Growth of massive nuclei beyond the freezing point by accreting thick hydrogen-helium shells
1. Beyond the cold
In protoplanetary disks, in a region beyond a certain distance from a star – often called frost line (snow line) – water and other volatile substances can freeze into ice grains. This has great significance for the formation of planets:
- Ice-enriched solids: Lower temperatures allow water, ammonia, methane, and other volatiles to condense on dust grains, increasing the total mass of solids.
- Larger particle nuclei: This increase in mass helps planetary embryos rapidly accumulate material and reach a critical mass to would attract nebula gases.
As a result, planets forming in the outer part of the disk may gain thick hydrogen-helium shells and become gas giants (like Jupiter or Saturn) or ice giants (Uranus and Neptune). While the terrestrial planets in the hot inner disk remain relatively low-mass and mostly rocky, these outer disk planets can reach tens or hundreds of Earth masses, significantly affecting the overall planetary architecture of the system.
2. Nuclear accretion model
2.1 Basic premise
Widely recognized nuclear accretions The model states:
- Hard core growth: A planetary embryo (an initially ice-enriched protoplanetary body) accretes local solids until it reaches ~5–10 MEarth.
- Gas aspiration: When a nucleus becomes massive enough, it rapidly gravitationally attracts hydrogen–helium from the disk, with the onset of uncontrolled mantle accretion.
- Uncontrolled growth: This is how Jupiter-like gas giants or intermediate-sized "ice giants" form if disk conditions are less favorable for mantle accretion or the disk disperses earlier.
This model convincingly explains the existence of massive H/He shells around the Jovian planets and the more modest shells in the "ice giants", which may have formed later, accreted gas more slowly, or lost part of their shell to stellar or disk processes.
2.2 Disk lifetime and rapid formation
Gas giants must form before as the disk gas dissipates (over ~3–10 million years). If the core grows too slowly, the protoplanet will not have time to accretize much hydrogen–helium. Studies in young star clusters show that disks decay relatively quickly, suggesting that giant planet formation must occur rapidly enough to exploit the short-lived gas reservoir [1], [2].
2.3 Shell shrinkage and cooling
Once the core exceeds critical mass, the initially shallow atmospheric layer transitions to uncontrollable The accretion stage. As the envelope grows, gravitational energy is radiated away, allowing the envelope to contract and attract even more gas. This positive feedback loop can eventually form ~tens to hundreds of Earth-mass planets, depending on the local disk density, time, and factors such as type II migration or gap formation in the disk.
3. The importance of frost lines and icy solids
3.1 Volatile compounds and increased particulate matter
On an external drive, where the temperature drops below ~170 K (for water, although the exact limit depends on the disk parameters), water vapor condenses, increasing the surface density of solid particles by a factor of 2–4.Also other ices (CO, CO2, NH3) fall out at even lower temperatures further away from the star, resulting in an even greater amount of solid material. This abundance of ice-enriched planetesimals results in faster-growing cores, which is a key gas and ice giants formation premise [3], [4].
3.2 Why do some become gas giants and others ice giants?
- Gas giants (e.g. Jupiter, Saturn): Their cores form quickly enough (>10 Earth masses) to have time to take over a huge layer of hydrogen-helium from the disk.
- Ice giants (e.g. Uranus, Neptune): They may have formed later, accreted more slowly or experienced greater disk dispersion, resulting in a smaller gas envelope, and a large portion of their mass is made up of water/ammonium/methane ices.
Thus, whether a planet becomes a "Jovian giant" or a "Neptunian ice giant" is determined by the density of solid particles, the rate of core growth, and the external environment (e.g., photoevaporation from nearby massive stars).
4. Growth of massive nuclei
4.1 Accretion of planetesimals
Based on the rigid nuclear accretions In the model, icy planetesimals (km in size and larger) form through collisions or streaming instability. When a protoplanet reaches ~1000 km in size or larger, it enhances gravitational collisions with the remaining planetesimals:
- Oligarchic growth: A few large protoplanets dominate the region, "sweeping out" the smaller body populations.
- Decay reduction: Lower collision rates (due to partial gas suppression) promote accretion rather than disintegration.
- Time scales: The nucleus must reach ~5–10 MEarth several million years to take advantage of the disk gas [5], [6].
4.2 "Pebble" accretion
Another mechanism is "pebble" accretion:
- Pebbles (mm–cm) drifts on the disk.
- A sufficiently massive protonucleus can gravitationally "capture" those pebbles, growing extremely rapidly.
- This accelerates the transition to a super-Earth or giant core, which is crucial for initiating mantle accretion.
When the core reaches a critical mass, uncontrolled gas accretion begins, resulting in the formation of a gas giant or an ice giant, depending on the final envelope mass and disk conditions.
5. Mantle accretion and gas-dominated planets
5.1 Uncontrolled shell growth
Once the core exceeds critical mass, the pro-giant planet initially has a thin atmosphere, which transitions to uncontrollable gas accretion phase. As the envelope expands, gravitational energy is radiated, allowing it to further pull in the nebula's gas. The key limiting factor is often to supply the disk and renew the gas or the planet's ability to cool and pull its shell. Models show that if ~10 MEarth the core forms, the mass of the shell can grow to tens or hundreds of Earth masses if the disk persists [7], [8].
5.2 Gap formation and type II migration
A sufficiently massive planet can to cut a gap in the disk through tidal rotations exceeding the local disk pressure forces. This changes the course of the gas supply and leads to Type II migration, where the orbital evolution of the planet depends on the magnitude of the disk viscosity.Some giants may migrate inward (forming "hot Jupiters") if the disk does not dissipate quickly enough, while others remain in their formation zone or further away if disk conditions inhibit migration or if several giants merge in resonances.
5.3 Various endings of gas giants
- Jupiter-like: Very massive, large shell (~300 Earth masses), ~10–20 The core of the Earth's masses.
- Saturn-like: Intermediate shell size (~90) Earth masses), however, there is a clear dominance of hydrogen-helium.
- Sub-juniors: Lower total mass or incomplete uncontrolled growth.
- Brown dwarfs: Upon reaching ~13 At Jupiter masses, a boundary appears between giant planets and substellar brown dwarfs, although the formation mechanisms may differ.
6. Ice giants: Uranus and Neptune
6.1 Formation in the far disk
Ice giants, such as Uranus and Neptune, have about 10–20 Total mass of the Earth's masses, of which ~1–3 MEarth in the core and just a few Earth masses in the hydrogen/helium shell. They are thought to have been born 15–20 AV, where the disk density is lower and the accretion rate is slowed by greater distance. The reasons for their formation are different from Jupiter/Saturn:
- Late formation: The core reached critical mass quite late, before the disk was already scattering, so a smaller amount of gas was attracted.
- Faster disk degradation: Less time or external radiation has reduced gas reserves.
- Orbital migration: Could have formed a little closer or farther away and been pushed into their current orbits by the interaction of other giants.
6.2 Composition and internal structure
Ice giants are rich in water/ammonium/methane ice — volatile compounds, which condensed in the cold outer zone. Their higher density compared to pure H/He giants indicates more "heavy elements". The internal structure may be layered: a rocky/metallic core, a watery mantle with dissolved ammonia/methane, and a relatively thin H–He layer on top.
6.3 Exoplanetary analogues
Many exoplanets, called "mini-Neptunes", occupies an intermediate position between super-Earths in terms of mass (~2–10 MEarth) and Saturn. This suggests that partial or incomplete shell accretion is quite common once a core of at least moderate size is formed—a dynamic similar to the formation of "ice giants" around many stars.
7. Verification of observations and theoretical considerations
7.1 Observing forming giants in disks
ALMA The ring/gap patterns detected may be carved by the cores of giant planets. Some direct imaging instruments (e.g. SPHERE/GPI) are trying to detect young giant objects that are still submerged in the disk. Such detections confirm the rates and mass accumulation predicted by the nuclear accretion theory.
7.2 Compositional clues from atmospheric spectra
Spectra of exoplanetary giants (transit or direct observations) reveal the "metallicity" of the atmosphere, which indicates how many heavy elements are present. Observations of the atmospheres of Saturn and Jupiter also reveal traces of the chemistry of the disks as they formed, such as the C/O ratio or the amount of noble gases. Differences may indicate the accretion of planetesimals or the path of dynamical migration.
7.3 Migration Impact and System Architectures
Exoplanet surveys show many systems with hot Jupiters or several Jovian planets near the star.This suggests that the formation of giant planets and the interaction of the disk or planets can significantly shift orbits. The outer gas/ice giants of our Solar System determined the final alignment by scattering comets and smaller bodies, and may have helped protect Earth from the threat of larger migrations (e.g., inward migrations into Jupiter or Saturn).
8. Cosmological implications and diversity
8.1 The influence of a star's metallicity
Stars with a larger metallicity (with a higher proportion of heavy elements) tend to have more giant planets. Studies show a strong correlation between the iron abundance of a star and the probability of giant planets. This is likely due to the higher amount of dust in the disk, which accelerates the growth of the core. Low-metallicity disks often form fewer or smaller giants, and perhaps more rocky/"ocean" worlds.
8.2 A "desert" of brown dwarfs?
When gas accretion moves to ~13 Jupiter-mass region, the boundary between giant planets and substellar brown dwarfs becomes unclear. Observations show a "brown dwarf desert" near Sun-like stars (brown dwarfs are rarely found at close distances), perhaps because bodies of such masses have a different formation mechanism, and disk fragmentation rarely yields stable orbits for that mass range.
8.3 Low-mass stars (M dwarfs)
M dwarfs (lower-mass stars) tend to have lower-mass disks. They are more likely to form mini-Neptunes or super-Earths than Jupiter-sized planets, although there are exceptions. The relationship between disk mass and stellar mass explains why we find Neptunes or rocky super-Earths more often around smaller stars.
9. Conclusion
Gas and ice giants – these are some of the most massive results of planetary formation that occur outside of frost lines in protoplanetary disks. Their powerful cores, rapidly forming from ice-rich planetesimals, attract thick hydrogen–helium shells until the disk is rich in gas. The final outcome—Jupiter giants with huge shells, ringed Saturn analogs, or smaller “ice giants”—depends on the properties of the disk, the rate of formation, and the course of migration. Observations of exoplanet giants and gaps in young dusty disks suggest that this process occurs widely, leading to a variety of orbits and compositions for giant planets.
Leading nuclear accretions In the model, the path appears to be nuanced: an ice-rich body spans several Earth masses, triggers uncontrolled gas accretion, and becomes a massive H/He reservoir that largely determines the arrangement of the entire planetary system—dispersing or arranging smaller bodies, creating a key dynamical context. As we continue to observe ALMA ring structures, spectral data from giant atmospheres, and exoplanet statistics, our understanding of how cold regions of protoplanetary disks grow the largest members of planetary families is deepening.
References and further reading
- Pollack, J. B., et al. (1996). "Formation of the Giant Planets by Concurrent Accretion of Solids and Gases." Icarus, 124, 62–85.
- Safronov, V. S. (1972). Evolution of the Protoplanetary Cloud and Formation of the Earth and Planets. NASA TT F-677.
- Lambrechts, M., & Johansen, A. (2012). "Rapid growth of gas-giant cores by pebble accretion." Astronomy & Astrophysics, 544, A32.
- Helled, R., et al. (2014). "Giant planet formation, evolution, and internal structure." Protostars and Planets VI, University of Arizona Press, 643–665.
- Stevenson, D.J. (1982). "Formation of the giant planets." Annual Review of Earth and Planetary Sciences, 10, 257–295.
- Mordasini, C., et al. (2012). "Characterization of exoplanets from their formation. I. Models of combined planet formation and evolution." Astronomy & Astrophysics, 541, A97.
- Bitsch, B., Lambrechts, M., & Johansen, A. (2015). "The growth of planets by pebble accretion in evolving protoplanetary discs." Astronomy & Astrophysics, 582, A112.
- D’Angelo, G., et al. (2011). "Extrasolar planet formation." Exoplanets, University of Arizona Press, 319–346.