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date: 17 January 2019

# The Formation and Evolution of the Solar System

## Summary and Keywords

The formation and evolution of our solar system (and planetary systems around other stars) are among the most challenging and intriguing fields of modern science. As the product of a long history of cosmic matter evolution, this important branch of astrophysics is referred to as stellar-planetary cosmogony. Interdisciplinary by way of its content, it is based on fundamental theoretical concepts and available observational data on the processes of star formation. Modern observational data on stellar evolution, disc formation, and the discovery of extrasolar planets, as well as mechanical and cosmochemical properties of the solar system, place important constraints on the different scenarios developed, each supporting the basic cosmogony concept (as rooted in the Kant-Laplace hypothesis). Basically, the sequence of events includes fragmentation of an original interstellar molecular cloud, emergence of a primordial nebula, and accretion of a protoplanetary gas-dust disk around a parent star, followed by disk instability and break-up into primary solid bodies (planetesimals) and their collisional interactions, eventually forming a planet.

Recent decades have seen major advances in the field, due to in-depth theoretical and experimental studies. Such advances have clarified a new scenario, which largely supports simultaneous stellar-planetary formation. Here, the collapse of a protosolar nebula’s inner core gives rise to fusion ignition and star birth with an accretion disc left behind: its continuing evolution resulting ultimately in protoplanets and planetary formation. Astronomical observations have allowed us to resolve in great detail the turbulent structure of gas-dust disks and their dynamics in regard to solar system origin. Indeed radio isotope dating of chondrite meteorite samples has charted the age and the chronology of key processes in the formation of the solar system. Significant progress also has been made in the theoretical study and computer modeling of protoplanetary accretion disk thermal regimes; evaporation/condensation of primordial particles depending on their radial distance, mechanisms of clustering, collisions, and dynamics. However, these breakthroughs are yet insufficient to resolve many problems intrinsically related to planetary cosmogony. Significant new questions also have been posed, which require answers. Of great importance are questions on how contemporary natural conditions appeared on solar system planets: specifically, why the three neighbor inner planets—Earth, Venus, and Mars—reveal different evolutionary paths.

# Introduction

In the recent decades great progress has been achieved in the study of our closest space environment—the solar system. Space exploration jointly with the advanced ground-based astronomical observations dramatically expanded knowledge about our star—the Sun and all eight major planets with their numerous satellites and rings, as well as about countless minor bodies—asteroids, meteoroids, and comets and interplanetary space surrounding the Sun—the heliosphere. We knew a lot about the nature of these bodies with implication to the basic ideas of fundamental scientific value concerning the solar system formation and evolution. The discovery of circumstellar discs and especially planetary systems around other stars put this challenging problem of modern astronomy on new ground and allowed us to integrate different theoretical views alongside the data of observations and computer modeling to more coherent concepts. This is one of the most intriguing branches of astrophysics that used to be referred to as planetary cosmogony (Marov, 2015). Being multidisciplinary by its essence, it stands at the frontiers of natural science involving mathematics, physics, and chemistry with close relevance to biology when addressing the problem of life origin and proliferation.

Planets formation is a widespread although very complex process, believed to be the succession of several stages affected by different mechanisms of physical interactions, chemical transformations, and numerous perturbations in the gas-dust disk. Scenarios and model approach to the origin of protoplanetary nebulae and evolution are generally backed by observational data. The mechanical, astrophysical, and cosmochemical characteristics of the solar system serve as the starting concept for the formation of planets around stars. The solar system planets and satellites architecture, as well as existing patterns in the systems of extrasolar planets definitely point to a unified process of every system formation though with different constraints. Data available on surface properties and matter composition for the solar system planets when confronting the samples of material from their embryos (small bodies) and “debris” (meteorites) provide an insight into the probable sources, paths, and chronology of this process.

It is generally accepted that like other planetary systems, our solar system formed from an original molecular cloud (protosolar cloud) consisting mostly of hydrogen and helium with a rather small admixture of heavier elements. The process started with the collapse of some fragment of a huge molecular cloud. A major part of its mass concentrated in the center, forming protosun while the rest flattened out into a compressed gas-dust disk, the whole system keeping rotation owing to conservation of angular momentum. In the follow-up process of the disc continuing evolution, the planets with their satellites and swarm of asteroids and comets emerged, which ultimately constituted the solar system family. The lab data on the meteoritic minerals formed during the condensation of chemical elements as well as remelting of the condensed phases allow us to judge the thermodynamic conditions in the circumsolar disk and, in turn, serve as the most important cosmochemical constraints imposed on the numerous analytical and computer models being developed.

# Basic Topics: Understanding and Context

## Historical Highlights

The first attempts to understand how the planets have born and solar system structured were undertaken in the Middle Ages. In the 16th century, Italian monk, doctor of theology, and author Giordano Bruno voiced against the church dogma that Earth is center of the World, arguing instead for a configuration of the solar system with Earth orbiting the Sun. But the truth is never free, and it is often necessary to pay a high price for personal conviction, sometimes with one’s life. This is what happened to Giordano Bruno: For this proclaiming of the truth, he was sentenced by inquisition to be burned on a fire. Nicolas Copernicus, who revolutionized the World system concept, had a more fortunate fate, and we refer to his concept as the real breakthrough in astronomy and philosophy in general. Immanuel Kant, father of the German classic philosophy, in 1755 published the book General Natural History and Theory of the Sky based on a hypothesis put forward in 1749 by Sweden mystic author Emmanuel Swedenborg who suggested that stars are formed in the eddy motions of space nebula matter. Kant hypothesized that planets set up of a dusty cloud that he associated with original Chaos. Famous French mathematician Pier Simon Laplace independently put forward a nearly analogous idea and gave mathematical support to it. Basically, these ideas were preserved until now and underlie the principal concepts of the solar system origin.

Indeed, the hypotheses of Kant and Laplace put forward in the 18th century about the simultaneous formation of the Sun and the protoplanetary cloud, along with the idea of rotational instability responsible for the successive separation of plane concentric rings from the cloud periphery, underlie the current views. The solar system is currently believed to have formed 4.567 billion years ago through the gravitational collapse of a dense fragment (core) of an interstellar molecular cloud with a density > 10−20 gcm−3, a temperature T~5–30K, a mass larger than the solar one by 10–30%, and a dust mass fraction of ~1% (see, e.g., Cassen, 1994; Cassen & Summers, 1984). It is also believed that after the central compressed core of the cloud collapses giving birth to the central star, material from the outer cloud regions continues to accrete onto the disk, causing strong turbulization of the gas-dust medium due to the difference between specific angular momentum of the falling matter and the disk particulate matter involved in the azimuthal (Keplerian) rotation. Observations backed the starting concept that a certain part of the material from the parent cloud (nebula), with an appreciable angular momentum, remains in orbit around the central clump and is incorporated into the protoplanetary disk in the process of stellar collapse. Concurrently, disk matter continues to accrete on the protostar during 1–5 Ma (Myr) and during this time the mass flow decreases by two–three orders of magnitude, while the overall process of first solid bodies formation and eventually their growing to planets take another 10–100 Ma (see Dorofeeva & Makalkin, 2004; Lissauer & de Pater, 2013; Safronov, 1969).

Schematic view of the solar system formation from a collapsed fragment of molecular cloud following by the formation of the proto-Sun and protoplanetary disk, its breakup into individual ring clumps of solid particles giving birth to planetesimals, and ultimately planets through collisional interactions are shown in Figure 1a. A more detailed diagram of the protoplanetary nebula evolution according to Otto Schmidt (Schmidt, 1957) who referred to the pioneering ideas about fragmentation of a primordial dust layer including critical wavelength and mass (Gurevich & Lebedinsky, 1950) is shown in Figure 1b.

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Figure 1a. A basic concept of the origin of the solar system. Scheme for the formation of the solar system, from the collapse of a molecular cloud fragment through the formation of the proto-Sun and protoplanetary disk (1,2), followed by its breakup into individual ring clumps of solid particles, eventually giving birth to planetesimals (3,4). Continuing collisional interactions of planetesimals ultimately leads to the formation of planets (5). Adapted from Wikipedia.

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Figure 1b. A basic concept of the origin of the solar system. Evolution of the protoplanetary nebula according to O. Schmidt. Left side: Sequence of transformations of the original gas-dust disk in blobs growing into rocks and coalescing in clumps of planetesimals. The time span is approximately 104–105 years. Right side: These embryos of planets continue to grow through mutual collisions, eventually to become protoplanets and ultimately a planetary system, here attributed to the solar system. The time span is about 108 years.

Source: O. Schmidt.

It involves the sequence of transformations of the original gas-dust disk in clumps due to growing instability and formation of planetesimals in mutual collisions. These basic ideas were later developed by several authors, forming the key publication (Goldreich & Ward, 1973; Safronov, 1969).

## Important Constraints

When discussing the problem of the solar system origin, we first of all address some of its obvious mechanical and cosmochemical features serving as prerequisites and placing important constraints on the developed scenarios:

• All planets orbit the Sun in the same prograde (anticlockwise when looking from the North World Pole) direction, in coincidence with the Sun’s intrinsic rotation around its axis. The orbits are nearly circular and have a very small inclination to the ecliptic—the imaginary plane containing the Earth’s circumsolar orbit. Similarly, all planets (except Venus and Uranus) rotate in prograde direction and the same is true for the majority of their satellites, which argues that planetary systems formed in a unified process from the same original disk matter. Satellites are locked in resonance with the planet’s intrinsic rotation and therefore they face the planet on the same side, similar to our Moon. The outermost satellites orbiting giant planets behave more randomly, exhibiting both prograde and retrograde orbits and rotations, and they are regarded as small bodies captured later on by the planet’s gravity field.

• There is a peculiar mass and angular momentum distribution in the solar system: While the Sun comprises 99.8% of the whole solar system mass, the planets comprise nearly 98% of its angular momentum. Basically, this resulted from the process of disk evolution and planets formation, though it is not yet clear how the angular momentum redistribution in early solar system history has occurred.

• There is similar cosmic abundance of non-volatile chemical elements in the Sun and most primitive meteorites (carbonaceous chondrites), which are viewed as original pristine substance partially inherited from the protosolar nebula and mostly lost. There is some evidence that inner planets were formed of the matter resembling that of chondrites meteorite composition and experienced dramatic transformations in the course of evolution, while gaseous-icy giant planets preserved their chemical composition essentially unmodified since the origin while the phase compositions have definitely changed as planets grew.

• There exists an obvious correlation of the planetary bulk composition with their distance from the Sun (with a small exemption for Uranus and Neptune), in support of the condensation theory that favors the emergence of different substances from the hot gas disk depending on radial temperature distribution and thus, on the distance from the Sun. Indeed, the theory of condensation, postulating the successive emergence of high temperature and low temperature condensates from the protoplanetary disk matter depending on radial distance from the Sun, may be recognized invoking some geochemical and dynamical constraints. This fractionation is believed to be responsible for the rocky inner planets close to the Sun and gaseous-icy outer planets farther away, that is, rocky composition of the terrestrial planets containing many refractory elements/compounds and the mostly gaseous and icy composition of giant planets.

• The composition of asteroids in the main asteroids belt between Mars and Jupiter orbits is intermediate between the silicate/metal rich inner planets and the volatile rich outer planets, which also brings support to the condensation theory and dynamical exchange. In turn, comets are mainly composed of water ice and other frozen volatiles, and these bodies retain the most pristine matter from which the solar system formed. Migration and collisional processes throughout the solar system history and matter transport appear to play the crucial role in the subsequent planet’s evolution. Surfaces of the terrestrial planets have been scarred by asteroidal and cometary impacts and painted with a veneer of volatiles and organic compounds made of potentially life-forming elements that under certain conditions transformed into a biological infestation, at least on Earth.

• Discovery of circumstellar protoplanetary gas-dust discs and extrasolar planets became the great milestone in the advancement of planetary cosmogony. Structure and composition of disks and different configurations of the exoplanetary systems placed important constraints on the origin of protosolar nebula and various scenarios of the planetary system evolution and, based on this onslaught, fueled refining theories and computer modeling of the solar system origin on the comparative approach.

## Basic Scenario

The cornerstone of the overall scenario is an origin of compact, rotating protosolar nebula itself that is fragmented from a primordial molecular cloud—one of the typical residents of the outer space (Figure 2).

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Figure 2. Sequence of protostar-disc formation from an original diffuse cloud. Changes of the parameters involved in the process of evolution are shown.

Source: Smithsonian Astrophysical Observatory/G. Fazio.

It steadily flattened down by intrinsic rotation resulting in differentially rotating gas-dust disk of hundreds of astronomical units across forming around the collapsed central core where the pressure and temperature progressively grew up until thermonuclear reactions were ignited (see Figure 1a). Original composition of the circumsolar cold gas-dust disk, which came out of the protosolar nebula, mainly consisted of the cosmically most abundant hydrogen and helium in the ratio 70.5% to 27.5% by mass (~10:1 by the number particles), while the remaining 1.5% were made of the heavier elements and compounds in either gaseous or solid (dust) states (Lodders, 2003). A part of them are the rock-forming elements such as silicon and metals that have been cooked inside stars from primordial hydrogen atoms. These products were sprayed out into interstellar medium in the final phase of massive stars evolution, some entering cold protoplanetary nebulae from which new stars and presumably planets may form, as it was apparently the case of the solar system origin with its rocky planets and gaseous planets with rocky cores.

The idea that the protosolar nebula was produced by a supernova explosion in the vicinity of a compact gas cloud initially formed through the fragmentation of a more massive gas cluster is acknowledged when addressing the solar system origin (Wasserburg, 1985). The support for this hypothesis comes from the observed enrichment of the Allende meteorite in 26Mg. This stable isotope is the product of radioactive decay of the short-lived radionuclide 26Аl having a half-life of only 0.74 Ma. Provisionally this and other short-lived isotopes produced in supernova nucleosynthesis were implanted into the protosolar nebula in the process of a very fast supernova products injection. Concurrently, there are indications that the solar system formed as part of a star cluster (Pfalzner et al., 2015) that is supported by the observed abundances of short-lived radionuclides implanted into protosolar nebula from a fairly large group of stars, with a caveat that stellar clusters are potentially dangerous environments for planetary systems (Kobayashi & Ida, 2001).

Both ideas favor general views on the important role of short-lived radionuclides in the early solar system evolution. The concept of a supernova explosion that triggered molecular cloud fragmentation is also favored by the modeling results, which suggest that excess pressure was needed to cause the gravitational collapse of a diffuse cloud causing the rapid (~103 yrs) core contraction, similar to the parent cloud of the solar system and the disk separation (Lissauer & de Pater, 2013). In principle, such an excess pressure, along with the process-accelerating turbulization of the interstellar medium, could be provided by the shock waves generated by a supernova explosion (Belloche, Hennebelle, & André, 2006). Before the onset or during the collapse, the rotating core of the molecular cloud can break up into fragments, which would give rise to a single, binary, or multiple star. An important factor contributing to the stability and counteracting the fragmentation of the proto-stellar core (or the collapsing proto-stellar object) is the magnetic field (Klein, Inutsuka, Padoan, & Tomisaka, 2007).

Our current ideas about evolution of the protosolar nebula involving original gas-dust disk formation are rooted in the comparison with evolving solar-type stars. Based on the results of astronomical observations and key astrophysical concepts, we argue that planets form in a common process of stellar origin and can be viewed as a more or less routine by-product of star formation, with the solar system not being an exemption. Basically, stars surrounded by a disk turned out to be quite a common phenomenon found in star formation regions (White, Greene, Doppmann, Covey, & Hillenbrand, 2007). Astronomical observations showed (see examples in Figures 35) that about 20–30% of newborn stars have disk-shaped objects around them but not all appear to evolve toward planet formation.

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Figure 3. The star-forming region NGC 1333 from Spitzer Space Infrared Telescope Facility (SIRTF) observations. The surrounding disks are clearly seen around several stars.

Source: JPL/NASA.

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Figure 4. Gas-dust disks around several stars. The dark bands between the bright regions are clearly seen.

Source: NASA.

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Figure 5. Disk around the star Beta Pictoris. Its extent in every direction from the star is 25 AU; the clearly distinguishable inhomogeneous structure is attributable to turbulent processes in the gas-dust medium on which gravitational perturbations from the planets forming inside the disk may be superimposed.

Source: European Observatory.

The probability of planets formation strongly depends on the mass and metallicity (abundance of elements heavier than hydrogen) of a star defining by its position on the Hertzsprung-Russell diagram of stellar evolution (Johansen, Youdin, & Mac Low, 2009). The mass constraint for a body to become a star (to ignite regular nuclear fusion reaction in the interior) is M $≥$ 0.08 MO. Bodies with M< 0.01 MO are regarded as planets (this threshold is 10 times larger than mass of Jupiter), while bodies in the intermediate range of mass (0.01 MO $≤$ M $≤$ 0.08 MO) are called brown dwarfs. The most relevant stars to possess planets are those of late spectral classes (G, K, M). One may speculate on the scenario of different objects formation proceeding from a part of the Hertzsprung-Russell (H-R) diagram in Figure 6 (Marov, 2015).

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Figure 6. Images of gas-dust disks obtained from STS OPO and Hubble Space Telescope observations.

Source: NASA.

Note that the main parameter defining the fate of a collapsing nebula and planetary system architecture is its specific angular momentum, which results in a single or binary star formation. Fast rotating single stars with protoplanetary disks are formed only from a nebula having some restricted range of (Cassen, 1994; Dutrey, Guilloteau, & Ho, 2007). During accretion of matter from the nebula, an angular momentum is transferred to the star, accelerating its rotation, as it was the case for the Sun, while an inverse process occurred in the course of a nebula stretching at later stages of accretion gas envelope decay, to satisfy the angular momentum conservation law. Indeed, the protoplanetary accretion disks have a significant viscosity, which, incidentally, in combination with the differential rotation of matter, leads to the presence of a constant “intrinsic” source of the internal thermal energy. It is believed that due to the viscous forces of friction (arising from turbulence accompanying the relative displacement of gas suspension elements during their orbital motion), the disk matter drifts toward the protosun along a very gently sloping spiral trajectory as its angular momentum with a minor part of the disc mass is transported outward from the inner disk regions to the outer ones causing the rotation velocity of the protostar to remain well below the instability threshold (Fridman et al., 2003; Königl & Pudritz, 2000; Pudritz, Ouyed, Fendt, & Brandenburg, 2007). This transport is most likely due to turbulent viscosity with α‎ coefficient (Shakura & Sunyaev, 1973) in a rotating, convectively unstable gas disk, which determines radial mass flux and momentum transport as well as the time scale of the disk expansion. Large viscous shear stresses emerging in the Keplerian disk between differentially rotating cylindrical layers were assumed as a source of turbulent motions (Dubrulle, 1993).

Basically, the most realistic source for the loss of angular momentum by the Sun at an early stage of evolution rotation is still debated. Nonetheless, nowadays it is mainly associated with the presence of a partially ionized disc medium and with the action of electromagnetic forces or the emergence of local shear turbulence in a poloidal magnetic field driven by the magnetorotational instability—MRI (Balbus & Hawley, 1991, 1998; Bisnovaty-Kogan & Lovelace, 2001; Suzuki, Ogihara, Morbidelli, Crida, & Guillot, 2016). Additionally, turbulence in the ionized gas medium can be triggered by hydrodynamical instability, such as baroclinic instability and act throughout the whole α‎ disc (Bitsch, Johansen, Lambrechts, & Morbidelli, 2015). Also, potential contribution to the viscous accretion and hence the loss of angular momentum owing to stellar wind outflow was suggested. Note that this mechanism, which was called magnetothermal disk winds from a protoplanetary disk, would decrease the role of MRI (Bai, Ye, Goodman, & Yuan, 2016).

The key role of electromagnetic forces with the turbulence involvement for explaining the transfer phenomenon is justified from the physical viewpoint. According to the present views, shear turbulence and chaotic magnetic fields with energy comparable (or higher) to the energy of hydrodynamic turbulence, are the most likely causes of viscosity in the differentially rotating disks. Besides regular magnetic field lines penetrating the disc, chaotic magnetic fields stretching with accreting plasma, mixed due to the differential rotation of the disk, and experiencing reconnection at the boundaries between chaotic cells should also contribute to the viscosity in the inner and outer disk regions. One may admit that both small- and large-scale magnetic fields (the latter responsible, in particular, for the collimated bipolar outflows, see Figure 8) play an important role in both the angular momentum transport and physical mechanism of accretion (Balbus & Hawley, 1998; Kolesnichenko & Marov, 2008; Marov & Kolesnichenko, 2013). Small-scale magnetic fields in the accretion disk as an important source of disk turbulent viscosity and mechanism of the angular momentum transport was confirmed by the respective numerical modeling (Marov & Kuksa, 2015).

Thermal history of the primordial protoplanetary disk is controlled by the several main processes crucially influencing its structure and composition. They include gas/particles heating and photo-evaporation by electromagnetic EUV-X-ray radiation from a protosun causing particles dispersion, turbulent energy release, and condensation of the gaseous phase upon decline of the disk temperature (temperature gradient) with radial distance. Radiative transfer from the protosun was stipulated by the variable disk matter opacity and spectral energy distribution, while turbulence most efficiently affected gas transfer of the differentially rotating disk matter and its viscous evolution with the account of the disk’s local parameters.

At high temperatures close to the Sun, gases could not be retained in the inner disc regions and were exiled outward leaving behind rocky bodies depleted with volatiles, the latter ultimately accumulated in giants. An interesting exercise is to estimate what mass the Earth would have had if volatiles have not been lost (Morrison & Owen, 1988). To do this one may scale the cosmic ratios of H and He to Si based on their cosmic abundances. For hydrogen we have: H/Si = 2.6 x104 by number, or 940 by mass. For helium we have: He/Si = 1.8 x103 by number, or 250 by mass. Let us recall that Earth contains 6 x 1026 g of Si (10% of the total Earth’s mass). Then, with the incorporated volatiles, the mass of Earth would be: (1+940+250) x 6x1026 = 7.1 x1029g. This is about 120 times the mass of the contemporary Earth (6x1027g), or more than the mass of Saturn!

In the process of evolution, accretion of matter from the nebula on the gas-dust disc and from the disc on protosun occurs. Disk matter (< 0.1MO) experiences compression/flattening accompanied by the formation of thin and relatively dense dusty subdisk due to particle settling down to the mid-plane, in combination with radial drift at the early stage of the disk evolution. In the subdisk, the internal gas pressure is not sufficient to prevent gravitational collapse of rather large dust particles in a region filled with gas-dust matter. If chaotic turbulent velocities of dust particles are not too high and surface density of the massive dust layer is large enough, a gravitational (Jeans) instability develops, in compliance with the classical Goldreich-Ward scenario of planetesimals formation (Goldreich & Ward, 1973). Gravitational instability is thought to be responsible for the appearance of primary dust clusters in the predominant ring-shaped subdisk configuration (Ziglina & Makalkin, 2016; Nakamoto & Nakagawa, 1994; Toomre, 1964; Youdin & Shu, 2002). Most recently amodification of the Jeans instability criterion for astrophysical disks was suggested based on generalization of Boltzmann-Gibbs statistics (non-extensive statistics, Tsallis, 1988) approach (Kolesnichenko & Marov, 2014). The criterion was derived from a modified kinetic equation with special form of the collision integral with application to uniform disc medium having fractal structure in the phase space.

An alternative (or rather complementary) approach is of hydrodynamic nature. The underlying concept is misbalance between surface gas-dust density and mass transfer. Two main scenarios of such instability have been suggested. The first one stems from an idea that disc/subdisc turbulence may produce local regions (patches) with the enhanced dust/gas ratios that grow and evolve eventually toward planetesimals (Youdin & Goodman, 2005). Basically, it is focused on a passive concentration of particles by turbulence on the large scale (comparable to the turbulent dissipation scale) either inside vortices serving as particle traps (Marov & Kolesnichenko, 2013) or in zonal flows (Johansen, Youdin, & Klahr, 2009) including aerodynamically promoted regions between vortices (Cuzzi, Hogan, & Shariff, 2008; Pan, Padoan, Scalo, Kritsuk, & Norman, 2011). The second scenario invokes an existence of feedback between gas and condensed particles in the two-phase stream, in other words, backward reaction of particles forcing in a gas stream. Such a coupling between the gas and dust is usually referred to as linear streaming instability (Youdin & Goodman, 2005; Youdin & Shu, 2002) responsible for generation of original pre-planetesimal seeds. In numerical modeling, dust/gas densities and some other parameters necessary for this mechanism to work were revealed. Large dusty clumps, specifically those containing cm-scale grains grown in the preceding collision/coagulation processes, can influence an efficiency of streaming instability. It was also shown that nonlinear evolution of streaming instability can be followed by gravitational instability under smaller dust/gas ratios (see Armitage, 2007; Bai & Stone, 2010; Chiang & Youdin, 2010; Drazkowska & Dullemond, 2014; Jacquet, Balbus, & Latter, 2011; Johansen et al., 2007; Johansen, Youdin, & Klahr, 2009; Yang & Johansen, 2014; for further discussion). Besides, shear turbulence caused by different gas and dust velocities in heterogeneous disk matter is responsible for the onset of Kelvin-Helmholtz instability (Garaud & Lin, 2004; Marov & Kolesnichenko, 2013).

Clusters resulting from streaming/gravity instabilities appear to contain micron-size grains including presolar dust and nebular condensates. The latter formed at different temperatures depending on radial distance—from refractory compounds in the proximity to protosun to ices farther away. Mutual collisions of clusters and dust particles with different size distribution therein are supposed to lead to further particles growing with the additional involvement of processes of coagulation/coalescence and the formation of more dense structures. The follow-up process involves continuing growth of forming bodies with emergence of the largest ones that accumulate most of the smaller bodies and dust through collisions and gravity attraction, while the remaining gas flowing inward is lost. The process eventually results in formation of numerous denser planetesimals of tens to hundreds of kilometers across and then planetary embryos from which planets ultimately are formed (see, e.g., Kolesnichenko & Marov, 2013; Marov, 2005; Weidenschilling, 2000; Wetherill & Stewart, 1989).

The protoplanetary accretion disk is supposed to be fully dissipated in about the first 4–5 million years after the solar system origin. During this period accumulation of primary solid bodies through runaway (oligarchic) growth while sweeping up residual planetesimals from their accretion region, as well as the process of gas accretion on the outer giant planets occurred (Lissauer & de Pater, 2013). A longer time (about 30–100 million years) was required for terrestrial planets formation through the classical collisional growth of bodies inherited from the former phase ensuring pumping up their relative velocities sufficient to mutual accumulation of the largest embryos into planets. The overall process of the solar system formation occupied altogether roughly 108 years. Asteroids and comets are regarded as the remnants of this process. Similar processes appear to occur in extrasolar planetary system formation around not only single but also binary and multiple stars with the peculiar systems’ dynamics (Marov & Shevchenko, 2014, 2017).

## Cosmochemistry and Chronology of Evolution

Of primary importance is an opportunity of getting insight into the chronology of the key physical and chemical mechanisms responsible for the early solar system evolution. Study of meteorites is the main tool of cosmochemistry aimed to reconstruct the processes of matter origin and transformations in the protoplanetary disc and forming bodies.

The time sequence was established based on the measurements of ratios of long- and short-lived isotopes and products of their decay in meteoritic materials. The main isotopic systems used in the study were U, Th-Pb, Sm-Nd, Al-Mg, Mn-Cr, Rb-Sr, I-Xe, Hf-W. Many undifferentiated meteorites (chondrites) contain the refractory inclusions of microns to cm in size enriched in refractory elements such as Al and Ca (Calcium Aluminum Inclusions or CAIs). They were assumed to belong to the ancient solid material that condensed out near the Sun (r < 0.5 AU) at Т ~2000–1700 K (Grossman, Ebel, & Simon, 2002; MacPherson, 2005; Meibom et al., 2007). These objects, including some ultra-refractory mineral nodules (Ivanova, Krot, Nagashima, & MacPherson, 2012; Ivanova, Lorenz, Krot, & MacPherson, 2015), enabled a determination of the absolute age of the solar system. The measured values vary from 4567.1 ± 0.1 Ma to 4568.67 ± 0.17 Ma (Amelin et al., 2010; Bouvier & Wadhwa, 2009; Shukolyukov & Lugmair, 2003), with the most reliable being 4567.30 ± 0.16 Ma (Connelly et al., 2012). Thus, the time of the solar system origin is determined with accuracy of better than ~1 Ma, or 0.02%. Concurrently, the absolute age of iron and stony meteorites of different petrological classes was defined from 1 to a few Ma younger CAI (McSween & Huss, 2010). Let us note that the submillimeter chondrules (spherules) embedded in stony meteorites and composed of ferromagnesian silicates are dated in the range from 4567.32 ± 0.42 to 4564.71 ± 0.30 Ma indicating an age gap between CAIs and chondrules with implication that chondrules formation lasted ~3 Ma. This time scale is in accord with protoplanetary disk lifetimes inferred from astronomical observations.

One may assume that during a few million years, interval accumulation and thermal evolution (differentiation) of the parent bodies of these ancient meteorites occurred. Provisionally the first primordial parent bodies of ~100 km in size formed in the very first few million years since the solar system origin. Such a size was sufficient for the body to experience differentiation due to intense heating by the short-lived 26Al and 60Fe nuclides with an iron core emergence. The subsequent core and silicate shell fragmentation caused by numerous collisions have been probably responsible for the existing iron and stony meteorites. Otherwise their existence is difficult to explain, in contrast to non-differentiated chondrites that experienced no melting by the exhausted short-lived isotopes heat source.

The above time scale is in accord with the results of computer modeling that argue that accretion of matter from the disk on the protosun terminated in 1–2.5 Ma after the system formation. The dust subdisk composed presumably of 1–10 cm particles is believed to form much earlier, in 0.01–0.1 Ma at radial distance r ~1 AU. Here critical density was achieved and gravitational instability developed. Evidently, this time was sufficient for accumulation and thermal evolution of the first solid bodies. Assuming that mass of the protoplanetary disc Md was ~0.1 MS and that with account for the disc partial dissipation ~0.1 Md ultimately entered the planets, we may estimate ~1010 of ~100 km original bodies were born in the first ~2 Ma. This idea is in accord with the models favoring distribution of asteroids from the initial generation of planetesimals of nearly similar size on which chondrules have been presumably accreted (Bottke, Nesvorny, Grimm, Morbidelli, & O’Brien, 2006; Morbidelli, Bottke, Nesvorny, & Levison, 2009; Matsumoto, Oschino, Hasegawa, & Wakita, 2017).

# Further Advancement and Current State

We shall now discuss the state of the art in our views on principal mechanisms of the solar system origin. In modern astronomy, the key consists of high resolution images and spectral features of objects relevant to planets formation at the different stages of evolution. In computer modeling, the focus is given to the theoretical treatment and development of robust models and effective algorithms allowing us to get insight into genesis of planetary system origin from primordial matter of the outer space involving disk formation, its radial/vertical compression, and dust distribution/size grow affecting the disc structure. Unfortunately, unlike protoplanetary accretion disks whose structure and evolution are accessible to astronomical observations, the mechanism of primary solid bodies set up in the gas-dust disk and their growing to planetary embryos remains rather speculative because cannot be yet tested experimentally. Hence, computer modeling is essentially the only tool to reconstruct the multiple processes involved with the use of observational constraints for models verification.

## Astronomical Observations

Generally, our current understanding of the mechanism of solar system origin is in accord with the experimental data available. The discovery of circumstellar disks through high-resolution visual, infrared, and submillimeter observations, and especially extrasolar planets, extend considerably our views of the discs structure and properties of emerging planetary systems with a variety of configurations. Space telescopes such as Hubble, Spitzer, and Herschel provided an exciting picture of how all the ingredients of the cosmic stew that makes planetary systems from a protostar nebula are blended together. The concept needs, however, more rigorous and augmented support and this is the focus of the progressively refined models with an ultimate goal to reconstruct a scenario of evolution and the processes involved.

The fact that a significant fraction of young stars is surrounded by disks had already become obvious by the early 1990s, though historically the first disks were discovered around stars more massive than the Sun, such as Vega (α‎ Lyra). The observations of young protostellar and stellar objects are currently performed over a very wide wavelength range: from X-rays to the radio band. One of the most informative methods for studying these objects is to analyze their spectral energy distributions. The studies of the infrared, submillimeter, and millimeter spectra have revealed gas-dust disks with Keplerian rotation around hundreds of T Tauri stars (young stars of less than 2 solar masses) with ages ranging from 105 to 107 yr. Gas-dust disks have been discovered around most of the observed T Tauri stars with ages 106 yr and around ~20–30% of the stars with ages 107 yr with a mean disk lifetime of 3–6 Ma. The disk masses turned ~0.01–0.2 МO while their extent up to ~100 AU (Andrews & Williams, 2005; Beckwith & Sargent, 1996; Cieza, Kessler-Silacci, Jaffe, Harvey, & Evans, 2005; Dullemond, Natta, & Testi, 2006; Eisner & Carpenter, 2006; Haisch, Lada, & Lada, 2001; Hueso & Guillot, 2005).

Nowadays it is recognized that both young (106–107yrs) and older (107–108yrs) stars possess disks either before entering or already residing on the Main Sequence of the H-R diagram. However, young stars (of T-Tauri type) are grouped in the regions of star formation (such as Orion Nebula) where they dominate (> 70–80%) and contain more gas and dust than the older ones. Obviously, this is because the process of planet formation completed in the older disks and respectively, the major part of matter is in the solid bodies while gas was lost. Dust in these disks appears to have secondary origin as the result of numerous collisions and debris left behind after planets formation and is partially depleted by accretion on growing bodies.

Thermal infrared gas and dust emission measurements and high-angular resolution observations in submillimeter and millimeter wavelength made the most significant contribution to the study of disks’ structure and chemistry, though the data interpretation is not straightforward. They revealed that the bulk of the matter is concentrated in an inner region with a radius of ~40 AU (inner boundary of Kuiper Belt Objects—KBO locations in the solar system) and this similarity of parameters per se suggests that these disks with ages 106–107 yrs are probable precursors of planetary systems (Beckwith & Sargent, 1996; Cieza, Kessler-Silacci, Jaffe, Harvey, & Evans, 2005). The accretion rate (total mass flux) from the disk onto the central star to be estimated: for most stars, it lies within the range $M˙$ ~10–9–10–7МO /yr with a mean value of ~10–8 МO/yr; in the range of stellar ages from 105 to 107, there is a tendency for the flux to decrease from 10–7 to 10–9МO /yr (Calvet, D’Alessio, Hartmann, Wilner, Walsh, & Sitko, 2002; Hueso & Guillot, 2005). A rather low gas content in the range of 10–2 to 10–3 disk mass was found indicating low gas to dust mass ratio of the order of 10 in contrast to an earlier estimate of nearly an order of magnitude higher (Williams & Best, 2014).

Many molecular species were identified and their isotopic compositions were measured (Dutrey, Guilloteau, & Ho, 2007; Rab, Baldovin-Saavedra, Dionatos, Vorobyov, & Gudel, 2016). Numerous molecules found in protoplanetary disks (such as H2O, СО, N2, H2CO, HCN, etc.) are probably genetically related to the volatiles contained in the frozen granules of primordial accreting material. They are supposed to be subsequently subjected to substantial chemical and thermal processing. Some of these molecules are apparently ionized or in non-equilibrium state due to the photolysis attributable to far ultraviolet and X-ray radiation from a young star. Observations carried out with the Spitzer Space Telescope allowed the discovery of several young stars surrounded by disks in a fairly small star-forming region (see Figure 3). The size of some disks is comparable with the Neptune orbit in the solar system (Figure 7).

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Figure 7. A part of the Hertzsprung-Russell diagram. Diagonal lines running from the upper left to the bottom right are disc radii from 10 AU to 0.1O. The solid curve represents the main sequence. Tracks for protostars of the solar (larger and lower) masses are shown. Objects having М<< МO do not reside in the MS.

Source: Marov (2015).

Note that the Kuiper belt could be regarded as analogous to the low-mass dusty debris disks observed around many Main Sequence stars where existence of planets is evidenced by some disk warping (Lagrange, Backman, & Artymovich, 2000).

Of great importance for understanding evolution of the protoplanetary accretion disk, in particular its inhomogeneous structure, thermal regime, and dynamics of its inner regions, are the data on dust composition and evolution (Alexander, Boss, Keller, Nuth, & Weinberger, 2007). Observations were carried out in the optical, near, and thermal infrared spectral ranges and included measurements of emission spectra with the long baseline interferometry in the millimeter wavelength. Many specific features in the thermal gas-dust emissions were revealed, including sources for chemical processing of disc gaseous matter and finding spectacular dust rings (ALMA Partnership) (ALMA Partnership, Brogan et al., 2015; Andrews et al., 2016; van der Marel et al., 2013; Perez, Isella, Carpenter, & Chandler, 2014; Pinte et al., 2016). The physical characteristics and mineralogy of dust particles were inferred assuming a close analogy with meteor particles in the Earth’s atmosphere. Interestingly, disk particles turned out to be much larger than micron-size dust in the diffuse interstellar medium: The largest are millimeters to centimeters across and resemble sand or even pebbles (Beckwith, Henning, & Nakagawa, 2000; Natta et al., 2007). Moreover, they exhibit the height stratification, with the smaller micron-size particles being concentrated near the disk surface. Such stratification is thought to persist for millions of years. Naturally, the 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 (see Figure 8).

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Figure 8. Scheme for the formation of a gas-dust accretion disk and a subdisk. The proto-Sun onto which matter from the protoplanetary nebula (the red color) continues to accrete is at the center. The green color indicates the forming dust subdisk, near which the outflow of gas and dust, including the formed high-temperature condensates in the inner zone, such as refractory CAIs, takes place. The blue color indicates the bipolar flows of matter attributable to the solar magnetic field.

Source: International Space University.

Based on observed particles’ properties, it may be reasonably assumed that their genesis is related to the formation very close to protostar and that some of them may have undergone the follow-up processes of evaporation-crystallization during radial motion in the disk. Besides, they may experience heating by shock waves in the accretion zone and subsequent rapid cooling. In accord with this concept is the finding the same type of rather refractory materials in comets, in particular those coming from the frigid outskirts of our solar system. Comets are known to have been born in regions beyond the line where water becomes frozen (called the snow line) and are referred to as remnants of the icy planetesimals. A probable scenario one may assume is that comets formed due to gravitational collapse of pebble clouds emerged through the streaming instability (Lorek, Gundlach, Lacerda, & Blum, 2016), which acquired the solids that would have been frozen into comets in the planet-forming disk regions.

## Computer and Lab Modeling

The matter of the protoplanetary gas-dust disk is a complex system of the different phase composition, densities, temperatures, and degrees of ionization, which vary with radial distance. Basically, it is an inhomogeneous medium composed of gas and dust particles of various sizes and origin. This matter, which is generally magnetized dusty plasma, is in a state of turbulence depending on the radial and azimuthal position of a parcel of matter (Marov & Kolesnichenko, 2013).When 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 certainly affect the condensation of volatiles, including first of all water, 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.

When the plasma effects are disregarded, the motion of a disk medium containing dust suspended in gas can be modeled most adequately within the framework of mechanics of heterogeneous turbulized media with allowance made for the physical-chemical properties of the phases, heat and mass transport, incident radiation/opacity changes, viscosity variations, chemical reactions, phase transitions, coagulation, fragmentation, etc. The rigorous mathematical treatment of the problem is presented in Marov and Kolesnichenko (2013). Specifically, it is focused on the dynamical interaction of turbulized gas and dust including modification of the turbulence energy of the carrier phase by solid particles (i.e., the reverse effect of the dust component on the turbulent and thermal regimes of the disk gas component); the influence of turbulence on the rates of phase transitions (evaporation, condensation); on the jump-like disperse particle accumulation processes such as coagulation and fragmentation during mutual collisions between particles in the mass flow; and, finally, on the settling of solid particles through the gas to the disk midplane, where they form a flattened dust layer—a geometrically thin subdisk.

Obviously, the presence of polydisperse (different particles’ size) admixture in a turbulized medium complicates significantly the disk hydrodynamics, contributing to the realization of additional regimes of cosmic matter flow. Note that the synergetic collective self-organization processes in the thermodynamically open system of the protoplanetary disk against the background of a large-scale shear flow of cosmic matter associated with its differential rotation are regarded as very important mechanisms shaping the properties of a viscous accretion disk at various stages of its evolution (Kolesnichenko & Marov, 2006b; Nakagawa, Sekiya, & Hayashi, 1986).

Whatever is the character of events under consideration, it is clear that complex physical and chemical processes accompanying evolution of the heterogeneous medium where dust particles collisions domain, are responsible for the first solids origin and planetesimal’s formation. The developed models include the sequence of changes in the aggregate state of the main protoplanetary matter components; the location of the condensation-evaporation fronts depending on the thermodynamic parameters of the disk; the role of particle sublimation and coagulation in the two-phase medium with the account for particle size distribution; the relative contribution of radiation and turbulence to the heat and mass transport; and the mechanisms for the development of streaming and gravitational instabilities with allowance made for the shear stresses in boundary layers and polydispersed, suspended dust particles (see, e.g., Armitage, 2007; Marov & Kolesnichenko, 2013).

In the most comprehensive approach, a continuum model of heterogeneous disk medium should take into account the joint influence of MHD effects and turbulence on the dynamics and heat and mass transport processes in differentially rotating matter with allowance made for the inertial properties of the polydispersed admixture of solid particles, coagulation, radiation, and changing partitioning of elements between gaseous and condensed phases. Turbulence generated at the boundaries of the protoplanetary disk layers and caused by shear flows corresponds in character to the parameters of a boundary (Ekman) layer and significantly affects the disc dynamics including the Kelvin-Helmholtz instability. It is important to emphasize that generation and maintenance of shear turbulence at various evolutionary stages of the disk involves a two-phase (gas-dust) medium with a differential angular velocity of rotation, different relative contents of dust particles, their size distribution, and coagulation processes. In general, a heterogenic mechanics approach should be applied to account for the emergence of coherent order against the background of random motions in large-scale turbulent structures. Also, the evolution of turbulence in the rotating accretion disk is supposed to be influenced by hydrodynamic helicity responsible for the cascade process of the inverse energy transfer from small to large eddies and negative viscosity appearance in the medium (Kolesnichenko & Marov, 2007).

Currently, a numerical solution of the bulk of problems with allowance made for the heterogeneity of a turbulent medium, radiation, diffusion, chemistry, and MHD effects is hardly possible and only limited approaches are feasible. Note that because terrestrial planets form close to the Sun, the focus in modeling is specially narrowed to the poorly resolvable inner disk regions within several astronomical units, where matter actively accretes onto the young star. This results in the dust/gas ratio, optical opacity, and the thermal regime changes, as well as the significant contribution of photochemical processes in transformation of the matter composition and transfer.

### Thermal Regime

Disc thermal regime is addressed as a key of its original inner structure and first solids formation. The viscous disc evolution with radial temperature lapse rate is regarded as the most realistic scenario of the solar system bodies’ formation (Alexander, Boss, Keller, Nuth, & Weinberger, 2007; Dorofeeva & Makalkin, 2004; Makalkin & Dorofeeva, 1995; Lynden-Bell & Pringle, 1974; Marov et al., 2013).

A hot rather than cold model of planets accumulation from the matter similar to chondriticmeteorites seems most plausible. It is supported by the established differences in the abundances of many elements and their isotopic ratios between the Sun, undifferentiated meteorites, and Earth. Indeed, all chondrites (except CI) and our planet are depleted in moderately volatile (Na, K, Rb, Sn, etc.) and highly volatile (Cs, Pb, etc.) elements relative to the solar abundances that are similar to their abundances in carbonaceous CI chondrites. The depletion is most pronounced in such elements as Bi, Cd, Cs, Hg, In, Pb, Se, Te, Tl, Zn, S, etc. (Lodders, 2003; Palme & Boyton, 1993) that was found to be typical not only for various types of chondrites but also for the bulk composition of the terrestrial planets and some large planetesimals, for example, for the parent bodies of basaltic achondrites—eucrites. Hence one may conclude that the differentiation of moderately and highly volatile elements was an important large-scale process at the early evolutionary stages of the protoplanetary accreting disk under relatively high temperature (Marov et al., 2013).

Basically, the observed depletion of highly and moderately volatile elements could result from either partial evaporation or incomplete condensation of the proto-matter of planets and the parent bodies of chondrites, because the higher the volatility of an element, the greater the depletion. Thermodynamic calculations showed that temperatures of no lower than 1200–900 K are required in both cases (Petaev & Wood, 1998; Saxena & Eriksson, 1986). Under such temperatures only non-equilibrium partial evaporation may occur and indeed, some CAIs show clear chemical and isotopic evidence of that. It is of interest to note that an experimental study of the fractional evaporation of the material of CI chondrites aimed at obtaining the material of chondrites of other types showed that, irrespective of the redox evaporation conditions, the residue obtained through heating differs radically from the actual chondrites material in the abundances of highly and moderately volatile elements (Lipschutz, Biswas, & McSween, 1983). These differences were claimed to be particularly true for the abundances of such pairs of elements as Zn and Se; Sn and Pb; Rb and Cs; etc., with similar degrees of depletion relative to the abundances in chondrites. The results, however, are not unambiguous because all chondritic meteorites are cosmic sediments; that is, their components have formed at very different conditions within the nebula and experienced different thermal history before being accreted together later.

The condensation mechanism for the differentiation of moderately and highly volatile elements accompanied by their incomplete accumulation in the proto-matter of planets and the parent bodies of chondrites seems more justified. For most elements, there is a clear correlation between the degree of depletion and the temperature of its condensation from a solar-composition gas. It is most likely attributable to the influence of the kinetic constraints on the heterogeneous reactions in a gas-solid system associated with the reduction of the reaction surface of small dust particles during their accumulation and some other factors (Fegley, 2000). This allowed us to conclude that much of the chondrites material formed through the condensation of the gas phase of the protoplanetary disk. Temperature initially increased at the disk formation stage, reaching the evaporation temperature of magnesian silicates and metallic iron at a distance of 1 AU (1400 K) and then decreased in the course of viscous disk evolution. In the formation region of the terrestrial planets, it has always remained well above the H2O condensation temperature—it did not dropped below 300–500 K.

Apart from mineral phases containing moderately volatile elements, there are crystalline Mg- and Fe-bearing silicates in chondrites that support the hot protoplanetary disk formation model. One may assume that these amorphous and crystalline silicates formed as a result of the condensation processes in the inner zone of the circumstellar disks. Amorphous silicates of the interstellar molecular cloud from the fragment of which the solar system formed are believed to have evaporated in its inner zone at the early evolutionary stages to be condensed as the nano-to-micrometer sized crystalline silicate grains during subsequent cooling of the disk gaseous phase (Arakawa & Nakamoto, 2016; Ciardi et al., 2005; Honda et al., 2003). One may suggest that the inclusions enriched in the most refractory elements (such as Са and Al composing CAIs, as well as the rare Hf, Sc, Lu, etc.) were the earliest condensates formed near the Sun (r < 0.5 AU) at Т ~2000–1700 K and partially carried outward through the radial drift up to the formation zone of the parent bodies of chondrites with refractory chondrules embedded in their matrix and entered rocky planetesimals. Obviously, a small fraction of them reached r ~5–10 AU, as evidenced by the findings of olivine crystals in the material of Halley and Hale-Bopp comets as well as in the Comet 9 P/Tempel nucleus investigated in the Deep Impact experiment (Wooden, Desch, Harker, Gail, & Keller, 2007).

Several important formation stages of the gas-dust disk around the proto-Sun and its subsequent dynamical, thermal, and cosmochemical evolution, including the non-equilibrium partial evaporation, condensation, and compaction of protoplanetary matter were traced in the framework of quite comprehensive self-consistent numerical model (Dorofeeva & Makalkin, 2004; Marov et al., 2013; Morbidelli et al., 2009). In particular, it yielded the distributions of thermodynamic parameters (Т—Р) in the viscous disk around the young Sun passing through the T Tauri stage, as a function of radial-vertical distance (the rz coordinates). Radial temperature profiles in the disk’s mid-plane at the different stages of its evolution were derived, as it is shown in Figure 9.

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Figure 9. Radial temperature distribution T(r) in the midplane of a protoplanetary disk between 10 and 0.5 AU. 1–4—formation stage between 0.12 and 0.45 Ma (measured in millions of years) from the disk origin; 5, 6—viscous dissipation stage between 0.65 и 1.8 Ma; 7а–7в—stages of dust subdisk compaction and dust clusters formation at about 2 Ma. Temperatures are controlled by the processes of condensation/evaporation of forsterite, enstatite, and iron; maximum values Tsi ≥ 1,600 К at r = 0,1 AU and Tsi ≤ 1,400 К at r = 1,4 AU. Water ice is formed at Tw ~140–160 К under gas pressure Р = 10‒7–10‒4 bar at about 3 AU (break in the dot-dashed curve). The green zone shows the range of possible temperatures at the stage of dust clusters formation.

Source: Marov et al. (2009).

Variation of subdisk dust surface density ρ‎d as a function of the radial distance r, the dust/gas densities ratio and size of dust particles is shown in Figure 10 as a sequence of subdisk dust density evolution, before critical surface density is achieved and the subdisc break up into dust clusters.

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Figure 10. Variation of subdisk dust density ρ‎d depending on the radial distance r from 100 AU for particles of mean size 10 cm (left) and 1 cm (right). Broad diagonal band—critical dust density ρ‎dcr corresponding to the disk gravity instability and its fragmentation into dust clusters. Curves 1–6 – time sequence 0, 1 × 103, 5 × 103, 2 × 104, 5 × 104 and 1 × 105 (yr) from the beginning of subdisk evolution.

Source: Marov et al. (2009). Note that in the refined model, ρ‎dcr approaches at larger r and the ρ‎d change at the snow line is more pronounced.

### Dynamics

It should be specially noticed that solar system formation was intrinsically related to the dynamical processes at all stages of origin and evolution including different kind of resonances defining the system’s structure, configuration, and stability. Complex nonlinear dynamical processes impose certain constraints on the models of disc evolution and planetary embryos origin. The role of dynamics is manifested, in particular, by observations of the formation of some peculiar configurations in the extrasolar planetary systems around the parent solar-type stars (see, e.g., Barucci, Boehnhardt, Cruikshank, Morbidelli, & Dotson, 2008; Ferraz-Mello, Michtchenko, Beaugé, & Callegari, 2005; Marov & Shevchenko, 2017; for further discussion).

The basic principles of the dynamical systems were derived by Anri Puankare and thoroughly developed by the numerous researchers (see Contopoulos, 2002, and citations therein). The main parameters defining planetary system configuration are resonances and dynamical chaos. The study is used to be performed as general N-body problem or in the framework of restricted three-body approximation with involvement of some constraints. Besides resonant and chaotic motions, this approach allowed us to describe periodic orbits, collisions, escape, and other processes of the long-term dynamics based on either analytical or (mostly) on the direct numerical integration of a set of ordinary differential equations. It was shown that orbits of the solar system planets with small eccentricities and inclinations are weakly chaotic and do not exhibit essential secular variations on the time scales comparable with the solar system age. Resonances (a near-exact relation between characteristic frequencies, e.g., orbital periods, of two bodies) and tidal oscillations are pronounced in the systems of small bodies and their tidal interactions with planets, which exerts strong influence on stability of their orbits being responsible for migration processes. The stability problems including interaction of nonlinear resonances in Hamiltonian systems were analyzed in detail in the framework of Kolmogorov-Аrnold-Мoser (КАМ-theory). Recently, these and some other studies (see Chirikov, 1979, 1982) laid the basis for investigation of the structure and dynamics of the systems of exoplanets around binary and multiple stars (Marov & Shevchenko, 2017).

Migration involving both forming planets and small bodies could play a major role in the history of early solar system affecting its configuration and planets composition. Great diversity of bodies revealed by compositional mapping of the main asteroid belt implies substantial mixing of bodies of different taxonomic classes through the various dynamical processes affected by planetary migration (DeMeo & Carry, 2014). The outer planets’ instability could cause massive influx of bodies to the inner solar system (e.g., Walsh, Morbidelli, Raymond, O’Brien, & Mandell, 2012). Hydrated C-type asteroids and comets transported from outer regions of the solar system would contribute to the above diversity and also be responsible for delivery of water and volatiles to the Earth and terrestrial planets deposited as a veneer at the final stage of these planets’ accumulation (Anders & Owen, 1977; Marov & Ipatov, 2005).

Unlike classical models of the terrestrial planets evolution with Jupiter–Saturn’s stable orbit positions (e.g., Raymond, O’Brien, Morbidelli, & Kaib, 2009; Wetherill, 1996), there were different scenarios developed in order to explain inner solar system’s water under action of the outer planets’ dynamical instability. Migration of bodies and dust from the disturbed trans-Neptunian regions in Jupiter Crossing Orbits (JCO) and then in the main asteroid belt to eventually become NEOs was studied in the numerical models (Marov & Ipatov, 2005, 2005). The mechanism involving unstable positions of the giant planets in the course of their formation was explored by several teams. Inward migration of Jupiter from ~ 20 to ~ 5AU and getting it captured in 2:3 or 1:2 resonance with growing Saturn (which could halt and reverse the inward migration of Jupiter) was considered in the model known as the Grand Tack scenario (Jacobson & Morbidelli, 2014; Mandell, Raymond, & Sigurdsson, 2007; Walsh, Morbidelli, Raymond, O’Brien, & Mandell, 2012). It was assumed that this process would shepherd outer belts’ bodies inward and exert influence on planetary embryos in the inner region. This would result in volatile implantation through planetesimals’ impacts during terrestrial planets formation and storage of remnant pristine bodies in the main asteroid belt, as well as the position and coexistence of asteroids of different compositions (Morbidelli, Lunine, O’Brien, & Walsh, 2009; Villeneuve, Chaussidon, & Liboured, 2009). Moreover, such a scenario was invoked to explain depletion of water in the zone of terrestrial planets’ formation in terms of a “fossilized” snow line position outside Jupiter’s precursor orbit beyond the snow line at ~3 AU preventing condensation of water and ice inside (Morbidelli et al., 2015) and/or mechanism of water delivery related to giant impacts (O’Brien, Walsh, Morbidelli, Raymond, & Mandell, 2014).

Protoplanets embedded in a gaseous disc would experience drift changing their orbital positions. The movement of Uranus and Neptune from the place of their initial formation close to the Jupiter–Saturn zone further away from the Sun was assumed to exert formation of the trans-Neptunian Kuiper belt. This scenario was justified by evaluating the time required for the accretion of Uranus and Neptune in their present-day orbits. Indeed, modeling showed that such a time would exceed the age of the solar system. The model, which is sometimes referred to as reconfiguration of giant planet orbits (“Nice model,” Morbidelli, Levison, Tsiganis, & Gomes, 2005; Tsiganis, Gomes, Morbidelli, & Levison, 2005) suggested an existence of the primordial disk of several tens of Earth masses made of comet-like objects residing just outside the initial orbits of the giant planets. The disk is thought to be scattered throughout the solar system by gravitational interactions between the giant planets leading also to their migration. It is worth noting that movement of Uranus–Neptune outward due to gravitational interactions with the planetesimals would ultimately eject them into hyperbolic orbits.

The dynamical models involving instability in the giant planets zone were associated with the dramatic event of Late Heavy Bombardment (LHB) of the Moon and terrestrial planets (Gomes, Levison, Tsiganis, & Morbidelli, 2005) and the Moon crater chronology. However, timing of the instability (well before the LHB or later) underlying these models remain unclear. Most recently (Morbidelli et al., 2017), instead of using the terminal cataclysm hypothesis that poorly explained the triggering flux of bodies from the outer asteroid belt, linked the source of LHB projectiles with leftovers of planetesimals (“tail end of planet accretion”) from the time of outer planets’ formation. In support of this idea, they brought some evidence of lunar craters’ records and matching density of craters with the Highly Siderophile Elements (HSE) in the lunar mantle. These “iron loving” elements were found in chondrite meteorites and presumably they were delivered with projectiles of similar composition after a major event of the lunar matter differentiation, with the core emergence and sinking of the original HSE in the core. Hence, geochemical constraints of large craters’ composition formed by projectiles and the timescale of mantle ocean crystallization (~ 4.35 Ma, with the account for Fe-S segregation), advocate for the imprint of LHB event at the tail end of planet accretion (Morbidelli et al., 2017). The modern model coupling LHB at ~ 3.9 Ma with the time of outer planets’ instability appears to accommodate the current knowledge with minimum assumptions.

The critical role of C-chondrites and water transport in the inner solar system could be played by the process of outer planets’ formation with no change of their orbital positions (Raymond & Izidoro, 2017). This is a kind of scattering model that postulates a slow accretion of gas in the broad outer belt rich of volatiles (~5–20 AU) by the giant’s cores until some threshold with the onset of Jupiter’s runaway growth. This process provides destabilization, gravitational scattering of nearby planetesimals by Jupiter and Saturn and their large-scale radial mixing, some of them moving inward and residing (resonance) orbits’ interior to that of Jupiter. As gas dissipates, orbits of the disc planetesimals become progressively eccentric, including those trapped in the main asteroid belt and crossing the region of growing Earth and terrestrial planets, thus delivering water with C-chondrites and other type of meteorites. Later implantation of these species by scattering triggered by growth and possible migration of Saturn and icy planets turns out to be non-efficient. This scenario with no or very limited key assumptions related to the Grand Tack or Nice models seems quite plausible and implies a close relationship of both inner and outer planets’ formation.

### Particles Growth and Solid Bodies Formation

The key problem of the solar system origin is how the solar system bodies (original dust and condensates, as well as those produced in coagulation) progressively grew on scales ranging from nano- and micron-size particles to planetesimals and planets thus ranging over dozens orders of magnitude in mass. As mentioned above, time-dependent modeling with the different particle size distribution functions and limited lab experiments is the only tool to gain insight into the problem. Numerous attempts to reconstruct the process taking into account nebula thermal structure; evaporation fronts (EFs’) position for different components depending on radial temperature lapse rates in the disc’s midplane; particle growth by sticking limited by bouncing; fragmentation and radial drift due to nebula headwind drag of growing bodies influencing mass redistribution; etc., have been undertaken (see, e.g., Birnstiel, Dullemon, & Brauer, 2010; Dominik, Blum, Cuzzi, & Wurm, 2007; Estrada, Cuzzi, & Morgan, 2016; Nakagawa, Sekiya, & Hayashi, 1986; Ormel, Spaans, & Tielens, 2007; Wada, Tanaka, Suyama, Kimura, & Yamamoto, 2008, 2009; Weidenschilling, 1980). Also, lab experiments with silicate and ice particles collisions in microgravity conditions revealed some important patterns of particles and particle aggregates formation. Some important constraints were deduced for particles bouncing and sticking, including translational energy and coefficients of restitution estimates depending on impact parameters (see, e.g., Beitz et al., 2011; Blum, 2004; Blum, Schrapler, Davidson, & Trigo-Rodriguez, 2006; Brisset et al., 2013; Chiang & Youdin, 2010; Güttler, Blum, Zsom, Ormel, & Dullemond, 2010; Hill, Heißelmann, Blum, & Fraser, 2015; Ida, Guilot, & Morbidelli, 2016; Lankowski, Teiser, & Blum, 2008; Schrapler, Blum, Seizinger, & Kley, 2012; Weidling, Güttler Blum, & Brauer, 2009; Weidling, Güttler, & Hium, 2011).

According to the modern views, the process started owing to the above-mentioned streaming/gravitational instability development in the dense subdisk formed out of the dust component settled down to the midplane of the gas-dust disk (Dorofeeva & Makalkin, 2004; Kolesnichenko & Marov, 2014; Makalkin & Dorofeeva, 1996; Marov et al., 2013; Youdin & Shu, 2002). This was followed by the primary porous dust clusters formation from which the first solid bodies of pebble-boulder size and eventually planetesimals of asteroid size have emerged. Some of these cm-size and larger pebbles were possibly assembled into porous clumps giving birth to comets; this approach accommodates the primordial rubble pile theory though other theory postulates that comets were made out of debris left over from the main planet-building phase, thus preserving remnants of the protosolar nebula matter. Nonetheless, collisional rubble pile theory better explains a rather small size of comet’s nucleus (~5–10 km) and even the bi-lobed shape of some of them, because of their gradual formation at low speed of leftover pebbles/grains after larger bodies have accumulated and gas in disc has disappeared, followed by gentle collisions owing to stirring the cometary orbits, specifically at the skirt of planetary system.

The sequence of solids growth and timescale of such a scenario is shown schematically in Figure 11;

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Figure 11. Sequence of the of protosolar disk evolution. (a) Disk formation due to accretion gas and dust from the protosolar nebula and protosun emergence in the center. (b) Disk flatteniand dust particle sedimentation toward the midplane and dense dust subdisc formation; particle growth. (c) Subdisc fragmentation into dust clusters due to streaming and gravity instability development, cluster collisional interaction and solid growth, including first proto-planetesimal accumulation with gravity domain. (d) Planetesimals and planetary embryo formation, gas dissipation, and original solar system architecture setup evolving ultimately to the contemporary configuration. Time span: (a)–(b) 105–106 yr; (c)–(d) 106–107 yr.

Source: Dorofeeva and Makalkin (2004).

the initial process is thought to last less than 105–106 years of the overall ~108 years of planets formation. Note that the same short timescale is assumed for comets’ formation as well as for initial growth phase of the TNOs probably influencing the cometary-like bodies origin and evolution. The shear turbulence mechanism would promote ring-like contraction of dust in protoplanetary cloud into a thin disc (h << r) of non-regular shape widening toward the periphery. Solid bodies becoming planet embryos are formed from initially “loose” gas-dust (porous) clumps filling the main part of their sphere of attraction (Hill’s sphere) and slowly contracting due to internal gravitational forces. Let us recall that whereas the growth of particles during their collisions is hampered in chaotic turbulence, their coalescence and enlargement can occur inside turbulent eddies’ coherent structures promoting dust clusters set up in vortexes of baroclinic nature in a broad range of Stokes (St) number defined by the ratio of particle drag in an ambient gas to characteristic time of the system (defined as inverse Kepler frequency Ω‎−1) and dependent on size and density of a particle. Solid particles may be also concentrated in the disks with quite weak turbulence where denser than average matter structures (with large dust-to-gas ratio) would create a large population of aggregates and trigger streaming instability. This could be the case in outer zone of massive discs where rapid growth of aggregates to planetesimals was suggested (Krijt, Ormel, Dominik, & Tielens, 2016).

Generally, both instability mechanisms support the basic Safronov and Goldreich-Ward ideas about disc viscous accretion and subdisk matter gravitational collapse. As we have seen, in the modern models, the focus is also given to the competing processes of gas and dust photo-evaporation by the solar EUV-X-ray radiation and gas condensation/condesate growth, as well as to dust trapping, clustering, and coagulation including particles size distribution and stratified turbulence. These processes are accompanied by dust aggregates formation/restructuring through particles sticking, gas-dust coupling decrease, solids growth, and radial drift resulting ultimately in gravitationally bound planetesimals and planet embryos origin (Armitage, 2007; Birnstiel, Fang, & Johansen, 2016; Carrera, Gorti, Johansen, & Davies, 2017; Johansen et al., 2014; Marov & Kolesnichenko, 2013; Raettig, Klahr, & Lyra, 2015; Schaefer, Yang, & Johansen, 2017).

Although the basic scenario of ongoing particle growth is generally understood, many details of the processes involved at the different stages remain unclear. First, still uncertain are the details of physical mechanisms responsible for primary small dust particles growth before gravitational interactions of hundred meters-kilometer size bodies become effective. The process of particles’ mutual collisions is usually invoked as the factor that presumably gave rise to the aggregation of small particles to yield either dense particle clumps (Carrera, Johansen, & Davies, 2015) or pebble/boulder-size compact aggregates migrating in the protoplanetary disc and controlling planetesimals’ growth (Güttler, Blum, Zsom, Ormel, & Dullemond, 2010; Ida, Guilot, & Morbidelli, 2016; Krijt, Ormel, Dominik, & Tielens, 2016; Nakagawa, Nakazawa, & Hayashi, 1981; Zsom, Ormel, Güttler, Blum, & Dullemond, 2010; Ormel, Spaans, & Tielens, 2007). However, a probability of destruction rather than growth of forming bodies may be higher if collisional relative velocities and bouncing barriers for particle aggregates are significant, until gravitational attraction of planetesimals becomes dominant. Hence, an efficiency of sticking of dust particles into aggregates through collisions is a rather delicate mechanism, specifically if equal size particles of ~mm size are considered (Blum & Wurm, 2000). The formation of larger objects limited by bouncing is thought to be augmented by the streaming instability, gravitational collapse, collective particle behavior, and/or by static compression of fluffy dust aggregates (Kataoka, Tanaka, Okuzumi, & Wada, 2013; Ward, 2000; Yang, Johansen, & Carrera, 2016).

As a compromise ensuring higher efficiency of agglomerates creation we advocate for collisional integration of fluffy clusters made up by micron-sized particles rather than individual particles themselves, in support of the lab experiments mentioned above. It is further assumed in the developed models that clusters and their individual particles have fractal structure. Such an approach was thoroughly explored and validated theoretically (Kolesnichenko & Marov, 2013) involving concurrence of gravitational and brownian coagulation of dust monomers, aggregates growth, and porous bodies interaction/growth.

The bottom line of our numerical model is the agglomeration of small particles in the primary fluffy dust aggregates of low-bulk density and fractal nature of the latter, giving rise to their compression and formation of first dense bodies of progressively larger size. Unlike an approach used in the previous simulations (e.g., Dominik, Blum, Cuzzi, & Wurm, 2007; Wada, Tanaka, Suyama, Kimura, & Yamamoto, 2008, 2009), the mode of particle on-head and offset collisions inside dust clusters was more strictly assessed in numerical N-body models (Marov & Rusol, 2011, 2015a, 2015b). Method of permeable particles and modified Newton model of collisions were utilized in terms of restitution coefficient Kr dependent on the distance between centers of particles and their relative velocity, taking into account internal structure of particles in fluffy clusters and complicated patterns of their interactions, specifically in the contact zone. This enabled us to examine collisional evolution of fluffy clusters beginning from nano-particles sticking together through electrostatic forces and growing up to compressed aggregates of larger size and different patterns. Example of 3D modeling of evolution of fractal dusty clusters with different numbers of populated submicron particles is shown in Figures 12 and 13.

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Figure 12. 3D-numerical modeling of submicron particles, collisional interaction, and growing within a grid in the primordial dusty cloud (density d = 1.5 × 10‒21 g/nm3. (a) An example of the original 3D structure of a selected grid. (b) Examples of agglomerate formation in the process of collisional evolution of particles in some grids.

Source: Marov and Rusol (2015a).

Click to view larger

Figure 13. 3D structure of fractal dusty clusters with different numbers of populated particles evolution (a–d) Red and blue colors denote positively and negatively charged particles of about 20-nm characteristic size in a quasi-neutral medium.

Source: Marov and Rusol (2015b).

Figure 14 is a snapshot of a cross-section of randomly selected grids for fractal dusty clusters with different numbers of populated particles in Figure 13.

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Figure 14. Snapshot of a cross section of a randomly selected grid when getting through fractal dusty clusters with different numbers of populated particles (clusters a and b, respectively).

Source: Marov and Rusol (2015b).

Of special interest is the evolution of fluffy dust clusters in mutual collisions that is critical for dusty agglomerates formation, as shown in Figure 15.

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Figure 15. Evolution of the structures of fluffy dust clusters; computer modeling of collisional interactions. (a) Fluffy clusters of characteristic size 50 nm, fractal dimension 2.55, and number of particles = 8,192. (b) Fluffy clusters of characteristic size 75 nm, fractal dimension 2.15, and number of particles = 3,072.

Source: Marov and Rusol (2016).

Examples of the respective numerical experiments carried out with clusters composed of various number of submicron particles of different fractal dimensions Dβ‎ ranging from 2.025 (very fluffy structure) to 2.975 (well-packed structure) are shown in Figure 16 (Marov & Rusol, 2016, in press). The results of modeling of cluster interactions reveals how Kr (restitution coefficient or its equivalent—collision recovery ratio) changes for clusters of different Dβ‎ depending on the relative distance—between colliding i-j particles (0–1), and collision energy Eij/Eint (Eij is kinetic energy of collision; Eint—the internal energy of molecular coupling preserving structure) ranging from 0.01 to 0.99. The strong dependence of Kr on the parameters involved and are bound threshold were found, for example, for dense colliding clusters with relative velocity less than the critical value(corresponding to the energy of plastic deformation)bouncing occurs at Kr> 0.87.

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Figure 16. Restitution coefficient Kr (collision recovery ratio) for clusters with various fractal dimensions $Dβ$ as shown here. Note: ri, rj — radii of i and j model particles; rij — distance between i and j colliding model particles; rcol = ri +rj — collision distance; $rijrcol$ — relative distance between i and j colliding particles; $Eint$ — cluster’s internal energy; $Eij$ — kinetic energy of collision; $EijEint$ — relative collision energy.

The results are regarded as an important milestone toward in-depth study of “cluster-cluster coagulation” at the initial stage of the protoplanetary gas-dust disc evolution and results are addressed as precursors of primary objects growing. They are in accord with the conclusion (Wada et al., 2008) that a cluster with a larger number of particles is harder to destroy (easier to survive) in energetic collisions. Nonetheless, the problem is still far from being solved, especially if one keeps in mind that the global qualitative effect of disk gravity further increases collision/impact velocities and adds additional jitter to the orbital evolution of the primary bodies.

The next stage of growth of primordial seeds of bodies to planetesimals, with the allowance for mechanism of self-gravitation, seems more conceivable. At the first approximation, the mass distribution of particle agglomerates and proto-planetesimals obeys the known Smoluhovsky coagulation equation (a sort of the Boltzmann kinetic equation when dealing with coagulation process) with the account for gravity mutual attraction and fragmentation in non-gentle collisions. This interaction along with the dust sedimentation onto the formed bodies residing on intersected orbits (with chaotic velocities superimposed on quasi-circular orbital velocities) results in further growth of these protoplanetary embryos followed by the gradual scooping up of smaller bodies in due course of the swarm evolution. It is supposed, however, that there is a sort of barrier at around one meter size-range (see, e.g., Nakagawa, Hayashi, & Nakazawa, 1983; Weidenschilling, 1977; Youdin & Kenyon, 2012) because of the effects of body destruction and their inward drift toward the central star. The latter is caused by aerodynamic braking of these bodies in the remaining gas whose rotation velocity becomes lower than the Keplerian one. Primordial bodies beyond the meter-size barrier to proto-planetesimals growth through “coagulation” after more complete gas evacuation seems more feasible.

Obviously, competitive processes of destruction and particle trapping during radial matter exchange, along with particle concentration via streaming and/or gravitational instability, eventually results in bodies’ growth. Based on the results of modeling supported by lab simulation (Jansson, Johansen, Syed, & Blum, 2017) millimeter- to centimeter-size pebbles in a gravitationally bound collapsed cloud (due to, for example, disk streaming instability) would experience numerous collisions with different outcomes depending on their relative speeds and the cloud density, resulting eventually in a quite intense formation of planetesimals. As far as a planet’s accumulation is concerned, gravitationally focused mutual collisions of asteroids and planetary embryos are thought to be responsible for the emergence of progressively growing proto-planets possessing larger gravitational potentials (oligarchs), such an oligarchic growth being accompanied by catastrophic fragmentation of other bodies in a swarm of planetesimals (Chambers, 2008; Greenberg, Hartman, Chapman, & Wacker, 1978; Weidenschilling, 2010;Youdin & Kenyon, 2012). A system of satellites around a proto-planet could be explained invoking the same mechanism (Canup & Esposito, 1996).

A possibility of the formation of bodies from dust clusters in mass range from 1020 to 1022 g (corresponding to asteroids of tens to hundred kilometers in size) was shown in the numerical model (Marov et al., 2013). A mechanism of gravitational collapse of massive swarms of small particles and their pile-up without passing through the intermediate phases of growing was proposed to explain early formation of the ~100 km bodies, a source of very old iron meteorites, thereby circumventing the meter-size barrier problem (Cuzzi, Hogan, & Shariff, 2008; Johansen et al., 2007; Morbidelli, Bottke, Nesvorny, & Levison, 2009). Similarly, a prompt planetesimal’s formation in regions beyond the snow line due to streaming instability-induced gravity collapse of radially drifting millimeter-size dust particles to ensure material deposition for the giant planet cores was suggested (Armitage, Eisner, & Simon, 2016). Anyway, whatever particular solution of the problem, further growth occurs through interaction of planetesimals with solid and gaseous components under gravity domain and sporadic mutual collisions (Chambers, 2010).

Note that in the numerical experiments, some constraints were placed on the value of angular momentum of the porous (low density) gas-dust clusters (pre-planetesimals) of about Hill sphere in size and their moving before collision along heliocentric orbits. The model aimed to assist dynamical formation of planetary/satellite bodies with application to trans-Neptunian system. Arguments were drawn for consistency of the properties of wide binaries in the Kuiper Belt with a primordial origin during gravitational collapse (Nesvorny, Youdin, & Richardson, 2010). As the outcome, origin of the Earth-Moon system was attempted to explain in terms of the compression of a low-density cluster of 0.1 mass of the contemporary Earth formed from the collision of two original clusters on the close heliocentric orbits, which allowed the system to acquire the necessary angular momentum (Ipatov, 2014).

As it was said above, significant role at the final stage of planet’s growth could play migration and resonances in the forming planetary system. The commonly adopted scenario of the solar system origin involving planetesimals growing to planet embryos together with asteroid-size and comet-like bodies as remnants of planets is illustrated in Figure 17.

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Figure 17. Artist’s concept of a planetary system formation, as seen from the outer edge of the gas-dust disc around an emerged central protostar. Planetesimals growing to planet embryos, together with asteroid-size and cometlike bodies as remnants of planets’ formation, are seen. The picture resembles the commonly adopted scenario of the solar system origins.

Source: NASA.

It reflects our current general understanding of how original bodies and then planets formed though we are still far from resolving this mysterious subject. Some fundamental bottlenecks in planets formation challenging future studies were most recently summarized in Morbidelli and Raymond (2016).

### Inner Planets Evolution

The key question intrinsically related to the origin of the terrestrial planets is why the three neighbor planets—Earth, Venus, and Mars—inheriting disc composition in a close neighborhood and basically, exhibiting similar chemistry in the formation (Saxena & Eriksson, 1986) took different evolutionary paths? Namely, what caused, unlike the pleasant climate of Earth, hostile thermal regime of Venus, and why the assumed original clement climate on Mars has drastically changed?

To answer this question, many complicated problems closely related to planetary cosmogony should be addressed. Some of them relevant to this important topic were considered in previous chapters of the paper and they are discussed in more detail in some reviews and monographs (see, e.g., Morbidelli, Lunine, O’Brien, & Walsh, 2009; Raymond, O’Brien, Morbidelli, & Kaib, 2009; Lissauer & de Pater, 2013; Armitage, 2007; Marov & Grinspoon, 1998). Here, we focus only on limited aspects of the problems involved that concerns a rather simple approach in the treatment of thermal regime formation on the inner planets and the fate of water as the key climatic factor impacting on their evolution.

Let us first note that Earth is located in a comparatively narrow zone of circumsolar space where the development of favorable (for life’s existence) climatic conditions is possible. This is the so-called habitable zone in the solar system whose inner boundary is located 10–15 million km closer to the Sun than the Earth’s orbit while its outer boundary extends to approximately the orbit of Mars (Figure 18). The orbit of Venus turns out to be outside this zone, at a distance that is almost triple the critical value. Obviously, if the Earth were moved to the place of Venus (actually, even less) then it would probably evolve according to the Venusians’ scenario.

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Figure 18. The habitable zone in the vicinity of Earth (adapted from Wikipedia). The zone is limited by only about 10–15 million km toward the Sun and extends outward to nearly the Mars orbit. The planet shifting closer to the Sun would meet runaway greenhouse similar to that on Venus (Ts = 735 K; Ps = 92 atm), whereas at Mars’s position, greenhouse gases would condense out and the atmosphere would collapse. Unlike Earth, the atmospheres of Venus and Mars consist mainly of carbon dioxide; their abundance is controlled by the carbonate-vollastonite equilibrium between atmosphere and crust, which is strongly dependent on surface temperature Ts . CO2 storage in the Venus atmosphere is the same as what is locked in the Earth’s crust, and it would release into the atmosphere amounting to Ps ~ 90 atm if the clement climate on the home planet irreversibly changed (temperature dramatically raised) and the CO2 balance maintenance ceased.

Based on the average annual balance of the solar radiation absorbed by the terrestrial surface and atmosphere with an account of its albedo the effective (equilibrium) temperature of Earth is Te~255 K, which is even below the freezing point of salt water. This means that favorable climate conditions could hardly have arose on the home planet unless the greenhouse effect caused by absorption of solar radiation in its relatively thick atmosphere would raise the mean temperature near the surface to the pleasant 288 K. This atmosphere of secondary origin, unlike the primary atmosphere captured from the protosolar nebula and composed of light atmophile elements that were lost, formed owing to degassing of volatiles from the interior and from collisions with remnant planetesimals and migrating bodies. It presumably contained carbon dioxide, nitrogen, water vapor, and some minor species including such greenhouse gas like methane.

Earth could therefore retain its water on the surface, which was mainly concentrated in the oceans. In turn, carbon dioxide would accumulate incarbonates of sedimentary rocks through its binding with metal oxides incorporated into the ocean crust and upper mantle (with the formation of aqueous silicates) and biogenically, through the deposits of lime skeletons of sea organisms. Dramatic change of the Earth’s atmosphere with its modern composition occurred much later, about 2.8 Ma, due to bacterial production of oxygen accumulated in the planet’s gas envelope, which made possible the life forms rich diversity and proliferation.

In contrast, equilibrium temperature of the early Venus is supposed to be not lower than Te~325 K, which is above the water boiling temperature in a low pressure environment. One may reasonably expect surface pressure on ancient Venus as an Earth-like plane to be substantially lower than 1 bar. Under these conditions, carbon dioxide would gradually accumulate in the atmosphere together with water vapors, which in turn, have contributed to a further rise in surface temperature. The runaway greenhouse eventually developed resulting in the transport of increasingly large amounts of СО2 and Н2О into the atmosphere, up to some equilibrium state corresponding temperature 735 K and pressure 92 atm. At such a temperature, carbon dioxide turned out to be not bound in carbonates of sedimentary rocks, as on Earth but was released into the atmosphere giving rise to very high pressure. According to the model estimates, the amount of carbon dioxide locked in the Earth’s sedimentary rocks is comparable to the content of СО2 in the Venus atmosphere and it would constitute nearly the same pressure had the Earth’s temperature raised to similar temperature and СО2 released in the atmosphere. The latter is characterized by the relationships between mineral phases and volatiles on the surface, with the carbonate-silicate interaction in the upper layer of the planetary crust being the most important. The above scenario is characteristic of a system with positive feedback and internal instability when initial perturbation is not suppressed but, on the contrary, fairly rapidly enhanced (see Marov & Grinspoon, 1998).

As far as water is concerned, its accumulation on Venus with the involvement of both endogenic and exogenic sources, likewise on Earth and Mars, would result in the initial amounts of water nearly equal to the volume of the terrestrial hydrosphere (Marov & Ipatov, 2005; Morbidelli, Lunine, O’Brien, & Walsh, 2009). However, water could not be preserved on the Venus surface at the temperature above the critical point (647 K), even as salty aqueous solutions (brines) with a slightly higher critical temperature (675–700 K). As to the atmosphere, the amount of water in it is negligible. Thus, the key problems of the planet evolution are whether water was on early Venus, where it was stored, and, if so, when and how was it lost. The deuterium-to-hydrogen ratio measured in the Venusian atmosphere, which turned out to be larger than that in the Earth’s atmosphere by two orders of magnitude, confirms the concept of ancient Venus ocean because high deuterium enrichment can be explained by an efficient thermal escape of the lighter hydrogen isotope and leaving behind heavier deuterium (Donahue, Hoffman, Hodges, & Watson, 1982). Note that adoption of this mechanism requires an assumption that enormous masses of liberated hydrogen and oxygen through dissociation by the solar EUV radiation were removed from the atmosphere by efficient dissipation and bound by surface rocks, respectively, which seems, however, hardly realistic (Marov & Grinspoon, 1998).

There is also a different viewpoint that Venus was initially formed as a “dry” planet, though the introduction of volatiles through the mechanism of heterogeneous accretion is assumed to play an important role as well. In this scenario, the water content was essentially constant throughout the geological history of Venus, remaining approximately at the current level while the efficiencies of heterogeneous accretion and hydrogen dissipation from the atmosphere were considerably lower. In such a case, the observed enrichment of the Venusian atmosphere in deuterium during the isotope fractionation in the process of their dissipation from the atmosphere can be also explained.

Addressing now the problem of Mars evolution, we start from a well-supported concept that the quite pleasant natural conditions presumably were on Mars at early epoch, which is backed by the morphological features preserved on the planet’s surface as well as by some other evidence. Since equilibrium temperature of early Mars would not exceed Te~220 K it would be able to retain only frozen water on its surface. However, there is widespread evidence of the presence of liquid water flows meaning considerably denser atmosphere and much more favorable climate ~3.8–3.5 billion years ago. Obviously a catastrophic drought suddenly occurred on Mars rather than a long-term evolution has resulted in the present-day natural conditions. This dramatic change cannot be explained by the fact that the planet is 0.5 AU farther away from the Sun than Earth. More likely it should be associated with the fact that the mass of Mars is almost an order of magnitude lower than that of the Earth implying a lower storage and an early depletion of the former in the long-lived radiogenic isotopes, which served as the main energy sources responsible for the thermal history of a rocky planet. Mars began to cool, volcanism ceased, atmosphere diminished. In other words, a limited inventory of radiogenic isotopes rather than the distance from the Sun has dramatically impacted the Mars evolution changing its geology and causing collapse of the atmosphere. Likewise Earth and Venus, Mars probably possessed an ocean, currently its significant fraction being preserved beneath the surface as underground water (Lissauer & de Pater, 2013; Marov, 2015).

It is important to emphasize that synergy of the Earth and planetary sciences is aimed at a better understanding of the present, past, and future of the Earth based on comparative planetology approach. It is intended to answer the key questions about feedback for the existing regulation mechanisms to maintain clement climate. Concurrently, this contributes to the cardinal problems of planetary cosmogony allowing us to put more stringent constraints on the range of parameters used in modeling of the origin and evolution of the solar and other planetary systems.

# Conclusion

The great advancement in our understanding of solar system origin and evolution was achieved during the recent decades owing to in-depth theoretical and experimental studies. The new data largely support the scenario rooted in the Middle Ages and provide much more rigorous evidence that formation of planetary systems is caused by the initial fragmentation of a molecular cloud. Its fragment (protosolar nebula) evolves into a newborn star surrounded by gas-dust disk from which eventually celestial bodies of different sizes, with the planets being largest, emerge.

Observation of the accretion gas-dust disks around stars of late spectral classes in different wavelengths and at various phases of evolution allowed us to resolve in much detail the structure of disks and their dynamics, which are generally in accord with such a scenario. The solar system’s age was firmly established from radiogenic isotope dating of the chondritic meteorites, with the CAI refractory inclusions dating the starting point of the solar system as 4567.30 ± 0.16 Ma ago. Chronology of these meteorites is intimately related to their parent body’s formation and heating, which in particular sheds light on the earliest stages of the protoplanetary disc evolution for the first ~3–5 million years.

Significant progress has been achieved in the theoretical study and computer modeling of protoplanetary accretion disk origin and early evolution, including its thermal regime, dynamics, evaporation/condensation processes, coagulation/clustering of dust and collisions of primary objects, with the strict observational constraints being taken into account. The key mechanisms of reconstruction concern compression of the protoplanetary nebula after collapse of its inner core giving rise to the fusion ignition in the protosun and evolution of the gas-dust disk formed around it. The disc evolution includes continuing accretion of protostellar matter onto the disk, evaporation-condensation of species in the original heterogeneous medium depending on radial temperature and primary solids formation as seeds of growing bodies. According to the currently adopted scenario, streaming and gravitational instabilities developed in the disk midplane (where dense dust-enriched subdisk was formed) resulted in fragmentation of its dusty component into fluffy dust clusters of fractal structure. Dust particles inside clusters progressively grew due to agglomeration of particles in the mutual collisions giving rise to the first dense bodies formation. How they grew to pebble-boulder size or larger bodies (specifically around the “meter-size barrier”) is not completely clear; however, it must have happened before proto-planetesimals of asteroid-like size with the gravitational interactions domain begin to form. The continuing numerous collisions are thought to be responsible for both growth and destruction of the swarm of such bodies resulting in a planetesimals suite from which a limited number of big oligarchs and smaller planetary embryos emerge. Such a scenario of the solar system origin is generally supported by the results of computer modeling and do not contradict astronomical observations of protoplanetary discs around other stars and exoplanetary systems architecture.

Of key importance is the problem of evolution of the three neighbor planets—Earth, Venus, and Mars, namely, why these closely located terrestrial planets presumably accreted similar disc composition followed different paths of their evolution. One of the basic concepts is that temperature in the formation region of the terrestrial planets has always remained well above the H2O condensation and hence these planets formed under water-depleted conditions. Indeed, the results of modeling argue for the idea that in the disc middle plane the temperature did not drop below 300–500 K during the entire period of early evolution. This means that the early Earth and Venus were very dry. Unfortunately, there are no firm constraints on the chemistry and mineralogy of terrestrial planet precursor materials in support of this concept. Water and other volatiles were probably delivered to Earth, Venus, and Mars at a later stage through the migration of small bodies of various sizes from the outer solar system, first of all, C-type asteroids. This statement does not exclude a possibility that some amount of water was stored in the planets’ mantle at the time of accumulation and partially exiled on the surface. Currently it is difficult to distinguish between exogenous and endogenous sources of water origin on the terrestrial planets. Nonetheless, contribution of the giant planets growth to the Earth’s water seems unavoidable.

As far as climatic conditions on these planets are concerned, a plausible scenario for the development of the Venus hostile climate is presumably related to its radial distance, which is beyond the habitable zone whereas drastic change of the ancient favorable climate on Mars ~3.5 Ma years ago was probably caused by the limited inventory of long-lived radionuclides in its interior because of a rather small mass of the planet. As the result, only Earth preserved its pleasant climate.

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. The following problems are of the principal interest (to mention a few):

• How the processes of the gas-dust disk evolution involving its fragmentation into dust clusters and emergence of the first compact bodies occurred during continuing accretion of gas and dust on disk and from the disk on the protosun?

• What was the concurrent role of streaming and gravity instabilities in the gas-dust disc midplane (dense subdisc)? What was the structure and density of primary fluffy dusty clusters and character of their evolution?

• How efficient were collisions of pristine submicron particles inside original fluffy dust clusters presumably of fractal nature rather than particles themselves to form the first compact objects through porous growth?

• What was the scenario of particles accretion onto primordial seeds of planetesimals after the latter exceed a “meter-size” barrier, but before a gravity-dominated growth of hundred meters-to-kilometer size bodies begins?

• What was the role of turbulence at the different stages of the protoplanetary gas-dust disk evolution? What was the role of turbulent eddies in concentration of particles and their integration in the dust clusters?

• What was the concurrence of turbulence and magnetic braking in the angular momentum transfer?

• What were protoplanetary disc chemistry and chemical evolution of disk matter and how the main processes responsible for different meteorites petrology can be reconstructed? How to incorporate chemical kinetics processes in the mass and energy conservation equations of heterogenic mechanics and magneto-hydrodynamics?

• 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?

• What role did migration of primordial bodies/planetesimals, forming planets and imposed resonances, play at the different stages of the solar system formation and evolution?

The list could be continued.

In summary, nowadays it is difficult to select between different models aimed to reconstruct the solar system origin and early evolution. New observations of the evolved disks around stars and exoplanetary systems will allow us to place stricter constraints on the developed models that are yet on shaky ground and to reconstruct the processes of solar system formation in a more coherent scenario. The basic concept is believed to remain unchanged, however, as it is shown in an artist’s view in Figure 18. Further progress in the field will be achieved by the synergy of astrophysics and planetary sciences jointly with computer modeling. Although significant strides were made in the area, we should learn more about primary disc structure and evolution, pebble accretion, role of giant planets formation in the inner planets’ Earth/volatiles delivery, geochemical constraints, planetesimals and planet embryos formation and dynamics. Undoubtedly, as the most intriguing goal, we are driven to understand the place of the solar system in the universe, the possible uniqueness of our home planet, and why it differs from other solar system bodies and, finally, the process that brought us to this world.

# Acknowledgments

This study was supported by the Grants of Russian Fund for Basic Research (RFBR) # 14–02–00319 and # 17–02–00507, and by the Fundamental Programs of the Russian Academy of Science # 7P. The author acknowledges multiyear fruitful collaboration with his colleagues in the field, anonymous reviewers, and especially the editor for valuable comments and corrections that helped to improve both content and style.

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