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Planet Formation: Disk Formation and Evolutionc Swinburne University of Technology, 2011

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Summary
In this Activity we will look at the formation and evolution of protoplanetary disks in which planets areformed. In particular we will discuss:• some of the constraints from the Solar System that planet formation models must explain;• the standard star formation paradigm and details of cloud collapse;• disk formation, evolution, and dispersal;• chemistry and dust grain condensation; and• grain growth via collisions.
c Swinburne University of Technology, 2011

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Introduction
The formation of the planets and the Solar System is one of the fundamental questions in modern
astronomy. It has been a question asked throughout the ages since it is really a question about ourown origin. We cannot hope to fully understand how life evolved on Earth if we do not know how the
Earth itself formed.
Throughout this course we have found many clues to help us build a general picture of the planet
formation process, as well as a number of constraints that any planet formation model must be able
to address. As well as planets in our own Solar System, we now know of hundreds of planets orbiting
other stars in the neighbourhood of our Sun. Assuming our Solar System in not cosmically special,a general planet formation paradigm should be able to understand the formation of the extrasolar
planets as well.
c Swinburne University of Technology, 2011

In this Activity we will start by looking at some of the constraints from our Solar System, and thenbriefly review the standard star formation paradigm, since planetary disks are a natural by-productof the star formation process. Once formed, protoplanetery disks go through a complex evolution
with can result in the formation of planets, satellites, asteroids and comets before it dissipates withina few tens of millions of years. We will look at disk evolution, as well as how grains form and growin these disks. In the next Activity we will look more closely at models of terrestrial and giant planet
formation.

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Constraints from the Solar System

The geometry of the Solar System provides important clues, as well as constraints, on formation
scenarios. The planets (major and minor) reside in the same plane and are relatively regularly
space; they all orbit the Sun in the same direction; most planets spin in the same direction in which
they orbit the Sun; and orbital periods increase with distance from the Sun. We also see a range ofdynamical structures in the asteroid belt and the Kuiper belt and these smaller bodies are in generalon more eccentric and inclined orbits than the planets.

c Swinburne University of Technology, 2011

If we take stock of what is in the Solar System,
we find a wide range of objects: the central
hot sun, rocky planet in the inner Solar System,
gas and ice giants in the outer Solar System,
a mix of rocky and icy satellites, as well asa mix of rock and icy minor planets, and icy
comets. Any model of planet formation needs
to explain all of the objects, and a modelfor our Solar System needs to include anevolutionary scenario that explains the current
state (location, composition, age, etc.) of all ofthese objects.

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In terms of the composition and bulk chemistry, we find the smaller rocky planets (Mercury, Venus,
Earth, Mars) in the inner part of the Solar System, while the larger gas/ice giants (Jupiter, Saturn,
Uranus, Neptune) reside farther out. The density of the planets decreases with heliocentric distance.
There is an inner ring of small rocky bodies, i.e. the asteroid belt (which has a chemical gradient)and an outer belt of icy bodies, i.e. the Kuiper belt. In the centre of the Solar System is the hot Sun.
There are clearly more refractory materials close to the Sun and more volatiles farther away.
Small bodies are generally irregularly shaped and undifferentiated, while large bodies are sphericaland differentiated. This tells us something about the history of internal heating of larger planetary
bodies. The surfaces of planetary bodies, which can be crater and/or lava covered, also provide
clues about their thermal history. Crater counts also provide information about impact rates in theearly Solar System.
c Swinburne University of Technology, 2011

Credit: NASA

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The refractory inclusions in the meteorite data tell us that the first solids in the
Solar System formed about 4.568 Gyrs ago. The chondrules and differentiatedplanetesimals formed a few million years later. Lunar rocks are between 3–4.4
Gyrs, and the oldest Earth rocks are about 4 Gyrs old (though terrestrial grains
with ages ∼4.4 Gyrs have been found).
We know that planets are formed around stars as a natural by-product of the starformation process. So before we move on to the details of planet formation, we
need to start with the general theory of star formation.
First

condensates:

calcium

aluminiuminclusions.
Credit:Sasha
c Swinburne University of Technology, 2011

Krot

c

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The standard star formation paradigm
Stars form in molecular clouds that are found in the spiral arms of
the Galaxy. Molecular clouds are cold, dense clouds of gas anddust, and stars form within them when they contract due to gravity.

In spiral galaxies, stars form in thearms which contain dense regions ofgas and dust.
Credit:NASA and The Hubble

Heritage Team (STScI/AURA)

c Swinburne University of Technology, 2011

The Milky Way contains a large number of molecular clouds, ranging
from giant systems with masses in the range of 105 –106 M andsizes in the order of 50–100 pc, down to small cores with masses
as low as a few M and a few pc in size. The small cores areusually embedded in larger complexes. Most molecular clouds havetemperatures between 10–50 K and as their name suggests containa wealth of molecules. Densities range from 103 particles per cm3
in molecular clouds to 105 particles per cm3 in dense cores.

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The generally accepted paradigm of low mass star formation (Shu et al. 1987) is as follows:
1. collapse phase: giant molecular clouds must contract to form molecular cores. This contraction
requires ambipolar diffusion to first carry away the magnetic fields which help hold the cloud up;
2. protostellar phase: the rapid inside-out gravitational collapse of molecular cloud coresconserves angular momentum, producing a protostar surrounded by a disk and an opticallythick infalling envelope;
3. outflow phase: a strong stellar wind breaks out at the rotational poles, reversing the infall andproducing bipolar outflows. This phase seems to be intimately connected with the disk formation
phase;

5. disk dispersal phase: the final stage is the clearing of the disk, via photoevaporation and stellar
winds.

c Swinburne University of Technology, 2011

4. T Tauri phase: the newly formed star/disk system becomes optically visible and the protostar is
identified as a T Tauri star;HET620-M09A01: Planet Formation: Disk Formation and
Evolutionc Swinburne University of Technology, 2011

To view a full-sized version of this diagram click here.

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Cloud collapse
Giant molecular clouds are held up by magnetic fields, thermal gas pressure and rotation. If theclouds become massive enough, they can collapse due to gravity. We will briefly look at each ofthese support mechanisms.

c Swinburne University of Technology, 2011

The role of turbulence in star formation is rather complex: it creates overdensities which can initiate
gravitational collapse and it can also counter the effects of gravity in these overdense regions (McKee& Ostriker 2007).

HET620-M09A01: Planet Formation: Disk Formation and
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PAGE 11 OF 51(i) Pressure support: Pressure is related to temperature via the gas equation of state. Therefore
inside cold molecular clouds the thermal pressure will not provide much support against
gravitational collapse. Some clouds, however, have observed supersonic motions1 and thermal
gas pressure which may contribute to their stability.
(ii) Rotational support: The gravitational force that is trying to make the cloud collapse also has toovercome rotation. The cloud’s rotation produces an outward centrifugal force perpendicular to therotation axis that keeps the cloud from collapsing. Observations of molecular clouds indicate thatthey rotate quite slowly, with rotational velocities equivalent to 0.3 km/s at a distance of 0.1 pc. Thisis similar to the thermal support, but many clouds rotate slower than this which suggests that rotation
provides little support2 .
1

Supersonic means faster than the speed of sound. The speed of sound in an ideal gas depends
on the density and pressure.
While rotation may not be important in holding clouds up against local collapse, we will see thatrotation has an important role to play in the star and planet formation process.

c Swinburne University of Technology, 2011

2

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PAGE 12 OF 51(iii) Magnetic support: Magnetic fields only affect charged particles in molecular clouds, making
them follow field lines rather than obey gravity (or dragging the field along with them). The fields
exert a magnetic force on the charged particles, which acts like a magnetic pressure. The magnetic
pressure is given by:
B2
Pmag =
8π
It is difficult to measure the magnetic field strength in molecular clouds. In a study of 27 clouds
Crutcher (1999) found field strengths B = 20–200 µG. This is generally thought to be enough to
support molecular clouds against gravitational collapse and is about ten times greater than thethermal support.

c Swinburne University of Technology, 2011

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In order for molecular clouds to collapse and commence the star formation process, they must rid
themselves of this magnetic support. The process which removes magnetic pressure from molecular
clouds is called ambipolar diffusion (Mestel & Spitzer 1956, Mouschovias 1976). In this process
there is a very slow slippage between the ions and neutrals in the cloud, and the ions carry themagnetic field with them (whereas the neutrals are unaffected by the magnetic field). Thus the ionsslowly diffuse away the magnetic field. Ambipolar diffusion is also known as “ion-neutral drift”.

c Swinburne University of Technology, 2011

Ion-neutral flows have been observed in molecular clouds (Greaves & Holland, 1999) supporting thetheoretical idea of ambipolar diffusion. Once the magnetic support has been fully removed, the cloud
can finally collapse due to gravity.

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Core collapse
For a cloud in equilibrium, the Virial theorem states that the gravitational potential energy is twice
the kinetic energy, | Egrav | = 2Ekin , where the kinetic energy mainly comes from thermal energy(unless the cloud is very turbulent or rapidly rotating).
When | Egrav | > 2Ekin the core can collapse. We can solve the Virial equation to find the minimum
mass - called the Jeans mass - of the cloud that will lead to gravitational collapse (if supported bythermal pressure alone):q
3
MJeans ∝ Tρc Swinburne University of Technology, 2011

Note that the Jeans mass, MJeans , decreases as the density, %, increases. Observations of cloud
cores indicate that they are dense enough to collapse to a stellar mass object, but we do not see
densities high enough that cores can collapse directly to produce Jupiter mass (i.e. planetary)objects.

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Fragmentation
Let’s assume that the Jeans criterion is satisfied and the cloud is unstable to gravitational collapse.
As the cloud contracts, different regions within the cloud will satisfy the Jeans criterion individuallyand start to collapse themselves. Therefore many smaller objects are formed, and this process isknown as fragmentation.

c Swinburne University of Technology, 2011

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Note that the density of the cloud increases by many orders of magnitude during the free fall process,yet the temperature remains nearly constant. The Jeans criterion tells us that the Jeans mass must
decrease as the collapse continues. Thus small regions of the collapsing cloud will satisfy the Jeans
criterion locally, resulting in many small stellar cores. This is supported by observations of star
forming regions, which show that stars generally form in clusters covering a range of sizes.

from Evans et al. (2009)
Credit: Tyler Bourke, CfA

c Swinburne University of Technology, 2011

Spitzer images of the star forming regions Ophiuchus and Serpens

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Protostar phase
As the molecular cloud core collapses, energy must be conserved andthe gravitational potential energy is converted into thermal energy. Whilethe dust in the core is optically thin, the core is transparent to infrared
wavelengths, and the thermal energy gained by the collapse will be radiatedaway and the core stays cool. This phase of contraction is called isothermal
collapse during which the temperature remains about constant.

Protostars shining throughthe Eagle Nebula in theinfrared.
Credit: M. McCaughrean“&

M.

AstrophysicalPotsdam, ESO.

Andersen,Institutec Swinburne University of Technology, 2011

The increase in density during the collapse, however, causes the opticaldepth to increase and eventually makes the cloud opaque to infrared,
trapping the thermal energy. This is called the adiabatic collapse phase,when energy is not radiated away and the temperature increases as thecore collapses. The trapped thermal energy heats the core, which builds
up the internal pressure until hydrostatic equilibrium is reached (i.e., gravity
balances pressure). As the temperature rises, the molecular hydrogen, H2 ,dissociates into separate hydrogen atoms. The end product is a quasi-static
protostellar core surrounded by an in-falling envelope. At this stage the core
is officially called a protostar.

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Once the central temperature reaches about 106 K, nuclear reactions begin in the core and convert
deuterium (D or 2 H) into helium (He) via the reaction:2

H + p → 3He + γThis nuclear energy heats the core and halts any further core collapse until the deuterium is
exhausted. Then the protostar shrinks again and heats up until the temperature reaches about
107 K. Finally hydrogen fusion is ignited in the stellar core, and a star is born!
41H → 4He + 2e+ + 2νc Swinburne University of Technology, 2011

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An aside: some definitions
There are a wide variety of terms used when referring to young stars, including protostar, pre-main
sequence star, T Tauri star, and young stellar object. In 1972, Steve Strom coined the term youngstellar object (or YSO for short) in recognition of the circumstellar material that strongly affects
and alters the appearance of young stars. The YSO can refer to T Tauri stars, Herbig Ae/Be stars,
protostars, and pre-main sequence stars. So what are all these objects?
• Pre-main sequence stars (or PMS stars) are stars that are in the process of contracting onto
the main sequence and are not yet burning hydrogen in their cores.
• A protostar is an embedded source that has not yet broken free from its parent cloud core
(while PMS stars are revealed sources, meaning that they have broken free from their parent
cloud core). Like PMS stars, protostars are not yet undergoing hydrogen fusion.

• High mass (2–10 M ) YSOs are called Herbig Ae/Be star (HAEBE).

c Swinburne University of Technology, 2011

• Low mass (M < 2 M ) YSOs are called T Tauri stars (TTS).

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Disk formation and evolution
During the gravitational collapse of a molecular
cloud core, the gas must contract by a factor
of about 106 in size to form a star. Due toconservation of angular momentum, the initialcloud rotation is enormously magnified, which
results in the small central protostar being
surrounding by a large rotating disk. It is inthese disks that planets form.

c Swinburne University of Technology, 2011

In this section we will discuss the three mainstages in the life of a protoplanetary disk:
formation, viscous evolution, and dispersal.

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An aside: some more definitions!
You will see various expressions used when reading about the disk out of which our Solar Systemformed.
• The solar nebula refers to the proto-Sun along with the surrounding disk, though it is often used(erroneously) in a way that means just the disk component.
• The disk itself is usually referred to as a protoplanetary disk.
• The minimum mass solar nebula is a theoretical disk that contains the minimal amount ofmass (with the appropriate composition) to form the planets3 .
3c Swinburne University of Technology, 2011

The term “minimum mass solar nebula” was coined by Weidenschilling (1977) and technicallydefines a mass distribution. This mass distribution can be integrated within a specific radius to get
the minimum mass, which is generally between 0.01–0.02 M .

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Disk formation
Protoplanetary disks form as a natural consequence of cloud collapse due to angular momentum
conservation. Angular momentum is given by→−−−
L = m→
r ×→v
So as the cloud contracts, r gets smaller thus v must increase and so the cloud spins faster. This
rapid rotation creates large centrifugal forces - just like you feel in a car when you go too fast arounda corner, and large sideways forces push you away from the corner. These centrifugal forces are
greatest at the equator and the rotating contracting cloud starts to spread out and form a disk:c Swinburne University of Technology, 2011

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The infalling gas rapidly reaches supersonic velocities as it falls to the
mid-plane, and passes through a shock front at the equator of thecollapsing cloud. The shock dissipates the kinetic energy of motion
perpendicular to the disk. If the shocked gas cools quickly, then thematerial will accrete onto the mid-plane and settle into a thin disk.
Evidence of accretion shock in protostellar disks was found in the system
Lynds 1157 (Velusamy et al. 2002)

Shocked

gas

in

the

disk

midplane due to infall.

c Swinburne University of Technology, 2011

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The disk will reach a quasi-equilibrium when all the forces balance: the inward gravitational forces
towards the centre must balance the outward centrifugal force, and the gravitational force towards
the disk centre must be balanced by the pressure gradient in the disk.

al. (1995). Equal density contour lines are shown in red.
Credit: H.W. Yorke, P. Bodenheimer, G. Laughlin (1995)

c Swinburne University of Technology, 2011

Results of a rotational cloud collapse simulation by Yorke etHET620-M09A01: Planet Formation: Disk Formation and
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Disk evolution
Observations of young stellar objects and T Tauri stars in particular are generally done at
sub-millimeter and infrared wavelengths. If we plot the spectral energy distribution of a T Tauri
star, we find that there is excess infrared emission. This is due to the dust in the protoplanetary disk,
which absorbs stellar radiation and re-radiates in the infrared. These disks are called “reprocessing”,“irradiated”, or “passive” disks.

Credit: NASA/JPL-Caltech/T. Pyle (SSC)

Some disks, however, are much brighter than can be accounted for by this reprocessing, andtherefore they must have some energy source of their own. These disks are called “active” or“accretion” disks since the source of energy comes from the accretion of material within the disk.

c Swinburne University of Technology, 2011

Excess infrared emission is seen in T Tauri stars due to their disks.

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During the accretion phase angular momentumis transferred outwards and material moves
inwards and accretes onto the protostar. The
efficiency of the angular momentum transport
determines the structure and evolution of the
disk. Lynden-Bell & Pringle (1974) consideredmass and angular momentum conservation tosolve for the density as a function of radius
and time. They showed that a viscous disk will
spread radially, redistributing the density so thatmaterial moves inwards and angular momentumis transferred outwards.
c Swinburne University of Technology, 2011

Various mechanisms have been proposed forthe transport of angular momentum and massin accretion disks, including viscous torques,
gravitational torques, and magnetic torques.

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Viscous torques
Gas in the disk follows approximately Keplerian orbits, so material in the inner part of the disk moves
faster than material further out. Collisions between neighbouring blobs of gas speed up the outerblobs and slow down the inner blobs. The inner blob will now be moving too slow for its orbit, and so
will fall inwards.

c Swinburne University of Technology, 2011

The reverse is true for the outer blob, which will move outwards.

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Thermal motions of the gas produce molecular viscosity, but this has been found to be too small toresult in any significant evolution over the disk lifetime. Turbulent viscosity is more likely to result inviscous disk evolution. Temperature gradients within the disk can cause convection, and convective
eddies can induce radial mixing of disk material while transferring angular momentum in the process.
The direction of the angular momentum transfer due to convection is debated.
Magnetohydrodynamic (MDH) turbulence, on the other hand, is much more promising (Balbus &Hawley 1991). Shear flows in weakly magnetised disks can lead to very strong local instabilities,
producing sustained turbulence which drives angular momentum outwards. Even a small amount ofphoton or cosmic ray ionisation in the disk will result in weak ionisation. Near the disk mid-plane,
however, the disk is well shielded from ionising radiation and MHD turbulence becomes ineffective.
These regions of very low viscosity are called dead zones (Gammie 1996) since accretion is inactive.

penetrate and viscosity is very low.

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Dead zone within an accretion disk, with ionising photons cannot

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Gravitational torques
Soon after its formation, the disk is likely quite
massive as it continues to accrete material fromthe infalling molecular cloud core. Massive disks
are prone to both local and global gravitational
instabilities. This can lead to the formation of spiraldensity waves which are very efficient at redistributing
angular momentum (and material) through the disk
until quasi-equilibrium is reached.

Credit: Sarah Maddison (Swinburne University)c Swinburne University of Technology, 2011

Simulation of massive disk with Mdisk = 0.5 M∗ .

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Magnetic torques
If the magnetic field lines from the protostar thread the disk, then the field tries to drive the disk tocorotation - which means it tries to make the disk spin at the same rate as the protostar’s rotation
period, P∗ . Disk material orbiting more rapidly than P∗ will therefore lose angular momentum, andmaterial orbiting slower than P∗ will gain angular momentum.
The hot inner disk will be ionised, and so the magnetic field couples the star to the disk. The rapidly
rotating protostar will be slowed down by magnetic breaking torques, and angular momentum will betransferred outwards from the star to the disk.

c Swinburne University of Technology, 2011

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Disk dispersal
The final stage of disk evolution is disk
dispersal.
The oldest observed (gas-rich)protostellar disks are about a few 106 –107 years
old (Haisch et al. 2001), so the disk must be
cleared within this time frame.
Obviously, the timescale of disk clearing
strongly constrains the planet formation
process, because once the disk has dispersed,
there is no more material available to makeplanets.

star forming regions. The disk fraction comes from IR excess
observations.
Credit: Swinburne, from Haisch et al. (2001)

c Swinburne University of Technology, 2011

Disk fraction as a function of mean cluster age of various

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Mechanisms for removing disk material include accretion onto the protostar (as we’ve been
discussing) as well as forming planets. Disk clearing is also assisted by the stellar wind andphotoevaporation of the surface of the disk by the high energy radiation from the young protostar(or nearby massive stars). It is quite probable that all of these processes play a role.
Hollenbach & Adams (2004) suggest that photoevaporation may be the dominant means of dispersal
for the outer regions of disks. UV photons, either from the central star or from a nearby luminous
massive star, heat the surface of the disk, evaporating the gas which drags the small dust particles
along with it. Gorti et al. (2009) model the effects of different forms of energetic radiation in a
viscous disk and show the importance of the highest energy photons (far-UV and X-ray) for matchingobserved disk dispersal timescales.
Once the disk has dispersed, we’re left with a new young hydrogen burning star, possibly surrounded
by a planetary system.
c Swinburne University of Technology, 2011

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Disk chemistry and grain condensation
The chemistry of the disk determines the composition of the raw materials - both the solids and gas- that go into making the planets. As the solar nebula radiated energy and gradually cooled, different
elements and compounds started to condense and form solid dust grains. Whether a substanceexists as a solid or a gas depends on the condensation sequence, which is depends on the local
pressure and temperature of the nebula.

c Swinburne University of Technology, 2011

The interior of the nebula was hotter than the outer regions, so refractory materials (stable atrelatively high temperatures) dominate in the hot inner Solar System. More volatile materials (easily
evaporated) condense out and dominate in the cooler outer Solar System.

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Condensation sequence

Right: Solar nebular condensation sequence at a fixedpressure of 104 bar, from Pignatale et al. (2011).

c Swinburne University of Technology, 2011

Starting with the elemental composition of the Sun, one
can assume chemical equilibrium to determine what solids
and molecules condense from the hot nebula. The mostrefectory solids are oxides of aluminum and titanium andcondense at ∼1700 K. Metals like iron, nickel and siliconcondense at ∼1450 K. Then the silicates, like forsterite(Mg2 SiO4 ) and enstatite (MgSiO3 ) condense at ∼1400
K. The first feldspars, including albite (NaAlSi3 O8 ), andplagioclase anorthite (CaAl2 Si2 O8 ) form once temperatures
drop below 1000 K. The sulphides, including FeS, condenseat temperatures ∼700K. The ices do not condense until
temperatures are below 270 K.

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This table shows the approximate condensation sequence for the solar nebula:
Material

Temp. (K)Corundum

1740

Gehlenite

1555

Fe and Si

1455

Silicates

1400

Anorthite

980

Trolite (FeS)

700

Carbonates

475–375

Ices

< 273
c Swinburne University of Technology, 2011

Once solids began to condense, this effectively set their “internal clocks”. Isotopic dating of
meteorites tells us that the metals began to condense as soon as the disk formed, about 4.55–4.56
Byr ago. The rocks (mostly silicates) condensed out a little later, about 4.4–4.5 Byr ago, once thedisk began to cool.

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Interior to the orbit of Mars, the nebulatemperature was greater than 400 K, while
exterior to the orbit of Mars the nebula was lessthan 270 K. Thus we can understand why theterrestrial and giants planets have very different
compositions.

c Swinburne University of Technology, 2011

HET620-M09A01: Planet Formation: Disk Formation and
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Jet flow model which forms and disperses chondrules throughthe inner Solar System. From Liffman (2010).
Credit: Kurt Liffman, CSIRO

There are various theories for the formation ofchondrules, including the X-wind model of Shu et al. (1994) and the jet flow model of Liffman& Brown (1995). In both models an outflowing wind launched close to the proto-Sun disperseschondrule and high refractory materials through the inner Solar System.
4

It should be noted that the CAIs themselves are not direct condensations, but they contain minerals
and metals that are high temperature condensates from a gas of solar composition (Marvin et al.
1970, Berg et al. 2009). The CAIs themselves clearly show evidence of remelting and reprocessing.

c Swinburne University of Technology, 2011

The existence of chondrules (small igneous
spheroid inclusions about 1 mm in size)
and their refractory inclusions4 in primitive
meteorites implies that there were more violent
processes occurring in the solar nebula thanjust gentle low speed collisions. Chondrules
must have formed in extreme temperatures
between 1500–1900 ◦ C and then cooled andsolidified very quickly - within a few minutes toan hour at the most. There is also evidenceof a remnant magnetic field at the time ofsolidification (Acton et al. 2007). Thus ahighly energetic and transient event must haveoccurred in the inner Solar System to explain
the existence of chondrules.

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Some primordial solar nebula material still survives in comets
as well. As comets make their way to the inner Solar System,
they’re heated by the Sun and some of their icy material
evaporates, which can be collected in the stratosphere byresearch aircrafts. These cometary grains are made of tiny
clusters of minerals, organics and nondescript amorphous5
material. The component grains are about 0.1 µm in size.

5

Amorphous grains have no inherent structure in the orderingof their atoms. Crystalline grains, on the other hand, have theiratoms arranged in a regularly repeating pattern.

Stardust mission to comet Wild 2.
Credit: Courtesy of NASA/JPL-Caltech

c Swinburne University of Technology, 2011

One of the most surprising discoveries of the Stardust mission
to comet Wild 2 was the discovery of refractory CAI-type grains
similar to those found in primitive meteorites (Zolensky et al.
2006). We know that the CAIs must have formed very close to
the Sun, while comets are found very far from the Sun. This
points to a global mixing of material in the early solar nebula.

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Grain growth
To form the Earth, the tiny grains that condense out of the cooling solar nebula need to grow in size
by at least 13 orders of magnitude! How does this happen? Grain growth is a multi-step process: first
the tiny grains stick electrostatically; then small grains grow via collisions; and finally planetesimals
grow via accretion.

10 micron interplanetary dust grain
Credit: Courtesy NASA/JPL-Caltech

c Swinburne University of Technology, 2011

The tiny sub-micron sized grains are held together by van
der Waals forces, which are weak short-range forces due touneven electric charge distributions. This generally leads tofractal aggregates, which must eventually compact to form
more spheroidal grains. Grains bound by van der Waals forces
are not very strong and collisions in turbulent zones can beenough to fragment them as they grow.

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The motions of small grains in the nebula are strongly coupled to the gas via adrag force due to the slight velocity difference between the dust and the gas.
Because the grains do not feel gas pressure, they are moving a little faster thatthe gas and so the grains effectively feel a “head wind” as they move throughthe gas disk. This removes some of their orbital angular momentum and as aresult the dust settles to the disk mid-plane and slowly spirals in towards theSun.
In the simulation shown in the image on the right, which shows the (R,Z) crosssection of a protoplanetary disk, red represents the gas while yellow represents
dust. As time progresses, the dust can be seen to vertically settle and radiallymigrate inwards. The time scale of the dust evolution depends on their size.

Dust(yellow)settling

and radial migration in agas (red) disk.
Credit:S. Maddison(Swinburne)
Humble (CITA)&R.

c Swinburne University of Technology, 2011

The rate of dust settling is proportional to the grain radius. It would take a 1 µm
grain about 107 yrs to settle to the mid-plane, which is very slow. In fact it is too
slow to form planets before the disk disperses. So other processes must be atwork. During the dust settling phase, collisional growth of grains will shorten
the settling time by a few orders of magnitude and result in differential settling(so larger grains settle faster than smaller grains). Models suggest that thebulk of solids at 1 AU will grow into macroscopic grains within ≤ 104 years.

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So how do the settling grains grow in size? As the dust settles towards the disk mid-plane thedensity of grains rises, which increases the likelihood of grain-grain collisions. There are threepossible outcomes of a grain-grain collision: the grains can stick, rebound or shatter. The probabilityof sticking depends on the relative velocity of the grains and their chemical and physical properties(Blum 2006). High speed collisions are more likely to result in shattering, while low speed collisions
are more likely to result in sticking. Icy and tarry grain surfaces are likely to enhance sticking.

Growth via collision have some problems. As
the grain size increases so does the mean
collision velocity, which is more likely to stall
the growth process or result in fragmentation.
So other mechanisms need to be invoked toenhance the grain growth process.

Range of potential grain-grain collision outcomes.
Credit: Swinburne, adapted from Güttler et al. (2010)c Swinburne University of Technology, 2011

Detailed laboratory experiments show a wide
range of possible outcomes of grain-grain
collisions (Blum & Wurm 2008, Güttler et al.
2010). Sticking can be via hit and stick, sticking
through surface effects, and sticking throughpenetration. Rebound or bouncing can include
bouncing with compaction and bouncing withmass transfer. Fragmentation and erosion canalso occur.

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Radial migration of the grains through the disk mid-plane begins to clear out the planetary regionof the nebula. Smaller sub-cm sized grains are swept up by larger grains as they spiral in and thetransition from cm to km sized bodies can occur rapidly.
Note on terminology: while it may seem strange to talk about ‘metre-sized grains’, when discussing
planet growth all bodies less than about a kilometre in size are called “grains”.

c Swinburne University of Technology, 2011

Another problem for planetesimal formation is what is known
as a the ”metre-sized barrier”. Once the growing grains havesettled to the mid-plane, they will migrate radially towards theSun. If the radial drift rate is too high, planets won’t have time
to form. Very small grains are strongly coupled to the gas andhence drift less (because the drift timescale for the viscous
gas in the accretion disk is generally very slow), while larger
km-sized planetesimals are mostly decoupled from the gas
and hence stay on their Keplerian orbits. Metre-sized grains
experience the highest rate of inward drift due to gas drag, withspeeds of up to 106 km/yr. A metre-sized grain at 1 AU will
spiral into the Sun in just 100 years (Weidenschilling 1977a,
1977b).

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A range of ideas proposed to get aroundboth the metre-sized barrier and the grain
fragmentation problems use that fact that grains
pile up at a pressure maxima.
This canstall radial migration and lower the rate ofgrain fragmentation, since the relative velocity
between grains is substantially lowered in thesepressure maxima and grain can therefore grow.
This means that if grains can become trapped ina pressure maxima they can grow at a rapid rate
and then decouple from the gas, which stops
their radial migration.
c Swinburne University of Technology, 2011

Several regions have been proposed to trap
dust in pressure maxima, including at the edge of the dead zone in the disk mid-plane (Johansen
et al. 2007) and at the ice-line where there is a jump in surface density (Brauer et al. 2008). Cuzzi
et al. (2008) also suggest that mm-sized grains can clump in the region between small eddies inturbulent disks.

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While the mechanism is not yet fully understood, the grains will eventually become kilometre-sizedplanetesimals. Once this size, the planetesimals are decoupled from the gas and move on
Keplerian orbits around the proto-Sun. Mutual gravitational interactions and collisions then become
important.
The solar nebula would have contained an enormous number of planetesimals, all on slightly
different orbits with a range of eccentricities and inclinations. While they would be widely separated,collisions did occur and close encounters gravitationally altered their orbits. Slow collisions would
have resulted in planetesimal growth, while fast collisions would have resulted in their fracture anddestruction.

c Swinburne University of Technology, 2011

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The more massive planetesimals have a larger gravitational collision cross-section so can accretealmost everything in their path. As long as the impacting velocities are smaller than the escapevelocity of the larger planetesimals, they can grow very rapidly. If the impacting velocity is larger
than the escape velocity, v ≥ v esc , then the planetesimal growth rate is proportional to the square of
the grain size, R 2 . When the impacting velocity is smaller than the escape velocity, v < v esc , theplanetesimals grow much faster with their growth rate proportional to R 4 .
This leads to a runaway accretion where larger bodies grow much faster than smaller bodies,
resulting in planetary embryos, or protoplanets, each several hundred kilometres in size. Eventually,
the protoplanets will accrete everything within their gravitational reach and the rapid growth phasethen ends.

c Swinburne University of Technology, 2011

Credit: P. Rawlings (Courtesy NASA/JPL-Caltech)

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In the inner Solar System, protoplanets were the size of asteroids and small moons, made up of
metals and rocky materials. In the outer Solar System, protoplanets grew much larger, between
1 and 15 MEarth . The large size jump in the size of protoplanets at the Mars-Jupiter boundary
was due to the availability of materials. Since the solar nebula contained a much higher proportionof volatiles than metals and silicates, this meant that there was much more material available in
the outer Solar System, resulting in much larger protoplanets. The formation timescale for the
protoplanets is thought to be a few 105 to a few 106 years.
After about a million years, the nebula began to clear through a combination of solar wind andphotoevapotation. This puts strong time constraints on the formation of the giant planets, since theirhuge atmospheres are made up of gas from the solar nebula. Therefore, the cores of the giants
must have formed within a million years.
c Swinburne University of Technology, 2011

The protoplanets continued to grow slowly via gravitational collisions, clearing up the remaining
solids in the disk. After about 10–100 million years, the Solar System was made, with 8 newly
formed planets in stable orbits, as well as some remaining debris - the asteroids, comets and Kuiper
belt objects (which includes Pluto).

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Summary
We have discussed how protoplanetary disks form from a rotating collapsing molecular cloud core
as a natural by-product of the star formation process. Once formed, protoplanetary disks evolveon a viscous timescale, slowly moving material inwards to help build the growing proto-Sun whiletransferring angular momentum outwards. We discussed various sources of disk viscosity, including
turbulent viscosity due to convection and MHD turbulence, gravitational torques in massive disks
which produce spiral waves, and magnetic torques that results in magnetic breaking. The disk
eventually disperses, with some material accreting on the proto-Sun, some material being blown
away by the solar wind, and most material being photo-evaporated.

In the next Activity we will look at the final process of terrestrial and giant planet formation in moredetail.

c Swinburne University of Technology, 2011

But before the disk disperses, some of the material must go into forming the planets. We talked about
the various stages of grain growth, which depend on the grain size: tiny grains stick electrostatically,large grains grow via collisions, and planetesimals and protoplanets grow via accretion. The
condensation sequence in the disk determines the initial chemical gradient in the dust.

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c Swinburne University of Technology, 2011