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Constraining the formation processes of small solar system bodies is crucial for gaining insights into planetesimal formation. Their bulk densities, determined by their compressive strengths, offer valuable information about their formation history. In this paper, we utilize a formulation of the compressive strength of dust aggregates obtained from dust N -body simulations to establish the relation between the bulk density and diameter. We find that this relation can be effectively approximated by a polytrope with an index of 0.5, coupled with a formulation of the compressive strength of dust aggregates. The lowest-density trans-Neptunian objects (TNOs) and main-belt asteroids (MBAs) are well reproduced by dust aggregates composed of 0.1 μ m sized grains. However, most TNOs, MBAs, comets, and near-Earth asteroids (NEAs) exhibit higher densities, suggesting the influence of compaction mechanisms such as collision, dust grain disruption, sintering, or melting, leading to further growth. We speculate that there are two potential formation paths for small solar system bodies. One involves the direct coagulation of primordial dust grains, resulting in the formation of first-generation planetesimals, including the lowest-density TNOs, MBAs, and the parent bodies of comets and NEAs. In this case, comets and NEAs are fragments or rubble piles of first-generation planetesimals, and the objects themselves or the rubble are composed of 0.1 μ m sized grains. The other path involves the further potential fragmentation of first-generation planetesimals into the compact dust aggregates observed in protoplanetary disks, resulting in the formation of second-generation planetesimals composed of compact dust aggregates, which may contribute to explaining another formation process of comets and NEAs. [ABSTRACT FROM AUTHOR]

Observations and theory suggest that core-collapse supernovae can span a range of explosion energies, and when sub-energetic the shockwave initiating the explosion can decelerate to speeds comparable to the escape speed of the progenitor. In these cases, gravity will complicate the explosion hydrodynamics and conceivably cause the shock to stall at large radii within the progenitor star. To understand these unique properties of weak explosions, we develop a perturbative approach for modeling the propagation of an initially strong shock into a time-steady, infalling medium in the gravitational field of a compact object. This method writes the shock position and the post-shock velocity, density, and pressure as series solutions in the (time-dependent) ratio of the freefall speed to the shock speed, and predicts that the shock stalls within the progenitor if the explosion energy is below a critical value. We show that our model agrees very well with hydrodynamic simulations, and accurately predicts (for example) the time-dependent shock position and velocity and the radius at which the shock stalls. Our results have implications for black hole formation and the newly detected class of fast X-ray transients (FXTs). In particular, we propose that a "phantom shock breakout"—where the outer edge of the star falls through a stalled shock—can yield a burst of X-rays without a subsequent optical/UV signature, similar to FXTs. This model predicts the rise time of the X-ray burst, t d, and the mean photon energy, kT, are anticorrelated, approximately as T ∝ t d − 5 / 8 . [ABSTRACT FROM AUTHOR]

Compressive strength is a key to understanding the internal structure of dust aggregates in protoplanetary disks and their resultant bodies, such as comets and asteroids in the solar system. Previous work has modeled the compressive strength of highly porous dust aggregates with volume filling factors lower than 0.1. However, a comprehensive understanding of the compressive strength from low (<0.1) to high (>0.1) volume filling factors is lacking. In this paper, we investigate the compressive strength of dust aggregates by using aggregate compression simulations resolving constituent grains based on Johnson-Kendall-Roberts theory to formulate the compressive strength comprehensively. We perform a series of numerical simulations with moving periodic boundaries mimicking the compression behavior. As a result, we find that the compressive strength becomes sharply harder when the volume filling factor exceeds 0.1. We succeed in formulating the compressive strength comprehensively by taking into account the rolling motion of aggregates for low volume filling factors and the closest packing of aggregates for high volume filling factors. We also find that the dominant compression mechanisms for high volume filling factors are sliding and twisting motions, while rolling motion dominates for low volume filling factors. We confirm that our results are in good agreement with previous numerical studies. We suggest that our analytical formula is consistent with the previous experimental results if we assume the surface energy of silicate is ≃210 ± 90 mJ m−2. Now, we can apply our results to properties of small compact bodies, such as comets, asteroids, and pebbles. [ABSTRACT FROM AUTHOR]