The equation of state (EoS) P = P (ρ, ...) -pressure as a function of density and other thermodynamical quantities -is what generates particularities of mass-radius distribution M (R) for super-dense compact stellar bodies, the remnants of cosmic cataclysms. In view of recent nuclear experiments, we propose one particular EoS, which admits the critical state characterized by density ρc and temperature Tc, and which under certain conditions permits a radial distribution of the super-dense matter in "liquid" phase. We establish such conditions and demonstrate that a stable configuration is indeed possible (only) for temperatures smaller than the critical one. Using Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium, we derive the mass-radius relation for the super-dense compact objects with masses smaller than the Sun, M ≪ M⊙. The obtained results are within the constraints established by both heavy-ion collision experiments and theoretical studies of neutron-rich matter.

Despite significant progress in the understanding of galactic nucleosynthesis and its influence on the solar system neighborhood, challenges remain in the understanding of enrichment of the solar system itself. Based on the detailed review of multi-disciplinary literature, we propose a scenario that an event of nucleogenesis—not nucleosynthesis (from lower nucleon numbers A to higher A) but nuclear-fission (from higher A to lower A)—occurred in the inner part of the solar system at one of the stages of its evolution. We propose a feasible mechanism of implementation of such event. The occurrence of such event could help explain the puzzles in yet-unresolved isotopic abundances, certain meteoritic anomalies, as well as peculiarities in the solar system’s composition and planetary structure. We also discuss experimental data and available results from existing models (in several relevant sub-fields) that provide support and/or appear consistent with the hypothesis.

The mechanisms and structural elements of the Rayleigh-Taylor instability whose evolution results in the occurrence of the collapse have been studied in the scope of the rotating shallow water model with horizontal density gradient. Analysis of the instability mechanism shows that two collapse scenarios are possible. One scenario implies anisotropic collapse during which the contact area of a collapsing fragment with the bottom contracts into a spinning segment. The other implies isotropic contracting of the area into a point. The rigorous integral criteria and power laws of collapses are found.

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