From Streaming Instability to the Onset of Pebble Accretion I. Investigating the Growth Modes in Planetesimal Rings

Irina L. San Sebasti\'an; Nicolas Kaufmann; Octavio M. Guilera; Yann Alibert

REVIEW 2 major objections 6 minor 2 cited by

From Streaming Instability to the Onset of Pebble Accretion I. Investigating the Growth Modes in Planetesimal Rings

T0 review · 2 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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

Pith's one-line read Planet seeds from streaming instability grow only inside about 10 AU

desk verdict Good, additive post-SI growth paper, but the §2.6 IMF normalization is not mass-conserving — the initial embryo is probably over-massive by ~2.5×, which shifts the headline timing claims without killing them. read the letter →

arxiv 2502.02124 v1 pith:CK7NXSNS submitted 2025-02-04 astro-ph.EP

Nicolas Kaufmann , Octavio M. Guilera , Yann Alibert , Irina L. San Sebastián This is my paper · ORCID

classification astro-ph.EP

keywords planetformationstreaminginstabilityplanetesimalringspebbleaccretionprotoplanetarydisksinitialmassfunctionlow-massstarsembryogrowth

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 whether planetesimal rings created by the streaming instability can build the seed bodies that later accrete pebbles fast enough to make planets before the protoplanetary gas disk disappears. The answer is a strong location bias: for a solar-mass star, the largest body in a ring reaches the pebble-accretion transition mass within the disk lifetime out to roughly 10 AU, while near 50 AU it barely grows. Around lower-mass stars the successful zone shrinks to about 3 AU for a 0.3-solar-mass star and about 1 AU for a 0.1-solar-mass star. The study matters because many planet formation models insert pre-assembled cores as initial conditions; this work maps where and when those seeds can actually arise. It also finds that once the embryo crosses the transition mass, pebble accretion quickly overtakes planetesimal collisions as the dominant growth mode.

What carries the argument

The load-bearing object is the mass threshold $M_{\rm tr}=\eta^3 M_\star/\sqrt{3}$, where $\eta$ is the dimensionless gas-pressure gradient; it marks the switch from slow Bondi-regime pebble accretion to fast Hill-regime accretion. The paper also uses the lower onset mass $M_{\rm on}$ below which pebble accretion is purely ballistic. Around these thresholds, the model follows one discrete embryo plus a fluid grid of planetesimal sizes, solving a continuity equation for the surface density with viscous diffusion, mutual collisions and fragmentation, and pebble accretion from a radially constant or time-dependent flux. The initial largest body is set by the streaming-instability initial mass function of Schäfer et al. (2017), which places it within a factor of about 1.5 of $M_{\rm tr}$ in the inner disk.

What would settle it

A direct test would be a streaming-instability simulation that resolves the high-mass tail of the planetesimal mass function for a filament with metallicity $Z=0.01$ to $0.1$: if the largest body at 1 to 10 AU is systematically more than a factor of about 2 below the mass given by Eq. (23), then the predicted transition times inside 10 AU would exceed the disk lifetime and the paper's central timing claim would fail. Observationally, high-resolution millimeter observations of rings at 30 to 50 AU around M dwarfs should show no signs of embedded pebble-accreting embryos if the prediction holds.

Watch

Extended reading notes

Core claim

The paper's central claim is that a ring of planetesimals produced by the streaming instability can build its largest body up to the pebble-accretion transition mass $M_{\rm tr}=\eta^3 M_\star/\sqrt{3}$ within the gas disk lifetime only in the inner disk: out to roughly 10 AU around a solar-mass star, to only a few AU around a 0.3-solar-mass star, and to about 1 AU around a 0.1-solar-mass star. At 50 AU, and generally around low-mass stars, the largest body stalls below the transition mass, so the seed for efficient pebble accretion does not form in time. Once the embryo does cross $M_{\rm tr}$, pebble accretion rapidly overtakes planetesimal collisions as the dominant growth mode. The paper reaches this conclusion with a semi-analytic model that evolves the full planetesimal size distribution on a radial grid together with the embryo, including viscous spreading, collisional fragmentation, and pebble accretion.

Load-bearing premise

The timing result rests on the assumed planetesimal initial mass function produced by the streaming instability: the largest body in a ring is taken to start within a factor of about 1.5 of the pebble-accretion transition mass in the inner disk, with a filament metallicity of $Z=0.1$ and a formation efficiency of $p_{\rm eff}=1$. If real filaments make smaller largest bodies or less total mass, the inner-disk success window shrinks or disappears, as the paper's own reduced-metallicity and reduced-embryo test cases show.

Editorial extensions

If this is right

For a solar-mass star, rings interior to about 10 AU can deliver a seed at the Bondi-to-Hill transition mass before the gas disk fades; interior to about 2 AU the embryo can consume the entire ring mass.
Diffusive spreading of the ring is a major brake on growth: if diffusion is switched off, the embryo reaches the transition mass out to about 25 AU instead of about 10 AU.
Pebble accretion contributes substantially even before the transition and accelerates growth at all separations, yet beyond about 25 AU the embryo never reaches the isolation mass within the disk lifetime.
Around a 0.3-solar-mass star only rings up to about 3 AU reach the transition mass, and around a 0.1-solar-mass star only up to about 1 AU, so low-mass stars have a much smaller window for forming pebble-accreting cores.
The timing of core formation is set mainly by semi-major axis and stellar mass, with initial embryo mass more influential than pebble flux; population models that insert pre-assembled embryos should adopt later insertion times in the outer disk and around low-mass stars.

Reading between the lines

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

If the true streaming-instability initial mass function is less top-heavy than the form used here, the inner-disk success window would narrow or vanish; the paper's reduced-embryo test suggests that forming giant-planet cores would then require earlier or more massive rings, or an additional growth channel.
The strong stellar-mass dependence offers a natural explanation for the scarcity of giant planets around M dwarfs: the same disk physics that delays pebble-accretion onset also shrinks the region where seeds can form.
Because the model assumes single-size pebbles with $\tau_s=0.1$, Bondi-regime accretion rates are likely underestimated; accounting for a distribution of pebble sizes would lower the effective onset mass and could partially rescue outer-disk and low-mass-star growth.
In a global disk with several rings, upstream rings would consume the pebble flux before it reaches outer rings, so the radial bias found here would be amplified rather than diluted.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things to know. First, this is a careful and genuinely additive paper: it models post-SI planetesimal-ring growth with an Eulerian continuity treatment, a full collision/fragmentation size distribution, and pebble accretion on top — a combination that Liu+19, Jang+22, and Lorek+22 do not have — and it ships a timing grid for when seeds of pebble accretion appear, plus stellar-mass scaling relations. The fragmentation sub-model is validated against Guilera+14 and matches well (Appendix A); the parameter table is honest; the output timings are on GitHub. Credit where due.

Second, there is a real normalization bug in §2.6, though the stress-test note overstates its size. The IMF is normalized with Ntot = M_fil/mmin and mmin = 10^-3 mp. That distribution is not mass-conserving: I integrated it and it carries roughly 40 times the filament mass. A mass-conserving normalization lowers the derived largest body from about 330 mp to about 130 mp — a factor of roughly 2.5, not orders of magnitude and not 'a few mp'. So the specific claim that the initial embryo sits within a factor 1.5 of Mtr out to 10 AU is wrong as stated; the transition times in Figs. 13–16 shift later; and the success boundary probably moves in from ~10 AU to a few AU. The qualitative picture — inner disk can make seeds within the disk lifetime, outer disk (about 50 AU) and low-mass stars cannot — survives. The paper's own 0.1×Mem test (Fig. 14) shows the result is fragile to exactly this input; that test is four times more extreme than the corrected mass, so it brackets but does not quantify the effect. The authors should fix the normalization before others use the timing grid.

The reader's other reservations are fair but minor in comparison: Z = 0.1 and p_eff = 1 are optimistic hand-chosen filament parameters and the abstract omits that caveat; the transition times carry no uncertainties; and only output data are released, not the full code. None of these is disqualifying. The derived masses come from published IMF and disk theory, not from fitting to the target result, so the circularity burden is low. The limitations section is honest about what is neglected (migration, fragment drift, poly-disperse pebbles).

This is for modelers who insert pre-assembled cores into global planet formation simulations, and for anyone comparing SI formation to pebble-accretion timelines. It deserves a serious referee. Send it out, and ask one referee to recompute the §2.6 quantile with a mass-conserving IMF and rerun the timing grid. That is a bounded, checkable fix; the rest of the machinery looks solid.

Referee Report

2 major / 6 minor

Summary. The paper presents a semi-analytic model for the early growth of the largest planetesimal in a narrow ring produced by the streaming instability. The model evolves a discrete embryo together with a size- and radially-resolved planetesimal population, including mutual collisions, fragmentation, viscous diffusion, and pebble accretion onto the embryo. It is applied to rings at 0.5--50 AU around 1, 0.3, and 0.1 solar-mass stars, with a nominal filament metallicity Z=0.1, formation efficiency p_eff=1, pebble Stokes number tau_s=0.1, and disk turbulence alpha=10^-2. The main finding is that the largest body can reach the pebble-accretion transition mass Mtr within the gas disk lifetime only in the inner disk (roughly up to 10 AU for a solar-mass star, and closer in for lower-mass stars), and that once pebble accretion turns on it quickly dominates over planetesimal collisions. The paper also provides scaling relations with stellar mass and a grid of transition times for use as initial conditions in global formation models.

Significance. If the quantitative results survive a corrected initial-condition treatment, the paper would be a useful constraint on when and where planet formation models may insert already-formed embryos, and it makes a falsifiable prediction about the radial and stellar-mass dependence of early core formation. The implementation is unusually transparent: the model equations are given in detail, the fragmentation treatment is validated against an independent model (Appendix A), the parameter choices are collected in Table B.1, and the simulation data are made available through a public GitHub package. The characteristic masses Mon and Mtr are taken from published theory rather than fitted to the target result, and the scaling relations in Section 3.3 are explicitly derived or labeled as fits to the model's internal outputs; I therefore see no circularity in the main argument. However, the headline quantitative result is controlled by an initial-mass normalization that is not mass-conserving, and the abstract's phrasing is broader than the model's own sensitivity study supports. For these reasons the result is currently conditional.

major comments (2)

[§2.6] The IMF normalization is not mass-conserving. With the adopted p=0.6, q=0.4 and m_min=10^-3 m_p, the cumulative distribution in Eq. (22) can be written G(z)=z^{-p} exp[δ(1-z^q)] with z=m/m_min and δ=(m_min/m_p)^q≈0.063. The mass-weighted mean is ⟨m⟩=m_min[1+∫_1^∞ G(z)dz]; substituting u=δ z^q gives ∫_1^∞ G(z)dz=(1/q)δ^{-1}=39.6, so ⟨m⟩≈40.6 m_min=0.0406 m_p. Setting N_tot=M_fil/m_min therefore overproduces the total planetesimal mass by a factor of about 40, and the accompanying statement that the mass budget is dominated by bodies of mass ~m_p is inconsistent with these exponents. Because the initial embryo is defined by N_≥(M_em)=1, the correct normalization changes the quantile: at the nominal ratio M_em/m_p≈330 quoted in Section 3, a mass-conserving normalization lowers M_em by roughly a factor of 2.6 (to about 125 m_p), and for smaller nominal ratios the reduction is larger. The initial embryo mass is exactly the quantity that controls the time to reach Mtr, as the authors' own sensitivity runs in Fig. 14 (Z=0.01 and 0.1 M_em) demonstrate. The authors should renormalize the IMF, recompute M_em and N_tot, and rerun the nominal runs and the grids of Figs. 13–16 before the radial and stellar-mass boundaries stated in the abstract can be supported.
[Abstract and §4.2] The abstract states that rings in the inner disk are able to produce protoplanetary embryos, without the qualification that this holds for the nominal filament metallicity Z=0.1 and p_eff=1. The model's own Fig. 14 shows that for Z=0.01 or for an initial embryo mass reduced by a factor of ten, the largest body fails to reach Mtr outside a few AU. Since Z=0.1 is ten times the adopted disk metallicity Z_0=0.01 and represents a strongly enhanced filament, the headline result should be stated as conditional on a high local enrichment. The body of the paper is careful about this, but the abstract and the first bullet of Section 4.2 are not; they should be reworded to reflect the parameter dependence that the paper itself demonstrates.

minor comments (6)

[§3.3, Fig. 9 caption, Fig. 1 caption] The text and captions refer to '0.3M⊕' stars in several places; the unit should be M⊙. For example, Section 3.3 says '0.3M⊕ (top)' and Fig. 1 labels a '0.3M⊕ star'.
[Table 1 caption] The caption reads 'Parameter gird'; this should be 'Parameter grid'.
[§3.5] The phrase 'transit timings' is used for the time to reach the transition mass; 'transition timings' would be clearer and is consistent with the surrounding text.
[Eq. (3)] In the typeset equation the left-hand side appears to be missing the '=' sign before the drift and diffusion terms; please check the formatting.
[§2.3] The pebble Stokes number is denoted τ_s in the text but τ_peb in places (e.g., in the discussion after Eq. (16) and in Fig. 2); the notation should be unified.
[§2.4] The sentence 'we do without the inclusion of pebble accretion and fragmentation' is awkward; consider 'we omit pebble accretion and fragmentation'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: initial embryo masses come from an external SI IMF, transition masses from pebble-accretion theory, and the growth model is validated independently.

full rationale

The derivation chain is self-contained: the initial embryo mass Mem is set by inverting the Schäfer et al. (2017) streaming-instability IMF, N≥(Mem)=1 with Ntot=M_fil/mmin (Eqs. 22–24), using externally published IMF parameters and stated filament assumptions, not by fitting to the target result. The transition and onset masses Mon and Mtr are computed from pebble-accretion theory (Ormel and Liu; Eqs. 17–18) with no free parameter tuned to the model's growth outputs. The growth model integrates collision, fragmentation, diffusion, and pebble-accretion rates, and the fragmentation implementation is checked against the independent Guilera et al. (2014) code in Appendix A. Self-citations (Kaufmann & Alibert 2023) supply standard collision and dynamical coefficients that are validated or replaceable and do not encode the conclusion that inner-disk rings reach Mtr. The paper's sensitivity runs (Fig. 14) show that inner-disk success depends on the assumed IMF normalization and filament metallicity, and the text explicitly flags that the choice of the initial mass function significantly shapes subsequent growth; transparent parameter dependence is not circularity. The strongest concern, that the Ntot=M_fil/mmin normalization may not conserve mass and could overestimate Mem, is a modeling-accuracy issue rather than a circular reduction, because Mem is not defined in terms of Mtr nor fitted to the headline transition-time result.

Assumptions & free parameters 11 free parameters · 6 assumptions · 0 invented entities

The central claim depends on a set of hand-chosen model parameters, most importantly the high filament metallicity Z=0.1 and p_eff=1, and on the prior streaming-instability IMF that sets the initial embryo mass near the transition mass. The paper tests the sensitivity of some of these (Z=0.01, reduced embryo mass, tau_s=0.03, diffusion off) but does not place error bars on the headline transition times. No new physical entities are introduced.

free parameters (11)

Filament metallicity Z = 0.1 (nominal), 0.01 (low case)
Directly sets the planetesimal ring mass (Eq. 24) and the initial embryo mass via the IMF; chosen by hand, not constrained by data.
Planetesimal formation efficiency p_eff = 1
Multiplies the ring mass; assumed to be 100% efficient.
Disk metallicity Z0 = 0.01
Sets the pebble flux normalization and dust growth timescale.
Gas turbulence alpha = 10^-2
Governs viscous disk evolution and the disk surface density profile.
Midplane turbulence alpha_z = 10^-4
Sets the pebble aspect ratio in the 3D pebble accretion efficiency.
Pebble Stokes number tau_s = 0.1 nominal, 0.03 variant
Fixes pebble aerodynamic size; motivated by drift-limited growth but not evolved self-consistently.
Dust growth efficiency epsilon_d = 0.5
Used in the pebble growth timescale and drift-limited Stokes number.
Fragmentation velocity v_frag = 1 m/s
Sets the fragmentation barrier for pebbles and thus the pebble size.
Bulk density rho_s = 2 g/cm^3
Converts masses to radii for planetesimals and pebbles.
Disk-to-star mass ratio M_gas/M_star = 0.1
Sets the gas disk mass and the characteristic radius r1.
Streaming instability collapse time t_SI = 500 orbital periods
Added to t0 to account for the collapse of pebbles into planetesimals; chosen from SI simulation literature.

assumptions (6)

domain assumption Streaming instability produces a planetesimal ring with the Schaefer et al. (2017) IMF and width Delta_w = eta * r0.
Section 2.6 assumes the IMF shape and normalization from prior collapse simulations; the paper does not derive them.
domain assumption The gas disk follows a viscously evolving alpha-disk with the Ida et al. (2016) temperature profile and a self-similar solution (Eqs. 20-21).
Standard disk model used in Section 2.5.
domain assumption The pebble flux is radially constant inside the growth radius and follows the Lambrechts & Johansen (2014) prescription (Eqs. 14-16).
Used for the time-dependent pebble flux in Section 2.3.
domain assumption Embryo migration and gas accretion are neglected; the embryo stays on a circular orbit.
Section 2.1 and Section 4.1; the authors note migration matters near isolation mass.
domain assumption Planetesimal radial drift is negligible; fragments smaller than 1 km would drift, so fragmentation runs are upper limits.
Section 2.1 and Section 4.1; the authors state this limitation explicitly.
standard math Collision outcomes follow the Benz & Asphaug (1999) / Morbidelli et al. (2009) fragmentation prescription with a power-law fragment size distribution.
Section 2.2; a standard parameterization of impact outcomes used in many planet formation codes.

how reviews work

0 comments

Cite this review

Pith. "Pith review of From Streaming Instability to the Onset of Pebble Accretion I. Investigating the Growth Modes in Planetesimal Rings." pith.science (2026). https://pith.science/paper/CK7NXSNS

@misc{pith2026250202124,
  author       = {Pith},
  title        = {Pith review of: From Streaming Instability to the Onset of Pebble Accretion I. Investigating the Growth Modes in Planetesimal Rings},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CK7NXSNS}},
  note         = {Machine review of arXiv:2502.02124}
}

read the original abstract

Context. The localized formation of planetesimals can be triggered with the help of streaming instability when the local pebble density is high. This can happen at various locations in the disk leading to the formation of local planetesimal rings. The planetesimals in these rings subsequently grow from mutual collisions and by pebble accretion. Aims. We investigate the early growth of protoplanetary embryos from a ring of planetesimals created from streaming instability to see if they reach sizes where they accrete pebbles efficiently. Methods. We simulate the early stages of planet formation for rings of planetesimals that we assume were created by streaming instability at various separations from the star and for various stellar masses using a semi-analytic model. Results. The rings in the inner disk are able to produce protoplanetary embryos in a short time whereas at large separations there is little to no growth. The growth of the largest bodies is significantly slower around lower-mass stars. Conclusions. The formation of planetary embryos from filaments during the disk lifetime is possible but strongly dependent on the separation from the star and the mass of the host star. It remains difficult to form the seeds of pebble accretion early in the outer disk \sim 50AU, especially for low-mass stars.

Figures

Figures reproduced from arXiv: 2502.02124 by the authors.

**Figure 1.** The resulting pebble fluxes from Eq. (16) for Z0 = 0.01 around a solar mass star (solid), a 0.3M⊕ star (dashed) and a 0.1M⊕ star (dotted) along with the t0 as described by Eq. (29) for filaments at different separations form the star Above the transition mass Mtr the accretion of pebbles is enhanced (in the 2D regime) as can be seen in Eq. (12). Finally, when the embryo is large enough and reaches its isolation m… view at source ↗

**Figure 3.** The total ring mass (dotted), the mass of the single largest (dashed) and characteristic (dashdotted) planetesimal mass for different stellar masses (colour) for filaments with different separations from the star growth timescale we follow the approach of Lorek & Johansen (2022). The growth timescale of the dust (Birnstiel et al. 2012) can be described by tgr = 2 √ πϵpZ0ΩK , (25) where the sticking efficiency given… view at source ↗

**Figure 5.** The mass of the largest body in the ring (embryo) (solid), the initial characteristic planetesimal mass (dash doted) and ring mass (dotted) where the background colours refer to the different pebble accretion regimes (red: ballistic/isolation regime, brown: Bondi regime and green: Hill regime) in the bottom panel of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

Figures from the paper (12 more)

**Figure 4.** Figure 4: The embryo masses for filaments at different separations from the star over time (top) and the surface density of planetesimals in the ring (bottom) as a function of time 3. Results We probed the formation of embryos in filaments at different locations ranging from 0.…

**Figure 7.** Figure 7: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

**Figure 9.** Figure 9: As we can clearly see the growth around both the 0.3 and 0.1 M⊙ mass star are significantly reduced. For the 0.3M⊙ star the filaments up 3 AU are able to reach the transition mass whereas for the 0.1M⊙ star, this only happens up to ∼ 1AU. This can easily be explained …

**Figure 10.** Figure 10: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

**Figure 9.** Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

**Figure 11.** Figure 11: The total mass of the embryo (solid), the mass budget of planetesimals accreted (dashed) and mass of accreted pebbles (dotted) tioned before but considering pebbles of a fixed lower stokes number of τs = 0.03. We show the results of these simulations in [PITH_FULL_I…

**Figure 12.** Figure 12: along with a comparison with the growth tracks considering the accretion of pebbles with different aerodynamic sizes. We see that initially the (aerodynamically) larger pebbles result in higher accretion rates, however at higher embryo masses this trend reverses, lea…

**Figure 13.** Figure 13: The time of the embryo reaching the transition mass for the nominal simulations without pebble accretion (solid), when considering the time-dependent pebble flux (dashed) and the fixed pebble flux (dotted) for different stellar masses (colour). The blue-shaded region…

**Figure 14.** Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]

**Figure 15.** Figure 15: , where for a fixed stellar mass, we plot the transition timing for the remaining parameter pairs. In the interest of brevity, the same plots for further stellar masses can be found in [PITH_FULL_IMAGE:figures/full_fig_p011_15.png]

**Figure 16.** Figure 16: The transition timing of for the grid at different stellar masses and separations where Fpeb = 100M⊕/Myr and Mem = 1Mem,0 Parameter Value Distance [AU] [0.5, 1, 5, 10, 25, 50 ] Stellar mass [M⊙] [1, 0.7, 0.5, 0.3, 0.1] Pebble flux [M⊕/Myr] [200, 100, 50, 20] Mass fact…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Solving for the 2D Water Snowline with Hydrodynamic Simulations. Emergence of gas outflow, water cycle and temperature plateau
astro-ph.EP 2025-02 conditional novelty 7.0 of 10

2D hydrodynamic simulations show vapor-driven outflows and a vertical water cycle strengthen ice pile-up at the water snowline, while latent heat cooling broadens the pile-up and creates a possible continuum dip.
The Influence of Dust Composition on Accretion Outbursts
astro-ph.EP 2026-07 conditional novelty 6.0 of 10

Using 1D simulations with dust evaporation and condensation, the paper shows that dead-zone accretion outbursts vaporize dust out to about 0.5 au and that higher dust sublimation temperatures produce stronger but less...

Reference graph

Works this paper leans on

98 extracted references · 69 canonical work pages · cited by 2 Pith papers

[1]

, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...
[2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....
[3]

, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.s...
[4]

W., & Dullemond, C

Güttler, C., Blum, J., Zsom, A., Ormel, C. W., & Dullemond, C. P. 2010, , 513, A56

2010
[5]

W., Guettler, C., Blum, J., & Dullemond, C

Zsom, A., Ormel, C. W., Guettler, C., Blum, J., & Dullemond, C. P. 2010, , 513, A57

2010
[6]

W., Dominik, C., & Tielens, A

Krijt, S., Ormel, C. W., Dominik, C., & Tielens, A. G. G. M. 2015, , 574, A83

2015
[7]

W., & Dullemond, C

Birnstiel, T., Ormel, C. W., & Dullemond, C. P. 2011, , 525, A11

2011
[8]

Stammler, S. M. & Birnstiel, T. 2022, , 935, 35

2022

Show all 98 references

[9]

2023, arXiv:2312.13287 [astro-ph]

Birnstiel, T. 2023, arXiv:2312.13287 [astro-ph]

2023 arXiv
[10]

Youdin, A. N. & Goodman, J. 2005, , 620, 459

2005
[11]

& Youdin, A

Johansen, A. & Youdin, A. 2007, , 662, 627

2007
[12]

2009, , 697, 1269, publisher: The American Astronomical Society

Johansen, A., Youdin, A., & Klahr, H. 2009, , 697, 1269, publisher: The American Astronomical Society

2009
[13]

& Stone, J

Bai, X.-N. & Stone, J. M. 2010, The Astrophysical Journal, 722, 1437, publisher: The American Astronomical Society

2010
[14]

2017, , 597, A69

Schäfer, U., Yang, C.-C., & Johansen, A. 2017, , 597, A69

2017
[15]

& Schreiber, A

Klahr, H. & Schreiber, A. 2020, , 901, 54

2020
[16]

& Klahr, H

Polak, B. & Klahr, H. 2022, arXiv:2211.13318 [astro-ph]

2022 arXiv
[17]

Stevenson, D. J. & Lunine, J. I. 1988, Icarus, 75, 146

1988
[18]

& Alibert, Y

Drążkowska, J. & Alibert, Y. 2017, , 608, A92

2017
[19]

& Ormel, C

Schoonenberg, D. & Ormel, C. W. 2017, , 602, A21

2017
[20]

P., Simon, J

Abod, C. P., Simon, J. B., Li, R., et al. 2019, , 883, 192

2019
[21]

Schneider, A. D. & Bitsch, B. 2021, , 654, A71

2021
[22]

& Tan, J

Chatterjee, S. & Tan, J. C. 2013, , 780, 53

2013
[23]

M., Sándor, Z., Ronco, M

Guilera, O. M., Sándor, Z., Ronco, M. P., Venturini, J., & Bertolami, M. M. M. 2020, , 642, A140

2020
[24]

& Alibert, Y

Shibaike, Y. & Alibert, Y. 2020, , 644, A81

2020
[25]

& Alibert, Y

Shibaike, Y. & Alibert, Y. 2023, , 678, A102

2023
[26]

M., Regály, Z., & Lyra, W

Sándor, Z., Guilera, O. M., Regály, Z., & Lyra, W. 2024

2024
[27]

2021, , 656, A69

Emsenhuber, A., Mordasini, C., Burn, R., et al. 2021, , 656, A69

2021
[28]

Chambers, J. E. 2006, , 652, L133

2006
[29]

B., Hubickyj, O., Bodenheimer, P., et al

Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62

1996
[30]

& Ormel, C

Jiang, H. & Ormel, C. W. 2021, , 505, 1162

2021
[31]

M., Dra̧żkowska, J., Birnstiel, T., et al

Stammler, S. M., Dra̧żkowska, J., Birnstiel, T., et al. 2019, , 884, L5

2019
[32]

Lau, T. C. H., Drążkowska, J., Stammler, S. M., Birnstiel, T., & Dullemond, C. P. 2022, , 668, A170, arXiv:2211.04497 [astro-ph]

2022 arXiv
[33]

2023, arXiv:2210.13314 [astro-ph]

Bae, J., Isella, A., Zhu, Z., et al. 2023, arXiv:2210.13314 [astro-ph]

2023 arXiv
[34]

Pinte, C., Teague, R., Flaherty, K., et al. 2022

2022
[35]

T., Klahr, H., & Birnstiel, T

Lenz, C. T., Klahr, H., & Birnstiel, T. 2019, , 874, 36

2019
[36]

2020, , 642, A75

Voelkel, O., Klahr, H., Mordasini, C., Emsenhuber, A., & Lenz, C. 2020, , 642, A75

2020
[37]

Lau, T. C. H., Lee, M. H., Brasser, R., & Matsumura, S. 2024, , 683, A204

2024
[38]

W., & Johansen, A

Liu, B., Ormel, C. W., & Johansen, A. 2019, , 624, A114

2019
[39]

2022, , 664, A86

Jang, H., Liu, B., & Johansen, A. 2022, , 664, A86

2022
[40]

& Johansen, A

Lorek, S. & Johansen, A. 2022, , 666, A108

2022
[41]

& Johansen, A

Lambrechts, M. & Johansen, A. 2014, , 572, A107

2014
[42]

M., Bertolami, M

Guilera, O. M., Bertolami, M. M. M., Masset, F., et al. 2021, , 507, 3638

2021
[43]

M., & Birnstiel, T

Drazkowska, J., Stammler, S. M., & Birnstiel, T. 2021, , 647, A15

2021
[44]

S., Mac Low, M.-M., et al

Johansen, A., Oishi, J. S., Mac Low, M.-M., et al. 2007, Nature, 448, 1022

2007
[45]

2017, , 606, A80

Yang, C.-C., Johansen, A., & Carrera, D. 2017, , 606, A80

2017
[46]

N., & Simon, J

Li, R., Youdin, A. N., & Simon, J. B. 2019, , 885, 69

2019
[47]

C., Zhu, Z., et al

Hu, X., Tan, J. C., Zhu, Z., et al. 2018, , 857, 20

2018
[48]

Carrera, D., Gorti, U., Johansen, A., & Davies, M. B. 2017, , 839, 16

2017
[49]

2006, Icarus, 180, 496

Chambers, J. 2006, Icarus, 180, 496

2006
[50]

2001, Icarus, 149, 235

Inaba, S. 2001, Icarus, 149, 235

2001
[51]

& Alibert, Y

Kaufmann, N. & Alibert, Y. 2023, , 676, A46

2023
[52]

R., & Ida, S

Ohtsuki, K., Stewart, G. R., & Ida, S. 2002, Icarus, 155, 436

2002
[53]

M., de Elía, G

Guilera, O. M., de Elía, G. C., Brunini, A., & Santamaría, P. J. 2014, , 565, A96

2014
[54]

& Tanaka, H

Ohtsuki, K. & Tanaka, H. 2003, Icarus, 162, 47

2003
[55]

2003, Icarus, 161, 144

Tanaka, H., Ohtsuki, K., & Daisaka, H. 2003, Icarus, 161, 144

2003
[56]

Morbidelli, A., Bottke, W., Nesvorny, D., & Levison, H. F. 2009, Icarus, 204, 558

2009
[57]

& Asphaug, E

Benz, W. & Asphaug, E. 1999, Icarus, 142, 5

1999
[58]

2000, in From Dust to Terrestrial Planets , ed

Benz, W. 2000, in From Dust to Terrestrial Planets , ed. W. Benz, R. Kallenbach, & G. W. Lugmair, Vol. 9 (Dordrecht: Springer Netherlands), 279--294

2000
[59]

Stewart, S. T. & Leinhardt, Z. M. 2009, , 691, L133

2009
[60]

Leinhardt, Z. M. & Stewart, S. T. 2012, arXiv:1106.6084

2012 arXiv
[61]

& Tanaka, H

Kobayashi, H. & Tanaka, H. 2018, , 862, 127, arXiv:1806.07354 [astro-ph]

2018 arXiv
[62]

V., Ide, A., Löhne, T., Johansen, A., & Blum, J

Krivov, A. V., Ide, A., Löhne, T., Johansen, A., & Blum, J. 2018, , 474, 2564

2018
[63]

Sebastián, I. L. S., Guilera, O. M., & Parisi, M. G. 2019, , 625, A138

2019
[64]

Ormel, C. W. & Kobayashi, H. 2012, , 747, 115

2012
[65]

Ormel, C. W. & Liu, B. 2018, , 615, A178

2018
[66]

& Ormel, C

Liu, B. & Ormel, C. W. 2018, , 615, A138

2018
[67]

2012, , 539, A148

Birnstiel, T., Klahr, H., & Ercolano, B. 2012, , 539, A148

2012
[68]

& Bitsch, B

Baumann, T. & Bitsch, B. 2020, , 637, A11

2020
[69]

N., et al

Izidoro, A., Bitsch, B., Raymond, S. N., et al. 2021, , 650, A152

2021
[70]

T., & Stammler, S

Pinilla, P., Lenz, C. T., & Stammler, S. M. 2021, , 645, A70

2021
[71]

Ormel, C. W. 2017, in Formation, Evolution , and Dynamics of Young Solar Systems , ed. M. Pessah & O. Gressel, Vol. 445 (Cham: Springer International Publishing), 197--228, series Title: Astrophysics and Space Science Library

2017
[72]

2018, , 612, A30

Bitsch, B., Morbidelli, A., Johansen, A., et al. 2018, , 612, A30

2018
[73]

2018, , 615, A110

Ataiee, S., Baruteau, C., Alibert, Y., & Benz, W. 2018, , 615, A110

2018
[74]

& Pringle, J

Lynden-Bell, D. & Pringle, J. E. 1974, , 168, 603

1974
[75]

2016, , 591, A72

Ida, S., Guillot, T., & Morbidelli, A. 2016, , 591, A72

2016
[76]

Armitage, P. J. & Kley, W. Saas- Fee Advanced Course , Vol. 45, 2019, ed. M. Audard, M. R. Meyer, & Y. Alibert (Berlin, Heidelberg: Springer Berlin Heidelberg)

2019
[77]

2016, Annual Review of Astronomy and Astrophysics, 54, 135

Hartmann, L., Herczeg, G., & Calvet, N. 2016, Annual Review of Astronomy and Astrophysics, 54, 135

2016
[78]

2020, , 638, A88

Liu, B., Lambrechts, M., Johansen, A., Pascucci, I., & Henning, T. 2020, , 638, A88

2020
[79]

A., Klahr, H., & Baehr, H

Gerbig, K., Murray-Clay, R. A., Klahr, H., & Baehr, H. 2020, , 895, 91

2020
[80]

Liu, B. & Ji, J. 2020, Research in Astronomy and Astrophysics, 20, 164

2020
[81]

Williams, J. P. & Cieza, L. A. 2011, Annual Review of Astronomy and Astrophysics, 49, 67

2011
[82]

& Ormel, C

Jiang, H. & Ormel, C. W. 2022, , 518, 3877

2022
[83]

2019, , 632, A7

Liu, B., Lambrechts, M., Johansen, A., & Liu, F. 2019, , 632, A7

2019
[84]

& Bitsch, B

Savvidou, S. & Bitsch, B. 2024, arXiv:2407.08533 [astro-ph]

2024 arXiv
[85]

M., Ronco, M

Venturini, J., Guilera, O. M., Ronco, M. P., & Mordasini, C. 2020, , 644, A174

2020
[86]

P., Guilera, O

Venturini, J., Ronco, M. P., Guilera, O. M., et al. 2024, , 686, L9

2024
[87]

2011, , 410, 293

Paardekooper, S.-J., Baruteau, C., & Kley, W. 2011, , 410, 293

2011
[88]

2020, , 494, 5666

Ida, S., Muto, T., Matsumura, S., & Brasser, R. 2020, , 494, 5666

2020
[89]

Tanaka, H., Takeuchi, T., & Ward, W. R. 2002, , 565, 1257, publisher: IOP ADS Bibcode: 2002ApJ...565.1257T

2002
[90]

M., Benitez-Llambay, P., Miller Bertolami, M

Guilera, O. M., Benitez-Llambay, P., Miller Bertolami, M. M., & Pessah, M. E. 2023, , 953, 97

2023
[91]

M., Brunini, A., & Benvenuto, O

Guilera, O. M., Brunini, A., & Benvenuto, O. G. 2010, , 521, A50

2010
[92]

Guilera, O. M. & Sándor, Z. 2017, , 604, A10

2017
[93]

E., Fuentes, C

Schlichting, H. E., Fuentes, C. I., & Trilling, D. E. 2013, The Astronomical Journal, 146, 36

2013
[94]

2024, arXiv:2409.03816 [astro-ph]

Pfeil, T., Birnstiel, T., & Klahr, H. 2024, arXiv:2409.03816 [astro-ph]

2024 arXiv
[95]

H., & Yang, C.-C

Lyra, W., Johansen, A., Cañas, M. H., & Yang, C.-C. 2023, arXiv:2301.03825 [astro-ph]

2023 arXiv
[96]

2021, , 653, A114

Sabotta, S., Schlecker, M., Chaturvedi, P., et al. 2021, , 653, A114

2021
[97]

Lau, T. C. H., Birnstiel, T., Drążkowska, J., & Stammler, S. 2024, arXiv:2406.12340 [astro-ph]

2024 arXiv
[98]

1981, Progress of Theoretical Physics Supplement, 70, 35

Hayashi, C. 1981, Progress of Theoretical Physics Supplement, 70, 35

1981

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

[3] [3]

, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.s...

[4] [4]

W., & Dullemond, C

Güttler, C., Blum, J., Zsom, A., Ormel, C. W., & Dullemond, C. P. 2010, , 513, A56

2010

[5] [5]

W., Guettler, C., Blum, J., & Dullemond, C

Zsom, A., Ormel, C. W., Guettler, C., Blum, J., & Dullemond, C. P. 2010, , 513, A57

2010

[6] [6]

W., Dominik, C., & Tielens, A

Krijt, S., Ormel, C. W., Dominik, C., & Tielens, A. G. G. M. 2015, , 574, A83

2015

[7] [7]

W., & Dullemond, C

Birnstiel, T., Ormel, C. W., & Dullemond, C. P. 2011, , 525, A11

2011

[8] [8]

Stammler, S. M. & Birnstiel, T. 2022, , 935, 35

2022