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REVIEW 3 major objections 6 minor 2 cited by

Three-dimensional simulations of accretion disks in pre-CE systems

T0 review · 3 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read A 3D simulation predicts that just before a red supergiant and neutron star enter a common envelope, the neutron star hosts an accretion disk of about 0.005 solar masses, about 40 solar radii across, accreting at about 0.004 solar masses…

desk verdict Solid 3D pre-CE disk simulation, but the factor-of-few mass claim is hostage to the fixed gamma=1.1 no-cooling thermodynamics; deserves review but needs that caveat front and center. read the letter →

arxiv 2502.02933 v3 pith:PP6CS7VV submitted 2025-02-05 astro-ph.SR astro-ph.HE

Ana L. Juarez-Garcia , Orsola De Marco , Fabio De Colle , Diego Lopez-Camara , Enrique Moreno Mendez , Jesus Carrillo-Santamaria , Mark Wardle This is my paper · ORCID
classification astro-ph.SRastro-ph.HE
keywords accretiondiskscommonenvelopeRochelobeoverflowneutronstarhydrodynamicsnumericalsimulationsredsupergiantmasstransfer
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 asks what the accretion disk around a neutron star looks like in the decades immediately before its binary companion's envelope swallows it. The authors simulate the Roche-lobe overflow from a 7-solar-mass red supergiant onto a 1.4-solar-mass neutron star in 3D, using a long 1D binary evolution calculation to set the mass-transfer rate. They predict that just before the common-envelope phase the disk holds roughly $5\times10^{-3}\,M_\odot$, extends to about $40\,R_\odot$, has a scale height near $5\,R_\odot$, and accretes onto the neutron star at about $4\times10^{-3}\,M_\odot\,\mathrm{yr}^{-1}$. These numbers matter because this disk may power jets that help decide whether the common envelope is ejected or the neutron star merges with the giant's core.

What carries the argument

The machinery is a compact-object-centred, co-rotating 3D hydrodynamic simulation with an L1 mass-injection nozzle: gas enters through a small elliptical nozzle at a rate interpolated from a 1D stellar evolution calculation covering 30,000 years, while a low-density background surrounds a spherical inner boundary at $1.3\,R_\odot$. The equation of state is quasi-isothermal with $\gamma=1.1$, chosen because earlier work found that RLOF and CE disks form only for $\gamma\lesssim1.2$; no self-gravity, magnetic fields, or explicit cooling are included. Disk radius is defined operationally as the first inflection point of the cumulative enclosed-mass profile, vertical density profiles define the scale height, and a specific-energy versus specific-angular-momentum diagram is used to show that the dense disk gas is bound and moving on low-eccentricity orbits.

What would settle it

Run the same binary through a 3D simulation with explicit radiative cooling and a realistic depth-dependent adiabatic index out to the onset of the common envelope: if the disk mass falls outside roughly $1.5\times10^{-3}$ to $1.5\times10^{-2}\,M_\odot$ or the radius outside $34$ to $46\,R_\odot$, the paper's stated uncertainties are wrong. Alternatively, identify an observed X-ray binary with a supergiant donor overfilling its Roche lobe and measure its accretion rate from X-ray luminosity; a rate more than an order of magnitude away from $4\times10^{-3}\,M_\odot\,\mathrm{yr}^{-1}$ would challenge the prediction.

Watch

Extended reading notes

Core claim

The central claim is that a pre-common-envelope disk around a neutron star fed through the inner Lagrange point should have $M_{\rm disk}\sim 5\times10^{-3}\,M_\odot$, $R_{\rm disk}\sim 40\,R_\odot$, and $H\sim 5\,R_\odot$ at the moment the in-spiral begins, with an inner-boundary accretion rate of a few $\times10^{-3}\,M_\odot\,\mathrm{yr}^{-1}$. The disk rotates at nearly Keplerian speed near the inner boundary and at 80 to 90 percent of Keplerian at its outer edge, where pressure support matters. Its mid-plane temperature falls as $T\propto r^{-1.1}$, steeper than the $T\propto r^{-3/4}$ law of the standard Shakura-Sunyaev thin-disk model, and the authors attribute the difference to their quasi-isothermal equation of state without explicit cooling. Based on simulations that vary the mass-injection rate, the nozzle velocity, the background density and temperature, and the mesh resolution, they argue the disk mass is reliable to within a factor of a few and the radius to within about 15 percent.

Load-bearing premise

The load-bearing premise is that a 21-year, quasi-isothermal ($\gamma=1.1$) 3D run without explicit cooling or self-gravity, driven by a 1D model of the donor's mass loss, captures the disk's state at the moment the common envelope begins; if the real envelope cools or compresses differently, or the donor responds to mass loss differently, the disk's mass and radius could move outside the stated factor of a few.

Editorial extensions

If this is right

  • The neutron star enters the common envelope carrying a disk of about $5\times10^{-3}\,M_\odot$, giving the in-spiral an immediate reservoir of mass and angular momentum that can feed jets or outflows.
  • Because the inner accretion rate is roughly a hundred times smaller than the L1 injection rate, most of the transferred mass is stored in the disk or leaves the domain rather than being accreted promptly.
  • A jet launched from the inner boundary of this disk could carry a mechanical luminosity near $3\times10^3\,L_\odot$, and a jet launched close to the neutron star surface could reach about $10^8\,L_\odot$, enough to affect envelope unbinding.
  • The disk's steeper-than-standard temperature profile implies that radiative cooling must be included before the Shakura-Sunyaev $T\propto r^{-3/4}$ prescription is used for pre-CE disk temperatures.
  • The convergence of disk mass, radius, scale height, and accretion rate across refinement levels indicates the predicted properties are numerical, not resolution artifacts.

Reading between the lines

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

  • If the disk is destroyed upon entering the common envelope, its measured mass and angular momentum set the starting budget for any disk that reforms around the in-spiralling neutron star, so these numbers anchor CE-feedback models even if the disk itself does not survive.
  • The simulations omit magnetic fields, and the paper notes that Gauss-level fields could be amplified by the magneto-rotational instability within a few orbits; if that happens, magnetic stress may raise the accretion rate above the measured value.
  • A comparison run at $\gamma=4/3$ already produces a five-times-smaller and hundred-times-less-massive structure, so if the real envelope contains zones of reduced compressibility, disk formation in this pre-CE phase could be marginal rather than assured.
  • Observing a candidate pre-CE system in unstable mass transfer and comparing its inferred accretion rate and disk signatures with these predictions would test whether the simulated 21-year window is representative of the full 30,000-year RLOF phase.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper presents 3D hydrodynamic simulations of Roche-lobe overflow mass transfer from a 7 M_sun red supergiant onto a 1.4 M_sun neutron star, targeting the phase immediately before common-envelope (CE) entry. A 1D MESA simulation supplies a 30,000-year mass-transfer history, while the 3D MEZCAL simulations follow only the last 21 years around the accretor, using a fixed quasi-isothermal equation of state with gamma=1.1 and no explicit cooling. The central claims are that the pre-CE disk has mass ~5e-3 M_sun, radius ~40 R_sun, scale height ~5 R_sun, and accretion rate ~4e-3 M_sun/yr, and that these values are robust to a factor of a few in mass and 15% in radius. The paper includes resolution, injection-rate, nozzle-velocity, background, and adiabatic-index sensitivity tests, as well as a comparison of the measured accretion rate and temperature profile with Shakura-Sunyaev theory.

Significance. If the central numbers hold, this would be a valuable quantitative constraint on accretion feedback in the poorly understood pre-CE phase, with direct consequences for studies of jet feedback and CE outcomes. The paper's strengths are its explicit stress testing: the resolution study (Section 4.4) shows convergence with only 12% mass variation across levels, and the parameter scans in Sections 4.1-4.3 cover several numerical and physical choices. The authors also openly state many limitations, including the absence of cooling and the short simulation window. However, the stated uncertainty budget does not include the dominant thermodynamic sensitivity, and the Shakura-Sunyaev comparison is circular; these issues bound the significance of the claimed numbers unless the claims are narrowed or the physics is extended.

major comments (3)
  1. [Section 4.5 and Figure 19] The claimed robustness expressed in the abstract and Section 5 ("reasonable within a factor of a few for the mass and 15% for the radius") is not supported for the dominant physical uncertainty. The paper's own 3D run with gamma=4/3 gives Mdisk=5.37e-5 M_sun and Rdisk=15.2 R_sun, versus Mdisk=5.5e-3 M_sun and Rdisk=39 R_sun for sim-0 -- a factor of ~100 in mass and ~2.6 in radius -- and the gamma=5/3 run yields no measurable disk. All variations in Sections 4.1-4.4 keep gamma=1.1 and no explicit cooling, so they cannot bound the sensitivity to the effective thermodynamics. The paper should either add simulations that vary the equation of state/cooling in a physically motivated range, or explicitly restate the central claim as conditional on a near-isothermal, no-cooling model, removing the factor-of-few and 15% statements as global robustness claims.
  2. [Section 3.1, Eq. (11)] The agreement between the simulated accretion rate and the Shakura-Sunyaev prediction is not an independent validation: Eq. (11) uses the simulation's own Mdisk, cs, and H, assumes Sigma = Mdisk/Rdisk^2, and adopts alpha=0.1 arbitrarily. The predicted rates are therefore partly determined by construction, making the comparison circular. The text should either derive alpha from the measured turbulent stress or shock dissipation in the simulation, or clearly label this as a consistency check rather than a prediction.
  3. [Section 2.2.2, Table 5, Figure 6] The extrapolation that the 21-year disk mass is "likely only a factor of a few smaller than if the entire phase were modelled" is not directly supported. The cumulative mass of sim-0 is still increasing at t=21 yr (Figure 6, bottom-right panel), and the sim-mdot-2 and sim-mdot-3 runs start at different times and run for different durations without reaching a secular plateau. The paper should quantify the disk growth rate at the end of the simulation and either show evidence of approach to saturation or reframe the CE-entry mass as an upper limit.
minor comments (6)
  1. [Section 2.2] There is a duplicated word in "We then use use the 3D hydrodynamic numerical code"; please correct.
  2. [Figure 15 caption] The caption states "Tbg = 105 cm s–1" for what should be a temperature; the units should be K, and the same typo appears in the legend context.
  3. [References] The Shakura & Sunyaev (1973) reference is listed twice with identical bibliographic data; please consolidate.
  4. [Section 4.5] The phrase "only slightly higher" for gamma=4/3 compared to gamma=1.1 is imprecise; a change from 1.1 to 1.333 is substantial in compressibility, so the sentence should be rephrased.
  5. [Section 3.1, Figure 9] The text uses alpha both for the Shakura-Sunyaev viscosity parameter and for the temperature power-law exponent; this is confusing and should be disambiguated with different symbols.
  6. [Appendix 1.1] The conservation test modifies the boundary conditions and removes the inner inflow boundary, so it does not verify conservation in the production setup; the discussion should acknowledge that this is a simplified check.

Circularity Check

1 steps flagged · score 3.0 of 10

Minor circularity: the Shakura-Sunyaev accretion-rate 'prediction' (Eq. 11) is assembled from the simulation's own disk outputs with an arbitrary α=0.1, so the agreement with the measured rate is a self-referential consistency test, not an independent check; the central disk mass/radius result remains a non-circular forward calculation.

  1. fitted input called prediction [Section 3.1, Eq. (11) and Table 4; restated in Section 5]
    "We can therefore compare the numerically-derived accretion rates to those theoretically predicted by Shakura & Sunyaev (1973): Mdot = 3πΣαcsHdisk, ... where we assume Σ = Mdisk/R2 disk). For thin disks, we arbitrarily assume α = 0.1. Using the aforementioned results at the 10.5 and 21 years, we predict accretion rates of 5.0 × 10–4 M⊙ yr–1and 3.7 × 10–3 M⊙ yr–1, respectively, consistent with the accretion rate measured at the same two points in the simulation (Table 4)."

    The 'predicted' Shakura-Sunyaev rate is assembled from the same simulation's measured Mdisk, cs, and Hdisk (Eq. 11), closed by an assumed Σ = Mdisk/Rdisk^2 and an arbitrary α = 0.1. The comparison target — 'the accretion rate measured at the same two points in the simulation' (Table 4) — is another output of that same run (Eq. 10). Neither side is independent: the prediction carries no information beyond the run's own disk properties, and the agreement only restates that the run's implied effective α is ≈0.1 under the assumed closure. Because every input to Eq. 11 is an output of the very simulation the check claims to validate, the 'prediction' is a self-referential consistency test, not a confirmation; with α free, the formula could absorb any discrepancy.

full rationale

The central claim (Mdisk ≈ 5×10^−3 M_sun, Rdisk ≈ 40 R_sun, H ≈ 5 R_sun just before CE) is the measured output of a forward 3D Euler-equation integration with a specified mass-injection history from MESA, γ = 1.1, and no explicit cooling (Sec. 2.2.2). No equation defines these outputs in terms of the inputs; they are obtained from cumulative-mass and vertical-density profiles (Sec. 3.1). That core derivation is not circular. The one self-referential step is the Shakura-Sunyaev 'prediction' (Sec. 3.1, Eq. 11): predicted Mdot = 3πα(Mdisk/Rdisk^2)csH is built from the same run's measured Mdisk, cs, H with an arbitrary α = 0.1 and compared to the same run's measured accretion rate (Eq. 10, Table 4). The agreement is a consistency test with a free efficiency parameter — it states that the run's implied effective α ≈ 0.1 — not an independent validation; but it is non-load-bearing for the headline disk parameters. The γ = 4/3 run (Sec. 4.5) lowering Mdisk by ≈100× and γ = 5/3 erasing the measurable disk is a real limitation of the quoted 'factor of a few' mass accuracy, and the paper itself concedes 'more reasonable cooling physics would need to be included'; this is a physical-robustness concern (correctness risk), not circularity, and it is disclosed rather than hidden. Self-citations (López-Cámara et al. 2019/2020/2022; Moreno Méndez et al. 2017/2022; De Colle et al. 2012) are contextual and non-load-bearing; the γ = 1.1 choice rests on external prior work (Makita et al. 2000; MacLeod & Ramirez-Ruiz 2015; Murguia-Berthier et al. 2017) and is explicitly stress-tested in Sec. 4.5. No uniqueness theorem is imported. Score 3: minor, non-load-bearing circularity in the SS cross-check; the central simulation stands on its own.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central prediction rests on several modeling choices: an almost isothermal equation of state, a nozzle prescription for L1 flow, a MESA-derived mass transfer rate, and no magnetic fields or radiation. None of these are fitted to the disk mass itself, but each can shift the result, which is why the authors quote only factor-of-a-few accuracy.

free parameters (4)
  • Adiabatic index gamma = 1.1
    Set at the start and fixed throughout; based on prior work (Makita et al. 2000, MacLeod and Ramirez-Ruiz 2015, Murguia-Berthier et al. 2017) but not derived in this paper. Controls gas compressibility and whether a disk forms; tested with gamma = 4/3 and 5/3 in Section 4.5.
  • Shakura-Sunyaev alpha = 0.1
    Arbitrarily assumed in Eq. 11 to compare the simulated accretion rate with Shakura-Sunyaev theory. The agreement is not an independent prediction because Mdisk, cs, and H all come from the simulation.
  • Nozzle injection velocity vL1 = 7.7e4 cm/s (sim-0)
    Chosen because gas must enter the domain at the prescribed rate; treated as arbitrary and tested with two other values in Section 4.2.
  • Background density and temperature = rho_bg = 2.6e-22 g/cm3, T_bg = 1e5 K
    Chosen as the lowest viable values for numerical stability, so that cells are never empty. Sensitivity tested in Section 4.3; high background pressure can reduce nozzle outflow.
assumptions (5)
  • domain assumption Ideal gas quasi-isothermal equation of state, P = (gamma - 1) rho e, with gamma = 1.1.
    State in Section 2.2.2. Central to disk formation; no radiation or explicit cooling is included.
  • domain assumption No self-gravity of the disk; only point-mass potentials of the donor and accretor in a rotating frame.
    Equations 4-6 in Section 2.1. Disk self-gravity is neglected throughout.
  • domain assumption The MESA 1D mass-transfer rate and binary parameters are accurate.
    Section 2.2.1. The 3D simulation interpolates its injection rate from this model; if the donor response to mass loss differs, the disk mass scales accordingly.
  • domain assumption The Lubow-Shu and Jackson nozzle prescription describes the mass stream through L1.
    Section 2.2.2, Eq. 8. Nozzle size and injection velocity are set by the isothermal sound speed and mass ratio.
  • domain assumption Inviscid Euler equations with numerical viscosity and turbulent shocks providing angular momentum transport.
    Section 2.1. There is no explicit viscosity, magnetic field, or MRI; the authors argue the measured accretion rate is physical rather than numerical.

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Cite this review

Pith. "Pith review of Three-dimensional simulations of accretion disks in pre-CE systems." pith.science (2026). https://pith.science/paper/PP6CS7VV

@misc{pith2026250202933,
  author       = {Pith},
  title        = {Pith review of: Three-dimensional simulations of accretion disks in pre-CE systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PP6CS7VV}},
  note         = {Machine review of arXiv:2502.02933}
}
abstract

Before a binary system enters into a common envelope (CE) phase, accretion from the primary star onto the companion star through Roche Lobe overflow (RLOF) will lead to the formation of an accretion disk, which may generate jets. Accretion before and during the CE may alter the outcome of the interaction. Previous studies have considered different aspects of this physical mechanism. Here we study the properties of an accretion disk formed via 3D hydrodynamic simulations of the RLOF mass transfer between a 7 M$_\odot$, red supergiant star and a 1.4 M$_\odot$, neutron star companion. We simulate only the volume around the companion for improved resolution. We use a 1D implicit MESA simulation of the evolution of the system during 30,000 years between the on-set of the RLOF and the CE to guide the binary parameters and the mass-transfer rate, while we simulate only 21 years of the last part of the RLOF in 3D using an ideal gas isothermal equation of state. We expect that a pre-CE disk under these parameters will have a mass of $\sim 5\times 10^{-3}$ M$_\odot$ and a radius of $\sim$40 R$_\odot$ with a scale height of $\sim$5 R$_\odot$. The temperature profile of the disk is shallower than that predicted by the formalism of Shakura and Sunyaev, but more reasonable cooling physics would need to be included. We stress test these results with respect to a number of physical and numerical parameters, as well as simulation choices, and we expect them to be reasonable within a factor of a few for the mass and 15% for the radius. We also contextualize our results within those presented in the literature, in particular with respect to the dimensionality of simulations and the adiabatic index. We discuss the measured accretion rate in the context of the Shakura and Sunyaev formalism and debate the viscous mechanisms at play, finishing with a list of prospects for future work.

Figures

Figures reproduced from arXiv: 2502.02933 by the authors.

Figure 1
Figure 1. Setup cartoon. The donor star is a red super giant of 7 M⊙ with a radius of 139 R⊙, orbiting a compact object of 1.41 M⊙, with a separation of 270 R⊙. The dotted line (centred on the compact object) represents the computational domain in our 3D simulations. 2.1 The hydrodynamic code and its governing equations To study the formation and stability of accretion disks during the RLOF phase, we run a series of 3D numeri… view at source ↗
Figure 2
Figure 2. Temporal evolution of the mass transfer rate from the primary to the secondary star in our long-term, MESA simulation of the binary system. The initial masses of the stars are 7 M⊙ and 1.4 M⊙; they have an initial orbital separation of 270 R⊙ and an orbital period of 177 days. We indicate with the orange box the mass transfer evolution that we are simulating in 3D. We then continue the MESA simulation for an additio… view at source ↗
Figure 3
Figure 3. Volumetric density rendering showing the accretion disk at four times (t = 0.3 yr, 1.5 yr, 10.5 yr, and 21 yrs). We can appreciate the 3D structure of the accretion disk, surrounding the companion star (represented by the white area in the middle of the accretion disk). After 10.5 yr the shock between the spiral arms has created a high density structure with a disk-like shape, surrounding the companion star (see bot… view at source ↗
Figures from the paper (16 more)
Figure 4
Figure 4. Figure 4: Density slices of the accretion disk on the orbital plane (top row) and perpendicular plane (bottom row) of sim-0 at times t = 0.3 yr, 1.5 yr, 10.5 yr, and 20.9 yr (from left to right). The letters in the third and fourth upper panels represent the positions used to ca…
Figure 5
Figure 5. Figure 5: Density profile of the accretion disk versus height at a radius of 26.7 R⊙ (1.86×1012 cm). Two times are shown: t = 10.5 yr (blue line) and 21 yr (red line). The readings were taken at four symmetric points around the companion indicated in [PITH_FULL_IMAGE:figures/fu…
Figure 7
Figure 7. Figure 7: ). We identify a cubic volume, 2Rin on a side, which contains the inflow boundary sphere. The total accretion rate is measured by calculating the mass flux through the cubic boundary, by taking the projection of the velocity of each cell surrounding the boundary onto t…
Figure 6
Figure 6. Figure 6: Cumulative mass as a function calculated from the companion star, at different times: t = 0.3 yr (top left panel, orange line), t = 1.5 yr (top right panel, maroon line), t = 10.5 yr (bottom left panel, purple line), t = 21 yr (bottom right panel, blue line). The black…
Figure 9
Figure 9. Figure 9: Temperature profile for sim-0 in the mid plane along the positive x-axis at t = 21 yr. The disk’s radius is indicated with a vertical grey dashed line, while the inner boundary’s radius is marked with a vertical black line. The solution for steady disks is indicated by…
Figure 8
Figure 8. Figure 8: Temperature slices for sim-0 in the orbital (top panel) and perpen￾dicular (bottom panel) planes of the disk at t = 21 yr. In [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 10
Figure 10. Figure 10: Slices of Mach number in the orbital plane (top panels) and per￾pendicular plane (bottom panels) of the disk at t = 10.5 yr (left panels) and t = 21 yr (right panels) for sim-0. of scatter in individual cells due to the gas there not moving entirely azimutally. Cells …
Figure 11
Figure 11. Figure 11: Velocity profile in the mid-plane along the positive and negative axes at 10.5 yr. The velocity is normalised to the Keplerian velocity (vk ). The inner boundary is marked by the black vertical solid line and the radius of the disk by the vertical grey dashed line. We…
Figure 12
Figure 12. Figure 12: Specific angular momentum versus specific orbital energy for every cell in the computational domain once the disk has formed (sim-0). The integration time corresponds to t = 10.5 yrs. The density colour table is the same as in [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 13
Figure 13. Figure 13: Densities slices on the orbital plane at the end of the 3D simulations. The models that are shown are: sim-0 (lower left panel), sim-mdot-1 (upper left panel), sim-mdot-2 (upper right panel) and sim-mdot-3 (lower right panel). Note how the density colour bar may have …
Figure 14
Figure 14. Figure 14: The cumulative mass as a function of radius (top panel) and the vertical density profile (bottom panel) for models with different injection velocities at t = 21 yr. Solid dark green line: vL1 = 7.75×104 cm s–1 (model sim-0), dotted green line: vL1 = 5.74×105 cm s–1 (s…
Figure 15
Figure 15. Figure 15: The cumulative mass as a function of radius (top panel) and the vertical density profile (bottom panel) for models with different back￾ground temperatures at t = 21 yr. Solid purple line: Tbg = 105 cm s–1 (model sim-0), dotted red line: Tbg = 104 cm s–1 (sim-bgT-1), d…
Figure 16
Figure 16. Figure 16: The cumulative mass as a function of radius (top panel), the verti￾cal density profile (middle panel) of the accretion disk at t = 21 yr for different resolutions. And the mass accretion rate onto the companion (bottom panel) as function of time for different resoluti…
Figure 17
Figure 17. Figure 17: Density in the orbital plane for 2D simulations with different adiabatic indexes. Adiabatic index γ = 1.1 is on the upper-left panel (a 2D version of the 3D sim-0), γ = 1.2 in the upper-right panel, γ = 4/3 in the lower-left panel, and γ = 5/3 in the lower-right panel…
Figure 18
Figure 18. Figure 18: Density slices in the orbital plane (upper panels) and perpendicu￾lar plane (lower panels) for 3D simulations with different adiabatic indexes (γ = 4/3 left, and γ = 5/3 right). The simulations are plotted at t = 21 yr, and can be compared with last panel of [PITH_FU…
Figure 19
Figure 19. Figure 19: The cumulative mass as a function of radius (top panel) and vertical density profile (bottom panel) for 3D models with different adiabatic index. The simulations are plotted at t = 21 yr. Density slices of these models are presented in the last column of [PITH_FULL_I…

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Forward citations

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