The perceived deficiencies of the Laplacian model stimulated scientists to find a replacement for it. During the 20th century many theories addressed the issue, including the planetesimal theory of Thomas Chamberlin and Forest Moulton (1901), the tidal model of James Jeans (1917), the accretion model of Otto Schmidt (1944), the protoplanet theory of William McCrea (1960) and finally the capture theory of Michael Woolfson. In 1978 Andrew Prentice resurrected the initial Laplacian ideas about planet formation and developed the modern Laplacian theory. None of these attempts proved completely successful, and many of the proposed theories were descriptive.
The birth of the modern widely accepted theory of planetary formation—the solar nebular disk model (SNDM)—can be traced to the Soviet astronomer Victor Safronov. His 1969 book Evolution of the protoplanetary cloud and formation of the Earth and the planets, which was translated to English in 1972, had a long-lasting effect on the way scientists think about the formation of the planets. In this book almost all major problems of the planetary formation process were formulated and some of them solved. Safronov's ideas were further developed in the works of George Wetherill, who discovered runaway accretion. While originally applied only to the Solar System, the SNDM was subsequently thought by theorists to be at work throughout the Universe; as of 17 April 2025 astronomers have discovered 5,943 extrasolar planets in our galaxy.
The physics of accretion disks encounters some problems. The most important one is how the material, which is accreted by the protostar, loses its angular momentum. One possible explanation suggested by Hannes Alfvén was that angular momentum was shed by the solar wind during its T Tauri star phase. The momentum is transported to the outer parts of the disk by viscous stresses. Viscosity is generated by macroscopic turbulence, but the precise mechanism that produces this turbulence is not well understood. Another possible process for shedding angular momentum is magnetic braking, where the spin of the star is transferred into the surrounding disk via that star's magnetic field. The main processes responsible for the disappearance of the gas in disks are viscous diffusion and photo-evaporation.
The formation of planetesimals is the biggest unsolved problem in the nebular disk model. How 1 cm sized particles coalesce into 1 km planetesimals is a mystery. This mechanism appears to be the key to the question as to why some stars have planets, while others have nothing around them, not even dust belts.
The initial collapse of a solar-mass protostellar nebula takes around 100,000 years. Every nebula begins with a certain amount of angular momentum. Gas in the central part of the nebula, with relatively low angular momentum, undergoes fast compression and forms a hot hydrostatic (not contracting) core containing a small fraction of the mass of the original nebula. This core forms the seed of what will become a star. As the collapse continues, conservation of angular momentum means that the rotation of the infalling envelope accelerates, which largely prevents the gas from directly accreting onto the central core. The gas is instead forced to spread outwards near its equatorial plane, forming a disk, which in turn accretes onto the core. The core gradually grows in mass until it becomes a young hot protostar. At this stage, the protostar and its disk are heavily obscured by the infalling envelope and are not directly observable. In fact the remaining envelope's opacity is so high that even millimeter-wave radiation has trouble escaping from inside it. Such objects are observed as very bright condensations, which emit mainly millimeter-wave and submillimeter-wave radiation. They are classified as spectral Class 0 protostars. The collapse is often accompanied by bipolar outflows—jets—that emanate along the rotational axis of the inferred disk. The jets are frequently observed in star-forming regions (see Herbig–Haro (HH) objects). The luminosity of the Class 0 protostars is high — a solar-mass protostar may radiate at up to 100 solar luminosities. The source of this energy is gravitational collapse, as their cores are not yet hot enough to begin nuclear fusion.
As the infall of its material onto the disk continues, the envelope eventually becomes thin and transparent and the young stellar object (YSO) becomes observable, initially in far-infrared light and later in the visible. Around this time the protostar begins to fuse deuterium. If the protostar is sufficiently massive (above 80 Jupiter masses (MJ)), hydrogen fusion follows. Otherwise, if its mass is too low, the object becomes a brown dwarf. This birth of a new star occurs approximately 100,000 years after the collapse begins. Objects at this stage are known as Class I protostars, which are also called young T Tauri stars, evolved protostars, or young stellar objects. By this time the forming star has already accreted much of its mass: the total mass of the disk and remaining envelope does not exceed 10–20% of the mass of the central YSO.
At the next stage the envelope completely disappears, having been gathered up by the disk, and the protostar becomes a classical T Tauri star. This happens after about 1 million years. The mass of the disk around a classical T Tauri star is about 1–3% of the stellar mass, and it is accreted at a rate of 10−7 to 10−9 M☉ per year. A pair of bipolar jets is usually present as well. The accretion explains all peculiar properties of classical T Tauri stars: strong flux in the emission lines (up to 100% of the intrinsic luminosity of the star), magnetic activity, photometric variability and jets. The emission lines actually form as the accreted gas hits the "surface" of the star, which happens around its magnetic poles. The jets are byproducts of accretion: they carry away excessive angular momentum. The classical T Tauri stage lasts about 10 million years. The disk eventually disappears due to accretion onto the central star, planet formation, ejection by jets and photoevaporation by UV-radiation from the central star and nearby stars. As a result, the young star becomes a weakly lined T Tauri star, which slowly, over hundreds of millions of years, evolves into an ordinary Sun-like star.
Under certain circumstances the disk, which can now be called protoplanetary, may give birth to a planetary system. Protoplanetary disks have been observed around a very high fraction of stars in young star clusters. They exist from the beginning of a star's formation, but at the earliest stages are unobservable due to the opacity of the surrounding envelope. The disk of a Class 0 protostar is thought to be massive and hot. It is an accretion disk, which feeds the central protostar. The temperature can easily exceed 400 K inside 5 AU and 1,000 K inside 1 AU. The heating of the disk is primarily caused by the viscous dissipation of turbulence in it and by the infall of the gas from the nebula. The high temperature in the inner disk causes most of the volatile material—water, organics, and some rocks—to evaporate, leaving only the most refractory elements like iron. The ice can survive only in the outer part of the disk.
The main problem in the physics of accretion disks is the generation of turbulence and the mechanism responsible for the high effective viscosity. The turbulent viscosity is thought to be responsible for the transport of the mass to the central protostar and momentum to the periphery of the disk. This is vital for accretion, because the gas can be accreted by the central protostar only if it loses most of its angular momentum, which must be carried away by the small part of the gas drifting outwards. The result of this process is the growth of both the protostar and of the disk radius, which can reach 1,000 AU if the initial angular momentum of the nebula is large enough. Large disks are routinely observed in many star-forming regions such as the Orion nebula.
The lifespan of the accretion disks is about 10 million years. By the time the star reaches the classical T-Tauri stage, the disk becomes thinner and cools. Less volatile materials start to condense close to its center, forming 0.1–1 μm dust grains that contain crystalline silicates. The transport of the material from the outer disk can mix these newly formed dust grains with primordial ones, which contain organic matter and other volatiles. This mixing can explain some peculiarities in the composition of Solar System bodies such as the presence of interstellar grains in primitive meteorites and refractory inclusions in comets.
Dust particles tend to stick to each other in the dense disk environment, leading to the formation of larger particles up to several centimeters in size. The signatures of the dust processing and coagulation are observed in the infrared spectra of the young disks. Further aggregation can lead to the formation of planetesimals measuring 1 km across or larger, which are the building blocks of planets. Planetesimal formation is another unsolved problem of disk physics, as simple sticking becomes ineffective as dust particles grow larger.
Planetary formation can also be triggered by gravitational instability within the disk itself, which leads to its fragmentation into clumps. Some of them, if they are dense enough, will collapse, which can lead to rapid formation of gas giant planets and even brown dwarfs on the timescale of 1,000 years. If these clumps migrate inward as the collapse proceeds tidal forces from the star can result in a significant mass loss leaving behind a smaller body. However it is only possible in massive disks—more massive than 0.3 M☉. In comparison, typical disk masses are 0.01–0.03 M☉. Because the massive disks are rare, this mechanism of planet formation is thought to be infrequent. On the other hand, it may play a major role in the formation of brown dwarfs.
Because planetesimals are so numerous, and spread throughout the protoplanetary disk, some survive the formation of a planetary system. Asteroids are understood to be left-over planetesimals, gradually grinding each other down into smaller and smaller bits, while comets are typically planetesimals from the farther reaches of a planetary system. Meteorites are samples of planetesimals that reach a planetary surface, and provide a great deal of information about the formation of the Solar System. Primitive-type meteorites are chunks of shattered low-mass planetesimals, where no thermal differentiation took place, while processed-type meteorites are chunks from shattered massive planetesimals. Interstellar objects could have been captured, and become part of the young Solar system.
After small planetesimals—about 1 km in diameter—have formed by one way or another, runaway accretion begins. It is called runaway because the mass growth rate is proportional to R4~M4/3, where R and M are the radius and mass of the growing body, respectively. The specific (divided by mass) growth accelerates as the mass increases. This leads to the preferential growth of larger bodies at the expense of smaller ones. The runaway accretion lasts between 10,000 and 100,000 years and ends when the largest bodies exceed approximately 1,000 km in diameter. Slowing of the accretion is caused by gravitational perturbations by large bodies on the remaining planetesimals. In addition, the influence of larger bodies stops further growth of smaller bodies.
Giant planet core formation is thought to proceed roughly along the lines of the terrestrial planet formation. It starts with planetesimals that undergo runaway growth, followed by the slower oligarchic stage. Hypotheses do not predict a merger stage, due to the low probability of collisions between planetary embryos in the outer part of planetary systems. An additional difference is the composition of the planetesimals, which in the case of giant planets form beyond the so-called frost line and consist mainly of ice—the ice to rock ratio is about 4 to 1. This enhances the mass of planetesimals fourfold. However, the minimum mass nebula capable of terrestrial planet formation can only form 1–2 ME cores at the distance of Jupiter (5 AU) within 10 million years. The latter number represents the average lifetime of gaseous disks around Sun-like stars. The proposed solutions include enhanced mass of the disk—a tenfold increase would suffice; protoplanet migration, which allows the embryo to accrete more planetesimals; and finally accretion enhancement due to gas drag in the gaseous envelopes of the embryos. Some combination of the above-mentioned ideas may explain the formation of the cores of gas giant planets such as Jupiter and perhaps even Saturn. The formation of planets like Uranus and Neptune is more problematic, since no theory has been capable of providing for the in situ formation of their cores at the distance of 20–30 AU from the central star. One hypothesis is that they initially accreted in the Jupiter-Saturn region, then were scattered and migrated to their present location. Another possible solution is the growth of the cores of the giant planets via pebble accretion. In pebble accretion objects between a cm and a meter in diameter falling toward a massive body are slowed enough by gas drag for them to spiral toward it and be accreted. Growth via pebble accretion may be as much as 1000 times faster than by the accretion of planetesimals.
Once the cores are of sufficient mass (5–10 ME), they begin to gather gas from the surrounding disk. Initially it is a slow process, increasing the core masses up to 30 ME in a few million years. After that, the accretion rates increase dramatically and the remaining 90% of the mass is accumulated in approximately 10,000 years. The accretion of gas stops when the supply from the disk is exhausted. This happens gradually, due to the formation of a density gap in the protoplanetary disk and to disk dispersal. In this model ice giants—Uranus and Neptune—are failed cores that began gas accretion too late, when almost all gas had already disappeared. The post-runaway-gas-accretion stage is characterized by migration of the newly formed giant planets and continued slow gas accretion. Migration is caused by the interaction of the planet sitting in the gap with the remaining disk. It stops when the protoplanetary disk disappears or when the end of the disk is attained. The latter case corresponds to the so-called hot Jupiters, which are likely to have stopped their migration when they reached the inner hole in the protoplanetary disk.
The region of a planetary system adjacent to the giant planets will be influenced in a different way. In such a region, eccentricities of embryos may become so large that the embryos pass close to a giant planet, which may cause them to be ejected from the system. If all embryos are removed, then no planets will form in this region. An additional consequence is that a huge number of small planetesimals will remain, because giant planets are incapable of clearing them all out without the help of embryos. The total mass of remaining planetesimals will be small, because cumulative action of the embryos before their ejection and giant planets is still strong enough to remove 99% of the small bodies. Such a region will eventually evolve into an asteroid belt, which is a full analog of the asteroid belt in the Solar System, located from 2 to 4 AU from the Sun.
Thousands of exoplanets have been identified in the last twenty years, with, at the very least, billions more, within our observable universe, yet to be discovered. The orbits of many of these planets and systems of planets differ significantly from the planets in the Solar System. The exoplanets discovered include hot-Jupiters, warm-Jupiters, super-Earths, and systems of tightly packed inner planets.
The hot-Jupiters and warm-Jupiters are thought to have migrated to their current orbits during or following their formation. A number of possible mechanisms for this migration have been proposed. Type I or Type II migration could smoothly decrease the semimajor axis of the planet's orbit resulting in a warm- or hot-Jupiter. Gravitational scattering by other planets onto eccentric orbits with a perihelion near the star followed by the circularization of its orbit due to tidal interactions with the star can leave a planet on a close orbit. If a massive companion planet or star on an inclined orbit was present an exchange of inclination for eccentricity via the Kozai mechanism raising eccentricities and lowering perihelion followed by circularization can also result in a close orbit. Many of the Jupiter-sized planets have eccentric orbits which may indicate that gravitational encounters occurred between the planets, although migration while in resonance can also excite eccentricities. The in situ growth of hot Jupiters from closely orbiting super Earths has also been proposed. The cores in this hypothesis could have formed locally or at a greater distance and migrated close to the star.
Super-Earths and other closely orbiting planets are thought to have either formed in situ or ex situ, that is, to have migrated inward from their initial locations. The in situ formation of closely orbiting super-Earths would require a massive disk, the migration of planetary embryos followed by collisions and mergers, or the radial drift of small solids from farther out in the disk. The migration of the super-Earths, or the embryos that collided to form them, is likely to have been Type I due to their smaller mass. The resonant orbits of some of the exoplanet systems indicates that some migration occurred in these systems, while the spacing of the orbits in many of the other systems not in resonance indicates that an instability likely occurred in those systems after the dissipation of the gas disk. The absence of Super-Earths and closely orbiting planets in the Solar System may be due to the previous formation of Jupiter blocking their inward migration.
The amount of gas a super-Earth that formed in situ acquires may depend on when the planetary embryos merged due to giant impacts relative to the dissipation of the gas disk. If the mergers happen after the gas disk dissipates terrestrial planets can form, if in a transition disk a super-Earth with a gas envelope containing a few percent of its mass may form. If the mergers happen too early runaway gas accretion may occur leading to the formation of a gas giant. The mergers begin when the dynamical friction due to the gas disk becomes insufficient to prevent collisions, a process that will begin earlier in a higher metallicity disk. Alternatively gas accretion may be limited due to the envelopes not being in hydrostatic equilibrium, instead gas may flow through the envelope slowing its growth and delaying the onset of runaway gas accretion until the mass of the core reaches 15 Earth masses.
However, that meaning should not be confused with the process of accretion forming the planets. In this context, accretion refers to the process of cooled, solidified grains of dust and ice orbiting the protostar in the protoplanetary disk, colliding and sticking together and gradually growing, up to and including the high-energy collisions between sizable planetesimals.
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Compare it with the particle number density of the air at the sea level—2.8×1019 cm−3.
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Motte, F.; Andre, P.; Neri, R. (1998). "The initial conditions of star formation in the ρ Ophiuchi main cloud: wide-field millimeter continuum mapping". Astron. Astrophys. 336: 150–172. Bibcode:1998A&A...336..150M. /wiki/Bibcode_(identifier)
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Stahler, Steven W.; Shu, Frank H.; Taam, Ronald E. (1980). "The evolution of protostars: II The hydrostatic core". The Astrophysical Journal. 242: 226–241. Bibcode:1980ApJ...242..226S. doi:10.1086/158459. https://doi.org/10.1086%2F158459
Montmerle, Thierry; Augereau, Jean-Charles; Chaussidon, Marc; et al. (2006). "Solar System Formation and Early Evolution: the First 100 Million Years". Earth, Moon, and Planets. 98 (1–4): 39–95. Bibcode:2006EM&P...98...39M. doi:10.1007/s11038-006-9087-5. S2CID 120504344. /wiki/Bibcode_(identifier)
Stahler, Steven W.; Shu, Frank H.; Taam, Ronald E. (1980). "The evolution of protostars: II The hydrostatic core". The Astrophysical Journal. 242: 226–241. Bibcode:1980ApJ...242..226S. doi:10.1086/158459. https://doi.org/10.1086%2F158459
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Montmerle, Thierry; Augereau, Jean-Charles; Chaussidon, Marc; et al. (2006). "Solar System Formation and Early Evolution: the First 100 Million Years". Earth, Moon, and Planets. 98 (1–4): 39–95. Bibcode:2006EM&P...98...39M. doi:10.1007/s11038-006-9087-5. S2CID 120504344. /wiki/Bibcode_(identifier)
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Andre, Philippe; Montmerle, Thierry (1994). "From T Tauri stars protostars: circumstellar material and young stellar objects in the ρ Ophiuchi cloud". The Astrophysical Journal. 420: 837–862. Bibcode:1994ApJ...420..837A. doi:10.1086/173608. https://doi.org/10.1086%2F173608
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Motte, F.; Andre, P.; Neri, R. (1998). "The initial conditions of star formation in the ρ Ophiuchi main cloud: wide-field millimeter continuum mapping". Astron. Astrophys. 336: 150–172. Bibcode:1998A&A...336..150M. /wiki/Bibcode_(identifier)
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Andre, Philippe; Montmerle, Thierry (1994). "From T Tauri stars protostars: circumstellar material and young stellar objects in the ρ Ophiuchi cloud". The Astrophysical Journal. 420: 837–862. Bibcode:1994ApJ...420..837A. doi:10.1086/173608. https://doi.org/10.1086%2F173608
Andre, Philippe; Montmerle, Thierry (1994). "From T Tauri stars protostars: circumstellar material and young stellar objects in the ρ Ophiuchi cloud". The Astrophysical Journal. 420: 837–862. Bibcode:1994ApJ...420..837A. doi:10.1086/173608. https://doi.org/10.1086%2F173608
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The T Tauri stars are young stars with mass less than about 2.5 M☉ showing a heightened level of activity. They are divided into two classes: weakly lined and classical T Tauri stars.[43] The latter have accretion disks and continue to accrete hot gas, which manifests itself by strong emission lines in their spectrum. The former do not possess accretion disks. Classical T Tauri stars evolve into weakly lined T Tauri stars.[44]
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As a variant they may collide with the central star or a giant planet.
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