A Feasible Mechanism for Appearance of Post-Post-Fe Elements in Solar System

Most people are unaware that traditional models do not explain chemical composition of the solar system fully. The presence of such elements as certain p-nuclei or post-post-Fe-nuclei, remains not yet understood. We propose a mechanism which can explain appearance of all non-native elements in the solar system. The hypothesis involves an explosive "collision" of a traveling from afar giant-nuclear-drop-like object (with specific equation of state of its matter) within the inner part of the solar system. The "nuclear fog" and debris, through the multitude of reaction channels (capture and fission) and nuclei transformations, enriched the solar system and led to the eventual formation of the terrestrial planets that pre-collision did not exist. This offers a possible explanation for the planets’ inner position and compositional differences within the predominantly hydrogen-helium rest of the solar system.


Introduction
We propose a hypothesis outlining a mechanism that could explain the observed presence of non-native elements in the solar system.The need for such mechanism is substantiated in Section 1 which articulates the problem -the existence of conceptual gaps in the current understanding of the composition and formation of the solar system.Section 2 outlines the proposed hypothesis in general, while Section 3 describes key elements of the potential scenario.Section 4 discusses the implications, provides comparisons with conventional models, and outlines the needs, directions, and challenges of further research.Section 5 concludes with a summary and additional considerations.Appendices contain details which are important for completeness of comprehension of the theoretical material involved, and thus are integral parts of this work.

Status of Current Understanding of Solar System Evolution
Despite the popular belief that formation and composition of the solar system are well understood and only nuances remain unresolved, serious conceptual gaps in the understanding continue to exist.The following quote succinctly sums up the current status of comprehension [67]: "The breakthroughs achieved during the recent few decades in our understanding of solar system formation are impressive.However, they are yet insufficient to clarify many problems intrinsically related to planetary cosmogony.Moreover, very important new questions have been posed that should be pursued before a robust theory of solar system origin and early evolution appears."One of these questions is "What was the original structure of the solar system, how did it evolved to the contemporary configuration, and what determines the planetary system final architecture?"Review of planet formation models brings to focus some specific areas of concern: "There remain considerable uncertainties at each step of planet formation.... even our most successful models are built on a shaky foundation" [69]."The solar system is characterized by a trimodal structure" containing terrestrial planets (rocky and relatively small), the asteroid belt (with cumulatively negligible mass), and the giant planets (beyond 5AU)."How this trimodal structure was set is still an issue of open debate" [69].Even (excluding asteroids) the "bimodal structure is puzzling.Assuming that planetesimals formed everywhere in the disk with comparable masses ... the subsequent process of planet growth by pebble accretion should favor the bodies closer to the Sun ... In other words, giant planet cores should have formed in the inner disk and Mars mass embryos in the outer disk!" [69] "The analysis of meteorites shows indeed that there were at least two generations of planetesimals in the inner disk.... It is unclear whether there was a gap in time in planetesimal formation and even whether the first and last generations of planetesimals formed in the same place" [69]."How they grew to pebble-boulder size or larger bodies (specifically around the "meter-size barrier") is not completely clear ..." [67].
Furthermore, while the rocky objects are thought to have formed by accretion (from dust grains into larger and larger bodies), two competing theories exist about formation of the giants -the core accretion model and the disk instability model.In either case, reconciliation of formation of two classes of planets has not been successful yet.The core accretion model presumes that rocky, icy cores of giant planets accreted in a process very similar to the one that formed the terrestrial planets and then captured gas from the solar nebula to become gas giants.This model explains why the giants have larger concentration of heavier elements than the Sun has, but numerical simulations yield formation times that are way too long (unless the mass of the primordial nebula is increased).The disk instability model posits that spontaneous density perturbations in the primordial disc could have caused clumps of gas to become massive enough to be self-gravitating and form the Sun and the planets [12].Formation scale is then much more rapid, but the model does not readily explain the observed chemical enrichment of the planets.
As the set of exoplanetary data continues to expand [11], the historical presumption that the solar system is "typical" (just an ordinary planetary system evolved in an ordinary way) becomes increasingly questioned [69]: " ... how typical was the solar system's evolutionary path?... Or was the solar system's path unusual in some way?... Based on statistically sound exoplanet observational surveys, the Sun-Jupiter system is special at roughly the level of one in a thousand.First, the Sun is an unusually massive star ... Second, only ∼ 10% of Sun-like stars have gas giant planets with orbits shorter than a few to 10 AU... Third, only about 10% of giant exoplanets have orbits wider than 1 AU and eccentricities smaller than 0.1.Taken together, these constraints suggest that the Sun-Jupiter system is a 0.1% case.... The numbers quoted here are a simple order of magnitude, but they clearly illustrate that the solar system is not a typical case in at least one regard: the presence and orbit of Jupiter" [69].
Indeed, the orbits of the solar system's giant planets are widely spaced and nearly circular, which is unusual [86], [31], [6].Remarkably, they also do not exhibit any resonance despite the fact that, as N-body studies of planetary formation and orbit positions indicate, due to the convergent planetary migration in times before the gas disk's dispersal, each giant planet should have become trapped in a resonance with its neighbor [54], [68].Some studies have also exposed the possibility that one more giant object initially might have been present in the solar system and then somehow disappeared at some point -dynamical simulations starting with a resonant system of four giant planets showed low success rate in matching the present orbits of giant planets [72] (see also discussion in Sec.4.4).
But the most significant deficiency in the understanding of the solar system's evolution concerns not its structural formation but the nuclear origination of its chemical elements.A number of anomalous for the solar system nuclides -varied in lifetimes (from stable to very short-lived) and produced by r-, s-, p-, or γ-processes (not natural for the solar system) -have been detected in the terrestrial and meteoritic material.Theoretically, these nuclei can be produced, directly or via chains of transformative reactions, in specific stellar events (each having its own "signature" -its own nuclei-generation profile).However, the ways in which these nuclides had mixed and solidified in meteoritic samples have imposed significant constraints on the timing (and location) of their origination.A number of Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 16 April 2019 challenges and inconsistencies exist in the models that have been proposed so far.Furthermore, some issues continue to remain unanswered.Here are the fundamentally important ones.
Challenges to Explanations of Short-Lived Nuclides Origins.The appearance of 26 Al, 41 Ca, 53 Mn, 60 Fe, and a few other nuclides, in the early solar system require their production at the same time, or just before, the "rocky" components of solar system formed (see, among others, reviews by [101], [100], and references therein).Various numerical models of stellar nucleosynthesis consistently show that one event by itself cannot provide the early solar system with the full inventory of short-lived nuclides.Depending on the model, certain isotopes are significantly over-or under-produced (see, among others, [34], [42], and references therein).
The conventional belief is that these nuclides were synthesized in a nearby supernova and/or a red giant and injected into the solar nebula just shortly before the solar system formation (see [16], [17], [13], [38], [64], and references therein).However, the Ivuna CI chondrite analysis detected simultaneous presence of at least five mineralogically distinct carrier phases for Mg and Ca isotope anomalies, leading to the explanation that they must represent "the chemical memory of multiple and distinct stellar sources" [89].
To reconcile various findings, the theory was advanced that the solar system formed as part of a star cluster [79] and therefore was enriched by multiple stars.The challenge is however that stellar clusters are potentially dangerous environments for planetary systems [67].The multi-source enrichment theory also faces a timing challenge.
To be able to provide the observed abundances of radioactive isotopes, multiple supernova must have been located not too far from the solar nebula, but the distance had to be great enough so that the shockwave of matter from the supernova did not destroy the nebula.For the stars with M ∼ 25M Sun shown to provide the best ensemble of short-lived radioactive nuclei, this optimal range is quite narrow, 0.1 − 0.3 pc [2].But stars within the cluster typically form within 1-2 Myr [45] and the clusters disperse in about 10 Myr or less [3].Since stars with mass M ∼ 25M Sun burn for ∼ 7.5 Myr before core collapse [103], to fit the supernova enrichment scenario the Sun must have formed several Myr after the progenitor [2].If located ∼ 0.2 pc from the progenitor, the early solar nebula could have been evaporated by the progenitor radiation [40].One way to reconcile this is to assume that the trajectories of the early solar nebula and the progenitor approached the 0.2 pc separation just before the supernova explosion [2].Such timing requirement lowers the odds for the supernova enrichment theory [102].The scenario in which multiple supernovae satisfied such trajectory and timing requirements has even lower odds.
Furthermore, when constraints imposed by the spread of calcium-aluminum inclusions (CAI's) condensation ages are taken into consideration, if the detected short-lived radionuclides were produced by multiple stellar sources (at least five [89]), all of these injection events, as well as the subsequent highly homogeneous mixing of isotopes, had to occur within the time-span of only about 20,000 years [42].
Inconsistent Abundances of 10 Be and 7 Li Isotopes.Furthermore, detection of 10 Be indicates that one more (high-energy) process, local to the solar system, must be added to the enrichment scenario. 10Be is not synthesized in stars.Indeed, in most stellar events Be is destroyed rather than produced.
Moreover, the discovered excess of 7 Li in CAI ( [20], [21]) points with certainty to its origin within the solar system, because 7 Li is produced by decay of 7 Be whose half-life is only 53 days.It was suggested that these elements were produced by spallation (high-energy nuclear reaction in which target nuclei are struck by bombarding particles) within the solar system as it was forming.Various research groups tested this scenario by comparing the modeled nuclear spallation yields with the inferred solar system initial ratios (e.g., [61], [39], [37], [62]).However, they failed to self-consistently explain the abundance discrepancies.
Unexplainable "Excess" of Proton-Rich Isotopes.Most significant, however, is the fact that anomalous for the solar system proton-rich nuclides (the so-called p-nuclei) have been detected in the terrestrial and meteoritic material ( [83], [80]).Their abundances are relatively tiny.(Before astronomical Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 16 April 2019 observations of isotopic abundances at the required discrimination level become feasible, if ever, it is impossible to determine p-abundances elsewhere [83].)The question of how these elements appeared in the solar system is not yet answered ( [83], [80]).Indeed, understanding the origin of proton-rich nuclei in general is the great challenge of stellar nucleosynthesis because p-nuclei cannot be made in the sand r-processes.
Conceptually, in stellar events, p-nuclei can be produced either by proton-capture from nuclei with lower charge number, or by photo-disintegrations.Both production mechanisms require high temperatures and presence of "seeds" (r-and/or s-process nuclides).Proton-capture process also requires a very proton-abundant environment.The conventionally considered scenario for creating these isotopes involves the post-supernova photodisinteration p-process -the so-called γ-processa complex network of reactions of photodisintegration (of the pre-existing intermediate and heavy nuclei) whose inputs are the outputs of the inverse reactions (proton-, α-and neutron-capture) that occur during the explosion of a supernova (mainly in explosive Ne/O burning during a core-collapse supernova.)Even so, the origin of the proton-rich post-post-Fe nuclei still remains one of the greatest puzzles of stellar nucleosynthesis ( [83], [80]).
Currently, the solar system abundances of p-nuclei have been best fitted into the combination of models of several stellar processes ( [83], [80]).Photodisintegration in massive stars Type Ia-supernova or a mass-accreting white dwarf explosion [83] and neutrino processes (for 138 La and 180 Ta), can perhaps explain the bulk of the p-nuclei abundances.However, the abundances of light p-nuclei in the solar system significantly exceed the model-simulated production from the stellar processes, and this problem has not been resolved yet [83].
Even though abundances of the p-nuclei detected in meteoritic and terrestrial material of the solar system are tiny, their unexplainable "excess" is very significant, because the quality of the understanding of what had contributed to the solar system's chemical composition is gauged by comparing (1) the "observed" profile of element abundances (consensus of direct/indirect measurements) with (2) the "simulated" profile that sums up outputs from all modeled mechanisms (superposition of models).A meaningful "mismatch" with respect to any one element (isotope) indicates that the understanding is incomplete -either (a) assumptions and superposition weights of contributing models may need adjustments (which may be difficult due to other physical constraints), or (b) a new mechanism/model is required to explain the mismatch.Since the detected p-nuclei abundances exceed best simulation results, it means that there has not been found a combination of model parameters that could match observations.Thus, a new model or mechanism is needed to explain the factual evidence.

Hypothesis
The above-mentioned puzzles -the unexplained trimodal structure of the solar system and the presence of p-nuclei, post-post-Fe-nuclei, and short-lived nuclei (explanations for which currently hypothesize quasi-simultaneous occurrence of numerous explosive stellar events that are unusual for the solar system neighborhood) -and other solar system peculiarities (not listed here but mentioned later on), indicate that a "fresh", more aggregating and more integrating, perspective is needed to explain the data.
The presence of p-nuclei in the solar system is the greatest conundrum on the list; it also offers perhaps the greatest pointer.According to the conventional view (see, for example, a recent review [80] and numerous references therein), p-nuclei can be produced via captures of various types and photodisintegration.However, they can also be produced via fission of heavy nuclei.Furthermore, in contrast with the commonly-considered fusion process of formation of heavy nuclei, fission of (super)-heavy nuclei (nuclear droplets) via spontaneous nuclear transformation cascades can yield not only p-nuclei, but also other types of nuclei, including post-post-Fe nuclei.
The p-nuclei and post-post-Fe nuclei detected in meteoritic and terrestrial samples can be explained if a "nuclear-fission-type event" happened in the solar system.Such event had to be "powerful" enough to create all the nuclei in question (forming and enriching terrestrial planets, Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 16 April 2019 asteroids, cores of gaseous planets, etc.), but not too "powerful" so the release of energy and matter did not destroy the solar system altogether.
For such nuclear-fission-type event to occur, a stellar body with particular characteristics (capable of phase-transitioning into unstable "nuclear-fog" state if perturbation of its inner matter is triggered, see Appendix A) had to cross the path of the solar system.Asking the questions -what kind of stellar body could that have been, how the nuclear fission could have been triggered, and how the scenario could have unfolded so the solar system ended up with the configuration and composition that we currently observe -is how we developed the hypothesis that we outline below.
We suggest that early on, more than 4.6 billion years ago, our solar system had no terrestrial but only jovian planets.Perhaps, it had a companion closest to the Sun, such as a dwarf or super-Jupiter.
We further propose that about 4.6 billion years ago (at the time currently defined as the birth of the solar system based on dating of meteoritic isotopes [67]), a traveling-from-afar object -perhaps born in an asymmetric catapulting cataclysm and already sufficiently cooled so its inner state was capable of phase-transitioning into unstable "nuclear fog" state if perturbed -crossed the path of the solar system and, once perturbed, "exploded" within the inner part of the solar system.Perhaps this explosion involved the possibly-then-existent companion of the Sun or the possibly-then-existent gaseous giant at the then-first orbit.We posit that, for the nuclear-fission-type cascades to unfold, the traveling object had to possess the characteristics of a "giant nuclear drop" (theoretical existence of such objects has been analyzed [96]).Such object could have been born as a result of destruction [97] of some neutron-rich stellar object (Sec.3.1) by the super-massive black hole located at the center of our galaxy. 1 Certain details of this scenario are fundamentally essential: As the nuclear-drop-like object entered the inner part of the solar system and experienced "sufficient" (see Sec. 3.3) perturbation (deceleration), the object's inner matter stratified -first the compression shockwave propagated from the front point towards the back, then (because the object's surface was strain-free due to extreme density contrast between the inner and outer media) the reflected shockwave reversed polarity and returned as the wave of decompression ([106], [58]; see Sec. 3.3 and Appendix B).Generally, in a nuclear-like medium, the shockwave propagation speed is comparable with the speed of light, so the stratification process develops very quickly.During such short time, the shape of the drop does not have time to change because propagation speed of surface perturbations is much slower than the speed of body waves.In the proposed scenario, in the zones of decompression, the matter that was previously (thermodynamically) weakly-stable (perhaps due to aging and cooling of the object), now became unstable and "preferred" not the homogeneous but the two-phased state (the state of "nuclear fog" where "nuclear droplets" coexist with "nuclear gas") -in other words, inside the object, the (locally) decompressed matter became a conglomerate of "droplets" of charge-neutral nuclear matter as well as "gas" of α-particles, protons, electrons, neutrons (see Appendix A).Such charge-neutral "droplets" (obviously with hyper-large nucleon numbers A) were structurally unstable and underwent spontaneous cascading fragmentation and fission (notably, with very abundant release of neutrons).Due to the nuclear mass-defect, this process released a lot of energy (see Sec. 3.2) -the system heated up -a "cloud" was formed composed of hyper-massive nuclei, α-particles, and protons and electrons to assure charge-neutrality of the system.All processes occurred at such fast nuclear-time-scales that the system exploded, and the matter became dispersed in the surrounding space.Overall, only insignificant mass remained at the orbit where the explosion occurred.The multitude of reaction channels led to transformations of nuclei (Sec.3.4).

1
A splattered mercury droplet (when an old-fashioned thermometer cracks) may perhaps serve as a helpful visual metaphor for the produced object, the "giant nuclear drop".Indeed, certain analogies between states of matter have been noted.For example, the equations of state for a nuclear system interacting through a Skyrme potential and a Van der Waals compressible liquid-gas system, exhibit remarkable similarities.See Appendix A.

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This mechanism of element-generation critically differentiates the proposed hypothesis from the conventional conception of element-formation in the solar system.In our hypothesis, the dominant mechanism is the process of fission (from large nucleon numbers A to moderate A), while in the conventional models the primary process is nucleosynthesis (from lower A to higher A).
Post-event, the final products of the nuclear transformations (that occurred via the enormous multitude and variety of random channels of reactions that were possible in such conglomerate of components exposed to such high-energy emissions) created the environment containing post-Fe elements, as well as the previously mentioned short-lived radionuclides, various isotopes, and so on, -with the element abundance profile as currently known.Later on, after the processes and the system settled, these nuclei became the building blocks of dust, grain particulates, pebbles, and later planetesimals, and eventually, the terrestrial planets and other "rocky" bodies.These nuclei also enriched the pre-existing jovian planets.
This hypothesis draws on the insight that over the course of its history the solar system could have undergone encounters with external objects of various mass (see, for example, a proposed explanation for the orbit of Sedna [53]), and also on the general acceptance that stellar "collisions" of dense objects do indeed happen (for example, neutron stars collisions, black-hole/neutron star mergers have been studied; see, among others, [59], [32]).But the idea of the solar system's path-crossing with an object capable of creating nuclear-fission-like transformations into nuclei that enriched the system, has never been advanced.
This hypothesis is also notable not just because it offers an explanation for how the exotic elements (and the unexplainably exotic ones, such as p-elements) appeared in our planetary system, but also because the proposed mechanism can occur in such way that it does not demolish the entire system.A different object would either not create the necessary effects, or be too destructive.That is why the object has to be of a special, although not a particularly unusual kind -the object had to have characteristics of a quasi-stable giant nuclear-drop.
Naturally, the proposed stellar path-crossing is a rare event, perhaps it is a completely unique one.But if another one already happened (or will happen) elsewhere, the implications can be breathtaking.For Earth, the presence of "exotic" elements at the "ideal" spot -at the perfectly habitable distance, next to the perfectly tranquil star (our Sun), in the perfectly quiet outskirt of our galaxy -has been key to development of many forms of life (as we know it).Indeed, human biochemistry critically depends on the non-native for the solar system iron, iodine, selenium, copper, molybdenum, or cobalt. 2  New hypotheses always lead to new ways of examining facts.The goal that many astro-and planetary researchers find most intriguing, is to understand the place of the solar system in the universe, the possible uniqueness of our home planet, why it differs from other solar system bodies and, finally, the process that brought us to this world.Perhaps, the proposed hypothesis contributes a meaningful insight towards such goal.

Traveling Object
Generally speaking, a number of exotic compact stars have been hypothesized, such as: "quark stars" -a hypothetical type of stars composed of quark matter, or strange matter; "electro-weak stars" -2 Iron (z = 26) is a key element in the metabolism of almost all living organisms.Copper (z = 29) is important as an electron donor in various biological reactions.Iodine (z = 53) is required for making of thyroid hormones, which regulate metabolic rate and other cellular functions.Iodine deficiency leads to goiter and mental retardation.Selenium (z = 34) is essential for certain enzymes, including several antioxidants.Molybdenum (z = 42) is essential to virtually all life forms.In humans, it is important for transforming sulfur into a usable form.Cobalt (z = 27) is contained in vitamin B12, which is important in protein formation and DNA regulation.Notably, among the listed elements, isotopes of selenium 74 Se and molybdenum 92 Mo and 94 Mo (detected in the solar system) are p-nuclei and cannot be produced by sand r-processes, and thus, could not have been produced by supernovae.a hypothetical type of extremely heavy stars, in which the quarks are converted to leptons through the electro-weak interaction, but the gravitational collapse of the star is prevented by radiation pressure; "preon stars" -a hypothetical type of stars composed of preon matter.Indeed, various objects could have existed five billion years ago.
Just as a reminder, the conventional neutron star forms as a remnant of a star whose inert core's mass after nuclear burning is greater than the Chandrasekhar limit but less than the Tolman-Oppenheimer-Volkoff limit.Due to certain aspects of their formation process, velocities of conventional neutron stars are never high (relative to their original frame of reference).However, during the rotating core collapse, one or more self-gravitating lumps of neutronized matter can form in close orbit around the central nascent neutron star [48].The unstable (in the phase-transition and nuclear-reaction sense) member of such transitory binary or multi-body system ultimately explodes, giving the surviving member a substantial kick velocity -as fast as ∼ 1600 km/s [25].
Small fragments of such stars can also be formed and kicked, or catapulted, if a black hole tears a neutron star apart [84].Fig. 1 illustrate such possibility (three scenarios depicted).
Figure 1.Illustration of the destruction process (three scenarios from [97]).A stellar body (depicted as the black dot near dimensionless coordinates (+6; +10)) that comes into vicinity of a rotating massive black hole (depicted as the black circle at the center) becomes torn apart by the fast-rotating black hole's gravity.Presumably, a part of plasma debris would remain trapped and funneled toward the black hole's event horizon.These viscously heated orbiting pieces of debris would start flaring up.Some fragments of the destroyed stellar body would escape the black hole's vicinity with high velocity.
Objects smaller (even significantly smaller) than conventional neutron stars can indeed (theoretically) exist -and stay as dense as a nucleus, without the crust, and remain stable (in the liquid-gas-phase-transition and nuclear-reaction sense, and therefore, structurally) -if their equation of state fulfills certain requirements [96].
In our hypothesis, the traveling object is essentially a giant "nuclear drop" (a hyper-nucleus) born in an asymmetric stellar cataclysm far away and catapulted with sufficiently fast velocity along the trajectory that crossed the solar system's path.

Explosive Energy Burst
High-energy nuclear experiments have demonstrated that the matter of a nuclei is characterized by critical parameters of temperature T c and density ρ c (see, for example, [49], [50], [51], [22], [52], [96], and references therein).In laboratory conditions, for nuclear samples, T T c ∼ Below the critical temperature T c , depending on its density, nuclear matter can exist in "nuclear liquid" phase (higher range of densities), or "nuclear gas" phase (lower range of densities), or as "nuclear fog" which is a mixture of both phases (within the "spinodal zone" of the density range corresponding to its T).See Appendix A.
In our scenario, for the traveling object, if the equilibrium state of the inner "nuclear liquid" is initially close to the boundary of the liquid/gas phase transition, then the liquid phase can decompress into the fog phase as the result of perturbation (deceleration).The matter would then exist as a mixture of two phases of nuclear matter -either liquid droplets surrounded by gas of neutrons, or generally homogeneous neutron liquid with neutron-gas bubbles.In such state, the matter can reach substantial further rarification, reducing density by a factor of 10 2 or more due to hydrodynamic instability.At this stage, cascading nuclear fragmentation of the nuclear-droplets and subsequent fission of the fragments may start.
Below density ρ drip -even if in some small physical domain within the objectβ-decay becomes no longer Pauli-blocked and significant amount of energy becomes released.Indeed, simulations of r-process nucleosynthesis in neutron star mergers demonstrated that from ρ drip -level, density decreases extremely fast -the matter initially cools down by means of expansion, but then heats up again when the β-decay sets in [32].
This process triggers cascading fragmentation of these supersaturated hyper-nuclei (see, for example, [7], [44], [65]).These reactions, known to release even more energy (∼ 1MeV per fission nucleon, as seen in transuranium nuclei fission events), proceed effectively at the same moments as the β-decay reactions.Everything happens very fast, practically with nuclear-time scales (∼ 10 −22 ÷ 10 −15 sec).When perturbations of the equilibrium of a "neutron liquid droplet" permit production of charged protons (even in small numbers, and in small localized regions), spontaneous cascading fission reactions commence.
Generally speaking, at different stages (with respect to applied energy/excitation of hyper-nuclei), different types of reactions occur [52].When a hyper-nucleus is excited (relatively) weakly, only γ-emission occurs.At a higher level of excitation, neutron-emissions start taking place.When even more energy is applied to the hyper-nucleus, it deforms and fission starts because, as known, for deformed charged nuclei with parameter Z 2 /A > 50, electrostatic repulsion starts exceeding surface tension of a nuclear drop.And finally, when injected energy is sufficiently high, fragmentation -splitting into fragments ("droplets" if the initial nucleus is a hyper-nucleus) -occurs, followed by the cascade of subsequent splitting into fragments and strong neutron emissions.

Deceleration and (Localized) Decompression as Trigger for Explosion
A number of mechanisms contribute to the object's deceleration as it penetrates a mediumclassical drag [58], dynamical friction [19], accretion [95], Cherenkov-like radiation of various waves related to collective motions [78] generated within the medium [76], [77], distortion of the magnetic fields, and possibly others.Obviously, some deceleration causes would be dominant and some would be negligible.Analytical and numerical treatment of the deceleration process can quickly become complex and cumbersome.Furthermore, as numerical studies of magnetized stars revealed, if the velocity, magnetic moment and angular velocity vectors point in different directions, the results become strongly dependent on model choices.
However, in the context of the question of whether explosion can be triggered by internal instability, the "strength" of deceleration should be defined not in the kinetic sense, but in the thermodynamic sense.Indeed, as already noted, if the initial phase state of the nuclear liquid is rather close to the boundary of the two-phase (spinodal) zone, deceleration with even "negligible" magnitude in the kinetic sense can in fact be a "significant" perturbation capable of triggering "sufficient" density stratification.In the (highly unstable) spinodal zone, even small perturbations develop extremely fast.(See Appendix B.) Since nuclear processes occur with even faster time scales (t ∼ 10 −22 ÷ 10 −15 sec) Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 16 April 2019 than thermodynamic processes, even "minor" localized decompression can trigger a cascade of spontaneous fragmentation and fission.
The lower are the nuclear-drop-like object's initial inner density and temperature "at birth", the less time will it take for its (T, ρ)-phase state to shift (via cooling) towards the nuclear-liquid/nuclear-gas phase-transition boundary.The closer is the (T, ρ)-phase state to the boundary, the smaller is the minimal perturbation (deceleration) magnitude necessary to produce decompression "sufficient" for triggering the cascade of nuclear transformations.
Theoretical plausibility of existence of small stable objects (spherical configurations) with the above-mentioned nuclear-drop-like properties has been demonstrated [96].Astronomically, however, such small and cool objects are difficult, if not impossible, to detect with current observational methods.The smaller (less massive) are the objects from the start, and the older they become, the lower are their temperatures (and densities).

Element Production
To attempt to simulate numerically the outcome of element production chains will be extremely challenging for several reasons.
First, the theory of fission (and even more so of fragmentation) of hyper-nuclei (lnA 1) is not developed at all, mostly because observational data are impossible to collect, and experimental studies are impossible at present to conduct.Split of nuclei with high A numbers into several with lower A numbers leads, via different channels, to the unpredictable composition of fission products, which vary in a broad probabilistic and somewhat chaotic manner.This distinguishes fission from purely quantum-tunnelling processes such as proton emission, α-decay and cluster-decay, which yield the same products each time.
Second, while r-process capture of free neutrons (leading to transformation of nuclei from the lower to higher A numbers) has been more studied and can be better modeled, the results strongly depend on the assumed equation of state (EOS) of absorbing matter [32], the neutron/seed ratio, and the composition of the seed, which in models are characterized by the proton/electron-to-nucleon ratio, Y p or Y e , of the ejected and expanding matter.The value of Y e has basically dual effect: (1) it determines the neutron-to-seed ratio, which finally determines the maximum nucleon number A of the resulting abundance distribution, and (2) it also determines the location (neutron separation energy) of the r-process path, and thus the β-decay half-lives to be encountered.This influences the process rapidity and the energy release.Thus, Y e of the ejected matter strongly depends on how much seed matter is contained in the domain of interaction of components.Also, various processes such as neutrino transport, neutrino captures, or positron captures, alter Y e evolution.Indeed, as well-acknowledged, in neutron star merger modeling, test calculations using different polytropic EOSs (a rather simple initial assumption) demonstrate strong dependence of the amount of ejecta on the adiabatic exponent of the EOS -stiffer equations result in more ejected material [32].
Finally, the data on the abundance yields from the observed supernovae are not useful for modeling the proposed event element production.The two processes (supernova and event) fundamentally differ in several aspects.
With respect to the nucleosynthesis reactions, the two processes have substantially different seed nuclei composition and neutron-seed ratios.In supernova explosions, when the core collapses once Coulomb repulsion can no longer resist gravity, the propagating outward shockwave causes the temperature increase (resulting from compression) and produces a breakdown of nuclei by photodisintegration, for example: 56 Fe 26 + γ → 13 4 He 2 + 4 1 n 0 , 4 He 2 + γ → 2 1 H 1 + 2 1 n 0 .The abundant neutrons produced by photodisintegration are captured by those nuclei from the outer layers (the "seeds") that managed to survive.Thus, the resulting abundances depend strongly on the characteristics of the star.Indeed, astronomical observations confirm that supernova nucleosynthesis yields vary with stellar mass, metallicity and explosion energy (see, for example, [73]).

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As for the production of gold, it occurs, for example, by free-neutron-capture of exited nuclei of mercury, which serve as seeds.Nucleus 198 Hg 80 captures a rapid free neutron, produces exited nucleus 198 The conventional theories of element-enrichment in the solar system posit that these seeds (mercury nuclei) and resulting elements (gold) are formed during supernova (and other stellar cataclysms).
In our scenario, they are (mostly) formed during the proposed event once the fragments of nuclear droplets had undergone fission (and subsequent transformations).
Overall, the proposed event and supernova explosion produce completely different distribution of seed nuclei available for subsequent reactions.The fact that in the proposed event scenario reactions of fission play dominant role in the element production process, while during supernova dominant are the reactions of nucleosynthesis, is also key fundamental distinction between the two types of events.
How exactly the chain reactions unfold in the proposed event scenario, is currently difficult to specify any further.The only thing that can be said at this point is that, in the framework of the outlined hypothesis, the observed abundances of the solar system represent the single outcome of such event known to us (of course, even with this event, the observed abundances also include contributions from stellar and other in situ sources).We do not have a statistical sample to make any comparisons.If the fission and nucleosynthesis reactions were better understood, the only subsequent approach would be to solve the inverse problem, i.e. to find out what the initial conditions had to be so the model resulted in the observed abundances.

Fission-Triggering Object
Our hypothesis proposes that an inner-galaxy-born fast-traveling nuclear-drop-like stellar object (capable of phase-transitioning into unstable "nuclear fog" state if perturbation of its inner matter is triggered) crossed the path of some accidentally-encountered stellar system (where subsequently the mankind evolved and which we now call "the solar system") and, as the result of this encounter, the traveling object "exploded" in a cascade of fragmentation/fission-type nuclear transformations.
At this point, we can envision three conceptual possibilities for how the object's perturbation was triggered.
(1) "The (Edge of) Sun".The object could have penetrated the "edge" of the star (the Sun), in which case the Sun is effectively the "fission-triggering object".In this scenario the encounter must have occurred in such a way that the Sun continued to exist as we know it.
(2) "Binary Companion".Perhaps the Sun had a companion -a dwarf, or a main-sequence star, larger or smaller than the Sun -which was destroyed as the result of the encounter.Indeed, a significant portion of solar-type stars are found in binary systems (see [1], [28], [55]).The well-known problems with angular momentum dispersal (e.g., [8] and references therein) indicate that protostars should end up in binary or multi-stellar formation.Furthermore, the 7 o misalignment between the Sun's rotation axis and the north ecliptic pole (see, e.g., [5]) may indeed be supportive of such scenario.In such case, both companions most likely formed a close binary and remained inside the orbit of Jupiter (wherever it was positioned at that time).
(3) "Super-Jupiter".Perhaps the Sun had another gaseous giant -a "super-Jupiter" (with the orbit located inside the Jupiter's orbit) -which was destroyed as the result of the encounter.Indeed, a number of independent analyses have pointed at the potential existence of one more giant in the early solar system (see, for example, [72], [4], [75]).In this context, at a quick glance, an argument may be raised that (within the conventional framework) near the Sun, inside the so-called snowline, no additional gaseous giant could have formed.But the location of the snowline is derived based on the assumed model of thermal regime.Because conventional models assume that gaseous and rocky bodies of the solar system formed contemporaneously, the models utilize meteoritic data as critical constraints shaping the view about the protodisc's thermal regime.Detection of high temperature condensates in meteorites has led to the acceptance of the hot model of thermal regime during formation of all solar system bodies [67].However, within the framework of the proposed hypothesis, the meteorites formed (as the result of the explosive event) after the gaseous objects had already formed.Obviously, constraints derived from the post-event data should not influence the pre-event evolution scenario.If meteoritic constraints are set aside, the least complicated scenario would seem to presume that all gaseous objects formed (before the explosive event) from the ("dust-less") protodisccomposed predominately of H/He, with infusion of whatever additional nuclei that were natural for the protonebula's "neighborhood", and presumably rather cold before viscous heating took place and later the Sun ignited -via local clumping and rapid gravitational collapse of the (marginally unstable) protodisc [12].Such scenario does not seem to preclude formation of another gaseous giant in the inner part of the solar system.Modeling of the process, however, is complex (see discussion in Sec.4.4).
To form an opinion about which solar system object was most likely "responsible" for triggering perturbation of the traveling-from-afar nuclear-drop-like object's inner mater (leading to explosive nuclear-fission-type transformations and eventual formation of rocky "debris"), the proposed alternatives should be analyzed and compared with several considerations in mind: (1) the thermodynamically "meaningful" perturbation / deceleration must have occurred (as described in Sec.3.3), (2) the location of the debris must have ended up forming the terrestrial belt, (3) the explosion must not have destroyed the Sun (and the rest of the solar system that apparently survived), and (4) to the extent the cascade of nuclear transformations may have required some hydrogen-rich environment, it should have been available.Numerical models specializing in planetary dynamics may perhaps be best equipped to bring further insights into which of the alternatives is most plausible, but the models need to re-examine and re-validate their inputs and assumptions before conducting any simulations (see discussion in Sec.4.4).

Hypothesis Summary
The entirety of puzzling peculiarities of the solar system -ranging from the availability of non-native chemical elements whose origins are difficult to explain, to the presence of atypical features in the planetary structure and dynamics -prompted us to inquire whether one event could have been responsible for all of the peculiarities at once.
We proposed that at first, more than 4.6 billion years ago, our solar system had no terrestrial but only jovian planets -perhaps, it had a companion closest to the Sun, such as a dwarf or super-Jupiter.We proposed that about 4.6 billion years ago (at the time currently defined as the birth of the solar system based on dating of meteoritic isotopes [67]), a traveling-from-afar object -perhaps born in an asymmetric catapulting cataclysm and already sufficiently cooled so its inner state was capable of phase-transitioning into unstable "nuclear-fog" state if perturbed -crossed the path of the solar system and, once perturbed, "exploded" within the inner part of the solar system.Perhaps this explosion involved the possibly-then-existent companion of the Sun or the possibly-then-existent gaseous giant at the then-first orbit.We proposed that, for the nuclear-fission-type cascades to unfold, the traveling object had to possess the characteristics of a "giant-nuclear-drop" (theoretical existence of such objects has been analyzed [96]).Such object could have been born as a result of destruction [97] of some neutron-rich stellar object by the super-massive black hole located at the center of our galaxy.As the nuclear-drop-like object entered the inner part of the solar system and experienced "sufficient" perturbation (deceleration), the object's inner matter stratified -first the compression shockwave propagated from the front point towards the back, then (because the object's surface was strain-free due to extreme density contrast between the inner and outer media) the reflected shockwave reversed polarity and returned as the wave of decompression [106], [58].In a nuclear-like medium, the shockwave propagation speed is comparable with the speed of light, so the stratification process developed very quickly.In the zones of decompression, the matter that was previously (thermodynamically) weakly-stable (perhaps due to aging and cooling of the object), became unstable and "preferred" not the homogeneous but the two-phased state (the state of "nuclear fog" where "nuclear Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 16 April 2019 droplets" coexist with "nuclear gas").Charge-neutral "droplets" (obviously with hyper-large nucleon numbers A) were structurally unstable and underwent spontaneous cascading fragmentation and fission (notably, with very abundant release of neutrons).Due to the nuclear mass-defect, this process released a lot of energy -the system heated up -a "cloud" was formed composed of hyper-massive nuclei, α-particles, and protons and electrons to assure charge-neutrality of the system.All processes occurred at such fast nuclear-time-scales that the system exploded, and the matter became dispersed in the surrounding space.Overall, only insignificant mass remained at the orbit where the explosion occurred.Post-event, the final products of the nuclear transformations (that occurred via the enormous multitude and variety of random channels of reactions that were possible in such conglomerate of components exposed to such high-energy emissions) created the environment containing post-Fe elements, as well as the detected p-elements and short-lived radionuclides -with the element abundance profile as currently known.After the processes and the system settled, these nuclear components became the building blocks of dust, grain particulates, pebbles, and later planetesimals, and eventually, the terrestrial planets and other "rocky" bodies.These nuclei also enriched the pre-existing jovian planets.
The described mechanism of element-generation critically differentiates the proposed hypothesis from the traditional conception of element-generation in the solar system.In our hypothesis, the dominant mechanism is the process of fission (from large nucleon numbers A to moderate A), while in the conventional models the primary process is nucleosynthesis (from lower A to higher A).

Likelihood: Plausibility vs Probability, Expectation vs Realization, and Meanings of Numbers
The very thought of an event occurrence often brings up a question of its likelihood.But in any context, it is very important to be clear what the term 'likelihood' is meant to describe.
The first kind of likelihood is 'plausibility', which inquires, in essence, whether the laws of physics permit the occurrence of the event in the first place.Understanding how a combination of various mechanisms can produce the event in question yields conclusion that the event is plausible -in other words, not impossible, not forbidden by the laws of physics.
The second kind of likelihood is 'statistical probability', which is about statistical odds of mental repetition of a similar event, not about whether the first (prior) event can happen.Questions about statistical probability always imply that the first event can or did happen.The concept of statistical probability of an event is connected with the concepts of the most expected outcome, the frequency of repeated events, and other related concepts.Generally speaking, the "statistical odds" have nothing to do with the question of whether the event proposed in our hypothesis could indeed have happened 4.6 Gyrs ago.Such event would have been (was) the first event.(And hence the only relevant inquiry is its plausibility.)And we humans should be very happy that the odds of the second event happening in our solar system are low.
Also, when talking about probabilities, it is important to remember the difference between "expectation" and "realization".For a collision, the often-used word "target" can mean two different things: the "intended-goal (specific aim for the path)" (like the rope for hanging that Clint Eastwood's hero was shooting from afar to release his co-conspirator in the movie "The Good, the Bad, and the Ugly") and the "accidental-result (random obstacle on the path)" (like the hole that is left in a wall by a blind-man's accidental gunshot).Using these metaphors, we can say that our scenario is not about "whether a bullet can hit the distant rope", but instead we note that "the hole in the wall looks like it came from a bullet", so what kind of bullet must that have been and what might have happened.For accidental-results (obstacles), post-event, statistical odds are irrelevant.Upon realization, P=1.
Nonetheless, let's look at the probability numbers for additional insight.The "frequency of collisions", ν ≡ τ −1 = n σV , gives indication about the chance of the occurrence of the event (collision) during some increment of time.Here, n is concentration of the obstacle population, σ is interaction cross-section, and V × 1 is the distance covered by the moving object over the unit of time.Properly speaking, expression P = ν∆t = nσV ∆t is defined over the large number of possible realizations (where symbol ... denotes statistical averaging, which is equivalent to ergodicity).Similar estimation Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 16 April 2019 is made, for example, for collisions between (microscopical) molecules of gas in a (macroscopical) container.Time increment τ should be compared with the full time of the experience ∆t (the traveling time of the object).If ∆t τ, i.e.P = ν∆t = n σV ∆t 1, it can be said then that a collision of the object with one of the (potential) obstacles during its journey most likely would not occur.
In our scenario, V∆t ∼ 3 × 10 4 light-years (distance from the center of our galaxy to the solar system).This is the distance that a traveling object with velocity V ∼ 3 × 10 −3 of light-speed, i.e. 10 3 km/sec, would cover in 10 7 years -not too long of a time in comparison with the age of the universe (∼ 10 10 years).Assuming n ∼ 1 −3 light-years −3 (based on the average distance between stars in the central part of our galaxy ∼ 1 light-year) and σ ∼ (10 −4 ) 2 light-years 2 (which corresponds roughly to the area within Jupiter's orbit, implying that a collision may in fact "perturb" the object and the system, and thus end the journey), the frequency of collisions is then P ∼ 10 −4 1.Even this (higher-end) estimate shows that the object could have reached the current solar system location in about ten million years, without an encounter with another system along the way -indeed our galaxy is very "scarcely populated".Such long journey would have allowed the object to sufficiently cool down, so its nuclear inner state could have approached its thermodynamical instability threshold (see Appendix B and [96]) -this condition allows for the "successful" explosion.In order words, lower "collision" odds actually imply higher "success" odds in our scenario.

Chemical Composition of the Solar System
To explain the chemical composition of the solar system, the conventional theory contemplates the following element-generation mechanisms in the scenario of the solar system evolution [33], [85]: (1) The Big Bang, which generated light elements up to Li.These elements are the basis of the gaseous solar system objects -the Sun and the giants.
(2) Continuous ejections from interiors of distant active stars, supernovae, and stellar collisions, which over the lifetime of the Universe, have created a (location-specific) interstellar background level containing (stable and long-living) elements from carbon to uranium.
(3) Continuous disintegration of heavier nuclei into lighter ones by cosmic radiation in interstellar medium, which presumably have filled the element-gap between Li and C.
(4) (Hypothesized) several supernovae that must have occurred not too far and not too close to the solar system (see Sec. 1).
(5) (Hypothesized) at least five, distinct and distant, contributing events which all must have occurred within the span of about 20 Kyrs.These events need to be presumed in order to explain the detected presence and mixing of certain isotopes in meteorite samples (see Sec. 1).
(6) (Hypothesized) local high-energy process (within the solar system) suggested to explain the detected presence of 7 Li in meteorite samples. 7Li is produced by decay of 7 Be whose half-life is only 53 days (see Sec. 1).
(7) (Unknown) "something" that must explain the excess (beyond the so far considered models) of certain proton-rich isotopes (see Sec. 1).
In the alternatively proposed (nuclear-fission-type event) scenario, the number of hypothesized events and mechanisms can be significantly reduced and the unresolved item ( 7) gains an explanation.Naturally, the Big Bang and the interstellar-background enrichment events (those that are typical for the neighborhood where evolution of the solar system took place) are the mechanisms that generated nuclei of the original protonebula -they are the natural formational basis of the solar system, identical in both scenarios.But events (4)- (7), conventionally hypothesized to explain the presence of nuclei that are anomalous for the solar system, are no longer required.While other stellar cataclysms may still have contributed to the full inventory of nuclei in the solar system, we proposed that just one eventthe nuclear-fission-type event -was the primary source of all exotic nuclei found in the solar system (and the material concentrated in the terrestrial belt).
To put it simply, the essence of the proposed event is that the arrived-from-afar "chunk" of nuclear matter -the (thermodynamical) state of which was "sufficiently" close to nuclear-phase-transition Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 16 April 2019 threshold (see Sections 3.2, 3.3, and Appendix A) -once became perturbed, partially or fully shifted into the (unstable) state of "nuclear fog" (mixture of droplets of nuclear "liquid" and "gas" of proton, neutron, α-particles, etc.).As known, once in the unstable state, the "droplets" (hyper-nuclei with super-large nucleon numbers A) experience spontaneous splitting (fragmentation and/or fission) into fragments of, generally speaking, random (not necessarily equivalent) mass.At each of the numerous subsequent steps, the resulting smaller "droplets" continue to spontaneously split until about A ∼ 200.The overall process self-organizes along random reaction channels.The environment is abundant with free protons and neutrons, powerful γ-radiation, etc.The "temperature" is enormous (this term is only conditionally used here because, as known, in rapid non-stationary processes this thermodynamical parameter is not properly introducible).Naturally, in such conglomerate of components, not only reactions of "fission" (transformations from large to small A) but also reactions of "fusion" (transformations from small to large A) take place.Importantly, these reactions can occur along any and all conceptually possible channels, thus leading to production of any and all of the detected isotopes (i.e. the entirety of the material observed in the terrestrial belt).This is how the proposed event can generate all the nuclei aimed to be explained by the conventionally hypothesized events ( 4)-( 6), as well as the not-yet-explained ones (7).
However, currently, to quantitatively analyze the process, a set of model equations is difficult to construct.The process is thermodynamically non-stationary, and therefore, in our opinion, even in the simplest semi-empirical form, such analysis would require development of a system of kinetic equations, the complexity of which would be mind-boggling.Obviously, the rates of concentrations' evolution (time-derivatives in the left sides of these equations) are defined by the mechanisms of inter-component interactions which are described (in their simplest forms) by pairwise-and crossproducts of components' concentrations (with possible emission and decay retardation effects) and by kernels/coefficients of interactions.But for the temperatures and densities characteristic for the hypothesized nuclear-fission-type event, no experimental data exist that could substantiate the structure of these kernels, even approximately.

Planetary Structure of the Solar System
Section 1 has listed a number of puzzles of the solar system' structure and configuration.They are unresolved in the conventional framework, but immediately make sense once the nuclear-fission-type event is hypothesized.
For example, in the conventional framework, the very existence of the bimodal planetary structure is perplexing and the process of formation of two classes of planets in the solar system is not fully understood [69].The consensus is unanimous that rocky planets formed by accretion, but two competing theories continue to exist about formation of gaseous planets because inconsistencies remain within each theory.With respect to the giants, the core accretion model explains why they have larger concentration of heavier elements than the Sun has, but numerical simulations yield formation times that are way too long unless the mass of the primordial nebula is increased.The disk instability model produces much more rapid formation rate, but does not explain the observed chemical enrichment of the planets.
Within the framework of the proposed nuclear-fission-event hypothesis, the evolution scenario is straightforward and self-consistent, accepting both accretion and disk-instability models but utilizing them sequentially: first the gaseous giants formed as the result of protodisc instability, and only after that, and after the proposed explosive event, the post-fission-cascade "debris" accreted into rocky bodies of the solar system and also enriched the original gaseous giants.
In favor of such scenario speak numerous features of the solar system.Indeed, if observed from afar, the set of terrestrial planets would be virtually unnoticed -mass-wise it is negligible (< 10 −5 M ) and distance-wise it is effectively lumped near the Sun.Unlike the bulk of known exoplanetary systems, the orbits of the solar system's giant planets are remarkably widely spaced, nearly circular, and show no resonance (see, for example, [31], [6], [54], [68]).To explain its present, stretched and relaxed Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 16 April 2019 state, in the conventional framework, an evolution scenario is required where the outer solar system underwent a violent phase when planets scattered off of each other and acquired eccentric orbits [98], [99], followed by the subsequent stabilization phase.Within the framework of the nuclear-fission-event hypothesis, the proposed explosion may be the one responsible for the "violence" implied by the observations.
The finding that model simulations struggle to find plausible evolution scenarios (that end up settling the existing giants at their current orbits) unless a fifth giant, eventually ejected or destroyed, is included [72], organically fits with the proposed nuclear-fission-event hypothesis.Indeed, such (destroyed) massive H/He giant could have served two purposes -it could have triggered the perturbation (deceleration) of the traveling object and supplied abundant protons and α-particles for nuclear transformations.
It is tempting to turn to numerical models of planetary dynamics to help examine the proposed scenario.For example, conceptually, simulations may perhaps clarify how the explosive "encounter" happened -which solar system's object was the most likely "trigger" for the explosion.As discussed in Sec.3.5, three candidates can be envisioned -the edge of the Sun, the then-existing binary companion, or super-Jupiter at the then-first orbit.(Indeed, simulations can perhaps also revisit -in the framework of the proposed hypothesis -the question of how the Sun obtained its 7 o tilt to the planetary plane.)However, to accomplish such simulations, the existing models must first carefully examine and revise their inputs, assumptions, and initial conditions.
The obvious revision is due to the proposed sequential formation of planets.In the proposed framework, during the first stage of the solar system evolution, only gaseous objects formed from the protodisc -via local clumping and rapid gravitational collapse -in line with the disk instability model but assuming longer lifetime for the solar system.(Recall that the currently-assumed age of the solar system -about 4.6 Gyrs -is derived based on dating of meteoritic isotopes.In the framework of our hypothesis, this would be the time when the proposed nuclear-fission-type event occurred.Therefore, the gaseous objects had to form much earlier.)In the second stage of the solar system evolution, after the explosive event, the "debris" accreted into the terrestrial planets (and other rocky objects).The nuclei generated by the event also enriched the pre-existing jovian planets.
The less obvious revisions, but critically important ones, must concern all basal-level assumptions.This is not a trivial exercise because most models are built using outputs of other models and many of the primary assumptions are buried under the layers of complexities.If such assumptions were conditioned or skewed by presumptions of the conventional framework, and if they happen to contradict the newly proposed framework, the erroneous biases will propagate and distort results.For example, as already noted in Sec.3.5, the conventional use of meteoritic data to constrain models has led to the selection of the "hot" rather than "cold" model of thermal regime during planet formation, but in the framework of our hypothesis, inclusion of the constraints derived from meteorites (which formed post-event) would be incorrect when modeling the pre-event stage of the solar system formation.
The need to re-examine all assumptions of the existing models starting from the very beginning -from the protodisc stage -greatly complicates any efforts to quantitately analyze the proposed hypothesis.As noted in [67], "[w]hen the main dynamical forces controlling the rotating disc flattening (gravitational and centrifugal) are in balance, weaker factors, such as the thermal/viscous processes, turbulence, and electromagnetic phenomena dominate the disk's evolution.They affect the condensation of volatiles, [...] and bear significant effect on the relative content and abundance of gaseous species and solid particles, as well as disk energetic and angular momentum transport."Furthermore, "[t]he content and size distribution of solid particles (granules) affects the disc medium opacity and turbulence flow patterns.They strongly influence the disk thermal regime, viscous properties, chemical transformations in a gaseous medium and, in the end, its evolution including the processes' dependence on the radial distance from the protosun and the early subdisk formation."[67] With this reminder, it seems apparent that because the proposed hypothesis posits that solid particles primarily formed after formation of gaseous objects completed, the protodisc evolution scenarios may Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 16 April 2019 meaningfully differ between the conventional and proposed frameworks.Differences in the (modelled) protodisc composition may lead to meaningful differences in how and where (and how many of) the gaseous bodies formed.The subsequent planetary dynamics would be affected.Other consequences may also follow.

Conclusion
Despite the widely popular belief that formation of the solar system is well understood and only nuances remain unresolved, serious conceptual gaps in the understanding continue to exist.These gaps concern both the chemical composition and the planetary structure of the solar system.The conventional models fail to resolve (at all, or self-consistently) such puzzles as the unexplained existence of the trimodal structure of the solar system and the presence of p-nuclei, post-post-Fe-nuclei, and short-lived nuclei (Sec.1).Currently, to explain the presence of the nuclei that are non-native for the solar system, quasi-simultaneous occurrence of numerous explosive stellar events (unusual for the solar system neighborhood) is hypothesized.(Notably, inconsistencies within and between the existing models still remain.) But as Occam's Razor principle suggests, simpler solutions are more likely to be correct than complex ones.In contrast with the multi-event framework, we propose that just one event can resolve all the existing puzzles altogether.All pieces of the "grand puzzle" fall in place if one presumes that a nuclear-fission-type event occurred within the inner part of the solar system at the time that we currently define as the birth of the solar system based on dating of meteoritic isotopes.Recall that so far conventional models considered mechanisms of nucleosynthesis and/or induced disintegration; the mechanism of fragmentation / fission has not been suggested yet (not in the solar system enrichment context, nor in any other enrichment context).
Conceptually, the nuclear-fission-type event could create all the nuclei defining "rocky" objects of the solar system -the terrestrial planets, meteorites, asteroids, and likely the cores of the gaseous giants.However, this event had to be such that it did not destroy the solar system, but impacted its composition and orbital structure to such degree that the system eventually settled into its present (much different from its original) state.
We defined and discussed the key elements of such scenario (Sec.3), but how exactly the details unfolded is not possible to say at this time.The challenges are rooted in the needs to (1) develop a valid model set of kinetic equations for the (non-stationary) nuclear transformation cascades, for which no substantiating experimental data exist due to enormous temperatures and densities of the nuclear matter involved in the scenario (Sec.4.3), and (2) examine and revise basal-level assumptions in all models of planetary formation and dynamics (starting with the protodisc evolution stage), which then face enormous uncertainties because, at minimum, the conventional constraints offered by meteoritic data must be set aside for the pre-event timeframe (Sec.4.4).Until these challenges are dealt with, any attempt at "quantitative analysis" or "numerical simulation" of the proposed scenario would be not just speculation, but profanation.
Instead, once the spectra of plausible cascades of nuclei transformations are (experimentally or at least theoretically) mapped out, one way to advance this hypothesis would be to solve the inverse problem: to find out (with proper correction for the fluctuations/uncertainties-driven "noise") what initial conditions had to be so the model resulted in the (actually measured) abundances of elements on Earth and in samples from other objects of the solar system.
Our current proposition is just a hypothesis.As more scientific data become available, certain aspects will certainly require adjustments, if not outright revisions.Nonetheless, the general idea can remain insightful.Conceptually, the proposed hypothesis is capable of explaining a great number of chemical and structural peculiarities of the solar system -peculiarities concerning the formation of two classes of planets, the configuration of the solar system, and the presence of non-native nuclei (and the unexplainably exotic ones, such as p-nuclei).Furthermore, the proposed scenario can even answer, at least conceptually, another intuitively troubling question: how is it that exogenous elements (such as iron, gold, uranium) managed to become clustered -like the deposits at mining sites, or the internally-uniform tonne-plus-sized chunks of the Sikhote-Alin meteorite (composed of 88% Fe, 5% Ni, and 2% Co [15], [18], [81]) -rather than become mixed quasi-uniformly with other granules as they presumably would have done if they had originated in distant stellar cataclysms.The proposed local cataclysm indeed produces "chunks".
To conclude, it is worth noting that, once/if proven to be true with certainty, scientifically speaking, the proposed hypothesis would serve as an important cornerstone in the overall understanding of the solar system evolution.But even now, it's a breathtaking thought that a stellar encounter could have created such marvel -our peaceful planet safely tucked at the perfect distance near a tranquil star on a quiet galactic periphery, the planet enriched with such variety of chemical elements that complex intelligent life forms were able to develop and prosper.How many other corners of the universe may be this fortunate?Possibly none.Indeed, while seeking scientific insights to solve nature's puzzles and developing technological advances to fulfill humans' wishes, it is important to remember to also seek comprehension of the gnoseological and moral implications of the discovered knowledge (and its power).We hope that this hypothesis contributes to these pursuits in multiple ways.

Appendix A
The fact that nuclear matter may in fact exist in the two-phase state has been known for a while.The equations of state of a multi-body system of nucleons interacting via Skyrme potential is presented in Fig. 2. The very steep part of the isotherms (on the left side) corresponds to the liquid phase.The gas phase is presented by the right parts of the isotherms where pressure is changing smoothly with increasing volume.Of special interest is the part of the diagram where the isotherms correspond to the negative compressibility, i.e. (∂P/∂V) T > 0. This is the so-called spinodal zone where the matter phase is unstable and can exist in both liquid and/or gas states.Within the spinodal zone lies a particularly unstable two-phased region (marked by the hatched line in Fig. 3), in which random density fluctuations lead to almost instantaneous collapse of the initially uniform system into a mixture of two phases.For nuclear matter, it is either liquid droplets surrounded by gas of neutrons, or homogeneous neutron liquid with neutron-gas bubbles (i.e. the spinodal zone where the square of adiabatical speed is negative, is inside the coexistence zone where the square of isothermical speed is negative).Critical temperature T c for the liquid-gas phase transition is a crucial characteristic of the nuclear equation of state.
A typical set of isotherms for an equation of state -pressure versus density with a constant temperature -corresponding to nuclear interaction (Skyrme effective interaction and finite temperature of Hartree-Fock theory, see Jaqaman et al [49]) is shown in Fig. 4. It exhibits the maximum-minimum The dash-dotted lines are the coexistence lines, the dotted lines are the spinodal lines.From Borderie [9].See also, Borderie and Rivet [10].
In a scenario when an object decelerates, significant stratification means s 2 /w < R s , where R s is the characteristic size of the object.The magnitude of deceleration, w, may be estimated as w ∼ (ρ t /ρ s )V 2 /R s .This gives Since R s R t and ρ t ρ s , it necessarily implies that for a significant density stratification to take place, the elasticity of the inner matter (characterized by s 2 = (∂p/∂ρ) T , calculated at constant temperature) must become "small" in the course of events.This is possible when the mono-phase state (liquid) of the matter approaches its thermodynamical (gas/liquid) stability threshold.

High-Velocity Collision of Drop with Obstacle
When a droplet collides with some object (obstacle), inside the droplet -as known -various motions arise, the velocity of which is comparable with the velocity of the droplet.If the droplet's initial velocity is comparable with the speed of sound within the droplet's matter, then compressibility becomes apparent.
The following effects arise inside the droplet upon collision: excitation and propagation of shockwaves of compression and decompression, interaction of the waves with each other and with free surfaces, formation and development of radial near-surface cumulative jet, formation and collapse of cavitation bubbles inside the droplet, and other complex hydrodynamic phenomena.
Quantitative numerical simulations of these effects show that results are strongly model-dependent, particularly, on the choice of the model EoS for the droplet's matter.Even the qualitative picture of a high-velocity collision is not yet fully understood.Understanding of many aspects remains incomplete, such as roles of viscosity and surface tension even in the case of the simplest model EoS of the liquid, mechanisms of development and destruction of the cumulative jet, estimates of velocity of the radial jet, mechanism of formation of cavities, strains experienced on the obstacle, and so on.
Qualitatively the process of high-velocity collision can be described as follows (see Fig. 6 taken from [23]): During the process of interaction of the droplet with the surface of the obstacle, the flow of fluid forms, which develops a strongly-non-linear wave structure and strongly deforms free surfaces.One of the features of collision of a convexly-shaped droplet is that at the beginning stage, the free surface of the droplet that does not touch the surface of the obstacle, does not deform.The region of compression is confined to the shockwave that forms at the edge of the contact spot (Fig. 6a).
Furthermore, there develops a near-surface wave.(The front of which is tangential to the front of the shockwave, and starts from the edge of the contact spot.It is not shown in Fig. 6a) This is explained by the fact that the speed of expansion of the contact spot V 0 (t) = V 0 cot β(t) (here V 0 is the initial velocity of the drop, β(t) is the angle between the drop's free surface and the obstacle's surface at moment t) is greater than the speed of propagation of the shockwave within the droplet's medium from time zero to the critical moment t c when these speeds match -the speed of the contact spot boundary diminishes from its infinite value at the moment of contact, but remains greater than the speed of the shockwave until the moment t c .Therefore, during this time perturbations expanding from the contact spot do not interact with the free surface of the droplet.At the edge of the contact spot, compression of the droplet's liquid is maximal.
At the critical moment of time t c , the shockwave detaches from the edge of the contact spot and interacts with the free surface of the droplet, and a reflective decompression wave forms which propagates inward (toward the central zone of the drop).The free surface becomes deformed, and a near-surface high-velocity radial jet of cumulative type forms (Fig. 6b).The time of formation of the jet depends on the viscous and surface effects within the liquid near the surface of the obstacle, its velocity substantially exceeds the velocity of collision.
Once the wave is reflected from the droplet's free surface, the change in polarity of impulse occurs.The reflective wave of decompression forms a toroidal cavity, the cross-section of which is qualitatively shown in Fig. 6c.
At the final stage of interaction, the wave of decompression collapses onto the axis of symmetry, and forms a vast cavity with most decompression occurring in the region near the axis (Fig. 6d).
During the propagation of the decompression wave toward the surface of the obstacle, the cavity fills almost the entire volume of the droplet, except for the thin layer near the droplet surface and the zone occupied by the near-surface jet.As the result of development of instability within this thin envelop, the droplet becomes shaped as a "crown", and the matter of the droplet becomes splashed out in small fragments.Thermodynamic Instability If a system is thermodynamically unstable, the rapidity of development of small spontaneous perturbations of density is determined by the parameter called "adiabatical sound speed".This parameter (dimensionless here) for relativistic fluid is calculated using expression V 2 s = (∂p/∂ε) s where p is pressure and is internal energy per particle.Quantity V 2 s is calculated in condition that entropy per particle, s, is constant.However, pressure and internal energy are frequently given as functions of density z = ρ/ρ c and temperature θ = T/T c .In this case, it is natural to calculate V 2 s using Jacobians and their properties (see [56], [87] for details): Once the expression for free energy f -the equation of state (EoS) -of the model is known, then pressure p, entropy s, and internal energy , as well as all derivatives in Eq. ( 2), can be found.Then V 2 s can be calculated using standard procedures.Plots of functions P(z) and V 2 s for several illustrative cases are shown in Fig. 7 and Fig. 8 (borrowed from [96]).The domain of inner matter where P(z) < 0 and V 2 s < 0 is the spinodal region in plane (z, θ) (shown in Fig. 9).When V 2 s < 0, the system becomes unstable with respect to small spontaneous perturbations (fluctuations).The lowest curve represents the hypothetical case where the thermal term in the expression for free energy is omitted.All curves below the critical isotherm, i.e. when θ < 1, possess two turning points (z 1 < z 2 ) where (∂ z p) z=z i = 0, i.e. s 2 (z i ) = 0.In the domain 0 < z < z 1 , the matter is in its gas state.In the domain z > z 2 , the matter is in its liquid state.Between z 1 and z 2 , lies the zone where the gas and liquid phases co-exist.
In view of certain limitations on thermodynamical functions, a thoughtfully-designed interpolating expression for the dimensionless free energy may be constructed from which all thermodynamical quantities can be found.
Here are the considerations for such interpolation [96]: For small densities, z → 0, the interaction between particles is weak, and the dominant term is the first term which describes a gas of non-interacting particles.As the density increases, the properties of the system differ more .Square of adiabatical sound speed V 2 s (z), normalized by the speed of light, as function of normalized density z, for the model of nuclear-drop-like object with equation of state described by interpolating expression permitting mono-and two-phase states [96].Several values of normalized temperature θ = T/T c are shown: critical isotherm θ = 1 (upper line), θ 0.84 (touching horizontal axis), and θ = 0 (lower line).Domain with V 2 s (z) < 0 (where sound speed V s (z) is imaginary, i.e. the system is unstable) is the so-called "spinodal" zone, in which small spontaneous initial perturbations of density will grow exponentially fast once triggered.Development of instability in homogeneous medium leads to formation of two-phase pockets where liquid (drops) and gas (vapor) states co-exist.Only the states with temperatures below some temperature θ * (unique for the medium), for which the curve V 2 s (z) touches the horizontal axis in plane (z, V 2 s ), may experience such instability.For the states with θ > θ * , the speed of sound is always real (V 2 s (z) > 0) and the matter remains in its mono-phase state.
and more from the properties of the ideal gas, the interaction (logarithmic term in expression for pressure) becomes more and more significant.With further increase of density, z 1, the gas enters its condensed state (liquid) -the term ∼ z in expression for f becomes most important.For high densities z, the equation of state has to be "hardened" to account for the dominance of the "repulsive core" in the potential of particle interaction.In such "hardened" state, repulsion between particles is very strong, and the properties of this interaction no longer depend on the specific type of the liquid, thus the corresponding term in the free energy has to have the universal form for the pressure p ∼ z 2 [104].
Furthermore, conceptually, and in view of specific experimental data, the interpolating expression incorporates the following considerations: (a) the equation of state (EoS) following from f has to have a form admitting the existence of the critical point where p = ∂ z p = 0; (b) the pressure p(z 1 ) = 0 for some value z 1 = 0; (c) the critical density ρ c is of order of (0.1 ÷ 0.4) ρ 0 , i.e. z 1 (3 ÷ 7); (d) compressibility factor K ∼ (240 ÷ 300) Mev; (e) the principle of causality must be respected -the adiabatical sound speed must be always smaller than the light speed [96].
Analysis of the model with such interpolating expression, demonstrated theoretical possibility of existence of the spinodal zone -where the square of the sound speed is negative -for temperatures below critical, for a nuclear-drop-like object of any (even very small) size [96].This signifies that, within the domain, small spontaneous initial perturbations of matter density do not propagate as acoustical waves in certain structures composed of nuclear matter, but grow exponentially fast (at the beginning of the process).This instability process leads to formation of the two-phase (coexisting liquid-gas) state.
It is important to underscore, that in the proposed model for free energy, the speed of sound is always less than the speed of light, V 2 s < 1 (the causality principle is respected).Spinodal region for the model of nuclear-drop-like object with equation of state described by interpolating expression permitting mono-and two-phase states [96].Inside the domain, V 2 s < 0; outside the domain, V 2 s > 0. On the (θ, z)-graph, pressure points p = 0 are shown as black dotstheir coordinates are (5.5, 0), (4.7, 0.3), and (1.74, 0.83).Any process that decompresses and cools the system adiabatically (along line θ = θ 0 (z/z 0 ) 2/3 ) from its initial mono-phase state (z 0 , θ 0 ) would trigger development of collective instability and fragmentation of nuclear matter, once the system is in the spinodal region.

Energy Effects
A stationary spherical configuration with the above-mentioned equation of state can indeed (theoretically) exist [96].
In general, a stationary spherical configuration exists only if the boundary condition for pressure p = 0 is respected for some z 1 = 0.This means that (in terms of Fig. 7 graphs) for a given θ 1 there must exist an intersection of curve p = p(z, θ 1 ) with horizontal axis p = 0.The intersection value z 1 = 0 is the boundary value of density which corresponds to p(z 1 , θ 1 ) = 0.
If some mechanism -collision-evoked deceleration, for example -heated up the colliding object, the object's inner state would shift into another state characterized by the new (higher) temperature, θ 1 → θ 2 > θ 1 .In terms of Fig. 7 graphs, the new p(z, θ 2 )-curve might rise above the horizontal axis p = 0 in such a way that no intersection points would theoretically exist.Physically, that would mean that no equilibrium spherical configuration would exist -the system would then disintegrate -the hyper-nucleus would split into fragments (likely unstable as well).Due to the nuclear mass-defect, such fragmentation/fission would release a lot of energy -since nuclear time-scales are extremely short, this would lead to a powerful explosion.

Figure 2 .Figure 3 .
Figure 2. The equations of state P(V) for a nuclear system interacting through a Skyrme potential and a Van der Waals compressible liquid-gas system (shown in relative units).From Jaqaman et al [49].

Figure 4 .
Figure 4. Equation of state for nuclear matter: pressure (isotherms, left panel) or temperature (isobars, right panel) as functions of density.(Parameters are normalized by their critical values).The dash-dotted lines are the coexistence lines, the dotted lines are the spinodal lines.From Borderie [9].See also, Borderie and Rivet [10].

Figure 5 .
Figure 5. Values of critical temperatures of nuclei T c measured by different techniques.From Karnaukhov et al [52].

Figure 7 .
Figure 7. Pressure p(z, θ) as a function of normalized density z = ρ/ρ c , for the model of nuclear-drop-like object with equation of state described by interpolating expression permitting monoand two-phase states [96].Several values of normalized temperature θ = T/T c , T c ∼ 15 Mev are shown: θ = 0 (lowest line), θ = 0.3 (second line from bottom), θ = 0.8255 (second line from top) which contains the point where p = ∂ z p = 0, and the critical isotherm θ = 1.0 (upper line) which contains the point where ∂ z p = ∂ zz p = 0.The lowest curve represents the hypothetical case where the thermal term in the expression for free energy is omitted.All curves below the critical isotherm, i.e. when θ < 1, possess two turning points (z 1 < z 2 ) where (∂ z p) z=z i = 0, i.e. s 2 (z i ) = 0.In the domain 0 < z < z 1 , the matter is in its gas state.In the domain z > z 2 , the matter is in its liquid state.Between z 1 and z 2 , lies the zone where the gas and liquid phases co-exist.

Figure 8
Figure 8. Square of adiabatical sound speed V 2s (z), normalized by the speed of light, as function of normalized density z, for the model of nuclear-drop-like object with equation of state described by interpolating expression permitting mono-and two-phase states[96].Several values of normalized temperature θ = T/T c are shown: critical isotherm θ = 1 (upper line), θ 0.84 (touching horizontal axis), and θ = 0 (lower line).Domain with V 2 s (z) < 0 (where sound speed V s (z) is imaginary, i.e. the system is unstable) is the so-called "spinodal" zone, in which small spontaneous initial perturbations of density will grow exponentially fast once triggered.Development of instability in homogeneous medium leads to formation of two-phase pockets where liquid (drops) and gas (vapor) states co-exist.Only the states with temperatures below some temperature θ * (unique for the medium), for which the curve V 2 s (z) touches the horizontal axis in plane (z, V 2 s ), may experience such instability.For the states with θ > θ * , the speed of sound is always real (V 2 s (z) > 0) and the matter remains in its mono-phase state.
Figure 9. Spinodal region for the model of nuclear-drop-like object with equation of state described by interpolating expression permitting mono-and two-phase states[96].Inside the domain, V 2 s < 0; outside the domain, V 2 s > 0. On the (θ, z)-graph, pressure points p = 0 are shown as black dotstheir coordinates are (5.5, 0), (4.7, 0.3), and (1.74, 0.83).Any process that decompresses and cools the system adiabatically (along line θ = θ 0 (z/z 0 ) 2/3 ) from its initial mono-phase state (z 0 , θ 0 ) would trigger development of collective instability and fragmentation of nuclear matter, once the system is in the spinodal region.