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The CO-Fuelled Time Machine: Tracing Birth Conditions and Terrestrial Planet Formation Outcomes in HD 163296 through Pebble Drift-induced CO Enhancements

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A single CO snowline measurement retrieves the birth mass of HD 163296's disk.

desk verdict Clever inversion of a CO snowline flux into a disk birth mass, but the quoted precision ignores the factor-of-four systematic in the imported flux. read the letter →

arxiv 2501.05316 v1 pith:AAF2RENZ submitted 2025-01-09 astro-ph.EP

Joe Williams , Sebastiaan Krijt This is my paper · ORCID
classification astro-ph.EP
keywords protoplanetarydiscspebbledriftCOsnowlineHD163296birthgasmassMCMCparameterretrievaldustfragmentationvelocityterrestrialplanetformation
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 claims that the observed gas-phase CO enhancement interior to the 70 au CO snowline of the disk around HD 163296 records the total mass of icy pebbles that drifted inwards over the disk's lifetime, and that a fast pebble drift model inverted by MCMC can turn this single number into a measurement of the disk's birth gas mass and its characteristic radius. The retrieval gives $\log_{10}(M_{\mathrm{disc}}/M_\odot) = -0.64^{+0.19}_{-0.24}$ (about $0.23$ solar masses) and $\log_{10}(r_{\mathrm{c}}/\mathrm{AU}) = 2.30^{+0.45}_{-0.46}$, the mass agreeing within $1\sigma$ with the value that thermochemical modelling of the SED and CO line observations had already inferred. The radius is not tightly constrained by a single snowline measurement, but the mass is robust because the cumulative pebble flux through the CO snowline is dominated by the disc mass. If this works, any disk with a resolved volatile enhancement near a snowline could have its birth conditions measured without relying on uncertain tracer abundances, and the same posteriors predict how much material reached the water snowline where terrestrial planets may be forming. A separate dust-mass comparison argues that the grains are fragile, with a fragmentation velocity near 100 cm/s, because more resilient grains exhaust the dust reservoir too early to match current millimetre-wavelength dust mass estimates.

What carries the argument

The central object is a fast one-dimensional model of dust growth, fragmentation and radial drift in a static gas disk, coupled to a Markov Chain Monte Carlo sampler over the two birth parameters $\log(M_{\mathrm{disc}}/M_\odot)$ and $\log(r_{\mathrm{c}}/\mathrm{AU})$. The model sets the maximum particle size by the turbulent or drift-induced fragmentation barrier or by the drift barrier, and computes the instantaneous pebble flux $\dot{m}_p(r,t)=2\pi r\,v_r(r,t)\,\Sigma_d(r,t)$; the time integral of this flux at the CO snowline is matched to the observed enhancement through a $\chi^2$ likelihood. At late times the integrated flux approaches the analytic limit $M_p(R,\infty)=Z_0\,M_{\mathrm{disc}}\exp[-(R/r_{\mathrm{c}})^{2-\gamma}]$, which is why a single cumulative flux measurement constrains the mass much more strongly than the radius. Because the CO snowline sits in the drift-limited regime, the retrieved mass is independent of the assumed grain fragmentation velocity, while the amount of dust remaining at 5 Myr is not.

What would settle it

Deep, radially resolved CO isotopologue imaging of HD 163296 interior to 70 au would settle the central conversion: if the enhancement is sharply localized near the snowline rather than filling the inner disk, the observed flux is not a clean record of continuous pebble drift, and the derived birth mass would have to be revised upward to compensate for a shorter delivery time.

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Extended reading notes

Core claim

The paper's central claim is that a single measured gas-phase CO enhancement inside the CO snowline functions as a time-integrated record of the pebble flux through that radius, and that inverting that record with a fast dust coagulation-and-drift model recovers the disk's birth gas mass. Applied to HD 163296, the inversion returns $\log_{10}(M_{\mathrm{disc}}/M_\odot) = -0.64^{+0.19}_{-0.24}$; the birth mass is roughly $0.23$ solar masses, higher than the current gas mass because it refers to the start of the class-II phase rather than the observed age near 5 Myr. The characteristic radius is only weakly constrained, with the posterior mostly following the prior except that very compact disks cannot supply the required flux. Extending the posterior to the water snowline, the model predicts cumulative fluxes at 5 Myr that mostly lie in the regime where the published planet-formation simulations produce Mars-like embryos and terrestrial planets, with super-Earths allowed but not favoured. The same simulations, compared with current dust mass observations, imply that dust grains must be fragile, with $v_f \approx 100$ cm s$^{-1}$.

Load-bearing premise

The load-bearing premise is that the observed CO enhancement inside 70 au equals the time-integrated mass of CO ice delivered by drifting pebbles, with the gas disk treated as static so that the fitted mass is interpreted as the birth mass even though viscous evolution, accretion and photoevaporation are not modelled.

Editorial extensions

If this is right

  • HD 163296's disk was born with roughly $0.23$ solar masses of gas, a value about twice the current tracer-based mass because the fit refers to $t=0$ rather than the observed age of roughly 5 Myr.
  • The characteristic radius cannot be pinned down by one snowline measurement; the posterior is close to the prior except for compact disks that cannot supply the required flux, so radius constraints will need flux measurements at several radii.
  • Fragmentation velocities above roughly 500 cm s$^{-1}$ deplete the dust reservoir too quickly and fail to reproduce the observed millimetre-continuum dust mass at 5 Myr, favouring fragile grains.
  • The model predicts a cumulative pebble flux through the water snowline at 5 Myr that mostly falls between about 40 and 200 Earth masses, corresponding in the comparison simulations to Mars-like and terrestrial-planet architectures, with super-Earths not excluded.
  • The retrieved birth mass is insensitive to the grain fragmentation velocity because the CO snowline is in the drift-limited regime, so the mass constraint and the grain-fragility constraint are independent.

Reading between the lines

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

  • If cumulative flux measurements from two or more snowlines were combined, the mass–radius degeneracy should break because each snowline samples a different part of the initial mass profile; this is a direct extension the paper does not carry out.
  • The fragile-grain conclusion predicts maximum grain sizes of order a few centimetres at 30–120 AU; scattering or polarimetric observations that place the grain size well below this would indicate missing physics in the coagulation model.
  • The water-snowline flux distribution is a testable prediction for JWST MIRI spectra of HD 163296: a cold-water reservoir far above or below the predicted range would point to a different drift efficiency or chemical processing timescale.
  • Because the model labels the fitted mass as the birth mass of the class-II phase, applying the same pipeline to younger disks with measured volatile enhancements could map how disk mass evolves from the embedded phase into the planet-forming disk.
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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

4 major / 5 minor

Summary. The paper presents a novel method to infer the birth gas mass and characteristic radius of the protoplanetary disc around HD 163296 by combining the fast pebble-drift model `pebble predictor` with MCMC sampling (`emcee`). The target observable is the time-integrated pebble flux through the CO snowline, which the authors import from Zhang et al. (2020), who estimated 150–600 M⊕ of CO ice must have drifted inward to explain the observed CO enhancement. The authors fit two parameters (log10(M_disc/M_sun) and log10(r_c/AU)) to this single flux value, obtaining log10(M_disc/M_sun) = -0.64(+0.19,-0.24) and log10(r_c/AU) = 2.30(+0.45,-0.46). They additionally use the current dust mass to argue for fragile grains (v_f = 100 cm/s) and forward-predict the cumulative pebble flux at the water snowline, comparing against the planet-formation simulations of Lambrechts et al. (2019) to speculate on terrestrial-planet architectures. A synthetic-disc test shows that the MCMC recovers known input parameters when the target flux is generated by the same model.

Significance. The idea of using a single, chemically motivated pebble-flux constraint to infer the initial gas mass of a protoplanetary disc is attractive and, if validated, would open a new observational window on disc birth conditions. The paper is commendable for using a fast, publicly available model (pebble predictor) in an MCMC framework, for performing a synthetic retrieval test, and for making explicit forward predictions (water-snowline flux, dust-mass evolution) that are falsifiable with future observations. The retrieved disc mass is consistent to within 1σ with the gas mass used by Zhang et al. (2019) to model the same system, which lends some credence to the method. However, the analysis has a load-bearing systematic: the imported flux range from Zhang et al. (2020) is itself model-dependent, and the Gaussian likelihood adopted in Eq. (12) does not propagate the full factor-of-four systematic uncertainty. Furthermore, the characteristic radius is explicitly shown in the paper to be unconstrained, yet it is presented as a headline result. These issues do not invalidate the method but require re-analysis and reframing before publication.

major comments (4)
  1. [§3.1, Eq. (12)] The likelihood in Eq. (12) treats the imported cumulative flux range of 150–600 M⊕ as a symmetric Gaussian 2σ interval with mean 375 M⊕ and σ=112.5 M⊕. Since the cumulative pebble flux is approximately proportional to the disc mass (Eq. 14), any systematic bias in the imported flux maps directly onto the retrieved mass: a factor-of-2 error in the flux changes log10(M_disc/M_sun) by about 0.3 dex, which is larger than the quoted 1σ uncertainty of +0.19/−0.24 dex. The authors acknowledge in §3.1 and §4.1.2 that the flux may be a lower limit, but the Gaussian likelihood does not propagate this systematic; the reported uncertainty on the disc mass is therefore understated. I recommend re-running the retrieval with the full factor-of-four range treated as a systematic (e.g., a wider or log-normal likelihood) or reporting the mass as a function of the assumed flux, so that the reader can see the dominant uncertainty.
  2. [§3.2.1 and Fig. 4] The paper explicitly states in §3.2.1 that “our results for the characteristic radius are not constrained,” and the synthetic test in §2.4.2 shows that the radius posterior is essentially identical to the uniform prior. Yet the abstract and Section 5 present log10(r_c/AU)=2.30(+0.45,-0.46) as a retrieved quantity. This is misleading: the result is an unconstrained parameter with a posterior inherited from the prior (with some filtering of gravitationally unstable solutions). The agreement with the Zhang+19 radius (red dashed lines in Fig. 4) is therefore a consistency check, not a validation of the retrieval. The abstract and conclusions should be reworded to state that the radius is not constrained by the current data, and the radius posterior should be shown with the prior bounds overplotted (as in Fig. 3) to make this clear.
  3. [§4.1 and interpretation of ‘birth mass’] The model assumes a static gas disc (Section 2.2): the gas surface density is fixed at the initial self-similar profile, and there is no viscous evolution, accretion, or photoevaporation. The parameter M_disc is therefore the mass of a non-evolving gas disc that, combined with the pebble model, reproduces the cumulative flux at 5 Myr. Labeling this the ‘birth’ mass is a strong interpretation that requires justification. A viscously evolving disc would have a different surface-density profile and a different pebble-drift history, so the fitted static-disc mass need not equal the initial mass of the real system. The paper acknowledges this limitation in §4.1.2, but the abstract and conclusions do not carry the caveat. I recommend either (a) performing a simple test with an evolving gas disc (e.g., a viscous evolution approximation) to quantify the bias, or (b) explicitly stating throughout that the result is a ‘static-disc equivalent mass’ rather than a true birth mass.
  4. [§2.4 and §3.1] The synthetic test in §2.4 validates only the internal consistency of the method: the target flux is produced by the same pebble predictor model that is used to fit it. The test does not validate the astrophysical mapping from the observed CO enhancement to a cumulative pebble flux, which is the most fragile premise of the analysis (as the reader’s report also notes). Contributions from chemical reprocessing, initial CO abundance gradients, gas-phase radial transport, or a different disc age could change the target flux by factors of a few. I suggest adding a simple sensitivity test that repeats the fit with the target flux shifted to 150, 375, and 600 M⊕ (or 1/2 and 2× the fiducial value) and reports the resulting shift in the retrieved mass. This would directly demonstrate the robustness (or lack thereof) of the headline mass to the dominant systematic.
minor comments (5)
  1. [§4.1.2] The text says “we assumed a cumulative flux value of 325 M⊕ based on the work of Zhang et al. (2020),” but Section 3.1 and the rest of the paper use 375 M⊕. Please correct this typo; if 325 M⊕ was actually used, the abstract and results must be updated.
  2. [Fig. 5 caption] The caption shows the target value as “375 ± 100 M⊕,” while the text (Section 3.1) defines it as 375 ± 112.5 M⊕. Please make the values consistent.
  3. [Abstract vs. Section 5] The abstract reports log10(M_disc/M_sun) = -0.64(+0.19,-0.24), while Section 5 reports -0.63(+0.19,-0.24). Please standardize the rounding.
  4. [§2.4.2] The sentence “The masses reported in Table 2 are independent of v_f as the dust dynamics are drift-dominated outside the CO snowline” appears in the synthetic-disc section, but Table 2 lists only one synthetic case. This statement is later verified for HD 163296 in §3.2.4, but it may confuse the reader on first reading. Consider moving or clarifying.
  5. [Fig. 3 and Fig. 4] The corner plots do not show the prior bounds (which are −3 < log(M/M⊙) < −0.3 and 1 < log(r_c/AU) < 3). Overlaying the prior range would make the unconstrained nature of the radius more immediately apparent.

Circularity Check

2 steps flagged · score 6.0 of 10

Birth mass retrieval is a rescaling of a model-dependent input flux; the Zhang+19 'agreement' is a closed loop.

  1. self definitional [Section 3.1 likelihood (Eq. 12); Eq. (14)-(15); Table 2]
    "Zhang et al. (2020) ... matched the observed line spectra with thermochemical models using models from Zhang et al. (2019) ... When fitting the cumulative pebble flux constraint, we decided to treat the estimated cumulative flux range as a data point with an associated Gaussian error 375±112.5 M⊕ at a measurement time of 5 Myr ... Since the cumulative pebble flux is directly proportional to the disc mass, ..."

    The 150-600 M⊕ target flux is not an independent observable: it was derived by Zhang+20 using the Zhang+19 thermochemical model whose log(M_disc/M_sun)=-0.82 and log(r_c/AU)=2.22 are exactly the reference values Table 2 assigns to HD 163296 and that the MCMC is designed to retrieve. In this paper's own model, Eq. (14) gives M_p = Z0 M_disc exp(-R/r_c), so the likelihood (Eq. 12) is effectively solved by M_disc = M_p,sample/[Z0 exp(-70/r_c)]. Because M_p,sample itself scales with the same Zhang+19 disc mass, the fitted M_disc is the input model mass rescaled by enhancement/Z0-type factors rather than an independently measured birth mass.

  2. self citation load bearing [Section 3.2.1 agreement discussion; Table 2 caption]
    "The agreement between the median solutions and the values of Zhang et al. (2019) is remarkable, considering the only constraints that we provided to emcee was a single measurement of the cumulative pebble flux at one location (70 AU) and one time (5 Myr), alongside fixing other parameters."

    This agreement is used as validation, but the 'single measurement' was produced with the Zhang+19 model whose gas mass and radius are the very values being compared, and Table 2 states that 'the reference values formed the basis for the initial MCMC guesses used during the burn-in phase.' Model choices such as gamma=0.8, M_star, and T0 are also imported from Zhang+19/20, and one present author is a co-author of Zhang+19. The agreement is therefore a closed loop through self-cited prior work rather than an independent external confirmation of the retrieval.

full rationale

The central mass retrieval for HD 163296 is not independent: the 150-600 M_Earth target flux was derived by Zhang+20 using thermochemical models based on Zhang+19, whose gas mass and characteristic radius are exactly the reference values this paper lists and against which the MCMC posterior is compared. Within the paper's own model, the cumulative flux is M_p = Z0 M_disc exp(-R/r_c), so fitting to a flux that itself scales linearly with the Zhang+19 M_disc makes the posterior mass a rescaled version of the input rather than a new measurement. The 'remarkable agreement' with Zhang+19 is thus partly a closed loop, reinforced by using those reference values as initial MCMC guesses. The synthetic-disc test is only a self-consistency check of pebble predictor. On the other hand, the water-snowline cumulative-flux distributions and the dust-mass/fragmentation-velocity comparison are forward predictions that go beyond the fitted input and are evaluated against external data (Lambrechts+19, dust mass observations), so the paper is not wholly circular. Score 6 reflects that the headline birth-mass claim reduces to a model-dependent input flux, while genuine independent content remains in the forward predictions.

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

This ledger itemizes what the paper assumes beyond the data. The dominant entries are the static gas disc (so 'birth mass' is really the static profile mass), the canonical Z0=0.01, and the Zhang et al. (2020) flux interpretation. The two fitted parameters are the birth mass and radius; the radius is unconstrained, and the fragmentation velocity is constrained qualitatively.

free parameters (5)
  • log10(M_disc/M_sun), HD 163296 birth gas mass = -0.64 +0.19 / -0.24
    Fitted by MCMC to a single cumulative CO snowline flux datum of 375 +/- 112.5 M_Earth at 5 Myr.
  • log10(r_c/AU), characteristic radius = 2.30 +0.45 / -0.46
    Fitted jointly with mass, but the posterior is essentially the uniform prior after excluding gravitationally unstable compact discs; the paper states the radius is not constrained.
  • Fragmentation velocity v_f = 100 cm/s fiducial; 250, 500, 1000 cm/s tested
    Not fitted formally; constrained qualitatively by comparing predicted current dust mass to literature values, giving v_f < 500 cm/s.
  • Turbulence parameter alpha = 1e-4 (fixed)
    Taken from Powell et al. (2022) based on vertical mixing and CO sequestration arguments; affects pebble growth and drift but is not sampled.
  • Initial dust-to-gas ratio Z0 = 0.01 (fixed)
    Canonical value assumed everywhere at t=0; the retrieved disc mass scales roughly as 1/Z0, so this choice directly sets the mass scale.
assumptions (8)
  • domain assumption The gas surface density is a static self-similar profile (Eq. 3) with gamma=0.8 for HD 163296.
    Adopted from Zhang et al. (2019); because the gas disc does not evolve, the fit constrains a static disc mass rather than a physically evolving birth mass.
  • domain assumption The midplane temperature is a fixed power law (Eq. 4) with T0=167.3 K chosen so the CO snowline is at 70 AU.
    Anchors the sublimation front without self-consistent thermal chemistry; the flux measurement is tied to this snowline location.
  • domain assumption The initial dust-to-gas ratio is Z0=0.01 everywhere at t=0.
    Canonical value; the inferred disc mass is inversely proportional to Z0, so a different Z0 changes the central claim linearly.
  • domain assumption Dust is a mono-disperse population of compact, silicate grains with material density 1.25 g/cm3 and growth limited by fragmentation or radial drift (Eqs. 5, 6, 8).
    Core simplification of the pebble predictor code (Drazkowska et al. 2021); excludes bouncing, porosity, vapour diffusion, and full size distributions.
  • domain assumption The Zhang et al. (2020) CO enhancement interior to 70 AU is caused by sublimation of CO ice on drifting pebbles, so the cumulative solid flux through the CO snowline is 150-600 M_Earth.
    This is the fundamental observable input; if the enhancement has chemical or non-pebble origins, the retrieved mass is not a solid flux.
  • domain assumption The gas disc does not lose or accrete mass over 5 Myr, so the model gas mass is the birth mass.
    No viscous evolution, photoevaporation, or accretion is modelled; the paper acknowledges that a more involved model may change the discrepancy with current-disc mass estimates.
  • domain assumption The gravitational instability limit, Eq. 16, filters out parameter solutions that would be unstable.
    Used to exclude massive compact discs; the prefactor f=1 and the temperature/radius choices affect which solutions are removed.
  • domain assumption The Lambrechts et al. (2019) thresholds of 38, 114, and >=190 M_Earth cumulative water-snowline flux map to final planetary architectures for HD 163296.
    The paper notes these simulations assume a Sun-like star and a fixed Stokes number, so the mapping is speculative.

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Cite this review

Pith. "Pith review of The CO-Fuelled Time Machine: Tracing Birth Conditions and Terrestrial Planet Formation Outcomes in HD 163296 through Pebble Drift-induced CO Enhancements." pith.science (2026). https://pith.science/paper/AAF2RENZ

@misc{pith2026250105316,
  author       = {Pith},
  title        = {Pith review of: The CO-Fuelled Time Machine: Tracing Birth Conditions and Terrestrial Planet Formation Outcomes in HD 163296 through Pebble Drift-induced CO Enhancements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AAF2RENZ}},
  note         = {Machine review of arXiv:2501.05316}
}
abstract

The architecture and composition of planetary systems are thought to be strongly influenced by the transport and delivery of dust and volatiles via ices on pebbles during the planet formation phase in protoplanetary discs. Understanding these transport mechanisms is crucial in building a comprehensive picture of planet formation, including material and chemical budget; constraining the birth properties of these discs is a key step in this process. We present a novel method of retrieving such properties by studying the transport of icy pebbles in the context of an observed gas-phase CO enhancement within the CO snowline in the protoplanetary disc around HD 163296. We combine Markov Chain Monte Carlo (MCMC) sampling with a fast model of radial drift to determine the birth gas mass and characteristic radius of the disc, and compare our results against observations and models in the literature; we find the birth-condition disc gas mass to be $\log_{10}(M_{\rm{disc}}/M_{\odot})=-0.64^{+0.19}_{-0.24}$ and the characteristic radius to be $\log_{10}(r_{\rm{c}}/\rm{AU})=2.30^{+0.45}_{-0.46}$. We additionally determine that dust grains must be `fragile' ($v_{f}=100~\mathrm{cms}^{-1}$) to retain enough dust to match current dust mass observations, with our lowest fragmentation velocity model providing a current-age dust mass of $\rm{M_{dust}}=662^{+518}_{-278} \rm{M_{\oplus}}$ based on the retrieved birth conditions. Using our retrieved birth conditions, we extend our simulations to mass of material reaching the water snowline in the inner disc, where terrestrial and super-Earth planets may be forming, and speculate on the nature of these exoplanets.

Figures

Figures reproduced from arXiv: 2501.05316 by the authors.

Figure 1
Figure 1. Schematic illustrating transport mechanisms of volatiles that produce the C/H enhancement seen within the CO snowline in HD 163296 as observed by Zhang et al. (2020). The process begins in the outer disc with dust growing to pebbles as the CO and water vapour freeze out onto the pebbles. As the grains grow, they decouple from the gas and drift inwards towards the CO snowline; within the snowline, the CO sublimates a… view at source ↗
Figure 2
Figure 2. The instantaneous pebble flux at 10 AU (equation 2) and cumulative pebble flux (equation 1) as functions of time for a disc of arbitrary properties, assuming 𝛼 = 1 × 10−3 and 𝑣𝑓 = 100cms−1 as calculated by pebble predictor. The colour of the curves correspond to discs with different masses (red for log(𝑀disc/𝑀⊙)= −3; yellow for log(𝑀disc/𝑀⊙)= −2; and blue for log(𝑀disc/𝑀⊙)= −1) and the line style corresponds to diff… view at source ↗
Figure 3
Figure 3. Corner plot of sample histograms for the synthetic disc of log(𝑀disc/𝑀⊙)= −1.8 and log(𝑟𝑐/AU) = 2.2. These ‘true’ values are shown as the red dotted lines. The median parameter from emcee’s sample is shown as the solid blue line, with one standard deviation shown as the blue shaded area. 3 HD 163296 3.1 Set-Up We now turn our attention to HD 163296. As in Sect. 2.4.1, we focus on the disc gas mass and characteristic… view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: Cumulative flux at the CO snowline (70 AU, top) and water snowline (1.3 AU, bottom) as a function of time for 50 randomly selected log(𝑀disc/𝑀⊙)and log(𝑟𝑐/AU) solutions from the posterior distribution. The target value derived from Zhang et al. (2020) provided to emcee…
Figure 6
Figure 6. Figure 6: Histogram of the cumulative pebble flux through the CO (blue) and water (red) snowlines at 5 Myr, using all of the solutions from the posterior distribution (solid) and excluding gravitationally unstable discs (dashed). The target value derived from Zhang et al. (2020)…
Figure 7
Figure 7. Figure 7: Dust and gas mass histories for 500 randomly selected values of log(𝑀disc/𝑀⊙)and log(𝑟𝑐/AU) from four different emcee runs, each with different fragmentation velocities (A: 100 cms−1 , B: 250 cms−1 , C: 500 cms−1 , D: 1000 cms−1 ). Each of the selected solutions were g…
Figure 9
Figure 9. Figure 9: Grain sizes as a function of radius for 500 randomly selected solutions at 5 Myr for fragmentation velocities of 100 cms−1 (red) and 1000 cms−1 (blue). The maximum grain sizes of an example scattering model from Guidi et al. (2022, [PITH_FULL_IMAGE:figures/full_fig_p0…
Figure 10
Figure 10. Figure 10: Prediction for the cumulative pebble flux through the water snow￾line by 0.5 Myr (purple dashed) and 5 Myr (red). The purple, dashed distribu￾tion represents a theoretically perfect pebble trap outside the water snowline and the red a smooth disc. Cumulative fluxes fr…

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Pith tools

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