It is now widely accepted that the breakup of comet Shoemaker–Levy 9 (SL9) was caused by tidal forces. This explanation applies to bodies that enter a planet’s Roche zone and have a loose ‘rubble pile’ structure with no internal strength. Observations from the Rosetta mission to comet 67P/Churyumov–Gerasimenko initially supported this hypothesis, as the comet’s surface strength was exceptionally low. However, beneath this loosely bound surface layer, a dense mixture of ice and rock was detected, as evidenced by deep cracks. Similar fractures on Mars yielded strength estimates of around 2 MPa. In this paper, we hypothesize the observed fragmentation pattern of comet SL9 caused by preliminary fracturing due to internal stresses. We calculate the internal thermal stresses using the analytical solution of the heat diffusion equation for bodies approaching the Sun along parabolic trajectories. The results indicate that upon reaching Jupiter’s orbit, thermal stresses develop within bodies composed of crystalline ice with radii ranging from 60 m to 5 km, exceeding the material’s tensile strength. When the tidal forces subsequently separated the fragments, they formed a chain of large bodies, with the central body corresponding to the inner core of the comet. The fragments closest to the surface were observed before and behind the central core. Therefore, the preliminary fracturing of the comet by thermal stresses, followed by the separation of resulting fragments due to tidal forces, appears quite plausible.

The termination of the slow neutron capture process (s-process) in the Pb--Bi mass region plays a key role in shaping the abundances of the heaviest stable nuclei produced in stellar environments. In this work, we revisit the classical description of the s-process termination developed by Clayton and co-authors, incorporating modern experimental neutron capture cross sections and exploring the sensitivity of the results to variations in neutron irradiation parameters. The reaction network describing the Pb--Bi--Po termination cycle is reformulated as a system of Bateman equations and solved numerically using the burn-up matrix formalism combined with the Pad\'e approximation for the matrix exponential. We investigate the influence of updated $(n,\gamma)$ cross sections for Pb and Bi isotopes, as well as variations in the shape and scale parameters of the neutron exposure distribution, on the isotopic abundances, the timescale required to reach equilibrium, and the behavior at maximum neutron exposure. Our results confirm the robustness of the quasi-stationary equilibrium condition $\sigma_A N_A = \mathrm{const}$ under modern nuclear data, while demonstrating that updated cross sections lead to a noticeable redistribution of isotopic abundances and modify the timescale for reaching the equilibrium plateau. The contribution of the s-process termination to the total abundances of Pb and Bi isotopes is further examined using different neutron exposure distributions. We find that the resulting s-process abundances are largely insensitive to the neutron capture cross section of $^{209}\mathrm{Bi}$ over the investigated range, confirming that $^{208}\mathrm{Pb}$ effectively acts as the termination point of the s-process. Among the considered exposure models, the exponential neutron exposure distribution provides the best overall description of the final s-process abundances. These results are in good agreement with observational abundance constraints and demonstrate that the main qualitative features of the classical Clayton scheme remain valid, while quantitative predictions are significantly refined by modern nuclear data and irradiation models.

We examine cyclic nuclear reactions in the lead–bismuth (Pb–Bi) system near the s-process termination point. We present a numerical investigation of the isotopic evolution and decay heat generation in an extended 60-isotope nuclear reaction network under continuous 30 keV neutron irradiation (${10}^{14}$–${10}^{28}$ n cm⁻² s⁻¹) using the Chebyshev Rational Approximation Method (CRAM). The network accounts for 88 transitions, utilising a hybrid data approach that combines neutron capture cross-sections from EAF-2010 and TALYS with fundamental decay properties from the ENDF/B-VIII.0. Our simulations reveal two distinct evolutionary regimes. At moderate fluxes (${10}^{14}$–${10}^{20}$ n cm⁻² s⁻¹), the system establishes a steady cyclic loop driven by the $\alpha$-decay of ${}^{210}\mathrm{Po}$, successfully reproducing the s-process termination isotopic distribution (${}^{208}\mathrm{Pb}{\gg }^{209}\mathrm{Bi}{>}^{207}\mathrm{Pb}{>}^{206}\mathrm{Pb}$), characteristic of low-metallicity AGB stars. As the flux exceeds ${10}^{22}$ n cm⁻² s⁻¹, the classical balance breaks down, propelling mass flow toward heavier trace isotopes and suggesting a potential transition into the intermediate neutron capture (i-process) regime. Heat density calculations demonstrate that while the energy release of the core cycle plateaus near ${10}^5$ W cm⁻³, the extended chain drives an energy surge to over ${10}^8$ W cm⁻³ at ${10}^{24}$ n cm⁻² s⁻¹ before the system enters an unstable transient state at extreme fluxes.

Thermal stresses in small bodies approaching the SunModern agglomeration models describe cometary nuclei as porous bodies with lowdensities ( 0.1 g/cm³), yet observations of comets Halley and Shoemaker–Levy 9 indi-cate significantly higher densities ( 0.6 g/cm³), suggesting a need to revise these models.Thermal stress has emerged as a plausible mechanism for fragmentation, capable of op-erating far from the Sun and without requiring tidal forces. Studies (Tauber and Kuhrt,1987; Shestakova and Tambovtseva, 1997; Tambovtseva and Shestakova, 1999; ˇCapekand Vokrouhlick´y, 2010) show that thermal stresses can exceed the tensile strength ofterrestrial materials.This mechanism is also relevant to the origin of meteorites and near-Earth ob-jects (NEOs). Research (Broˇz, M. et al., 2024) highlights the role of asteroid familieslike Karin, Koronis, and Massalia in generating NEOs and ordinary chondrites. Car-bonaceous chondrites are linked to bodies such as 3200 Phaethon, which may undergothermal disruption near the Sun.We apply both analytical and numerical solutions of the heat diffusion equationwith one initial and two boundary conditions (Shestakova and Tambovtseva, 1997).The analytical approach assumes constant thermal diffusivity and is restricted to ide-alized parabolic orbits with zero perihelion, whereas the numerical model accountsfor temperature-dependent thermal diffusivity and realistic orbital configurations withnon-zero perihelion distance.Spherical bodies made of crystalline ice, basalt, and chondrites are modeled alongparabolic orbits. Initial uniform temperatures are set at Tbb ≈ 150 K (3.45 AU) forsilicates and Tbb ≈ 30 K (86 AU) for ice, with final distances of 0.0345 AU (Tbb ≈1500 K) and 4.95 AU (Tbb ≈ 125 K), respectively. Results show rapid internal heatingfor small bodies, while larger ones retain cold interiors (see Fig. 1).Comparison with strength lines (see Fig. 2) suggests that bodies with radii of 30 mto 5 km may undergo fragmentation, even at distances from 10 AU to 40 AU.Smallerfragments (with radii less than 30 meters) are unlikely to undergo thermal destruc-tion, as they experience nearly uniform heating throughout their volume, resulting innegligible internal temperature gradients and stress accumulation. Nevertheless, suchbodies are subject to active sublimation(Shestakova and Serebryanskiy, 2023) as theyapproach the Sun. In contrast, larger nuclei (more than 1 km) retain a cooler interior and exhibit critical thermal stresses in the near-surface layers, which is consistent withthe observed onset of coma formation during solar approach. The breakup of cometShoemaker–Levy 9 was likely initiated by this mechanism, with thermal fracturingpossibly preceding the tidal disruption (Shestakova et al., 2025).According to Fig. 3, destructive internal stresses arise in basaltic, carbonaceous, andordinary chondritic bodies at heliocentric distances of approximately 2.5 AU, 2 AU,and 1 AU, respectively. These stresses affect bodies with radii not exceeding 10 meters,whose fragmentation is unlikely to produce observable dust clouds unless they passclose to Earth such as ordinary chondrites with radii around 10 m. Near Earth’sorbit, carbonaceous chondrites (40 m) and basaltic bodies (80 m) may also undergofragmentation ( ˇCapek and Vokrouhlick´y, 2010).Larger objects tend to break up closerto the Sun, initiating a cascade of fragmentation. The resulting smaller fragmentscontinue to disintegrate, forming clouds of fine dust that may reach the sublimationzone and become detectable via optical or infrared observations.Figure 1: Temperature profiles from the center (x/r = 0) to the surface (x/r = 1) insidebodies of various sizes at the final heliocentric distances of 0.0345 AU (7.42 R⊙) and 4.95 AU,for chondritic material (left) and crystalline ice (right), respectively.Figure 2: Thermal stresses at the center (x/r → 0, left) for the radial component and at thesurface (x/r = 1, right) for the tangential component, computed analytical and numerical atvarious heliocentric distances from the initial position at 86 AU to the final point at 4.95 AUfor ice bodies.Figure 3: Thermal stresses at the center (x/r → 0, left) for the radial component andat the surface (x/r = 1, right) for the tangential component, computed analytically andnumerically at various heliocentric distances from the initial position at 3.45 AU to the finalpoint at 0.0345 AU (≈ 7.42 R⊙) for chondritic and basalt bodies.ReferencesBroˇz, M., Vernazza, P., Marsset, M., Binzel, R. 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