AIAA Journal, 59, 3261

    Loth, E., Tyler Daspit, J., Jeong, M., Nagata, T., & Nonomura, T. 2021, AIAA Journal, 59, 3261

    work page 2021

  49. [49]

    2017, ApJ, 838, 56

    MacLeod, M., Antoni, A., Murguia-Berthier, A., Macias, P., & Ramirez-Ruiz, E. 2017, ApJ, 838, 56

    work page 2017

  50. [50]

    2018, ApJ, 853, L1

    MacLeod, M., Cantiello, M., & Soares-Furtado, M. 2018, ApJ, 853, L1

    work page 2018

  51. [51]

    & Ramirez-Ruiz, E

    MacLeod, M. & Ramirez-Ruiz, E. 2015, ApJ, 803, 41

    work page 2015

  52. [52]

    Occurrence, mass distribution and orbital properties of super-Earths and Neptune-mass planets

    Mayor, M., Marmier, M., Lovis, C., et al. 2011, arXiv e-prints, arXiv:1109.2497

    work page arXiv 2011

  53. [53]

    D., Giannios, D., & Spiegel, D

    Metzger, B. D., Giannios, D., & Spiegel, D. S. 2012, MNRAS, 425, 2778

    work page 2012

  54. [54]

    2013, Dissertation, Technische Universität München

    Miczek, F. 2013, Dissertation, Technische Universität München

    work page 2013

  55. [55]

    K., & Edelmann, P

    Miczek, F., Röpke, F. K., & Edelmann, P. V . F. 2015, A&A, 576, A50

    work page 2015

  56. [56]

    Miller, D. G. & Bailey, A. B. 1979, Journal of Fluid Mechanics, 93, 449 O’Connor, C. E., Bildsten, L., Cantiello, M., & Lai, D. 2023, ApJ, 950, 128

    work page 1979

  57. [57]

    M., Brewer, J

    Oh, S., Price-Whelan, A. M., Brewer, J. M., et al. 2018, ApJ, 854, 138

    work page 2018

  58. [58]

    Ostriker, E. C. 1999, ApJ, 513, 252

    work page 1999

  59. [59]

    2016, A&A, 593, A128

    Privitera, G., Meynet, G., Eggenberger, P., et al. 2016, A&A, 593, A128

    work page 2016

  60. [60]

    J., Glanz, H., Bildsten, L., Perets, H

    Prust, L. J., Glanz, H., Bildsten, L., Perets, H. B., & Röpke, F. K. 2024, ApJ, 966, 103

    work page 2024

  61. [61]

    E., Lin, D

    Sandquist, E., Taam, R. E., Lin, D. N. C., & Burkert, A. 1998, ApJ, 506, L65

    work page 1998

  62. [62]

    L., Dokter, J

    Sandquist, E. L., Dokter, J. J., Lin, D. N. C., & Mardling, R. A. 2002, ApJ, 572, 1012

    work page 2002

  63. [63]

    1986, MNRAS, 221, 687

    Shima, E., Matsuda, T., & Inaguchi, T. 1986, MNRAS, 221, 687

    work page 1986

  64. [64]

    & Osher, S

    Shu, C.-W. & Osher, S. 1988, Journal of Computational Physics, 77, 439

    work page 1988

  65. [65]

    Silverman, B. W. 1986, Density estimation for statistics and data analysis

    work page 1986

  66. [66]

    Soares-Furtado, M., Cantiello, M., MacLeod, M., & Ness, M. K. 2021, AJ, 162, 273

    work page 2021

  67. [67]

    Stevenson, D. J. 1991, ARA&A, 29, 163

    work page 1991

  68. [68]

    Syrovatskii, S. I. 1954, Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 27, 121, in Russian

    work page 1954

  69. [69]

    2016, A&A, 589, A10

    Thun, D., Kuiper, R., Schmidt, F., & Kley, W. 2016, A&A, 589, A10

    work page 2016

  70. [70]

    F., Spruce, M., & Speares, W

    Toro, E. F., Spruce, M., & Speares, W. 1994, Shock Waves, 4, 25 van der V orst, H. A. 1992, SIAM Journal on Scientific and Statistical Computing, 13, 631

    work page 1994

  71. [71]

    2013, ApJ, 769, 1

    Viallet, M., Meakin, C., Arnett, D., & Mocák, M. 2013, ApJ, 769, 1

    work page 2013

  72. [72]

    & Sneden, C

    Wallerstein, G. & Sneden, C. 1982, ApJ, 255, 577

    work page 1982

  73. [73]

    T., Marcy, G

    Wright, J. T., Marcy, G. W., Howard, A. W., et al. 2012, ApJ, 753, 160

    work page 2012

  74. [74]

    2026, ApJ, 998, 118

    Yang, M., Lai, D., Wu, F., & Zhang, J. 2026, ApJ, 998, 118

    work page 2026

  75. [75]

    B., Murguia-Berthier, A., et al

    Yarza, R., Razo-López, N. B., Murguia-Berthier, A., et al. 2023, ApJ, 954, 176 Article number, page 14 of 18 Mike Y . M. Lau et al.: Continuous mass ablation of planets engulfed in stellar envelopes Appendix A: Grid stretching functions The computational coordinates are mapped from a logically Cartesian space to physical space using normalised power-law s...

    work page 2023