Positive YORP effect induced by lateral heat conduction in a crater

(2) Macau University of Science; (3) Shanghai Aerospace Control Technology Institute); Hailiang Li (2); Li-Yong Zhou (1) ((1) Nanjing University; Technology; Yangbo Xu (3); Yining Zhang (1); Zehua Qi (1)

arxiv: 2604.08699 · v1 · submitted 2026-04-09 · 🌌 astro-ph.EP

Positive YORP effect induced by lateral heat conduction in a crater

Zehua Qi (1) , Yining Zhang (1) , Hailiang Li (2) , Yangbo Xu (3) , Li-Yong Zhou (1) ((1) Nanjing University , (2) Macau University of Science , Technology , (3) Shanghai Aerospace Control Technology Institute) This is my paper

Pith reviewed 2026-05-10 16:58 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords YORP effectasteroid craterslateral heat conductionspin torqueobliquitythermal modelingasteroid rotation

0 comments

The pith

Lateral heat conduction around a crater on an asteroid generates a consistently positive YORP torque.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper investigates the YORP torque produced by a circular crater on a spherical asteroid, focusing on how lateral heat conduction breaks thermal symmetry. Three-dimensional finite element simulations show that this internal conduction creates a net positive spin torque while shadowing and self-heating remain negligible. The torque stays positive at all crater latitudes and reaches 10 to 100 percent of the conventional YORP torque for small craters. It also steers the spin axis toward obliquity equilibria at 0, 90 or 180 degrees. The persistent positivity supplies one mechanism that could account for the observed tendency of asteroids to accelerate their rotation.

Core claim

The crater-induced spin torque is consistently positive because lateral heat conduction inside the asteroid occurs only in the three-dimensional model and produces an asymmetric temperature field that yields a net torque; shadowing and self-heating contribute negligibly, while the effect for small craters amounts to 10-100 percent of normal YORP torque and drives the obliquity toward equilibria at 0, 90 or 180 degrees.

What carries the argument

Three-dimensional finite-element simulation of temperature distribution and thermal emission around a single circular crater, where lateral conduction breaks symmetry to produce net torque.

If this is right

The crater torque remains positive at every latitude and depth examined.
Obliquity is driven toward stable points at 0, 90 or 180 degrees.
For small craters the torque reaches 10 to 100 percent of the usual YORP magnitude.
The mechanism is produced by internal conduction and persists when surface shadowing is ignored.
The positive bias may contribute to the statistical prevalence of accelerating asteroid spins.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If craters are widespread, their collective conduction torques could systematically shift the spin-period distribution of small bodies.
Similar lateral-conduction effects may arise from other irregular surface topography and could be tested by comparing spin states of cratered versus smooth asteroids of comparable size.
On bodies where YORP already dominates, adding this always-positive component would narrow the range of possible long-term spin outcomes.

Load-bearing premise

The asteroid is a perfect sphere containing only one circular crater and lateral internal conduction dominates the torque while self-heating and shadowing are negligible.

What would settle it

A simulation or observation in which the crater torque reverses sign with changing latitude, depth, or thermal parameters, or in which asteroids with many craters show no excess of positive spin acceleration.

Figures

Figures reproduced from arXiv: 2604.08699 by (2) Macau University of Science, (3) Shanghai Aerospace Control Technology Institute), Hailiang Li (2), Li-Yong Zhou (1) ((1) Nanjing University, Technology, Yangbo Xu (3), Yining Zhang (1), Zehua Qi (1).

**Figure 1.** Figure 1: Temperature variations along a radius on the equatorial plane at sunset. Two thermal conductivities κ = 0.001 and 0.01 (given in W m−1 K −1 ) are adopted. The depth is measured downward from the surface. The solid and dashed lines denote the depths, from which the temperature variation with respect to the next layer of mesh is less than 0.1% for κ = 0.001 and 0.01, respectively. show in [PITH_FULL_IMAGE:f… view at source ↗

**Figure 2.** Figure 2: Mesh model for the crater. The interior is composed of tetrahedrons, wrapped by a layer of triangular prisms near the surface. and mass of the crater is very small (the ratio between them is ∼10−4 ), therefore we simply assume that the changes in the moment of inertia and in the principal axis caused by the crater are both ignorable. Using COMSOL, we simulate the thermal evolution in the asteroid with a … view at source ↗

**Figure 3.** Figure 3: YORP accelerations (dω/dt in left panel and dε/dt in right panel) of the asteroid due to the crater as a function of obliquity ε. The cases of crater at ten different latitudes from ϕ = 0 ◦ to ϕ = 90◦ are plotted in different colours, as indicated by the colour bar. ubov et al. (2014) named the torque generated by the same terrain without boulders as normal YORP (NYORP). The dimensionless normalized spin… view at source ↗

**Figure 4.** Figure 4: illustrates that the spin acceleration dω/dt and the obliquity change rate dε/dt both exhibit a positive correlation with the depth q. Specifically, increasing q from 0.1 to 0.5 results in a significant enhancement of approximately one order of magnitude for both of them. A bigger q value indicates a deeper crater that has a relatively steeper wall. And the same amount of irradiation energy absorbed and t… view at source ↗

**Figure 4.** Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: Spin YORP acceleration produced by a crater on equator as a function of rotation period P. Other model parameters are as in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 8.** Figure 8: Spin YORP torques produced by the western (yellow) and eastern (blue) halves of the crater. The total torque (the summation of both halves) is also plotted in red. The solid and dashed lines are for thermal conductivity κ = 0.001 and 0.01 W m−1 K −1 , respectively. a distinctive ‘tail’ in the net positive spin torque (red lines) after sunset (phase 3π/2), which constitutes the primary contribution to the … view at source ↗

read the original abstract

The YORP effect plays an important role in the spin evolution of asteroids. Although craters are ubiquitous surface features, their influence on YORP torque has received limited attention. In this paper, we investigate the YORP torque of a circular crater on a spherical asteroid, focusing specifically on how lateral thermal conduction breaks symmetry to produce a net torque. Using three-dimensional finite element simulations, we calculate the resulting spin and obliquity accelerations and examine their dependence on the crater's location, depth, and thermal parameters. Our results show that the crater-induced spin torque is consistently positive, and craters at different latitudes drive the spin axis toward obliquity equilibria at 0, 90 or 180 degree. We demonstrate that the spin torque arises primarily from the lateral heat conduction inside the asteroid that occurs only in 3D model, while the contributions from self-heating and shadowing effects are negligible. While the YORP effect induced by internal heat conduction may be overtaken by torque components arising from shadowing and crater orientation, particularly on large asteroids, our numerical results show that for small craters, this spin torque amounts to approximately 10 to 100 percent of the normal YORP torque. Its persistent positivity may help explain the observed prevalence of positive spin accelerations in asteroids.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Lateral conduction in 3D crater models gives a consistently positive YORP torque that simpler treatments miss, but the numerics lack convergence checks.

read the letter

The key takeaway is that lateral heat conduction inside a crater on an asteroid can generate a consistently positive YORP spin torque in three-dimensional models. This effect, which simpler models miss, might account for why more asteroids show positive spin accelerations than expected. The authors set up finite-element simulations of a spherical asteroid with one circular crater. They solve the heat equation in 3D and compute the torque from the resulting temperature distribution and thermal radiation. The torque comes out positive for craters at various latitudes, and it drives the spin axis toward obliquity values of 0, 90, or 180 degrees. For small craters, the magnitude reaches 10 to 100 percent of the normal YORP torque. They also test that self-heating and shadowing contribute little compared to the lateral conduction term. This is new relative to the cited literature. Prior YORP work with craters used 1D or 2D approximations that do not capture the internal lateral heat flow unique to 3D geometry. The parameter study on crater location, depth, and thermal properties is a useful addition. The simulations are the strength here. Direct numerical solution of the 3D problem lets them isolate the conduction effect without fitting to observations. The main concern is numerical validation. The abstract and stress-test note indicate no mesh-convergence tests, time-step checks, or zero-crater control runs are presented. Because the torque arises from a subtle asymmetry at the crater rim, insufficient resolution could create artificial positive bias. That weakens confidence in the exact percentages reported. The model assumptions are another limitation. A single crater on a perfect sphere is far from real asteroid surfaces, which are irregular and covered in many features. The paper acknowledges that on large asteroids other torques may dominate, but the idealized setup still restricts how far the results can be applied. This paper is for researchers in planetary science who model asteroid spin evolution and YORP effects. Anyone working on rotational disruption or long-term dynamics would find the proposed mechanism relevant. It should go to peer review. The idea is worth exploring and the 3D approach is appropriate, but referees will want to see the convergence data and perhaps tests with more complex geometries before accepting the quantitative claims.

Referee Report

1 major / 1 minor

Summary. The manuscript uses 3D finite-element thermal simulations of a spherical asteroid with a single circular crater to show that lateral heat conduction produces a consistently positive YORP spin torque (10–100% of the reference YORP torque for small craters). This torque drives the spin axis toward obliquity equilibria at 0°, 90°, or 180° depending on crater latitude, while self-heating and shadowing contributions are stated to be negligible.

Significance. If the numerical results hold, the work identifies a purely 3D conduction-driven mechanism that supplies an inherently positive torque component, offering a potential explanation for the observed prevalence of positive spin accelerations in asteroids. The approach relies on direct numerical solution of the heat equation rather than parameter fitting, which is a methodological strength.

major comments (1)

[Finite-element simulation description and results] The central claim that lateral conduction produces a robust positive torque rests on 3D FEM results, yet the manuscript provides no mesh-refinement studies, time-step convergence tests, or zero-crater control runs demonstrating that the torque vanishes to machine precision in the absence of a crater. Because the reported effect is a small 3D correction whose magnitude reaches 10–100% of the reference YORP torque, the absence of such validation leaves open the possibility that numerical diffusion or boundary-layer resolution at the crater rim artificially breaks symmetry.

minor comments (1)

[Abstract] The abstract states that self-heating and shadowing are negligible but does not quantify the relative magnitudes or show the corresponding torque components; a brief comparison table or figure would clarify this assertion.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive criticism. We address the single major comment below and will revise the manuscript to incorporate the requested numerical validations.

read point-by-point responses

Referee: The central claim that lateral conduction produces a robust positive torque rests on 3D FEM results, yet the manuscript provides no mesh-refinement studies, time-step convergence tests, or zero-crater control runs demonstrating that the torque vanishes to machine precision in the absence of a crater. Because the reported effect is a small 3D correction whose magnitude reaches 10–100% of the reference YORP torque, the absence of such validation leaves open the possibility that numerical diffusion or boundary-layer resolution at the crater rim artificially breaks symmetry.

Authors: We agree that explicit numerical validation is essential for establishing the robustness of a small 3D effect. The original manuscript did not include these tests. In the revised version we will add a new subsection under Methods (or Results) that presents: (i) mesh-refinement studies showing that the spin torque converges to within a few percent as the element size at the crater rim is reduced by successive factors of two; (ii) time-step convergence tests confirming that the integrated torque is insensitive to the chosen time step once the thermal skin depth is adequately resolved; and (iii) zero-crater control simulations performed on identical meshes and time steps, in which the net torque falls to machine precision (typically < 10^{-12} of the reference YORP torque). These controls will demonstrate that the reported positive torque is not an artifact of numerical diffusion or inadequate boundary resolution. We believe the addition will directly address the referee’s concern and strengthen the paper. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from forward 3D numerical simulation

full rationale

The paper computes crater-induced YORP torques by solving the 3D heat equation via finite-element discretization on a spherical asteroid geometry. The reported positive spin torque and obliquity equilibria are direct numerical outputs from the temperature field and resulting thermal recoil, not algebraic reductions, fitted parameters, or self-citations that define the target quantity. No self-definitional loops, ansatzes smuggled via prior work, or renaming of known results are present. The derivation is a standard forward model whose central claim (lateral conduction produces net positive torque) is independent of the inputs and can be falsified by mesh refinement or zero-crater controls.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The simulation rests on standard heat-conduction physics and a simplified asteroid geometry; no new physical constants or entities are introduced, but several modeling choices function as free parameters that are varied numerically.

free parameters (2)

crater depth and radius ratio
Crater geometry parameters are varied to examine dependence; specific values are not listed in the abstract.
thermal diffusivity and conductivity
Dependence on thermal parameters is stated but numerical values and ranges are not provided.

axioms (2)

domain assumption The asteroid is modeled as a perfect sphere containing one circular crater.
Geometry assumption stated in the model description.
standard math Heat transport obeys the three-dimensional heat equation with constant thermal properties.
Implicit in the finite-element formulation.

pith-pipeline@v0.9.0 · 5569 in / 1480 out tokens · 55970 ms · 2026-05-10T16:58:18.430096+00:00 · methodology

discussion (0)

Reference graph

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