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Collision-induced mass loss and mass gain on an extremely massive star. An analytical approach and a static proto-globular cluster test-case

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that collision-induced mass loss on an accreting extremely massive star is substantial and strongly structure-dependent, and that in a compact aEMS model with low to intermediate gas accretion the star reaches a…

desk verdict First collision mass-loss/gain grid for 10^3-10^4 M_sun accreting stars; qualitatively plausible, but the conveyor-belt numbers rest on a static-structure prescription that the paper itself shows is violated. read the letter →

arxiv 2506.12132 v1 pith:PLC4EJVZ submitted 2025-06-13 astro-ph.SR astro-ph.GA

Laura Ramírez-Galeano , Corinne Charbonnel , Tassos Fragos , Zoubaïr Tazakkati , Jaime Roman-Garza , Mark Gieles This is my paper · ORCID
classification astro-ph.SRastro-ph.GA
keywords accretingextremelymassivestarscollision-inducedmasslossmultiplestellarpopulationsinglobularclustersconvectiveenergytransportMESAmodelsMonteCarlosimulationsbudgetproblemproto-globular
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

The paper asks whether collisions with ordinary stars can remove or add significant mass to an accreting extremely massive star (an aEMS, roughly 1,000 to 10,000 solar masses), and whether such stars can supply the chemically processed gas that globular clusters show in their second stellar populations. It builds a grid of one-dimensional stellar evolution models with different treatments of super-adiabatic convection, derives analytical prescriptions for how much mass a single collision unbinds, and runs Monte Carlo simulations of repeated collisions in a dense proto-globular cluster. The central result is that the outcome depends strongly on the target's structure: bloated stars tend to lose mass in collisions while compact stars tend to gain it. In the compact models with low or moderate gas accretion, the star settles into a conveyor-belt quasi-equilibrium that processes up to about $10^{5}$.5 solar masses of material in roughly 5 million years. If correct, accreting extremely massive stars could be the polluters behind the abundance anomalies observed in old globular clusters.

What carries the argument

The load-bearing object is an analytical energy-budget criterion for an inspiraling star moving inside the envelope of a target aEMS. The inspiraling star releases orbital energy $E_{\rm rel}^{\rm orb}(r)=E_{\rm ini}^{\rm orb}-E_{\rm orb}(r)$ locally in a spherical shell, and mass is lost when this released energy exceeds the binding energy of the layers above the orbit while the inspiral timescale $\tau_{\rm dr}$ is longer than the local thermal timescale $\tau_{\rm th}$. Two geometric conditions determine where the inspiraling star merges rather than strips material: its virial temperature must remain above the local envelope temperature, and its radius must stay inside its Roche lobe, computed with the Eggleton formula. This criterion turns stellar structure into concrete mass-loss and mass-gain predictions across the target-inspiraling mass plane.

What would settle it

A 3D radiation-hydrodynamical simulation of one inspiraling star entering the envelope of a compact 1000-solar-mass target would settle whether the analytical mass-loss criterion predicts the right direction and amount of mass change; if the simulated star gains mass where the grid predicts loss, or vice versa, the conveyor-belt mass budget fails. A second test is to run a cluster simulation using the paper's grid and check whether the ejected gas mass, up to $10^{4}$.9 solar masses in 5 million years, and its H-burning composition match the observed second-population fraction and abundances.

Watch

Extended reading notes

Core claim

The paper claims that collision-induced mass loss on an accreting extremely massive star is substantial and strongly structure-dependent, and that in a compact aEMS model with low to intermediate gas accretion the star reaches a conveyor-belt state where collision-driven ejection plus winds balances accretion plus mergers. Under the most favorable parameters, the star ejects up to $10^{4}$.9 solar masses in 5 million years, roughly an order of magnitude more than its initial mass, which the authors say is sufficient to address the mass-budget issue for the multiple populations observed in old globular clusters. It also shows that the treatment of super-adiabatic convection in radiation-dominated layers changes the radius and binding energy of these stars enough to flip the sign of the net collision outcome from mass loss to mass gain.

Load-bearing premise

The calculation assumes the target star's pre-computed structure stays fixed while collision energy is dumped into a thin shell and radiated away, even though collisions can arrive faster than the star can re-adjust; if the true dynamical and thermal response differs, the predicted amount and even direction of mass change could flip.

Editorial extensions

If this is right

  • In the extended (MLT) models, a single 30 $M_\odot$ inspiraling star can unbind about 14% of a 1000 $M_\odot$ target, and a 100 $M_\odot$ inspiraling star can remove about 25% of a 1000 $M_\odot$ target; over large parts of the parameter space the target ends up lighter after the collision.
  • In the compact (MLT++ and MLT++L.I.) models, collisions are much less destructive: for targets above about 6000 $M_\odot$ the mass loss cannot exceed roughly 0.5%, and the target almost always gains mass after a merger.
  • In Monte Carlo runs for a compact aEMS with gas accretion rates between $10^{-4}$ and $10^{-2}\,M_\odot\,\mathrm{yr}^{-1}$, the star reaches a quasi-steady conveyor belt at roughly 7,500 to 16,000 $M_\odot$, with total mass ejected up to about $4\times10^4\,M_\odot$ in 5 million years.
  • For the most extended aEMS structure, the star reaches the imposed $2\times10^4\,M_\odot$ upper limit in 10 to 68 thousand years, with mergers rather than gas accretion dominating the mass gain.
  • The paper provides a grid of mass-radius-structure and collision mass-loss and mass-gain predictions that can be inserted directly into hydrodynamical and N-body simulations of dense star clusters.

Reading between the lines

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

  • If the conveyor-belt balance holds, the same mechanism would operate in clusters that are somewhat less dense than the static test case, because the equilibrium mass is set by the ratio of collision rate to the star's ability to radiate injected energy; the ejecta yield would scale accordingly.
  • The paper's grid invites a direct test: run a collisional N-body or hydro cluster simulation with multiple potential targets rather than a single central aEMS, using the paper's mass-loss prescription, and compare the total processed mass and chemical composition of the ejecta with observed first-to-second population ratios and abundance anticorrelations.
  • Because the authors assume circular inspirals and instantaneous spherical spreading of deposited energy, real hyperbolic encounters may deposit energy more inhomogeneously; this could increase per-collision stripping or trigger partial envelope loss, widening the parameter space in which a conveyor belt operates.
  • The strong sensitivity to the treatment of super-adiabatic convection suggests that three-dimensional radiation-hydrodynamic simulations of near-Eddington massive envelopes are the decisive next experiment; they may confirm or rule out the compact structures that produce the conveyor belt.
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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 / 4 minor

Summary. This paper computes MESA models of rapidly accreting extremely massive stars (aEMS) for three treatments of super-adiabatic convection and three metallicities, and uses the resulting mass-radius and binding-energy profiles in an analytical prescription for collision-induced mass loss. A single-collision grid maps mass loss and net mass change for inspiraling masses 0.1-500 M_sun and target masses 140-20000 M_sun. These maps are then inserted into a Monte Carlo simulation of an initially 1000 M_sun aEMS in a static proto-globular cluster, with gas accretion and wind mass loss, to estimate total mass ejected over 5 Myr. The paper concludes that extended (MLT) targets grow by mergers, compact (MLT++) targets mostly gain mass, and intermediate (MLT++L.I.) targets at low/intermediate accretion rates reach a 'conveyor-belt' quasi-equilibrium that may eject up to about 10^4.9 M_sun, which the authors argue is sufficient to address the globular-cluster multiple-population mass-budget problem.

Significance. If the conveyor-belt result held, it would provide a concrete mechanism for a single polluter to process enough mass to explain multiple populations in globular clusters, linking collision dynamics to the mass-budget problem. The paper's strengths are its use of public stellar-evolution code, a broad parameter grid, and open acknowledgment of caveats; the qualitative finding that envelope compactness controls the sign of collision-induced mass change is physically plausible and useful for future N-body and hydro implementations. However, the quantitative yield is not yet robust: the static-structure prescription is applied on timescales shorter than the thermal relaxation time, and the paper's own quoted yields are inconsistent. As a result the mass-budget conclusion should be treated as a testable prediction of an idealized model rather than an established result.

major comments (3)
  1. [§3.1, §4.4, §5] The mass-loss map from Section 3.1, Eqs. (3)-(7), is evaluated on pre-computed accreting model structures and then applied at every Monte Carlo step, but Section 4.4 states that in the relevant cases the time between collisions is shorter than the Kelvin-Helmholtz timescale. Under repeated collisions faster than thermal relaxation, the envelope should be hotter, more extended, and less tightly bound than the static model used to build the grid; both the collision cross-section (Eq. 10) and the mass-loss efficiency are expected to change accordingly. The authors acknowledge this in Section 5, yet the headline 'conveyor-belt' ejected masses are still quoted as the outcome of the static prescription. Because the mass-budget conclusion rests on these numbers, a sensitivity test or a substantial downgrade of the quantitative claim is required.
  2. [Abstract, §4.4, §5] The paper quotes three different values for the same headline result: the abstract says 'processing up to 10^5.5 M_sun of material in ~5 Myrs'; Section 4.4 reports a maximum total mass lost of approximately 4×10^4 M_sun for Ṁacc,gas = 10^-2 M_sun/yr; and Section 5 says 'up to 10^4.9 M_sun were ejected in 5 Myrs'. These numbers differ by factors of 2-8 and mix 'processed', 'mass lost', and 'ejected'. Since the mass-budget argument depends on the ejected mass, the paper should harmonize these numbers, define what is counted, and specify the convection treatment and accretion rate for the quoted maximum.
  3. [§4.1, §4.3] In the Monte Carlo loop, after each collision the target's new radius and internal structure are taken from the mass-radius relation of the preparatory accreting models, but the target has not followed that continuous-accretion sequence: it has lost mass through collisions and then continued accreting. There is no reason that its entropy profile, radius, and binding-energy profile coincide with those of an unperturbed accreting model of the same instantaneous mass. This couples the collision rate (through Eq. 10) and the mass-loss prediction (through Eq. 4) to an additional structural assumption that is not tested in the paper. The authors should either justify this assumption or present a sensitivity calculation with, for example, artificially inflated or deflated envelopes.
minor comments (4)
  1. [§4.2] The quantity l is used in Eq. (9) with the explanation 'inversely proportional to the dispersion of relative velocities' only after the equation; it should be defined before first use.
  2. [§3.2] The paper does not state the mass step used for the target mass grid in Fig. 4, although the results are claimed to be obtained by linear interpolation over the whole domain; this should be specified for reproducibility.
  3. [Fig. 6] In Fig. 6, the vertical axis is labelled only 'Mass of the target' with no units; add (M_sun) to the axis label.
  4. [Appendix A.1] There is a typo: 'combinaisons' should be 'combinations'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the collision mass-loss prescriptions and conveyor-belt totals are forward-model outputs from stated energy-deposition assumptions, not fits or results imported from self-citations.

full rationale

The paper's derivation chain is self-contained. The collision-induced mass-loss map is built by comparing the orbital energy released by an inspiraling star (Eq. 3) with the binding energy of the target envelope (Eq. 4), plus virial-temperature, Roche-lobe, and timescale criteria stated in Section 3.1. These are forward physical assumptions, not parameters fitted to reproduce the final ejected-mass numbers. The Monte Carlo simulation in Section 4.3 applies this grid to a target whose mass is updated by collisions, winds, and accretion; the resulting 'conveyor belt' equilibrium and the quoted 10^4.9 M_sun ejected in 5 Myr are outputs of that stated model, not quantities equivalent by construction to the inputs. The paper does cite the same group's aEMS scenario (Gieles et al. 2018, 2025), and the aEMS formation premise and the 'conveyor belt' nomenclature come from that prior work, but the collision calculations and the mass-budget estimate are new and independent of the success of those citations. The acknowledged limitation that the target structure is not dynamically updated between collisions is a modeling assumption and caveat, not a circular step. No equation or fitted parameter reduces to the paper's conclusions, so the circularity burden is low.

Assumptions & free parameters 5 free parameters · 8 assumptions · 0 invented entities

The paper's predictions rest on a chain of explicitly stated modeling choices: an ad hoc 10x accretion-rate scaling, three bracketing convection treatments, a simplified energy-budget collision criterion, static pre-computed target structures, and a static cluster geometry. These are not measured inputs; they are assumptions that the authors transparently list as caveats. The central "conveyor belt" result follows from the interplay of these choices and is not an independent empirical claim.

free parameters (5)
  • Accretion rate scaling for preparatory aEMS models = 10x CH relation, ~1e-4 to 0.1 M_sun/yr
    The Churchwell-Henning accretion rate is scaled up by a factor of 10 (Section 2.1) to reach 10^3-10^4 M_sun with limited He enrichment; this choice sets the stellar radius and internal structure that drive all collision results.
  • Gas accretion rate during collision phase = 10^-4, 10^-3, 10^-2, 10^-1, 1.0 M_sun/yr
    The Monte Carlo simulations assume constant accretion rates spanning five orders of magnitude (Section 4.1); the conveyor belt appears only for the lower values, so the rate is a controlling input rather than a measured quantity.
  • Super-adiabatic convection treatment = MLT, MLT++, MLT++L.I.
    Three energy-transport choices bracket the uncertainty in radiation-dominated layers (Section 2.2); MLT++ and MLT++L.I. are explicitly described as 'stellar-engineering' modifications, and the paper shows they change radii by factors of several and reverse the sign of collision-induced net mass change.
  • Upper and lower mass limits in Monte Carlo = 2e4 M_sun upper, 150 M_sun lower
    Simulations stop when the target reaches 2e4 M_sun or drops below 150 M_sun (Section 4.3); in the MLT case the upper limit is reached quickly, truncating mass loss, so the limits affect the reported totals.
  • Initial seed mass for aEMS models = 0.7 M_sun
    Preparatory models start from a 0.7 M_sun seed and accrete to the EMS regime; the initial seed mass affects the early thermal structure and thus the exact radius evolution.
assumptions (8)
  • standard math Hydrostatic, spherically symmetric 1D stellar structure equations as implemented in MESA, with standard mixing-length theory.
    Used throughout Section 2 to construct the aEMS models; these are standard approximations but unverified for super-Eddington, radiation-dominated stars near the Eddington limit.
  • ad hoc to paper The inspiraling star is on a circular orbit just below the target's surface from the outset.
    Section 3.1 states this as the initial condition; real cluster encounters are hyperbolic, as acknowledged in Section 4.4, which may underestimate the encounter velocity and change energy deposition.
  • ad hoc to paper Mass loss is triggered when the released orbital energy exceeds the binding energy of the layers above the orbit and the inspiral timescale exceeds the thermal timescale.
    This is the core criterion in Section 3.1 (Eqs. 3-5); it is a simplified energy-budget condition that ignores shock dynamics, mixing, and asymmetric ejecta.
  • ad hoc to paper Energy released by the inspiraling star is instantaneously distributed over a spherical shell at the orbital radius.
    State in Section 3.1 as an implicit 1D assumption; realistic energy deposition is anisotropic and time-dependent.
  • ad hoc to paper The aEMS structure is taken from the pre-computed fast-accreting models and is not dynamically updated for the energy injected by collisions.
    Used in Sections 3 and 4; the paper notes in Sections 4.4 and 5 that the target does not have time to relax between collisions and that hydrodynamical response is not modeled.
  • ad hoc to paper Static, unsegregated proto-cluster with Kroupa IMF and a single aEMS target at the center; no other stars grow or lose mass.
    Section 4.1 states the cluster is static and the aEMS is the only target; the paper acknowledges this is a simplification (Section 5).
  • domain assumption The collision rate follows the Hills & Day (1976) formula with gravitational focusing and a Maxwellian velocity distribution.
    Section 4.2 uses Eqs. (8)-(12); this is a standard treatment for a relaxed cluster but ignores mass segregation and binary interactions.
  • domain assumption The Vink (2018) wind prescription applies to aEMS.
    Section 4.1 uses log Mdot_winds = -9.13 + 2.1 log(M) + 0.74 log(Z/Zsun); this is extrapolated to 10^3-10^4 M_sun, far beyond the calibration range.

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Pith. "Pith review of Collision-induced mass loss and mass gain on an extremely massive star. An analytical approach and a static proto-globular cluster test-case." pith.science (2026). https://pith.science/paper/PLC4EJVZ

@misc{pith2026250612132,
  author       = {Pith},
  title        = {Pith review of: Collision-induced mass loss and mass gain on an extremely massive star. An analytical approach and a static proto-globular cluster test-case},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PLC4EJVZ}},
  note         = {Machine review of arXiv:2506.12132}
}
read the original abstract

The objective of this study is to analytically explore mass loss and gain induced by stellar collisions on a gas-accreting extremely massive star (aEMS, 10^3 <= M/M_sun <= 10^4). We also consider its contribution to the mass budget in the context of forming multiple stellar populations in a typical protoglobular cluster. We used MESA to build a series of aEMS models up to 2e4 M_sun for three [Fe/H] values, covering the metallicity range of Galactic GCs, with different treatments of super-adiabatic convection. We set analytical prescriptions to quantify collision-induced mass loss when a star spirals in and deposits energy into the envelope of the aEMS. We used a Monte Carlo approach to simulate the effects of multiple collisions on an aEMS of initial mass 10^3 M_sun in a static proto-GC, accounting for mass loss and gain from collisions, gas accretion, and stellar winds. We show that assumptions on super-adiabaticity in radiation-dominated layers significantly impact aEMS properties and their collision responses: extended stars tend to lose mass, while compact ones are more likely to gain it. Our MC simulations predict total mass lost and gained, along with timescales and contributions from winds and collisions. The results depend on both the aEMS structure and the gas accretion rate during the collision phase. Under certain conditions, the EMS shows a "conveyor belt" behavior, processing up to 10^5.5 M_sun of material in 5 Myr. This study provides theoretical predictions supporting aEMSs as contributors to the abundance anomalies observed in GCs. It emphasizes the need to include collision dynamics and mass transfer in aEMS formation and evolution models in dense stellar environments. We provide a grid of predictions for stellar M-R-[Fe/H]-structure relations and collision-induced mass loss and gain, suitable for hydro and N-body simulations.

Figures

Figures reproduced from arXiv: 2506.12132 by the authors.

Figure 1
Figure 1. Evolution of the key properties of the accreting models starting from 0.7M⊙ and reaching 2 × 104M⊙ (the circles, squares and triangles indicate the points at which the accreting models reach a mass of 1000M⊙ for reference). The models are computed with the same accretion rate and no mass loss, for the reasons discussed in the text. tostars that are highly inflated and red (see the blue tracks in the Hertzsprung-Russ… view at source ↗
Figure 2
Figure 2. Kippenhahn diagrams in radius and mass coordinates (left and right respectively) showing the evolution of the internal structure of the accreting models with [Fe/H]=-2 dex as in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Comparison between |Ebin| within an aEMS of 1000M⊙ and the orbital energy |E rel orb| of a 30M⊙ inspiraling star (blue full and orange dotted lines respectively), for models computed with MLT and [Fe/H]=-2.00 dex, with the abscissa in mass and radius in the left and right panels, respectively. The red-dotted lines show the coordinates where |E rel orb| is higher than |Ebin|. The green-dotted lines represent the poin… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Color maps of the mass loss (upper row) and net mass change (lower row) due to a collision with inspiraling stars with minsp between 0.1 and 500 M⊙ as a function of the mass of the target stars with MaEMS between 140 and 20.000 M⊙. The three panels in each row correspo…
Figure 5
Figure 5. Figure 5: Top: Respective contributions of gas accretion and collisions to the total mass gain of the 1000M⊙ target for different gas accretion rates in the Monte Carlo simulations (mean values). Bottom: Respective contributions of winds and collision-induced mass loss to the to…
Figure 6
Figure 6. Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.