Angular Momentum Drain: Despinning Embedded Planetesimals

A.C. Quillen; Adam E. Rubinstein; Maggie Ju; Stephen Li

REVIEW 3 major objections 4 minor 14 references

Angular Momentum Drain: Despinning Embedded Planetesimals

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Low-velocity headwind impacts spin down young planetesimals by 30–50%, helping pebble-cloud collapse without completing it.

desk verdict A careful extension of angular momentum drain to low-velocity embedded planetesimals; the mechanism is real and the 30-50% estimate is plausible but rests on unvalidated ejecta extrapolations. read the letter →

arxiv 2412.03533 v2 pith:5IOZFH6A submitted 2024-12-04 astro-ph.EP

Stephen Li , Maggie Ju , A.C. Quillen , Adam E. Rubinstein This is my paper · ORCID

classification astro-ph.EP

keywords ejectaimpactphenomenacollisionalprocessesplanetesimalsangularmomentumdrainobliqueimpactscraterscalingprotoplanetarydisk

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 low-velocity impacts from particles in a protoplanetary disk can spin down a young, embedded planetesimal. The authors combine crater-scaling ejecta laws with azimuthally asymmetric ejecta distributions for oblique impacts, integrate over a realistic headwind impact population, and compute the torque on an Arrokoth-like body. They find that the asteroidal angular-momentum-drain mechanism operates at 10–65 m/s impact speeds, with an angular-momentum transfer efficiency near unity for many parameter choices. Integrating over the expected collisional mass during a streaming-instability epoch, they estimate that impacts remove 30–50% of the initial spin angular momentum. That is real but partial: it can help a pebble cloud collapse into a single planetesimal only when the cloud starts with low angular momentum.

What carries the argument

The load-bearing machinery is a numerical integration that combines four ingredients: normal-impact crater ejecta scaling laws that give ejecta velocity and mass as functions of radial distance from the impact point; analytic functions (Equations 20–23) that modulate the scaling parameters $\mu$, $C_1$, crater radius $R_{cr}$, and the mass coefficient $k$ with impact angle $\theta_{\rm imp}$ and azimuthal angle $\zeta$, capturing the asymmetry of oblique-impact ejecta curtains; gravitational focusing via hyperbolic projectile orbits, which changes impact location, velocity, and angle; and a dimensionless efficiency $\epsilon_L$ that measures fractional spin angular momentum lost per unit projectile mass. Escaping ejecta are identified by comparing their inertial-frame speed to the escape velocity; because the surface rotates, ejecta leaving the trailing side move faster in the inertial frame than those on the leading side, so more trailing-side ejecta escape and spin angular momentum is carried away. The same integration yields the mass loss ratio $\epsilon_M$, separating accretionary from erosional regimes.

What would settle it

Run oblique-impact experiments into weakly cohesive and strengthless granular targets at impact speeds of 10–65 m/s and impact angles down to grazing, measuring the azimuthal ejecta mass and velocity distributions; compare the measured distributions to Equations 20–23. If the low-speed, high-obliquity ejecta do not follow these functions, the predicted spin-down efficiency, the 30–50% estimate, and the spin-up reversal for strengthless bodies would all need revision.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the angular-momentum-drain mechanism, in which escaping ejecta carry away spin angular momentum preferentially from a rotating body, works in the low-velocity, embedded-planetesimal regime, extending a mechanism previously studied for high-velocity asteroid impacts. Using crater scaling laws modified for oblique impacts and for ejecta azimuthal angle, the authors compute the mass loss ratio and the dimensionless angular momentum transfer efficiency $\epsilon_L = -|\langle\Delta L_a\rangle|/(L_a/M_a\, m_{pj})$. They find $\epsilon_L \approx 1$ across a wide range of parameters, with stronger drain when the headwind is fast, when the projectile density exceeds the planetesimal density, and when cratering operates in the gravity regime. For the fiducial Arrokoth-like parameters, most impacts cause net accretion rather than erosion, yet the drain still operates; over the collisional era the expected total projectile mass is less than the planetesimal mass, giving a total spin-down of roughly 30–50%. The paper concludes that this partial despinning can facilitate collapse of pebble clouds with low initial angular momentum but is insufficient by itself to explain single-planetesimal formation.

Load-bearing premise

The results depend on ejecta functions that were fit to km/s-scale impact simulations and roughly 100 m/s sand impacts but are applied here at 10–65 m/s and at more extreme impact obliquities; if those functions fail in this regime, the computed torque, and even its sign, could be wrong.

Editorial extensions

If this is right

Angular momentum drain works at 10–65 m/s impact speeds, not just at the km/s speeds typical of asteroid impacts, and it operates in both accretionary and erosional impact regimes.
The most favorable conditions are a fast headwind, a projectile denser than the planetesimal, and a planetesimal weak enough that cratering follows gravity-regime scaling; varying the projectile-to-planetesimal density ratio is the strongest lever on efficiency.
For an Arrokoth-like body at 45 AU over a 10^4-year streaming-instability epoch, about half the planetesimal's mass in pebbles impacts it, and the integrated effect is a 30–50% reduction in spin angular momentum.
That reduction is large but does not solve the angular momentum problem by itself: at 45 AU roughly 93% of the pebble cloud's angular momentum must be removed for collapse into a single planetesimal, so additional drain mechanisms are needed.
The pebble-cloud velocity gradient, even at its assumed upper bound, changes the drain efficiency and mass loss ratio by less than detectable amounts, so a unidirectional headwind is a good approximation.

Reading between the lines

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

Beyond the paper, a direct test of the azimuthal ejecta functions at 10–65 m/s into weakly cohesive granular targets would clarify whether the 30–50% estimate stands; the paper itself flags the low-velocity, high-obliquity regime as uncalibrated.
Beyond the paper, the same integration framework could be extended to compute the linear momentum transfer, effectively an impact-induced drag, on an embedded planetesimal; the paper notes this could tighten binaries or assist binary merging during the high-flux streaming-instability epoch.
Beyond the paper, if the predicted spin-up reversal for strengthless bodies at small radii is physical, it would mean extremely low-strength planetesimals are not efficiently despun, narrowing the conditions under which single-planetesimal collapse can occur.

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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

Quick take. This is a genuine extension of Dobrovolskis and Burns to a regime they never touched: planetesimals embedded in a protostellar disk, hit from a preferred direction at 10-65 m/s. The central claim—that low-velocity impacts can drain a substantial fraction of spin—is plausible and survives a skeptical read. The headline 30-50% number, though, is an order-of-magnitude estimate resting on extrapolated azimuthal ejecta functions and a rough disk mass-flux model, not a robust prediction.

What's actually new: the paper integrates ejecta distributions with modern azimuthal sensitivity (Raducan et al. 2022, Quillen and Doran 2024), includes gravitational focusing via hyperbolic orbits, and treats a unidirectional headwind perpendicular to the spin axis. That combination matters because at low velocity the ejecta escape fraction is sensitive to rotation and impact angle. The efficiency epsilon_L is computed from crater scaling, not fitted to a desired spin-down, and the paper covers density ratio, strength, headwind speed, spin rate, and a filament velocity gradient. Credit where due: the integrals are internally consistent, and the authors are unusually candid. Section 5.4 flags the possible unphysical spin-up reversal from the butterfly pattern, Section 2.9 lists neglected physics, and they explicitly note their adopted Raducan functions are inconsistent with that paper's Figure 12.

The soft spots are real but not fatal. The load-bearing issue: Eqs. 20-23 are fitted to km/s iSALE simulations and ~100 m/s sand experiments, and are applied at 10-65 m/s and impact angles below the 30-degree calibration limit. Since a large fraction of impacts on a sphere are oblique, the net torque's sign and magnitude are controlled by exactly this unvalidated territory. The stress-test note lands here; if the azimuthal asymmetry weakens at low velocity, epsilon_L could drop well below the near-unity values used for the 30-50% claim. There is no uncertainty quantification, and the mass-flux normalization depends on fp~100 and a 10^4 yr streaming-instability epoch—reasonable but soft. Minor: the code archive is just the arXiv page, not a runnable repository, and the ejecta angle is fixed at 45 degrees.

Overall: the mechanism operates, and the paper does a service by showing it is partial—30-50% drain is not enough to collapse a single planetesimal from typical cloud angular momentum at 45 AU. That conclusion is probably robust even if the exact percentage is not.

Recommendation: send to peer review. A serious referee should push for sensitivity tests of the azimuthal functions at low velocity/obliquity and some uncertainty range on the final estimate. If those tests show the qualitative result survives, this is a solid contribution to planetesimal formation.

Referee Report

3 major / 4 minor

Summary. The paper applies crater ejecta scaling laws to compute the mass loss and angular momentum transfer experienced by a planetesimal bombarded by low-velocity headwind particles (10–65 m/s) in a protoplanetary disk. The authors integrate oblique-impact ejecta distributions over a distribution of impacts on a spherical planetesimal, including gravitational focusing, and define an angular momentum transfer efficiency ϵL and a mass-loss ratio ϵM. They report that the Dobrovolskis and Burns (1984) spin-down mechanism operates in this low-velocity regime, with ϵL ∼ 1 for a wide range of parameters, and that under assumed pebble mass-flux conditions the cumulative angular momentum drain is 30–50% of the initial spin. The paper closes with caveats about highly oblique impacts and notes that the adopted oblique-impact scaling functions are inconsistent with one source figure.

Significance. If the result holds, the paper provides a quantitative pathway by which low-velocity impacts can remove a substantial fraction of a planetesimal's spin angular momentum before pebble-cloud collapse, connecting impact ejecta physics to the angular-momentum problem in streaming-instability planetesimal formation. The work has clear strengths: the transfer efficiency is computed rather than fitted to a target spin-down, the gravitational-focusing treatment is explicit, the code is archived with the submission, and the paper identifies its own most fragile assumption in Section 5.4. These strengths make the paper a useful contribution even though the headline 30–50% number inherits uncertainty from the ejecta-scaling extrapolation.

major comments (3)

[Sec. 5.4 and Eqs. (20)–(23)] The central quantitative claim — ϵL ∼ 1 and the resulting 30–50% spin-down — is controlled by the azimuthally asymmetric ejecta functions μ(ζ,θ), C1(ζ,θ), Rcr(ζ,θ), and k(ζ,θ). These functions are calibrated to km/s-scale iSALE simulations (Raducan et al. 2022) and roughly 100 m/s sand-crater measurements (Quillen and Doran 2024), yet they are applied here at 10–65 m/s and to impact angles below the 30° calibration limit. As the authors note, the resulting spin-up reversal for strengthless bodies may not be physical. Because a large fraction of impacts on a sphere occur at highly oblique angles, the sign and magnitude of the net torque are set by exactly this unvalidated part of the model. I ask the authors to either (a) add a sensitivity test that suppresses or reverses the butterfly-pattern asymmetry and shows how ϵL changes, or (b) bound ϵL using the low-velocity experimental data available for oblique impacts, or (c) explicitly degrade the 30–50% claim to a qualitative statement pending such tests. This is an extrapolation risk rather than an internal inconsistency, but it is load-bearing for the paper's main numerical conclusion.
[Sec. 2.4.1, Eq. (22)] The text states that Eqs. (20)–(23), taken from Raducan et al. (2022), 'are not consistent with their Figure 12 but appear consistent with the distributions shown in their other figures.' This is an explicit admission that the adopted crater-radius asymmetry function Rcr(ζ,θimp) (Eq. 22) disagrees with a stated calibration figure. Since Rcr sets the integration domain in Eq. (31), the inconsistency is not cosmetic. The authors should either reconcile the adopted functional form with the source's Figure 12, show quantitatively how much the discrepancy changes Rcr and hence ϵL, or replace Eq. (22) with a form that is actually consistent with the cited calibration. At minimum, the source of the discrepancy needs to be explained, not merely noted.
[Sec. 7 and Eq. (57)] The 30–50% total spin-down estimate combines the computed ϵL with the pebble mass flux estimate in Eq. (57), but the paper provides no uncertainty quantification on either factor. The mass-flux estimate depends on fp = 10^2, Δt = 10^4 yr, the disk model of Quillen et al. (2024), and the neglect of gas drag on incoming and outgoing particles; the ϵL values enter near unity in the fiducial regime. Because the authors do not propagate uncertainties or show how the 30–50% range follows from the parameter ranges explored in Figure 8, this headline number is presented with unjustified precision. I recommend adding a short propagation or bracketing calculation that translates plausible ranges in fp, Δt, and the oblique-scaling uncertainty into a range for the cumulative spin-down, with the caveats of Section 5.4 folded in.

minor comments (4)

[Figure 8 caption] The caption says 'Panels (a,b) varies π4, (b,c) varies planetesimal strength Ya, (e,f) varies the distant headwind velocity uhw, and (g,h) varies the planetesimal spin rate.' The panel labels are inconsistent: the second pair should be (c,d), not (b,c). Please correct the caption.
[Throughout] There are many typographical artifacts from the manuscript preparation, such as 'ine fficient', 'su fficiently', 'di fferent', and 'e ffect'. These should be cleaned up before publication.
[Sec. 2.9.1 and Sec. 5.2] The paper says in Section 2.9.1 that neglecting gravitational defocusing 'does not influence our estimate of the angular momentum transfer efficiency', but in Section 5.2 it suggests that gravitational defocusing 'could be an even stronger effect on the escaping ejecta than on the incoming projectile.' Please clarify whether defocusing affects the angular momentum computation or only the linear momentum computation; the current statements are easy to read as contradictory.
[Acknowledgements] The code is said to be 'archived at https://arxiv.org/abs/2412.03533', which is the paper's own arXiv page rather than a code repository. Please provide a persistent code repository (e.g., Zenodo or GitHub) with a version identifier.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction: the spin-down efficiency is computed by integrating ejecta-scaling laws calibrated to independent experiments and simulations, and the 30-50% total drain is a product of that computed efficiency with an externally anchored disk mass flux, not a fit to the claimed result.

full rationale

The paper's central object, the angular momentum transfer efficiency epsilon_L (Eq. 36), is obtained by integrating ejecta velocity and mass distributions (Eqs. 24-25, 30-33) built from Housen and Holsapple (2011) normal-impact scaling laws and the Raducan et al. (2022) / Quillen and Doran (2024) oblique-impact functions (Eqs. 20-23). These functions are empirical calibrations from independent iSALE simulations and sand-crater experiments; the paper does not fit any parameter to a target spin-down. The headline 30-50% drain (Section 7) multiplies this computed epsilon_L by the collisional mass fraction Delta M_a / M_a ~ 0.52 (Eqs. 55-57), whose disk model and headwind velocity are taken from Quillen et al. (2024) with overlapping authorship. That citation is load-bearing for the normalization but not circular: the disk model is an externally published, MMSN-based prescription, and the spin-down claim scales linearly with it rather than being defined by it. The main scientific risk is extrapolation of the oblique-ejecta functions to 10-65 m/s and to impact angles below 30 degrees, which the authors explicitly acknowledge in Sections 4.2 and 5.4 ("further work is needed in low-velocity, low-strength/strengthless, highly oblique impacts"); extrapolation risk is a correctness concern, not a circularity. No equation in the derivation reduces by construction to its input, and no self-citation is used to forbid alternatives.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central claim rests on externally calibrated crater scaling laws, a set of chosen fiducial scenario parameters, and several domain simplifications that the authors explicitly flag. No new physical entities are introduced. The load-bearing extrapolation is the use of high-velocity, moderate-obliquity ejecta functions at low velocity and extreme obliquity.

free parameters (6)

Crater scaling coefficients (C1,N, kN, μN, ν, H1, H2, p) = C1,N=0.55, kN=0.3, ν=0.4, μN=0.4 (SFA) / 0.41 (sand), H2=0.4, H1=0.59, p=0.3 (Table 2)
Empirical fits from Housen and Holsapple (2011), treated as inputs to the ejecta model.
Oblique impact azimuthal function coefficients (Eqs. 20-23) = μ: 0.5 cosζ cosθimp; C1: exp(-5 cosζ cosθimp); Rcr: factor involving (9 - 18θimp/π)cosζ/2; k: exp(-0.02 cosζ cosθimp)
Fitted by Raducan et al. (2022) to iSALE simulations and by Quillen and Doran (2024) to sand impact experiments.
Ejecta angle θej = 45°
Assumed constant despite observed 30-60° variation; affects which ejecta escape and the torque.
Fiducial planetesimal properties = Ra=10 km, ρa=235 kg/m^3, Ya=100 Pa, Ωa=Ωbreakup
Chosen based on Arrokoth and disk wind estimates; the spin-down magnitude scales with these values.
Headwind velocity and projectile density = uhw=30 m/s, ρpj=235 kg/m^3, apj=1 m in gravity regime
Scenario choices; Section 5 shows the angular momentum transfer efficiency is sensitive to both.
Streaming instability scenario parameters = fp=100, Δt=10^4 yr, a=45 AU, gΣ=gT=1
Used to convert efficiency into the total 30-50% spin-down estimate; particle concentration and duration are uncertain.

assumptions (7)

domain assumption The planetesimal is spherical, homogeneous, and in solid-body rotation.
Section 2.1; non-spherical shape and surface heterogeneity are neglected, as flagged in Section 2.9.2.
domain assumption Projectiles arrive from one direction and the spin axis is perpendicular to the headwind.
Section 2.1; motivated by prograde pebble accretion simulations; other directional components are assumed to average to zero.
domain assumption Ejecta escapes if its inertial-frame speed equals or exceeds the escape velocity.
Section 2.6; gas drag on ejecta and gravitational deflection of ejecta are neglected (Sections 2.9.1 and 2.9.3).
domain assumption Ejecta launch angle is constant at 45°.
Section 2.5; experiments show 30-60° variation, and the choice affects escape fractions and the torque.
domain assumption Projectile trajectories follow hyperbolic orbits with gas drag neglected.
Section 2.8; gravitational focusing is included, but the effect of the gas flow on incoming projectiles is not.
domain assumption The streaming instability epoch supplies impacts for about 10^4 years at 45 AU.
Section 5.2; used with the chosen disk model to estimate total projectile mass and the 30-50% spin-down.
ad hoc to paper Oblique impact scaling laws extrapolate to 10-65 m/s and to obliquities below the 30° calibration range.
Equations 20-23 are applied outside the parameter range where they were calibrated; the authors flag possible artifacts in Section 5.4.

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Cite this review

Pith. "Pith review of Angular Momentum Drain: Despinning Embedded Planetesimals." pith.science (2026). https://pith.science/paper/5IOZFH6A

@misc{pith2026241203533,
  author       = {Pith},
  title        = {Pith review of: Angular Momentum Drain: Despinning Embedded Planetesimals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5IOZFH6A}},
  note         = {Machine review of arXiv:2412.03533}
}

read the original abstract

Young and forming planetesimals experience impacts from particles present in a protostellar disk. Using crater scaling laws, we integrate ejecta distributions for oblique impacts. For impacts at 10 to 65 m/s, expected for impacts associated with a disk wind, we estimate the erosion rate and torque exerted on the planetesimal. We find that the mechanism for angular momentum drain proposed by Dobrovolskis and Burns (1984) for asteroids could operate in the low velocity regime of a disk wind. Though spin-down associated with impacts can facilitate planetesimal collapse, we find that the process is inefficient. We find that angular momentum drain via impacts operates in the gravitational focusing regime. The angular momentum transfer is most effective when the wind speed is high, the projectile density is high compared to the bulk planetesimal density, and the planetesimal is sufficiently weak that cratering is in the gravity regime. We find that angular momentum drain due to impacts within a pebble cloud may, in those specific conditions, facilitate collapse of single planetesimals.

Figures

Figures reproduced from arXiv: 2412.03533 by the authors.

**Figure 2.** We illustrate how rotation affects impact angle and velocity in as seen in frame rotating with the surface. Black shows rotation. Blue shows wind speed. Green shows wind particle velocity in the frame rotating with the planetesimal. From the perspective of a viewer on the surface on the leading side, rotation causes the wind particle to impact the surface at higher velocity and at lower (closer to grazing) impact an… view at source ↗

**Figure 3.** In the frame rotating with the surface, we illustrate variables relevant for describing crater, projectile, and ejecta. The variables [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: We illustrate how rotation affects the ejecta velocity as seen in an inertial frame. Black arrows show rotation, Brown shows ejecta particle velocity in the frame rotating with the surface at an angle from normal of about 45◦ . To transfer into the inertial frame, we a…

**Figure 5.** Figure 5: We plot the transition between strength and gravity regime, [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: We show a polar plot of an impact with projectile density [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: We show a polar plot of the ejecta distributions as a function of ejection position for an impact with impact parameter [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

**Figure 8.** Figure 8: Mass loss ratio and angular momentum transfer e [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 9.** Figure 9: We plot a histogram of the angular momentum transfer e [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]

**Figure 11.** Figure 11: Angular Momentum Transfer Efficiency and Mass Loss Ratio for a planetesimal and projectile with fiducial values shown in [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]

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