Introduction
There are currently many models for the formation of planets and in particular gas giants,
such as core accretion, disk instability, the modern Laplacian etc. Each of these models have
their own strengths and weaknesses. While some models can co-exist, others will prove to
be either right or wrong. Scientists have being seeking an answer to how the planets formed
in our solar system for hundreds of years, as it is just one small part to the age-old question
of how we came to be here.
The purpose of this review is to compare and contrast competing theories for gas giant
formation, with a brief look firstly at solar system formation.
Background
Before planets can be formed the solar system must be formed. It is important to look at
these mechanisms as they can give insight into the conditions that the planets are required
to form in. This places constraints that the competing theories need to include in order to
be considered as correct. For example some theories require a metallicity conditions be
satisfied (disk instability theories), that is a certain amount of the material that makes up
the solar system must be non-hydrogen or helium.
Forming a Solar System
The mechanism for forming stars and solar systems is known much better than the
individual formation of the planets. This may be due to the fact that astronomers have
millions of stars to view at varying ages, but only one solar system to observe that formed
approximately 4.6 billion years ago.
Early theories for the formation of the solar system include the nebular hypothesis and the
catastrophic hypothesis. The catastrophic hypothesis has now being disregarded in favour of
the nebular hypothesis. One of the first theories of this type was the cometary collision
hypothesis formulated by Georges-Louis Buffon (1749), a French biologist turned
cosmologist. In his theory, he proposed that large comets collided with the sun, tearing off
large streams of material that was to create the planets and their moons. Another
catastrophic hypothesis was later put forward by Alexander Bickerton in 1880, this time the
collision was said to have being of another star with our sun. He even went so far as to say
that observed spiral nebulae were the results of such collisions, but spiral nebulae actually
turned out to be far away spiral galaxies.
The general theory for the formation of solar systems is called the Nebula hypothesis
(Immanuel Kant 1755). This theory starts out with a large gas cloud, or giant molecular
cloud. A nearby supernova explosion is thought to have disrupted the cloud causing a region
of it to become gravitationally unstable and collapse. These giant molecular clouds have a
slight rotation, so that when the cloud contracts it begins to rotate faster, this is due to the
conservation of angular momentum. This faster rotation flattens the cloud into a disk. At the
centre the contraction causes the cloud to become denser – eventually becoming so dense
that hydrogen fusion starts and a star is formed. Meanwhile in the disk, the planets formed
via the gradual build up of material through collisions. Due to these collisions, eventually the
planets would sweep clean their orbits and the surrounding space through gravitation
attraction. This process is called accretion.
Fundamental observations support the disk/accretion model, such as:
- All of the planets rotate the sun in the same direction
- All of the planets and moons, except Venus, rotate on their axis in this same
direction
- All the planets, except Pluto, have approximately circular orbits.
- All the planets, again except Pluto, orbit the sun in roughly the same plane.
Although Pluto is a counter example to two of the above points, it has recently being reclassified
as a dwarf planet and in the future it may be found that Pluto did not form in the
same way as the rest of the planets.
Later Pierre-Simon Laplace also formed a nebular hypothesis, which differed from Kant’s. In
his hypothesis, Laplace postulated that as the giant gas cloud contracts it will shed gas rings.
It is these concentric gas clouds that he proposed would then form the planets through
accretion. This idea of concentric gas rings gives an explanation for why the ratio of the
orbits from one planet to the next is approximately the same. It wasn’t until last century
that Andrew Prentice was able to show that if supersonic turbulence is present in the gas
cloud, it can lead to the formation of concentric gas rings (Prentice 1978). The renewed
theory was coined ‘The Modern Laplacian Theory’.
Core Accretion
When considering gas giants, the core accretion model has being the long standing accepted
theory. The core accretion model states that as the disk formed by the protostellar cloud
rotates, planetismals (the predecessors of planets and in this, case gas giant cores) will start
to accrete from dust and ice under the force of gravity. This will continue to happen and
collisions between many planetismals will eventually yield larger protoplanets. As these
protoplanets get larger, they gain more gravitational attracting force. This causes them to
eventually, over time, sweep clean their orbital path. When these protoplanet cores get
large enough they will start to accrete gases. This gas forms an envelope around the core in
hydrostatic equilibrium – the gas pressure force equally but oppositely balances the
gravitational force. When enough gas has being accreted, the force of gravity overcomes the
gas pressure force and the equilibrium is broken, forcing the planet to contract into a gas
giant.
While core accretion is the currently favoured theory, it has some issues that need to be
addressed if it is to remain the accepted theory. Simulations have shown that the time taken
for a gas giant in the order of Jupiter’s mass to form is around 1-10 million years (Pollack et
al. 1996). This is too long, since it is currently thought that the sun will have formed and the
solar wind would have blown the gas and dust in the disk into interstellar space before the
gas giant can have formed. Although in some different systems the proto-planetary disk may
have a lifetime in the order of 10 million years, on average it is less and thus core accretion
cannot explain the formation of gas giants in these systems.
Another problem with the core accretion model is what is known as inward migration. As
the planetismal core gets larger it experiences a breaking effect from collisions. This lowers
its angular momentum and makes the current orbit unstable, forcing the planetismal to
migrate inwards. This inward migration presents problems when trying to model our own
solar system. Currently all extra-solar planets observed have being hot Jupiters. They were
given this name because they are gas giants orbiting their parent stars very tightly in
comparison to our system. The inward migration occurs over approximately 104 initial
orbital periods (Nelson et al. 2000). This places a maximum possible amount of gas that can
be accreted in this time, calculated to be approximately 5 times the mass of Jupiter2 when
the gas giant reaches the vicinity of the parent star. Recent observations by the Galileo
space probe suggest Jupiter may only have a core of around three times Earths mass. This is
a problem because for core accretion to occur it would need the core to be more like ten
times Earths mass. Hence the core accretion model may not describe the local solar system,
but it can be used to describe observed extra-solar systems. A survey of the current
detected extra-solar planets showed that 90% of them could be explained by the core
accretion model (Matsuo et al. 2007). The remaining 10% did not fit core accretion models
and could have only formed via a different mechanism.
While this is a good result it may be due to a selection effect. The selection effect manifests
itself because using current techniques for extra-solar planet detection don’t actually detect
the planet itself, but instead observe periodic ‘wiggles’ of parent stars. These ‘wiggles’ are
observed as the periodic back and forth motion of a star in the sky, they are due to the tug
of gravity from the planets on their parent star. All planets will effect the movement of their
parent star but the larger, closer orbiting planets (hot Jupiters) will produce a more
pronounced ‘wiggle’ in the parent stars motion. This larger movement caused by hot
Jupiters is easier for our telescopes to pick up here on Earth, hence it is no surprise that
currently all the extrasolar planets detected are thought to be of this type.
Disk Instability
The crux of disk instability theories is that the protoplanetary disk will not remain stable and
allow accretion to occur over long time periods. Instead the disk fragments, clumping into
what are called arclets. This has been shown via simulation (Durisen 2004). It is uncertain
whether these arclets are stable and if they will eventually become protoplanets over time,
simulations of impeccable accuracy need to be run (Durisen 2004).
The idea of the protoplanetary disk being unstable is not new, it dates back to 1964 when
Alar Toomre came up with the Toomre's Stability Criterion (Q). Only more recently has disk
instabilities being looked at as a mechanism for the rapid formation of gas giants. In 1997
Alan Boss put forward the first Disk Instability theory and henceforth has being the biggest
competitor with the core accretion model.
Toomre was able to show that a protoplanetary disk would be unstable unless the random
root mean square velocity of particles in the disk was adequately large to overcome self
gravity (Toomre 1964). The stability criterion consists of such parameters as the speed of
sound, epicyclic frequency and surface mass density of the disk. Numerical analysis has
shown that disks become prone to instabilities when Q is less than 1.5 to 1.7 (Durisen et al.
2005).
Matsuo’s study found that the remaining 10% of the catalogued extra-solar planets that
could not be explained by core accretion, where in accordance with the disk instability
theory. This was done by first deriving the upper and lower limits for the mass of gas giant
formed by both disk instability or core accretion. These values where then plotted as a
function of the metallicity. Once these conditions where set the, data of known extra-solar
planets could be interpreted. They concluded most planets formed via core accretion while
a minority formed by disk instabilities.
Disk instability Theory (first proposed by Yoji Osaki 1996) is able to explain the formation of
gas giant planets in a much shorter time span than that of the core accretion mode – “High
spatial resolution, three-dimensional hydrodynamical models of `locally isothermal' disks
have shown that gas giant protoplanets may form in such a marginally unstable disk, with
masses comparable to the more massive extra-solar planets, and well within expected disk
lifetimes”4 (Boss 2001). This is far from saying that gas giant planets can form via this
method, though it does look promising.
Using disk instability models it has being shown that the disks can become unstable and
rapidly clump. The main issue is that within simulations these protoplanetary clumps form
relatively quickly and remain stable, but no one has, as yet, being able to follow through the
simulations long enough to see if the clumps form gas giants.
Hybrid Theories
A new third direction is approaching the problem taking ideas from both core accretion and
disk instability theories, to create a hybrid theory. It has being shown in simulations that
even if the disk instability cannot create a fully formed planet, it is possible that instabilities
will create rings about the star (Durisen et al. 2005). The simulations showed that disk
instabilities leave the ring of material in a state that fosters quicker gas giant formation.
Such as increasing the gas density and decreasing the gas opacity. Hence these rings would
be able to form a gas giant much quicker than if it purely formed by accretion.
The Modern Laplacian Theory
The main premise of the Modern Laplacian theory is the formation of concentric gas rings
around the contracting protosolar cloud. For the protosolar cloud to have shed such a
relatively small amount of mass while still shedding significant angular momentum, the
surface must have being under turbulent stress causing supersonic convective velocities. In
this case the speed of sound is referring to the local isothermal sound speed. The idea of
turbulent stresses where first put forward by ter Haar in 1950. This is where the theory runs
into some problems. The Modern Laplacian Theory requires speeds around mach 5, five
times that of the adiabatic sound speed (sound speed at constant temperature), while
simulations only come up with values of mach 3 (Prentice Dyt 2003). This isn’t the only
simulated value that falls short, the vertical dynamical stress to gas pressure ratio was found
to be 3-4. While the Modern Laplacian theory requires it to be ~35 for gas rings to form.
Prentice was able to show that if these gas rings form then they should form with the ratio
of one orbit to the next being a constant (1978). This is observed not only in the solar
system, but also in the Saturnian and Jovian systems. No other theory currently gives an
explanation for this constant ratio.
While the Modern Laplacian theory does not primarily describe gas giant formation, it is a
much more complete theory. If these problems can be rectified the Modern Laplacian
theory gives a quick route to the formation of concentric gas rings that would eventually
form the planets.
Disk or Rings?
It is evident that there is something amiss when one theory proves rings should exist around
a protostar, while another theory insists on there been a disk. The Modern Laplacian theory
is able to show mathematically that these rings should be shed under certain conditions, it is
yet unknown whether our young solar system was under such conditions. Further data
about the early solar system needs to be collected, from such sources as asteroids or
perhaps kuiper belt objects. Since these objects have remained relatively untouched and the
conditions they evolved in confidently known, it is possible to extrapolate back to the
beginning of the solar system.
Observations of the star Beta Pictoris have shown it to be surrounded by a flat disk. The disk
has been swept clear within 40Au of the star; this may be due to the presence of a planet
(Lagage, P.O., & Pantin, E. 1994). Such an observation seemingly supports theories in which
a disk forms around the star and accretion then occurs within the disk. The problem is there
is not enough examples of this, more data needs to be collected before one can conclusively
say whether a disk, ring or perhaps both can form around a protostar.
Conclusion
The theories for the formation of gas giants have reached a crossroad. While core accretion
can explain the formation of Jupiter and perhaps Saturn (as well as other extra-solar hot
Jupiters), the time scales required for it to form Uranus and Neptune are longer than the
lifetime of the protoplanetary disk. This shows that core accretion cannot be the sole
mechanism that we use to describe the formation of gas giants. There are a few alternatives
that must be considered:
- Either core accretion must be let go and a new theory be used to explain the
formation of all the gas giants, this may be a version of a disk instability theory or
modern Laplacian theory.
- Multiple theories may be accepted; where core accretion is accepted as the
mechanism for the formation of some gas giants (under the correct conditions) and
other theories, currently known or unknown, are used to explain the formation
process where core accretion is not sufficient.
- Finally a hybrid theory that combines both disk instability and core accretion and is
able to be used as a definitive solution to the gas giant formation problem in all
situations.
It is clear that further research is needed in this area. Specifically more data is needed
pertaining to the conditions in our early solar system. With this data in hand and using
improved computer models of higher precision, it may then be possible to show
conclusively whether a gas giant can form via disk instabilities, core accretion or the Modern
Laplacian theory.
References
1. Boss, A.P., Gas Giant Protoplanet Formation: Disk Instability Models with
Thermodynamics and Radiative Transfer. The Astrophysical Journal, 2001. 563(1), p.
367-373.
2. Durisen, R.H., Gravitational instabilities in disks: From polytropes to protoplanets.
First Astrophysics meeting of the Observatorio Astronomico Nacional, 2004.
3. Durisen, R.H., Cai K., Mejía, A.C., & Pickett, M. K., A hybrid scenario for gas giant
planet formation in rings. Icarus, 2005. 173 (2), p. 417-424.
4. Lagage, P.O., & Pantin, E., Dust depletion in the inner disk of Pictoris as a possible
indicator of planets. Nature, 1994. 369, p. 628 - 630
5. Nelson, P.R., et al, The Migration and Growth of Protoplanets in Protostellar Discs,
Monthly Notices of the Royal Astronomical Society, 2000. 318 (1), p. 18–36.
6. Matsuo, T., et al., Planetary Formation Scenarios Revisited: Core-Accretion versus
Disk Instability. The Astrophysical Journal, 2007. 662: p. 1282 - 1292.
7. Pollack, J.B., et al, Formation of the Giant Planets by Concurrent Accretion of Solids
and Gas, Icarus, 1996. 124, 62.
8. Prentice, A.J.R, Towards a modern Laplacian theory for the formation of the solar
system, The origin of the solar system, 1978.
9. Prentice, A.J.R., & Dyt, C.P., A numerical simulation of supersonic turbulent
convection relating to the formation of the solar system. Monthly Notices of the
Royal Astronomical Society, 2003. 341(2), p. 644–656.
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