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A 3D thermophysical model for binary asteroid systems: Application to the BYORP effect on (175706) 1996 FG3

T0 review · 2 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read For the binary asteroid 1996 FG3, eclipses alter the BYORP coefficient B by about 7 percent, lowering the radiation torque on the secondary and changing its predicted orbital contraction.

desk verdict A credible first step toward including eclipses and thermal inertia in BYORP calculations, but the headline 7% number is computed at perihelion only and is not yet established as the secular effect. read the letter →

arxiv 2508.18568 v1 pith:KJ7MEQ4V submitted 2025-08-26 astro-ph.EP

Kya C. Sorli , Paul O. Hayne , Rachel H. Cueva , Chloe J. Long , Jay W. McMahon , Daniel J. Scheeres This is my paper · ORCID
classification astro-ph.EP
keywords binaryasteroidsBYORPeffectthermophysicalmodelthermalinertiaeclipsesmutualradiation1996FG3YORP
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 develops a 3D thermophysical model for binary asteroid systems that combines heat conduction, insolation, visible-light reflection, ray-traced shadows and eclipses, and mutual infrared radiation between the two bodies, and applies it to the binary (175706) 1996 FG3. The authors aim to show that thermal effects that standard BYORP theory ignores, chiefly eclipses but also thermal inertia and mutual radiation, change the BYORP coefficient B in measurable ways. For 1996 FG3 they find eclipses alter B by about 7 percent, lowering the radiation torque on the secondary, while thermal inertia adds a smaller correction and mutual radiation a still smaller one. The point of the claim is that binary evolution models should include these thermal corrections, and that the coming wave of spacecraft infrared data on binaries will need such a model to be interpreted.

What carries the argument

The central machinery is the Binary Thermophysical Model: a 1D heat-conduction solver coupled to a 3D ray tracer and view-factor calculator that tracks insolation, self-shadowing, eclipses, and mutual visible and infrared scattering between the two asteroid meshes. The load-bearing quantity is the BYORP coefficient B, defined as the normalized zeroth-order Fourier coefficient of the solar-radiation-pressure force parallel to the secondary’s orbital motion, computed by integrating the along-track force over one mutual orbit and dividing by the solar pressure and the secondary’s volume-equivalent radius squared. Eclipses enter through ray-traced shadows, thermal inertia through the subsurface conduction equation, and mutual radiation through single-scatter view factors using the M2 method. The model is validated against analytical crater temperatures and against Bennu thermophysical results before being applied to 1996 FG3 under the assumption of a circular, zero-inclination mutual orbit.

What would settle it

Measure the semimajor-axis drift of 1996 FG3's mutual orbit precisely enough to separate BYORP from tidal forces, or observe the eclipse-induced temperature dips on the secondary with spacecraft infrared data; if the drift or temperature pattern matches the standard no-eclipse theory rather than the BTM prediction, the claimed 7 percent reduction in B is wrong. A shorter test: recompute B with the mutual orbit's true eccentricity and inclination once they are measured; if the approximately 7 percent eclipse signature disappears, the result is an artifact of the assumed geometry.

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Extended reading notes

Core claim

On its own terms, the paper claims that the Binary Thermophysical Model (BTM) reproduces the analytical BYORP coefficient B to better than 0.01 percent when thermal effects are switched off, and that turning them on changes B in a systematic way. For 1996 FG3 at perihelion, including eclipses makes B about 7 percent less negative, meaning less torque on the secondary, by cooling facets on the leading and trailing sides whose thermal emission contributes to the along-track force. Thermal inertia produces a small non-monotonic correction: it first increases torque by introducing a phase lag, then decreases it by damping diurnal temperature amplitudes, with a tipping point between 160 and 320 tiu. Mutual radiation from the primary changes B by roughly 0.2 percent, an order of magnitude smaller. Over 10,000 years and in the absence of tides, the eclipse-induced reduction in B would shrink the semimajor axis by about 20 meters less than the standard theory predicts.

Load-bearing premise

The model assumes a circular mutual orbit with zero inclination, and the eclipse geometry that drives the 7 percent shift in B depends directly on that assumption, while the real eccentricity is only bounded at e≤0.07 and the inclination is unconstrained.

Editorial extensions

If this is right

  • BYORP coefficients computed from shape models alone will overestimate the radiation torque for eclipsing binaries by up to several percent.
  • Binary evolution models that ignore thermal inertia miss a small but nonzero torque that changes sign with thermal inertia, so the effect cannot be absorbed into a single B value.
  • Mutual radiation can safely be neglected for most binaries, but not for close, low-thermal-inertia systems where it patches a few percent of temperature and a fraction of a percent of B.
  • Spacecraft infrared observations of binaries can be interpreted with the BTM to constrain thermal inertia and regolith properties, not just shape.
  • The eclipse-driven reduction of B weakens the BYORP contraction of the mutual orbit, which shifts the inferred balance of tides and BYORP in tidal-BYORP equilibrium systems like 1996 FG3.

Reading between the lines

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

  • For binaries with larger secondaries or tighter separations than 1996 FG3, the eclipse-induced shift in B could be substantially larger than 7 percent, making thermal corrections mandatory rather than optional.
  • The non-monotonic dependence of B on thermal inertia suggests a testable prediction: a binary with very low thermal inertia should show a smaller eclipse-driven torque reduction than one with moderate inertia, a difference that spacecraft infrared light curves could detect.
  • The same ray-tracing machinery could be applied to single rubble-pile asteroids with strong topography, where self-shadowing plays the role of eclipses, to check whether YORP coefficients likewise shift with thermal inertia.
  • Because the secondary’s synchronously locked face is eclipsed every orbit, the model implies a persistent day-night asymmetry on that hemisphere, which may affect regolith mobility and observable photometric behavior.
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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

2 major / 6 minor

Summary. The paper presents a new 3D thermophysical model ("BTM") for binary asteroid systems, coupling 1D heat conduction with 3D ray tracing to include self-shadowing, eclipses, visible-light reflection, and mutual infrared radiation between the two bodies. The model is validated against analytical bowl-crater temperature solutions, against global temperature maps of Bennu (within about 1 K for the maximum), and against the analytical BYORP coefficient of McMahon and Scheeres (to better than 0.01%). Applying the model to the binary near-Earth asteroid (175706) 1996 FG3 at perihelion, the authors find surface temperatures of roughly 100 to 475 K, find that eclipses and thermal inertia can alter secondary surface temperatures by up to 14%, and find that mutual radiation is a small effect. Using a new force-integration method, they compute the BYORP coefficient B for different thermal inertias, with and without eclipses and mutual radiation. They report that eclipses change B by about 7% (making it less negative, i.e., lower torque), that thermal inertia alone changes B by up to about 0.2%, that the combination of eclipses and thermal inertia at Gamma = 160 tiu gives a change of about 6.3%, and that mutual radiation changes B by about 0.2%. They estimate that, absent tidal effects, the eclipse-induced change would reduce the semimajor-axis contraction by about 20 m over 10,000 years.

Significance. If the reported corrections are robust, this is the first quantitative treatment of second-order thermal effects on the BYORP coefficient for a real binary system, with direct relevance to interpreting measured orbital drift rates (e.g., the Scheirich et al. 2015 value for 1996 FG3) and to planning binary evolution models. The paper's strengths are the multiple validation benchmarks (analytical crater solution, Bennu temperatures within 1 K, and the analytical BYORP limit to 0.01%), the physical transparency of the model, and the fact that the new effects are genuine predictions based on stated physical parameters rather than fitted values. The BYORP comparison is a self-consistency check with the same theoretical framework (McMahon and Scheeres, two coauthors) rather than an independent validation of the new eclipse and thermal-inertia terms, but the temperature validation against Bennu provides independent support for the core thermal model.

major comments (2)
  1. [§2.4, Eq. (7); §4, Eqs. (10)-(11)] The BYORP coefficient B used in the secular evolution estimates is computed from a single model run at perihelion (Section 2.4: 'Each BTM run returns ... the BYORP coefficient B, measured at perihelion'). In the zero-thermal-inertia limit the ratio F_y/P(R) in Eq. (7) is independent of heliocentric distance because emission is instantaneous and proportional to insolation, but for Gamma > 0 the sigma*epsilon*T^4 term in Eq. (6) carries memory of prior insolation, so F_y/P(R) can depend on R. Given the system's heliocentric eccentricity e = 0.3497 (insolation at aphelion is about 25% of that at perihelion), the perihelion-only 7% value is not automatically the secular B used in Eqs. (10)-(11). The paper's own caveat in Section 2.4 ('if the magnitude of BYORP is sensitive to thermophysical properties, we expect it to be most pronounced near perihelion') confirms the issue. Please compute B at multiple heliocentric distances and average over the heliocentric orbit, or demonstrate quantitatively that B varies by less than the claimed precision.
  2. [§2.4] The model assumes a circular mutual orbit with zero inclination, although the observational bound is e <= 0.07 and the inclination is unconstrained. Eclipse duration, depth, and phase, which drive the dominant reported 7% change, depend directly on the assumed geometry. To make the 'approximately 7%' claim about 1996 FG3 rather than about the assumed geometry, the paper should include sensitivity runs over e in [0, 0.07] and over a plausible range of mutual inclinations. In addition, Table 1 notes that pole positions are given in ecliptic coordinates, but no pole values appear in the table or text; without the primary's pole orientation relative to the heliocentric orbit, the Sun's elevation above the mutual orbit plane, and hence the eclipse pattern, is not reproducible.
minor comments (6)
  1. [§3.3, paragraph on Figure 7] The sentence 'Holding the thermal inertia steady at 0 tiu and not including eclipses, the BYORP coefficient is altered by approximately 7%' appears to be a typo; it should read 'including eclipses' (or 'with eclipses enabled'), since the same paragraph attributes the 7% change to the inclusion of eclipses.
  2. [Abstract and §5] The 'approximately 7%' eclipse change is computed at perihelion and for zero thermal inertia; please state these conditions in the abstract and conclusions so that readers do not take it as the secular value for the realistic thermal inertia (the paper reports about 6.3% for eclipse plus thermal inertia at Gamma = 160 tiu).
  3. [Table 1] The word 'Assummed' should be 'Assumed'; in addition, the table's note that 'Pole positions are given in ecliptic coordinates' is not supported by any pole values in the table, so either add the pole coordinates or remove the note.
  4. [§2.1.2 and §3.1] Two wording errors: 'shape models derived from from Earth-based radar data' has a duplicated 'from', and 'This causes a an irregular drop' has a doubled article.
  5. [Figure 7 and Table 2] The reported B values and temperature metrics lack uncertainty or numerical precision estimates; given the authors' own sphere test showing numerical B errors at the ~10^-5 level (Section 4), a statement of the numerical precision of the quoted percent changes would help the reader judge their significance.
  6. [Eq. (7)] The normalization constant and the meaning of the integral (why dividing by 2*pi*R_RES^2 yields the A0(2) coefficient) could be explained in one sentence or with a specific reference to the McMahon-Scheeres definition, to make the paper more self-contained.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the BTM's thermal corrections are genuine model outputs, not fitted parameters or imports from the authors' own theory.

full rationale

The paper's central derivation is the Binary Thermophysical Model: it solves the 1D heat diffusion equation (Eq. 1) with a surface energy balance, ray-traced insolation, view factors, eclipses, and mutual radiation, and then computes the BYORP coefficient B from the simulated facet forces via Eq. 7. No parameter is fitted to the target quantity B: thermal inertias are varied over a range chosen from the literature, and albedo, emissivity, shape, and orbital parameters are taken from published observations or stated assumptions. The validation step reproduces the analytical BYORP theory of McMahon and Scheeres (2010b) in the limiting case of zero thermal inertia, no eclipses, and no mutual radiation, matching Bo to better than 0.01%. Although two coauthors are authors of that theory, the theory is an independently derived analytical benchmark whose assumptions explicitly exclude the effects under study; using it as a numerical consistency check does not make the new eclipse, thermal-inertia, or mutual-radiation corrections equivalent to the theory's inputs. The headline 7% eclipse effect is obtained by toggling eclipses on and off in otherwise identical model runs, not by fitting or by renaming a prior result. The perihelion-only evaluation is a scientific caveat about secular averaging, not a circularity. The paper is therefore self-contained against its benchmark and the new claims have independent content, so the circularity score is 0.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central BYORP calculation rests on adopted thermophysical parameters (thermal inertia, Bond albedo, emissivity), the circular zero-inclination orbit assumption, and several standard domain assumptions (1D conduction, Lambertian scattering, single scattering, no absorption torque). No new physical entities are introduced.

free parameters (4)
  • Thermal inertia Gamma = 0, 40, 80, 160, 320, 700, 2500 tiu
    Literature estimates for 1996 FG3 are 80 +/- 40 and 120 +/- 70 tiu; the paper sweeps a range, and B responds non-monotonically to Gamma. The secondary value is especially unconstrained.
  • Bond albedo A_B = 0.011
    Derived from geometric albedo 0.044 using an assumed phase integral of 0.25; enters the reflected-light force term in Eq. 6.
  • Emissivity epsilon = 0.95
    Assumed in Table 1; enters the thermal emission force sigma * epsilon * T^4 in Eq. 6 and the surface energy balance.
  • Mutual orbit eccentricity and inclination = e = 0, i = 0
    Assumed for simplicity; inclination is unconstrained and eccentricity upper limit is 0.07. This sets the eclipse geometry that drives the 7 percent B shift.
assumptions (6)
  • domain assumption 1D heat conduction is sufficient for modeled facets
    Section 2.1.1 argues 3D conduction can be neglected when topography is larger than the thermal skin depth, which the paper estimates at 1-4 cm.
  • domain assumption Lambertian diffuse reflection and emission with tangential forces canceling
    Section 2.3, Eq. 6: the force is normal to the surface with a 2/3 Lambertian factor; no specular component is included.
  • domain assumption Single scattering suffices for view factors
    Section 2.1.2 notes that with Bond albedo 0.011, double-scatter contributions are below 0.1 percent of incident insolation.
  • domain assumption Absorption of radiation has no secular effect on BYORP
    Section 2.3 cites Rubincam and Paddack (2010) to exclude absorbed photons from the force model.
  • domain assumption Zeroth-order BYORP coefficient is independent of heliocentric distance
    B is evaluated at perihelion and used in secular evolution estimates; Section 2.4 and 3.3 acknowledge this but do not test it.
  • ad hoc to paper Circular, zero-inclination mutual orbit
    Section 2.4 assumption; inclination is unconstrained and e <= 0.07. The eclipse calculation, and thus the largest correction, depends on this geometry.

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Cite this review

Pith. "Pith review of A 3D thermophysical model for binary asteroid systems: Application to the BYORP effect on (175706) 1996 FG3." pith.science (2026). https://pith.science/paper/KJ7MEQ4V

@misc{pith2026250818568,
  author       = {Pith},
  title        = {Pith review of: A 3D thermophysical model for binary asteroid systems: Application to the BYORP effect on (175706) 1996 FG3},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KJ7MEQ4V}},
  note         = {Machine review of arXiv:2508.18568}
}
read the original abstract

Differential heating and radiation on asymmetric asteroids can cause measurable changes in their rotation rates and spin axes, known as the YORP effect. In binary systems, such radiation-driven torques can change the mutual asteroid orbits, termed the binary YORP or BYORP effect. To study how binary asteroid shapes and thermophysical properties affect surface temperatures and BYORP, we developed a new 3D thermophysical model which balances insolation, 1D conduction, visible light reflection, and mutual heating through scattered infrared radiation. Using 3D ray tracing, we include eclipses, shadowing from horizons and topography, and mutual radiation exchange between the primary and secondary asteroids. We perform global modeling of the binary asteroid (175706) 1996 FG3, a Janus mission target. At perihelion, we find that the 1996 FG3 system experiences temperatures between 100 and 475 K. We find that eclipses and thermal inertia can alter secondary surface temperatures by up to 14%, with a mean difference due to radiation from the primary of just over 1%. We also present a model for calculating the BYORP effect using binary thermophysical model results. This model compares well to analytical approximations of the BYORP coefficient B, and suggests that thermal effects like eclipses and thermal inertia can reduce torque in the 1996 FG3 system and alter the BYORP coefficient by up to several percent. For 1996 FG3, eclipses alter B by approximately 7%, resulting in a lower torque on the secondary. Though small, in the absence of tidal effects this would reduce the contraction of the semimajor axis by about 20 meters over 10,000 years. Our findings suggest that thermal effects can alter temperatures and BYORP calculations sufficiently that they should be included when modeling binaries. The relative importance of each effect is predicted to vary with the properties of the studied system.

Figures

Figures reproduced from arXiv: 2508.18568 by the authors.

Figure 1
Figure 1. Binary thermophysical schematic, demonstrating flux exchange between both bodies, incoming solar radiation and re-radiated heat. Light can also be scattered between parts on the same body due to local topography. from the primary for certain systems, especially for low-inclination binaries. They also find the binary Yarkovsky effect can be a powerful mechanism for synchronizing secondaries in a prograde orbit, or ma… view at source ↗
Figure 2
Figure 2. Maximum facet temperatures (panels a, b), and diurnal amplitudes (panels c, d) for the northern and southern hemispheres of Bennu using the BTM. Lambertian reflectance factor is 2/3. Ai is the area of the facet. The first term describes the recoil force from reflecting flux, given by the bond albedo times the intensity incident on the facet, or Qref = ABQinsolation. This includes both insolation and scattered light … view at source ↗
Figure 3
Figure 3. Surface temperature maps for a selection of model runs with varying surface thermal inertias. From left to right, each row shows the progression of the secondary about the primary, first in a state with no eclipses (leftmost column), an eclipse of the primary by the secondary (center column) and a total eclipse of the secondary (rightmost column). The top panel, labeled (a), shows modeled temperatures for the case u… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Diurnal temperature curves for a single facet that experiences eclipsing on (a) the primary and (b) the secondary. Each shows a thermal inertias of Γ = 40, 160 and 320 tiu, encompassing a range of estimated values for 1996 FG3 (see [PITH_FULL_IMAGE:figures/full_fig_p0…
Figure 5
Figure 5. Figure 5: The maximum percent change in temperature caused by mutual radiation for each facet on the primary (a) and the secondary (b). Results shown on both bodies use a thermal inertia value of Γ = 160 tiu. Note that the scale bars for each body are different, as the primary e…
Figure 6
Figure 6. Figure 6: The force experienced by the secondary parallel to the direction of movement in the secondary fixed frame, or the y component of the force Fy for three model runs. The vertical axis is the force acting on the body in Newtons, and the horizontal axis is the time over wh…
Figure 7
Figure 7. Figure 7: BYORP B coefficients for various model runs plotted against the theoretical validation value Bo (shown with the solid line). The validation case uses no thermal inertia, no eclipses and no mutual radiation. Above the validation line indicates a smaller B, or smaller to…
Figure 8
Figure 8. Figure 8: BYORP B Coefficients for a spherical secondary. The data points shown do not include eclipses. The three colors denote different resolutions of spherical shape model. Note that the B values are over two orders of magnitude smaller than the normal BTM runs. The axis on …

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Reviewed August 15, 2026 · model on record in the stance chip above.