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The influence of interior structure and thermal state on impact melt generation upon large impacts onto terrestrial planets

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Melt efficiency peaks when melting depth equals lithosphere thickness.

desk verdict A systematic, internally consistent simulation study that gives planetary scientists a practical empirical scaling law for impact melt volume, with the main caveat that the law's absolute calibration leans on unvalidated latent-heat compensation. read the letter →

arxiv 2506.18718 v1 pith:MYUINVGU submitted 2025-06-23 astro-ph.EP physics.geo-ph

Lukas Manske , Thomas Ruedas , Ana-Catalina Plesa , Philipp Baumeister , Nicola Tosi , Natalia Artemieva , Kai Wünnemann This is my paper · ORCID
classification astro-ph.EPphysics.geo-ph
keywords impactmeltingefficiencythermalevolutionlithospherethicknessdecompressionplasticworkempiricalscalinglawterrestrialplanets
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish a rule for how much melt a large planetary impact produces, given only the target planet's size, core fraction, and thermal age. By combining thermal-evolution models with more than 200 two-dimensional impact simulations, it finds that melting efficiency — melt volume divided by impactor volume — is controlled mainly by the ratio of the impact's melting depth to the planet's lithosphere thickness, with a peak when those two lengths are comparable. It packages this into an empirical law (Eqs. 16–21) that predicts melting efficiency for planets whose interior reaches the solidus. If the law holds, melt volumes for basin-forming impacts on stagnant-lid planets—rocky planets with one rigid surface shell—can be estimated from radial structure and thermal age without running full impact simulations.

What carries the argument

The carrying machinery is the pair of normalized length scales $d'_m = d_m/d_L$ and $d'_T = d_T/d_L$, where $d_m$ is the depth below the impact point where shock melt is most abundant (set by impactor size), $d_L$ is the lithosphere thickness, and $d_T$ is the center of the supersolidus depth range — the depth interval where the geotherm is at or above the solidus. The empirical law combines a hyperbolic-tangent baseline that interpolates between a cold crustal melting efficiency $\pi^c_m \approx 10.1$ and a cold mantle melting efficiency $\pi^m_m \approx 5.81$ with a Gaussian peak term; the peak position $d'_0$, amplitude $A$, and width $c$ are linear functions of $d'_T$ (Eqs. 19–21). These two ratios collapse melting-efficiency data from planets with radii 0.1–1.5 $R_E$, core size ratios 0.2–0.8, and ages 1–4.5 Gyr onto a single family of curves.

What would settle it

Run the same impact scenarios with a thermodynamic model that includes the energy absorbed by melting explicitly and no ad hoc cutoffs; if the resulting melting efficiencies differ from the compensated values by more than the scatter around Eqs. 16–21, the empirical law's amplitudes need recalibration.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that the normalized melt production (melting efficiency $\pi_m = V_\mathrm{melt}/V_\mathrm{impactor}$) for impacts on stagnant-lid terrestrial planets is governed by the ratio $d_m/d_L$ of the depth of melting to the lithosphere thickness, not by impactor size alone. Melting efficiency peaks when $d_m$ is roughly equal to $d_L$ or up to about three times larger, and the peak amplitude is set by the ratio $d_T/d_L$ of the supersolidus depth to lithosphere thickness. This reproduces the otherwise counterintuitive observation that larger planets are melted most efficiently by smaller impactors, while smaller planets are melted most efficiently by larger impactors, and explains why melting efficiency maxima are typically highest on Earth-size planets. The paper further claims that shock melting dominates but decompression and plastic-work melting contribute significantly (up to about 50% and 20–35%, respectively), and that classical scaling laws that account only for shock melting underestimate melt production once the impactor's length scale approaches the target's thermal structure. The empirical law of Eqs. 16–21 summarizes the result for planets with $d'_T > 1$.

Load-bearing premise

The results depend on the assumption that discarding barely melted material at the edges of the melt zone roughly cancels the overestimate caused by ignoring the energy that melting itself absorbs; if that cancellation is wrong, every reported melting efficiency and every fitted peak amplitude is off in absolute terms.

Editorial extensions

If this is right

  • For basin-forming impacts on stagnant-lid planets, melt volume can be estimated from a planet's radial thermal structure and thermal age alone, using Eqs. 16–21, without a new full impact simulation.
  • Each planet size has a specific impactor-size window, corresponding to a melting depth of roughly 1–3 lithosphere thicknesses, in which craters are especially prone to melt overflow because melting efficiency is maximal there.
  • Older, cooler planets produce substantially less impact melt: about 40% less for large planets and 60% less for small planets between 1 and 4.5 Gyr after formation.
  • Large cores reduce melting efficiency only on old planets, through more efficient cooling of the mantle, rather than through any direct mechanical effect of the core itself.
  • Under a lunar-like impactor flux, Moon-sized planets accumulate the most melt relative to their volume over 4.5 Gyr, despite also cooling efficiently.

Reading between the lines

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

  • Testable extension: if Eqs. 16–21 survive testing with codes that include latent heat explicitly, they offer a fast way to estimate impact melt production for stagnant-lid exoplanets from interior-structure retrieval, and to bracket magma-ocean generation during accretion.
  • The ratio framework suggests that the same $d'_m$ curve might hold for targets with thin or mobile lithospheres, such as early Mars or resurfaced Venus-like planets, if the mechanical boundary-layer thickness is substituted for $d_L$; this is not tested in the paper.
  • Because the empirical law was fit only for $d'_T > 1$, applying it to cold, conductive bodies like the smallest modeled planets is an extrapolation, and extending the fit to $d'_T \le 1$ would require additional simulations.
  • The flux projection probably underestimates early melt production because thermal profiles younger than 1 Gyr were not modeled; including post-accretion profiles could raise the cumulative melt estimate for Moon-sized planets.
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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

3 major / 5 minor

Summary. The paper investigates impact-induced melt production on generic terrestrial planets by combining 1D parameterized thermal evolution models with 2D iSALE hydrocode impact simulations. It spans planet radii 0.1–1.5 R_Earth, core-to-planet radius ratios 0.2–0.8, thermal ages 1, 3, and 4.5 Gyr, and impactor diameters 1–1000 km (more than 200 runs). The central quantity is the melting efficiency π_m = V_melt/V_impactor, and the authors show that peaks in π_m occur when the depth of melting d_m is comparable to the lithospheric thickness d_L (d_m/d_L ≈ 1 to 3), that larger planets are most efficiently melted by smaller impactors while smaller planets favor larger impactors, and that core size has little effect except for old, large-core cases. They propose an empirical scaling law (Eqs. 16–21) expressing π_m as a function of d'_m = d_m/d_L and d'_T = d_T/d_L, and they use a lunar impactor flux to estimate cumulative melt production over 4.5 Gyr, concluding that Moon-sized planets produce the most melt relative to their volume. The paper also compares its results with classical homogeneous-target scaling laws and argues that those laws underestimate melt production when target thermal structure and pressure gradients are important.

Significance. If the qualitative trends survive scrutiny, this is a substantial advance: it extends impact melt scaling from homogeneous targets to thermally and structurally layered stagnant-lid planets, systematically includes decompression and plastic-work melting alongside shock melting, and provides a compact parameterization that could be applied without new hydrocode runs. The study is unusually comprehensive in its parameter coverage, the qualitative regime separation (crust melting, peak-efficiency, and deep mantle regimes) is physically plausible and internally consistent, and the authors have published replication data, which strengthens reproducibility. The main significance risk is that the quantitative, absolute calibration of the empirical law and the cumulative melt volumes inherits an unquantified systematic bias from the melt diagnostic and from fitting the law to the same simulation suite, so the predictive power beyond the calibrated cases is not yet demonstrated.

major comments (3)
  1. [Section 2.3, Eq. (8) and following truncations] The melt diagnostic neglects latent heat because of ANEOS limitations, and the three ad hoc truncations (melt domain cut at 5L, 25 K below the solidus, and discard of melt fractions below 2%) are not calibrated. The manuscript states that melt volumes are 'likely an overestimate' and that the truncations 'should help to compensate for it to some extent,' but no test against an energy-conserving melt estimate is provided. Because every π_m value entering the empirical law (Eqs. 16–21) and the cumulative melt volumes in Fig. 10 inherit this bias, this is a load-bearing uncertainty for the paper's quantitative claims. I request either an explicit calibration of the truncations against at least a subset of runs with a latent-heat-corrected melt calculation, or a clear error budget that propagates a plausible range of latent-heat corrections through the fitted amplitude A in Eq. (20).
  2. [Eqs. (16)–(21), Fig. 9] The 'predictive' empirical law is a least-squares fit to the same simulation data it is compared with in Fig. 9, so the agreement in that figure is by construction. The paper is transparent that the formulas are empirical, but the abstract and Section 4.1 present them as 'predict[ing] melt generation as a function of radial structure and thermal age.' Please rephrase the claim as an interpolation/parameterization of the explored parameter space, and ideally validate the law on withheld cases (e.g., a subset of runs not used in the fit) or on independent data such as basin melt volumes on Mars or the Moon. At minimum, provide the fit uncertainties on Eqs. (19)–(21) so users can judge extrapolation risks.
  3. [Appendix A and Fig. 10] The velocity scaling exponent b = 0.986 is calibrated on data from a single Mars-like target structure (Manske et al. 2021) over only three impact velocities (10, 15, 20 km/s), but it is applied to all planet sizes, thermal ages, core ratios, and scaled up to 23.85 km/s in the cumulative melt production estimates of Fig. 10. The manuscript acknowledges that the scaling 'may be strongly dependent on the impact and target conditions,' but does not quantify the resulting uncertainty. Please add a sensitivity test that uses alternative scaling exponents (e.g., the value from Pierazzo et al. 1997 or a range bracketing the fitted slope) and show how the accumulated melt volumes and the conclusion about Moon-sized planets change.
minor comments (5)
  1. [Section 3.2.1] The text near the discussion of shock melting says 'shock melting, which is the dominant melting mechanism at vi≥15 km/s'; the symbol 'vi' should be 'v_imp' for consistency with the rest of the paper.
  2. [Section 2.3] The description of the melt-domain truncation is ambiguous: 'truncated the entire melt domain at a fixed radius of 5 impactor diameters L around the depth of one impactor diameter' could be read as centered at depth z = L or as a cylindrical/spherical cut; please state the exact centroid and geometry used.
  3. [Section 4.1] When the thermal profile does not intersect the solidus, d_T is set equal to d_L, which gives d'_T = 1, but the empirical law is restricted to d'_T > 1. Please clarify how users should handle planets with no supersolidus depth, and whether the restriction is physical or a fit-range limitation.
  4. [Figure 14 and Eqs. (19)–(21)] The fit parameters d'_0, A, and c are shown with standard deviations in Fig. 14, but the standard deviations are not propagated into the final scaling law; please state that the plotted lines are the mean regression and either include confidence bands or explicitly note their absence.
  5. [Appendix B.1, Eqs. (24)–(25)] The cubic polynomial approximations to the solidus and liquidus are used only in the thermal evolution models, while the impact models use Eq. (7); this is stated but easy to miss. Please add a sentence in the main text (Section 2.1) reiterating that the impact simulations use the Simon–Glatzel forms, not the cubics.

Circularity Check

1 steps flagged · score 6.0 of 10

The empirical π_m scaling law (Eqs. 16-21) is a least-squares fit to the same simulation data it is presented as predicting, so the Fig. 9 agreement is built in; the central new deliverable is partly a re-description of the input data.

  1. fitted input called prediction [Section 4.1 ("Melting efficiency parameterization", Eqs. 16-21) and Appendix D ("Melting efficiency scaling")]
    "We parameterize our numerically determined melting efficiencies as a function of d′m and d′T, as shown in Figure 9 as thick, dashed lines. ... The following fit may be used to estimate the melting efficiency on planets with similar structure and thermal profiles ... In our approach to parameterizing our melting efficiency data, we fit each relevant melting efficiency curve (d′T >1), consisting of multiple runs with varying impactor size ... Finally, we fitted the parameters by a linear regression as a function of d′T, resulting in the introduced scaling law."

    Eqs. 16-18 define π_m as a tanh baseline plus a Gaussian peak whose parameters d′_0, A, c are then linearly regressed on d′_T in Eqs. 19-21. Each of those parameter curves is obtained by fitting the melting-efficiency data from the same set of hydrocode runs that are shown as filled dots in Fig. 9. The agreement between the dashed fit curves and the data is therefore guaranteed by construction: the 'empirical law' is a compression of the simulation output, not an independent prediction of it. The abstract's claim that the paper proposes formulas 'to predict melt generation as a function of radial structure and thermal age' is, for this law, a re-description of the fitted simulations rather than an out-of-sample test.

full rationale

The physical content of the paper—the existence of a melting-efficiency peak near d_m ≈ d_L, the shift of that peak with planet size, and the significant contributions of decompression and plastic-work melting—is a genuine output of the hydrocode simulations and is not circular. The latent-heat neglect and the ad hoc truncations described in Section 2.3 are a calibration/correctness risk, not a circularity. The velocity-scaling slope b = 0.986 is calibrated on the authors' own earlier dataset (Manske et al. 2021), but that is a separate published dataset and the power-law form is taken from Pierazzo et al. (1997); I treat it as calibration rather than circularity. The substantial circularity is confined to the presentation of the empirical scaling law: Eqs. 16-21 are obtained by least-squares fits to the very melting-efficiency curves they are then said to predict, so the match in Fig. 9 is built in. Because this fitted law is one of the paper's central practical deliverables, the circularity is partial rather than total, and the qualitative mechanism-based conclusions remain independent.

Assumptions & free parameters 7 free parameters · 8 assumptions · 0 invented entities

The central results depend on the parameterized thermal evolution model (initial temperatures, plume fraction, chondritic heat sources), the iSALE/ANEOS impact model with the ROCK strength law, the melt reconstruction that neglects latent heat and is truncated ad hoc, the single-velocity impact ensemble scaled by a power law fitted to prior data, the lunar-flux projection, and the empirically fitted scaling law. No new physical entities are postulated; the depth of melting and supersolidus depth are diagnostic metrics, not entities.

free parameters (7)
  • Initial potential temperature T_pot = 1400 K (R_P = 0.1, 0.25 R_E); 1600 K (R_P >= 0.5 R_E)
    Chosen by hand to avoid mantle temperature exceeding the CMB temperature for small planets; controls the thermal profile and thus lithosphere thickness and melt efficiency (Section 2.1, Table 2).
  • Plume surface fraction = 0.01
    Adopted from Grott et al. (2011) for melt and crust production in the thermal evolution model; affects crustal thickness and hence the crustal melt contribution (Section 2.1).
  • Velocity scaling slope b = 0.986
    Slope of the power law lg π_m = a + b lg(v_imp^2/E_M), fitted to only three velocities (10, 15, 20 km/s) on a Mars-like target from Manske et al. (2021); applied to all planets up to 23.85 km/s and used in the lunar-flux cumulative melt calculation (Appendix A, Eq. 23, Table 4).
  • Empirical fit coefficients d'_0 = 0.2432, 0.6791
    Linear regression of the offset parameter d'_0 versus d'_T in the melting efficiency scaling law (Eq. 19); fitted to the authors' own simulation data (Section 4.1).
  • Empirical fit amplitude A = 10.5774, 15.3064
    Linear regression of the Gaussian peak amplitude A versus d'_T (Eq. 20); fitted to the authors' own simulation data (Section 4.1).
  • Empirical fit width c = 0.023, 0.5364
    Linear regression of the Gaussian width c versus d'_T (Eq. 21); fitted to the authors' own simulation data (Section 4.1).
  • Melt truncation thresholds = 5L radius, 25 K below solidus, 2% melt fraction cutoff
    Chosen by hand to compensate the overestimate from neglecting latent heat; directly sets the tracked melt volume and affects all π_m values (Section 2.3).
assumptions (8)
  • standard math The peak shock pressure method reconstructs the thermodynamic path using Rankine-Hugoniot curves and isentropic release, and this path determines melt fraction.
    Section 2.3 and Figure 1; this is the foundation of the melt quantification method.
  • domain assumption 2D vertical impacts at 90 degrees are representative of melt production; obliquity effects are only accounted for by heuristic reduction factors.
    All simulations are axisymmetric vertical impacts; Section 4.3 discusses angle effects but does not model them, so the empirical law implicitly assumes vertical impacts.
  • domain assumption A single impact velocity of 15 km/s is representative, with power-law scaling to other velocities.
    Section 4.4 and Appendix A; chosen from Chyba (1991) Earth estimate; scaling to 23.85 km/s uses b = 0.986 from Manske et al. (2021).
  • domain assumption M-ANEOS and the ROCK strength model with the listed parameters describe the dunite, basalt, and iron behavior in the impact simulations.
    The EOS and strength model control shock pressures, plastic work, and hence melt volumes; parameters in Table 3.
  • domain assumption The lunar Neukum Production Function and Holsapple-Housen scaling describe the impactor flux on all generic planets over 4.5 Gyr.
    Section 4.2; the NPF is extrapolated for D_cr > 2300 km with lg N = 5.1398 - 4.6589 lg D_cr.
  • domain assumption Stagnant-lid thermal evolution with a plume area fraction of 0.01 captures the thermal state of generic terrestrial planets.
    Thermal profiles and crustal thicknesses from the parameterized model are inputs to the impact simulations; Earth-like mobile lid is excluded (Section 2.1).
  • ad hoc to paper The melt overestimate from neglecting latent heat is adequately compensated by the adopted truncations.
    Section 2.3: 'the amount of melt is likely an overestimate, and the aforementioned truncations should help to compensate for it to some extent'. This is a stated ad hoc compensation.
  • ad hoc to paper The empirical scaling law is valid only for planets whose geotherm intersects the solidus (d'_T > 1).
    Section 4.1: 'only data have been considered where the thermal profile at some part aligns with the solidus (d'_T > 1)'; colder profiles are excluded from the fit.

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Pith. "Pith review of The influence of interior structure and thermal state on impact melt generation upon large impacts onto terrestrial planets." pith.science (2026). https://pith.science/paper/MYUINVGU

@misc{pith2026250618718,
  author       = {Pith},
  title        = {Pith review of: The influence of interior structure and thermal state on impact melt generation upon large impacts onto terrestrial planets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MYUINVGU}},
  note         = {Machine review of arXiv:2506.18718}
}
abstract

We investigate the melt production of planetary impacts as a function of planet size ($R/R_\mathrm{Earth}$=0.1-1.5), impactor size ($L$=1-1000 km), and core size ratio ($R_\mathrm{core}/R$=0.2-0.8) using a combination of parameterized convection models and fully dynamical 2D impact simulations. To this end, we introduce a new method to determine impact-induced melt volumes which we normalize by the impactor volume for better comparability. We find that this normalized melt production, or melting efficiency, is enhanced for large planets when struck by smaller impactors, while for small planets, melting efficiency is elevated when impacted by larger impactors. This diverging behavior can be explained by the thickness of the planets' thermal boundary layer and the shapes of their thermal and lithostatic pressure profiles. We also find that melting efficiency maxima are usually highest on Earth-size planets. We show that the melting efficiency is only affected by core size ratio for large cores and older planets, where melt production is decreased significantly compared to smaller core size ratios. Projecting the lunar impactor flux on the generic planets, we find that Moon-sized planets produce the most melt throughout their evolution, relative to planet volume. Contrary to previous scaling laws, our method accounts for melt production by decompression or plastic work in addition to shock melting. We find that traditional scaling laws underestimate melt production on length scales where variations in the target planets' lithology, temperature, and lithostatic pressure become significant. We propose empirical formulas to predict melt generation as a function of radial structure and thermal age.

Figures

Figures reproduced from arXiv: 2506.18718 by the authors.

Figure 1
Figure 1. Schematic illustration of the initial thermal profile and a set of Rankine–Hugoniot curves starting from [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Evolution of the thermal profiles (1–4.5 Gyr) and crust formation for the generic terrestrial planets in the upper [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Impact on a 3 Gyr-old Earth-sized planet with a small core [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Melting efficiency πm along with the contribution of the melting mechanisms µ and melt composition are plotted for different planet ages and planet sizes against the depth of melting dm for a medium-sized core (Rc = 0.5RP). The depth of the lithosphere dL and the super…
Figure 5
Figure 5. Figure 5: The fraction of different melting mechanisms [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Melting efficiency πm as a function of the depth of melting dm for different planet sizes RP for all simulations [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Melting efficiency πm as a function of the depth of melting dm for different core size ratios Rc/RP [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Comparing melting efficiency scaling laws from the literature with our data. In the upper panels, we compare [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: Melting efficiency fitted as a function of [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Accumulated melt production over a 4.5 Gyr time interval based on the lunar impactor flux. Here the [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]
Figure 11
Figure 11. Figure 11: Melting efficiency as a function of the melt number [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: Solidus and liquidus fits for the chondritic and basaltic/eclogitic compositions, and the underlying experi [PITH_FULL_IMAGE:figures/full_fig_p025_12.png]
Figure 13
Figure 13. Figure 13: Plots of xesc(g) (Eq. 30) and results for the target planets and impactors of this paper, for different vimp. xesc is the maximum distance from the point of impact at which the vertical component of the velocity of the ejecta surpasses the target’s escape velocity, no…
Figure 14
Figure 14. Figure 14: Individual scalings of the melting efficiency curves (A) and scaling parameters (B, C and D) used to [PITH_FULL_IMAGE:figures/full_fig_p032_14.png]

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Pith tools

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