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IV
Planet formation
http://sgoodwin.staff.shef.ac.uk/phy229.html
4.0 Introduction
Here we examine how planets form and how planetary systems can
change.
Much of this was covered in PHY106.
The key here is to see how that model is adapted in light of exoplants:
in particular Migration.
It is important to be clear on two modern theories of movement and
restructuring of the Solar System: the Grand Tack model (during
formation), and the Nice Model (500Myr after formation).
4.1 Protoplanetary discs
Planets form in gas/dust discs around young stars (see the disc of HL
Tau below). The discs are roughly 10% of the mass of the star, and
roughly 1% of their mass is in solid dust grains (micron-sized initially).
They are heated by the star and the temperature falls-off strongly as a
function of distance as the disc self-shields (>1000K at 0.1AU, to 10sK
at >50AU).
Gas discs last <10 Myr, so that is the
timescale for gas/ice giant formation.
4.1 Core accretion theory
Planets form from dust grains:
Coagulation:
Coagulation Dust particles interact, sticking together to form larger
and larger particles.
Runaway growth:
growth The larger a particle becomes, the faster it grows
as it has a larger surface area. Once these condensations reach ~10s
km in size they become 'planetesimals' and gravity becomes important.
Oligarchic growth:
growth The largest planetesimals grow faster, and the
larger they become the more dominant their gravitational attraction
becomes, allowing a small number to grow to planetary masses.
Giant planet formation:
formation In the outer solar system a planet can grow
large enough to attract a significant H-He envelope (planet mass >a
few Earth masses).
4.1 Core accretion theory
Core accretion theory predicts that:
In the inner parts of the disc planets will be fairly small, rocky bodies
(most volatiles having been gaseous leaving only rocky dust):
Terrestrial planets (e.g. Mercury, Venus, Earth & Mars). <4au
In the middle of the disc large planets can form that will collect large
H-He envelopes: Gas Giants (e.g. Jupiter & Saturn). 5-10au
In the outer disc large icy planets will be able to form, but the low
density will mean they do not collect very massive H-He envelopes: Ice
Giants (e.g Uranus & Neptune). Remember the Nice model! 10-20au
There will be significant amounts of debris remaining which will be
rocky in the inner system (e.g. Asteroids), and icy in the outer system
(e.g. Pluto, Kuiper Belt and the Oort Cloud). Everywhere, esp. >20au
4.2 Formation of the Moon
As we shall see later the Moon might be an important factor in the
development of advanced life on Earth.
The Moon is thought to have formed after the collision of a Mars-sized
body with the early Earth. This body presumably formed during the
oligarchic growth phase in a Lagrange point in the same orbit as Earth.
It was then perturbed from its Lagrange point and eventually collided
with the Earth.
This scenario suggests that large moons around terrestrial planets
might not be rare as this should happen fairly (?) often in the core
accretion scenario. Estimates are that maybe 10% of Earth-like
planets will have a large Moon.
4.3 Hot Jupiters
Core accretion says that gas giant planets can only form beyond the
ice line at ~3-5 au. However, most of the planets discovered so far are
gas giants well within the ice line.
How can we explain hot Jupiters?
Ice line
4.3 Migration: Type I
High-mass planets (more than a few
Earth masses) interact weakly with
the discs causing a spiral density
wave in the disc. At this point the
discs are much more massive than
the planets they contain.
The planet interacts more strongly
with the outer wave causing it to
loose angular momentum/energy
(transferring that angular
momentum/energy to the wave) and
so moves inwards.
4.3 Migration: Type I
The dominant gravitational force of the
outer (trailing) wave decelerates the
planet causing it to move inwards as it
looses kinetic energy.
(Note it also gains some kinetic energy
as it moves inwards by releasing
gravitational potential energy, but the
deceleration from the wave dominates).
4.3 Migration: Gap Clearing
As the planet increases in mass, the
strength of the interaction with the disc
grows stronger. The transfer of angular
momentum (outwards through
interaction with the trailing wave, and
inwards through interaction with the
leading wave) causes the disc around
the planet to clear.
4.3 Migration: Type II
Once a planet has reached the mass of
a small gas giant planet, the area
around that planet will have been
completely cleared.
Some gas continues to accrete, caught
by the planet's gravitational field. As the
disc slowly moves inwards accreting
onto the star, the planet will also slowly
move inwards (the disc looses a.m. by
viscous transport, and new material
accreted by the planet will have lower
a.m., causing the planet to move
inwards also).
4.3 Migration: Type II
Spiral structure and gaps (presumably due to planets) have been
observed in a number of discs around young stars:
4.3 Migration: Problems
Migration appears to solve the hot Jupiter problem: massive planets
can move in from beyond the ice line to close to stars. However,
migration suffers from two major problems:
Firstly, the timescale for rapid (type I) migration is very short (O(105)
yrs) – why do planets not fall into their parent star? Why are so many
Jupiters at 1-3au?
Secondly, why did migration not occur in the Solar System? It is argued
that Jupiter and Saturn reached a resonance as they migrated so
stopping migration. Is another gas giant required? How often does
this happen? Some systems have hot Jupiters and distant Jupiters (55
Cnc, HD125612,Ups And, and others) – why?
4.4 Problems in the Solar System
The Solar System sort-of fits the predictions of the core accretion
model but there are some problems.
1. Why do the Terrestrial planets have volatiles (especially water)?
They formed well within the ice line and so should be very depleted in
volatiles.
2. Why is Mars so small? Mars should be much bigger than the Earth
given where it is now.
3. Why are Uranus and Neptune where they are? They are too far out
to have formed where they are (they have H-He envelopes so must
have formed while the gas disc was in place). And why is Neptune
more massive than Uranus?
4.5 Grand Tack model
The Grand Tack model suggests that Jupiter and Saturn both migrated
whilst forming.
Jupiter migrated in to ~2AU. Its migration was stopped and reversed
by the inward migration of Saturn to a 3:2 resonance.
The inward migration of Jupiter brought volatile-rich material from
~5AU which was incorporated in the formation of the terrestrial planets.
It also cleared much of the material from Mars' orbit meaning that the
planet that formed there was low mass.
4.5 Grand Tack model
4.6 Nice model
The Nice model suggests that the outer Solar System was restructured
about 0.5Gyr after the formation of the Solar System (ie. much later
than the Grand Tack model).
Initially the outer Solar System was Jupiter-Saturn-Neptune-Uranus
(and maybe another ice giant).
The Kuiper Belt was more massive and extended in to the orbit of
Jupiter. Over ~500Myr interactions with comets caused the planets to
move orbit slightly.
This is quite gentle until Jupiter and Saturn hit a 2:1 resonance which
pumps energy into the orbits of the ice giants throwing them to a larger
distance (Neptune further as it was closer to them). It also pushes J-S
out of the resonance and clears the early Kuiper Belt.
This also explains the Late Heavy Bombardment.
4.6 Nice model
The Solar System before, during, and after restructuring in the Nice
model.
4.5 Summary
The core accretion model states that planets form from the build-up of
dust into larger and larger bodies.
But planet formation is not simple. Interactions with the disc can cause
the migration of massive planets, and multiple massive planets can
interact in complex ways.
Planetary systems can also restructure themselves long after
formation.
An important point for astrobiology is how often do significant amounts
of volatiles get introduced to the inner solar system? Grand Tack does
this early, but Nice can do it later.
A common question is: how 'special' is our Solar System?