Download Notes 3 - 1 Notes 3: Formation of the solar system 3.1 Starting

Notes 3: Formation of the solar system
3.1 Starting Ingredients
The first thing we need to do is look at the material out there – what is available for the
formation of the solar system and where did it all initially come from? The periodic table shown
here provides a general breakdown of the sources of these elements.
Major elements in the solar system, in order of solar composition by mass, with their most
common form in the galaxy, and the most likely origin:
5 most important:
H
78%
He
20%
O
0.8%
C
0.3%
N
0.2%
Common form:
atomic, molecular
atomic
molecule
molecule
molecule
And other elements that are rather common:
Ne
0.2%
atomic
Si
0.06%
molecule (dust)
Fe
0.04%
molecule (dust)
Source:
Big Bang
Big Bang/Fusion
He Fusion
He Fusion
CNO cycle
C Fusion
O Fusion/Supernovae
Si Fusion/Supernovae
Notes 3 - 1
Mg
S
Ar
Al
Ca
Na
Ni
0.015%
0.04%
0.006%
0.006%
0.009%
0.003%
0.2%
molecule (dust)
molecule (dust)
molecule (dust)
molecule (dust)
molecule (dust)
molecule (dust)
molecule (dust)
Fusion/Supernovae
Fusion
Fusion
Fusion/Supernovae
Fusion
Fusion
Supernovae
Generally hydrogen, and helium are found in atomic form (as individual atoms), though
hydrogen can also be found commonly as H2, it is usually most often observed in the galaxy as H
I (neutral atomic form). Hydrogen and helium are thought to be originally from the Big Bang
rather than as by-products of fusion, though some helium is produced by fusion. Pretty much
every other element originated in stellar processes, such as fusion, supernovae events or
processes involving high energy particles. So having only minute amounts of those elements is
not too surprising since the material would first have to be created in a star and then dispersed
out into space. Some material produced by stars is never actually dispersed into space through
the regular processes of distribution such as stellar winds, condensation of material in the outer
atmosphere of cool giant stars, ejection during the planetary nebulae phases or blowing out in a
supernova event, but instead remains trapped in stellar remnants such as white dwarfs, neutron
stars or black holes. Generally speaking stars may eject 30-90% of their mass out into space
where it may be incorporated into the next generation of stars and their planets.
Even though stars tend to be comprised of atomic species of elements, once particles get far
enough away from stars, they tend to form into molecules. About 150 molecules have been
found in space (more found all of the time), mainly through observations by radio and infrared
telescopes. The most common molecules are H2, carbon monoxide (CO), O2, and water. Other
molecules found in space include hydrogen cyanide (HCN), ammonia (NH3), methane (CH4),
ethanol, formaldehyde, benzene, and the list goes on…
Generally most molecules will form while in a gas phase or will be formed while on the surface
of dust grains. So the presence of dust is often an important component to create some
molecules – and of course dust itself is a molecule. The type of molecules that form will depend
upon the environment that is present, specifically the values of the pressure, and temperature.
Depending upon the values of temperature and pressure, you can have rather complex molecules
forming, or there will be a depletion of specific molecules. It is not a simple task trying to
determine which molecules will or will not form in a given location. Generally speaking, most
of the interstellar medium is in a gas form (99%) and only 1% is tied up in the form of dust
grains. While dust is a pretty small part, it is a very important part of the interstellar medium.
Typically dust grains are around 1 micron in size (10-6 m). And like many molecules, dust grains
are often detected with infrared telescopes.
3.2 Collapse of Solar Nebula
The formation of the solar system will require an ample amount of the raw material that
eventually went into the creation of the objects in the solar system and the collapse of that cloud
of material. Of course it isn’t easy to get a cloud of material to just collapse in on itself, since
Notes 3 - 2
there is a natural resistance to collapse due to gas pressure. The higher the temperature, the
greater the resistance (the atoms are moving faster). But if you have enough gravitational pull,
you can collapse it. To determine the conditions for gravitational collapse of a gas cloud, you
can use the relationship known as the Jean’s Mass, which provides a value for the minimum
mass needed to collapse a cloud with a particular temperature and density. It is given by the
following relationship -
 T 

M  M Jeans  
 G 
3/ 2
1/ 2
 3 
 
 4 
1
3-1

G, =constant
=average density
T=temperature
=mean molecular weight, usually around 1
So if you have a mass M>MJeans then it will collapse (so long as nothing other than gas pressure
is involved with the cloud). Occasionally things like magnetic fields or winds from nearby stars
could alter the collapse of clouds, but we’ll just stick with the basics here.
Once the collapse starts, it can go rather quick – and that rate will depend upon the density of the
material. Assuming just a straight freefall of material, you get a collapse time of
 3 

t ff  
 32G 
1/ 2
3-2
This is the free-fall time (again, this is based upon the assumption that no other forces are
influencing the collapse).
One thing that will often complicate situations is rotation, which can lead to fun aspects of
angular momentum. Depending upon the collapse rate and the rotation rate of the cloud, you can
also have situations where the cloud fragments into multiple stars, or perhaps just a single star.
Generally if it rotates very fast you are likely to get multiple stars rather than just one. But let’s
stick with the not so fast rotation that leads to the formation of our solar system and one star.
As the material falls in, it heats up the cloud since there is the conversion of gravitational energy
to kinetic energy. This can obviously influence the density of the material. At first the energy of
the collapse is lost quickly, since at the onset the cloud is rather transparent (literally not
opaque). This will allow the collapsing material to cool down quickly and the density of the
cloud will increase faster (since the material is not fast moving – easier to clump together).
Eventually you’ll get to the point where the density will be large enough to trap energy in (the
cloud is not so transparent anymore, but is now more opaque), and this helps to heat the central
proto-star. As the proto-star is heated up, there will be a build-up of the internal pressure in the
proto-star (hotter, denser, higher pressure). Eventually it gets hot enough for some deuterium
fusion to occur (2H + 3H  4He+n+). This would happen at a temperature of around 1 million
K. The release of energy through this short term fusion process will slow down the collapse for
a while, at least until the deuterium runs out. Once the deuterium fusion stops, the collapse will
continue on until the internal pressure/temperature of the proto-star builds up to the point where
“real” fusion can start.
Notes 3 - 3
All of the fusion activity is really only happening at the very center of the cloud, where the “sun”
will be found. To an outside observer, you wouldn’t really see much of this activity since you
would only see the outer layers of the cloud, which are emitting a good deal of energy at long IR
wavelengths. But as time goes on, and the inner proto-star gets hotter and hotter, this effect will
eventually work its way out to the outer layers of the cloud and the peak of the emission for the
cloud shifts to shorter wavelengths. Technically the light is still IR, but not as long wavelength
as it was at the start of the collapse.
3.3 Observational Evidence
Okay, time for a reality check - does any of this really happen? What evidence is out there that
shows stellar formation and/or planetary system formation?
First there are small clouds of gas in our galaxy known as Bok globules. These are very small
gas clouds, between 10-50 M, and only about 0.3 pc in diameter. Bok globules are scattered
about the galaxy and would be the objects associated with the formation of only a few stars.
These clouds can collapse and form small stellar system, creating stars of about the size of the
sun, or only a few stars at once, so long as they are given a push, usually in the form of a shock
wave from a supernova or a compression wave from a spiral arm. The formation of the star
though is buried deep inside of a Cocoon nebula, which is basically the cloud of gas and dust
around newly forming stars. We find evidence for this process by looking for objects that emit
quite a lot of energy at IR wavelengths. An example of this is seen in the star R Mon, which is a
variable star emitting energy at a peak of 2.4 microns. R Mon is thought to be a cocoon nebula
with a diameter of about 200 AU surrounding a forming stellar/planetary system. Similar objects
are observed with a strong IR signature, and observations of the spectra show that the dust in the
cocoon has silicates and/or ice particles in it – this is the type of material that can go into the
formation of planets.
IR observations are good, but visible light images are even better. Now we have that! Direct
observation of these cocoon clouds have been observed with the Hubble Space Telescope in the
Orion nebula. The clouds that were observed there were given the name proplyds, which
actually stands for proto-planetary disks. There are quite a few proplyds in the Orion star
forming region, and due to that environment, they experience a great deal of heating from the hot
nearby massive stars. The hot stars ionize the outer layers of the cocoons. As expected the
proplyds have sizes of a few hundred AU, and in some cases it is possible to see the central star
that is being formed. These objects are similar to how our solar system may have looked during
its first few million years.
Several of the Orion proplyds look very dark, which isn’t surprising. It is true that dust is not
very abundant in the interstellar medium, but it is very efficient at blocking light. Even a small
amount of dust can cause an object to appear rather dark. While it may make objects look dark,
it will also help trap heat quite effectively, and help temperatures rise within the cocoon.
Often during various stages in the formation of a star there will be a large outflow of material
from the polar regions, perpendicular to the disk of material that is forming around the star.
Notes 3 - 4
These blobs of material are known as Herbig-Haro Objects (HH objects) and they are often
seen near Bok globules. Around 400 HH objects are known in our galaxy. They are typically ½
pc away from their proto-star, moving outward at speeds of 100-1000 km/s. They are just short
term objects, since they can disperse relatively quickly and fade away as the gas cools off.
So as the proto-star is contracting and blowing off material as HH objects, there is the formation
of a disk of material around the proto-star. This is just a side-effect of rotation (and conservation
of angular momentum) leading to the formation of a disk around most proto-stars. The collapse
time is inversely proportional to mass, such that a larger mass will have a faster collapse (takes
less time). And of course not every cloud that collapses will form a star, since very low mass
objects will not have enough mass to fuse elements. Typically the cut-off for the lowest mass
star is around 0.008 M.
Further evidence of star formation is the observation of T Tauri stars. This is a proto-star with
a very strong wind. This phase can remove many of the light weight gases/particles from near
the proto-star, and help clean out the system. Often T Tauri stars are observed near HH Objects,
but some T Tauri stars are on their own.
T Tauri characteristics:
 Irregular variability/brightness
 Brighter than regular stars (large radii, R ~ 3 x Sun’s radius)
 Found close to nebula (region of star formation)
 Spectra has emission features, excess of IR light, evidence of silicates
 Teff ~ 4000 K (cool)
 Lots of lithium in their spectrum (an indication of young objects)
 Show signs of mass loss, high winds, flares, etc.
 Sometimes show signs of infall (material falling towards proto-star)
 Masses typically only at most 2 solar masses
 Typically found in binary system – seems to help cause bi-polar outflow
 strong magnetic fields – large starspots (sunspots)
 phase lasts for ~100 million years
How do we know these are young stars? They have excess lithium in their spectra – this material
is destroyed in stars gradually during a stars life, so any substantial amount of lithium indicates a
young star.
About ½ of T Tauri stars are observed to have disks around them. This is probably the end of the
formation stage for the star, and close to the end of the formation stage for the planetary system
as well, since the T Tauri stage can result in a large amount of mass loss from the stellar system.
An important aspect of the T Tauri stage is the observation of a strong magnetic field – what
effect does that have? One thing that can happen is the transfer of angular momentum from the
star to the disk (or to the planets). Technically in the collapse of the gas cloud, the distribution of
angular momentum should have the majority of it located within the star that forms – since that
has most of the mass, and it should just spin faster and faster as it collapses down. However
most stars are not very fast spinners, so there must be a way for them to lose their angular
momentum, or more likely to transfer it elsewhere. It is possible for this to happen through
magnetic braking. This happens when the star’s magnetic field “connects” with the ionized
Notes 3 - 5
material in the disk that surrounds the proto-star. The breaking/connecting of the magnetic field
is primarily on the inner part of the disk forming around the star.
While the T Tauri stage is a good cleaning-up stage for the solar system, there are also other
things happening in the disk of the star. Disks of material have been observed around many stars
since the first one was discovered around beta Pictoris. This is a very large disk, (1500 AU
wide), and also shows warping in the inner parts, possibly due to the presence of large objects
like a planet or brown dwarf companion to the star. More observations by the HST have shown
quite a few disks around stars, which vary in size and development stage. Disks around these
stars tend to be several hundred AU in size, which is just where we think the Kuiper belt ends!
Observations of disk spectra show that the material is quite similar to that found in the dust of
cometary material, grains thought to be composed of minerals such as olivine and pyroxene –
which are important for the formation of planets. Usually the disk is not complete – there is
often a gap between the star and the inner edge of the disk, which is logical given the high
velocity winds and temperatures near that part of the star forming region. The gap is usually
observed in slightly older objects.
Recently the disk around the star Fomalhaut has been shown to contain a planetary body. The
Fomalhaut disk is quite large, much larger than our solar system, and extends out to a distance of
about 110 AU from the star. Within the disk is an object that appears to have moved in orbit
about the star, located about 100 AU from the stars. The orbital period for this mass is about 872
years for one orbit. Expect more observations of this object in the future.
Disks that have been observed contain only a small fraction of a solar mass, around 0.001 to 0.1
M. Some disks are rather narrow, more ring-like. This type of structure may indicate the
presence of unseen planets that are shepharding the material around the star into a ring.
Material in the disk goes to various places depending upon its angular momentum. Material with
little angular momentum falls towards the center, while other stuff will stay further out, and is
basically in orbit about the proto-star. Material that falls in towards the star will help to generate
heat due to the infall of the material, and the inner part of the disk will be heated up by this
process (as well as being heated directly by the protostar). There will be a gradient in the
temperature of the disk, with temperatures up to 1500 K at a distance of 1 AU, while at 10 AU it
is closer to 100 K.
There will also likely be temperature variations up/down within the disk (from mid-plane to disk
surface) and this gradient can lead to energy transport, most likely via convective transport. This
will help to mix the material in the disk and make the disk have a uniform composition for
regions that are undergoing convective mixing. It is also possible for turbulent eddies to mix
material radially out from the star, so that compositions in those directions also get homogeneous
to a certain degree.
3.4 Formation of minerals
Before we talk about how the planets formed, we first need to nail down when the planets
formed. This is done by not looking at the planets but the material out of which they formed.
Notes 3 - 6
We determine the age of the formation of the solar system through radiometric dating, based
upon radioactive decay of elements within rocks. The ages derived in this way would be the
time since the material was first put into its present form, which could be when it solidified from
a gas or liquid state into a solid.
While current estimates for the age of solar system vary from about 4.52-4.58 billion years ago,
the time for the formation of the material into its current form was relatively quick, only 50-100
million years.
One thing that is known is that there was quite a large quantity of short lived radioactive
elements in the material out of which the solar system formed (and a lot of different forms of
them). Of course this material has to come from some source, and the likely source is a
supernova or similar large stellar event in our neighborhood occurring relatively close to the start
of our solar system’s formation. Short lived radioactive elements (half-lifes indicated) such as
41
Ca (0.15 Myr), 26Al (1.1 Myr), 60Fe (2.2 Myr), 53Mn (5.3 Myr), 107Pd (9.4 Myr), 182Hf (13
Myr), 129I(23 Myr), and many more have been studied in meteorites to determine the age of the
solar system and determine the rate of planet formation. A supernova could have made these
elements, or they could have been ejected from the outer layers of an evolved red giant star.
Counter arguments to this idea is the possibility that these isotopes came from spallation
reactions (this is the interaction of atoms with energetic particles from the proto-sun that causes
these isotopes to form). Odds are it is likely that both phenomena had a role to play, since the
isotope ratios don’t conform to just one of these scenarios being present.
Regardless of the actual cause, there is still the need to have some source of material to enrich
the solar nebula with radioactive material, though it is not the main material of course. Once the
material is here it has to form into objects, generally into a solid form. But how was the material
distributed or what form was it in, in the early pre-formation solar system?
For example, you can have oxygen present in many different forms. It exists as a gas such as in
O2, CO, CO2, H2O, etc., and as a liquid/solid, such as H2O, CO2, etc. and as a solid, such as
within silicates, ferrous oxide, olivine, serpentine, and similar minerals. But wait a minute, is a
mineral the same as a rock? What is a mineral, what is a rock? (I’m assuming you know the
difference between a gas/solid/liquid).
Put simply minerals are the things that come together to make rocks. Minerals have specific
chemical compositions and rocks can be made up of a variety of different minerals. Rocks can
also be made of just one mineral, but that’s not too common. Different minerals may also be
made of the same element, for example carbon has several mineral forms. The various forms of
these different minerals that are made of the same elements depends upon how the atoms are
arranged in the mineral. So rocks can be made of a single mineral or many, depends upon the
rock. Okay, back to the question of where these elements end up.
Here are some common minerals -
Notes 3 - 7
Silica, often in the form of quartz, (SiO2), density ~ 2600 kg/m3. These are very low density, and
in the molten interior of planets, these minerals would float up towards the surface. For this
reason they are very common on the surface of planets.
Feldspars, a group of various minerals with different elemental configurations.(K,Na,
Ca)AlSi3O8 with a density between 2800-3700 kg/m3. In its various forms you have K, Na, Ca
in varying amounts of the feldspars. Like silica, these are also relatively low density minerals
and tend to be found close to planetary surfaces.
Pyroxenes: (Mg, Fe)2 Si2O6 are made up of silicates of various elements, including augite,
enstatite, hypersthene, etc. A similar density to the feldspars, (~2700-3700 kg/m3).
Amphiboles: Mg, Fe, Ca silicates, similar to pyroxene, but with a different crystal structure.
Micas: K, Al, Mg silicates with an intermediate density of ~3200 kg/m3, and are common in
igneous rocks. You can find them in a rather sheet-like structure (biotite, muscovite are
examples)
Other minerals commonly encountered in planets and other places are
Olivines (Fe,Mg)2SiO4, fairly heavy so they are found under the crust or lower crust layers.
Density is around 3300-4400 kg/m3.
Magnetite (Fe3O4) and maghemite (Fe2O3) are iron oxides that are likely on the Martian surface.
These have been picked up by magnets on various Mars landers. Other iron – oxides include
hematite (Fe2O3), goethite (HFeO2), and limonite (FeOnH2O). These are common iron ore
sources. Generally these are the things we suspect of coloring Mars its various shades of red and
orange, since these minerals tend to have those colors. Densities of these vary from 3000 to
about 5000 kg/m3.
Ilmenite (Fe,Mg,Mn,Ti)O3 is a mineral that is fairly common in the Moon’s mare – the titanium
rich version. Density is around 4700 kg/m3.
Armalcolite (Mg,Fe)Ti2O5 is a mineral that was initially discovered on the Moon, but later found
on the Earth. It is named for Armstrong, Aldrin and Collins, the Apollo 11 crew. Density is
around 3600 kg/m3.
There are also clay minerals which are basically hydrous aluminum silicates, which are produced
in erosion on the Earth and Mars. They may make up a good fraction of Martian dust.
And of course in the outer solar system the surface minerals would be comprised of various
forms of carbon (graphite usually), and the common ices of H2O, CO2, NH3, and CH4
And if you have minerals, then you can also make rocks out of those. Odd are we all learned
there are three basic types of rocks, igneous, sedimentary, and metamorphic. Let’s see some of
those common forms.
Notes 3 - 8
Igneous rocks form from cooled magma. And just to clarify things, “lava” is magma above the
ground. When it is in the ground and still fluid it is magma. Igneous rocks comprise the vast
majority of the rocks on the surface of the Earth – about 95% of the surface layers are made up
of igneous rocks. All of the rocks on the surface of the Moon are igneous and it appears that the
dominant rocks on Mars and Venus are also igneous. So igneous rocks pretty much dominate
terrestrial planet surfaces. There is a great variety of igneous rocks based upon their cooling
rates, where they form and composition. Intrusive igneous rocks form inside of the object.
These tend to cool down slowly and produce rocks such as granite, diorite, anorthosite, gabbro,
and peridotite. Extrusive igneous rocks form outside of the object, so after material gets to the
surface as lava. This includes rocks such as rhyolite, andesite, obsidian and basalt. These
various types of rocks are distinguished according to their mineral grain sizes (crystals).
In general basaltic rocks like basalt and gabbro seem to be very common, since they are observed
on the Earth, the Moon, Venus, Mars and even on asteroids. Granitic rocks are not commonly
observed on other worlds, since they aren’t formed immediately near the surface. They may be
present on Venus, and are of course observed on the Earth.
Sedimentary rocks appear to dominate the Iowa landscape, but they are not found at great depth,
so they are not as abundant as the igneous rocks in the Earth’s crust. And of course they are
formed due to weathering processes, such as
Chemical weathering (chemical reactions break down original rocks)
Mechanical weathering (wind/water abrasion break down rocks)
On the Earth the most important sedimentary rock is shale, while sandstone is another common
rock. The grains that make up shale and sandstone tend to be rounded due to long-term
abrasions. This is seen in both Earth and Mars rocks (remember, you need water to form these
rocks so don’t expect them on the Moon). Another important type of sedimentary rock are the
evaporites – these form after water or a similar solution has evaporated. Basically the scum left
behind when the liquid is gone. Common rocks that are evaporites include halite (rock salt),
gypsum, and calcium carbonate. On Mars there was a great deal of excitement concerning the
presence of concretions, spherical rocks that form within voids which in this case were made up
of hematite. This has been considered a very strong indicator of liquid water existing on the
surface of Mars in the past.
Metamorphic rocks are basically other rocks that have been altered and re-crystallized beneath
the surface of a planet. The change in temperature, pressure and chemical environment can alter
the form of the minerals. Examples of metamorphic rocks include marble, quartzite, gneiss,
schist, slate, and shocked quartz (something produced by impacts).
Another type of rock produced by impacts are breccias, which are formed when rocks break
apart and are cemented together again. It is possible to produce breccias by means other than
impacts, but since impacts were pretty common in the past and still occur in some places in the
solar system, these are still a significant rock form. Breccia make up most of the rocks in the
lunar highlands. So, what type of rock is breccias – igneous, sedimentary or metamorphic?
Take a guess (and perhaps I’ll tell you in class)!
Okay, enough of the detour into geology, back to the formation of the solar system….
Notes 3 - 9
The state of the various elements depends upon the chemistry of the environment in which the
element is located in. And this includes factors such as how many other elements are available
for it to interact with, and the temperature and pressure of the area, which determines which
interactions can and cannot occur. And as one element starts to change its state or get put into a
particular form, that process will likely influence what happens to other elements. For example,
if you’re in a region where oxygen is able to bind with carbon, then you also deplete the
available carbon in that area, and limit the options for carbon’s various states/forms. Generally
speaking the formation of material is strongly temperature/pressure dependent, which is a
function of the distance of the star. So look at those features to figure out what forms where.
Remember the situation that you are starting from here for creating the planets - the solar nebula
was likely composed of what the sun is composed of, mainly H, He, C, N, O, etc. Where does
this stuff go? Most of it (H, He) doesn’t go into the planets, the composition of the planets
doesn’t have the same distribution as does the solar nebula (Sun). It is the case that a large
fraction of this material was lost from the solar system during the early mass loss phases possibly
as much as 0.5 M was lost. Also, the current mass of the solar system (apart from the Sun) is
pretty small compared to the Sun. Generally speaking the material in meteorites is very similar
in abundance to that found in the Sun, though there are some differences (which need to be
explained).
3.5 Temperature Gradient
Let’s look at where things formed. For simplicity we’ll look at the temperature dependence of
the formation of various minerals.
To complicate things what actually forms depends upon both the temperature and whether it has
the time to go into a certain form – whether it reaches chemical equilibrium. For example:
At T> 700, Carbon is most stable as CO, at cooler temperatures CH4 dominates
At T>300, Nitrogen is mainly as N2, at cooler temperatures it is more likely to form NH3
So logically you would expect to find carbon in the form of carbon monoxide in the inner solar
system, while carbon is mainly in methane in the outer solar system. However we find things
like CO and N2 ices in the outer solar system, such as on the surfaces of Triton and Pluto. How
is that possible? It is likely that there was not enough time for chemical equilibrium to occur
before those bodies formed, so the preferred form of carbon isn’t found. As with many things in
science, there are always some exceptions to the rules.
With that in mind the general distribution of elements, and minerals is the following At locations >2000 K, everything is evaporated so no minerals/solids would form. This would
have been in the area closest to the proto-star.
T ~ 1700 K, you have the formation of rare earth elements, high temperature refractory
compounds such as tungsten (W) and various oxides containing aluminum, calcium, titanium
(corundum, Al2O3, perovskite, CaTiO3, spinel, MgAl2O4) condense. These minerals are found in
Earth’s mantle and crust.
Notes 3 - 10
T ~1400 K, nickel, iron form an alloy. These are of course a major part of the Earth’s interior.
For T slightly less than 1400 K, magnesium silicates appear, including fosterite (Mg2 SiO4), and
enstatite (MgSiO3). These minerals are found in meteorites, and the mantle of the Earth.
T<~ 1200, the first feldspars appear, the first of which are plagioclase anorthite (CaAl2Si2O8),
and as the temperatures continue to go down you have other feldspars forming, for example at
temperatures of around 1100 K sodium and potassium feldspars ((Na, K)AlSi3O8) form.
Feldspars make up about 60% of the Earth’s crust.
T~700, iron and H2S react to form troilite (FeS), which is found in meteorites and thought to be
in the cores of terrestrial planets.
T~500, iron reacts with water to form iron oxide (Fe+H2O  FeO+H2)
Iron oxide is important since it reacts with enstatite and forsterite to form olivines and pyroxenes
((Mg,Fe) 2SiO4; (Mg,Fe)SiO3), common minerals on the Earth and in other places in the solar
system.
There are of course some problems with this scheme. We find high temperature minerals as
inclusions in low temperature matrices, usually within carbonaceous chondrites – carbon rich
meteorites, thought to be from the outer asteroid belt region. There must have been some sort of
migration mechanism that allowed the higher-temperature forming minerals to move to the
cooler areas of the solar nebula for later inclusion into the rocks that formed at those locations.
Again, there are always exceptions to the rules. Speaking of which, here are some more
formation guidelines.
At temperatures below 500 K, water is a major player as a gas.
Water reacts with olivines and pyroxenes to form hydrated silicates such as serpentine
Mg6,Si4O10(OH) 8, talc Mg3Si4O10(OH) 2, tremolite Ca2Mg5Si8O22(OH) 2 as well as hydroxides
such as brucite Mg(OH) 2.
Below 200 K, water ice forms. Now don’t forget, that’s a mineral!!!
At even cooler temperatures, you get ammonia, and methane to condense as hydrates and
clathrates respectively (methane hydrates NH3 H2O, ammonia hydrate CH4 8H20). A clathrate is
a “cage” of one molecule around/trapping another molecule. So methane clathrate is a methane
molecule trapped within a lattice of water molecules.
Below 60 K, CO, N2 can form clathrates with water ice (they are trapped in the ice).
Below 40 K, CH4 and Ar ices form.
Below 25 K, CO, N2 form ice.
It must be remembered that the temperature structure of the solar nebula changed over time.
Initially with many small dust particles scattered about, the temperature drops off with distance
Notes 3 - 11
quickly, since the dust absorbed most of the light. As large objects formed, the starlight could
travel further out and interact directly with material in the outer solar system, possibly melting
(subliming) some of the ices.
When the Sun entered the T Tauri phase, this
ended the large scale chemistry – whatever
formed in terms of the minerals at the various
distances from the Sun were stuck there. The
image shown here shows how the planet are
located relative to the temperature/density
graph of which minerals formed under those
conditions.
This sort of scenario is supported by not only
having the appropriate main composition
come out of this but also isotopic ratios of
things such as 16O/18O – which varies
uniformly through the solar system, which
says that there wasn’t large scale mixing.
There could be some mixing (to account for
unusual inclusions in meteorites), but not
really large scale mixing which would have
made compositions of more objects very
similar to one another. So mixing of material over the entire breadth of the solar system is not
likely.
3.6 Growth of Planets
Once the minerals have formed it is possible to start to make the planets.
First you will have grain sized particles (dust like) all over the place. These have to get larger to
form into the next sized objects, though they have a hard time doing that. Why? Objects would
have to be brought together but not with high speeds so that they’d destroy each other and you
end up with even smaller pieces. Objects orbit about the Sun at pretty high velocities and there
must be a way to bring them together into similar orbits and to stabilize them. There are a
variety of effects that can influence these objects, such as corpuscular drag, electrostatic forces,
and good old gravitational perturbations. These effects can bring the material into close contact,
at least close enough so that they can come together at a reasonable speed and not destroy
themselves when they meet. Electro-static forces are surprisingly efficient at bringing material
together, and this is actually seen in zero-gravity situations. I guess that means it is really
difficult to clean dust from the International Space Station.
Any ways, the particles get together and form larger and larger pieces. Once they reached the
size of planetismals (between 0.001 m to 1000’s of m ) they can withstand collisions, and not be
affected by gas drag. These objects will continue to grow into larger forms often via collisions.
Notes 3 - 12
There are statistical ways to calculate the rate of growth of the planetismals and the resulting
planets. These depend upon the density of the material, the velocities of the stuff, and some
rough guesswork. For a distance of 1 AU, you can create the Earth in 107 to 108 years, with most
of the growth occurring during the early stages of the formation process.
But as you get further from the Sun, the density of the solar nebula decreases, and so does the
growth rate for the planets. At Jupiter’s distance you will need typically 108 years to form that
planet, while at Neptune’s distance the growth rate age ends up being greater than the age of the
solar system! Obviously there is a problem here. Also you need to have Jupiter and Saturn
form before the T Tauri stage so that they need to form within about 107 years or so. The need to
get them to form before the T Tauri stage is due to the strong stellar winds that will develop and
which will deplete the material in the solar system – you can’t build large planets without a lot of
material on hand!
The big problem with these calculations is the velocity. If the relative velocity between objects
is much less than the escape velocity, that leads to run-away growth rate for the planetismals, via
run-away accretion. This does limit the region of the material that can be accreted onto the
planet to an annulus of its orbit, but that should be enough material to make the planets. Even
things that are beyond the planetismal’s Hill radius can be drawn in to the process, but anything
that is brought in should be pulled into the growing body and not just trapped into a tadpole or
horseshoe orbit. It is also possible for additional material to be brought in by perturbations, or
gas drag.
3.6.1 Formation of terrestrials planets
As the planets form, they also heat up. This heating is due to collisions (on the surface mainly,
but the heat migrates inward), radioactive decay, gravitational energy, and chemical processes.
The planet also loses energy mainly out into space, but it can also lose energy if it expands, or if
water freezes (or other phase changes occur). Depending on the internal structure, energy
transport within the planet is via conduction or convection. Convection is a better method of
energy transport since it is faster, and gets rid of energy much more efficiently, but requires a
level of fluidity.
While the body of the planet is undergoing all of these changes due to heating, cooling and
impacts, it can also have a temporary early atmosphere from the evaporation of water, and CO2.
This can lead to further surface heating due to the trapping of heat, so long as the atmosphere is
thick enough. The formation of a thick atmosphere depends upon the mass of the planet
(gravity), and you usually need a planet mass that is about 0.1 M to have a blanketing
atmosphere. By the time the mass is 0.2 M, the surface temperature will be around 1600, which
pretty much melts all materials on the surface. The hot surface and interior leads to
differentiation with the heavier elements/minerals sinking inwards.
The planet’s atmosphere previously mentioned isn’t the same as the current one of course. Most
likely the atmosphere evolved over time, with the loss of H, and He to space, and the retention of
mainly the heavier molecules. Impacts, and outgassing are likely to have provided the material
for the atmospheres seen on the terrestrial planets, and other things will have affected the
Notes 3 - 13
evolution of the atmospheres later on. It is likely that the planet didn’t get emplaced until near
the end of the entire formation process which likely took ~108 years.
3.6.2 Formation of gas giants
The large H, He content in these objects requires quick formation, within 107 years, since those
elements would be quickly lost with strong solar winds during the T Tauri phase. The amount of
the other common elements such as C, N, and O is greater in these objects than in the Sun, so
that abnormality has to be explained as well. It is thought that these objects accreted solids at a
higher rate than they accreted gas. One scenario is to have the cores of these objects form first,
which would have been similar to terrestrial formation process previously outlined (taking a few
million years). Once the mass gets to be around 10-20 M, the infall of gaseous material
becomes significant. When the amount of gaseous material is greater than the amount of solid
material, the gas accretion accelerates into a run-away event. When this ends, the object that
would be Jupiter is a few hundred times its current radius, such that it fills its Hill sphere. When
accretion stops, the planet will contract, initially rapidly, then less rapid. This heats up the
interior, leads to convection throughout, and homogenizes the material. Contraction slowed
down after only around 10,000 years. The temperature and IR luminosity became stable – it is
still losing energy today, but not at the rate at which it was earlier in its history. Overall the
time for the formation of a gas giant is only a few million year, but less than 10 million based
upon simulations.
3.6.3 Formation of ice giants
The formation of Uranus and Neptune is similar to that of the gas giants, but you have even more
of the heavy elements in these objects and that needs to be explained. There is actually about
300x more CNO relative to the solar hydrogen content. During the planetismal accretion phase,
there was less material available out at the distance of these objects, so that the cores that formed
were less massive and that resulted in less massive gas accretions. In the case of the ice giants,
they never reached the runaway level that the gas giants did. When accretion stopped, the
planets started to contract. After about 200,000 years the contraction rate dropped off and these
objects became stable in their temperature and IR emission afterwards.
3.6.4 Additional formation details
There are a few other things that formed along with the planets when the Sun formed. First of all
there is the asteroid belt. People often suppose that this is a broken up planet. If you were to
take all of the material here you’d find that it doesn’t add up to much. It is possible that in the
past there were more objects here, but they have been pulled out of their locations by Jupiter’s
gravitational influence. This would have led to their being accreted into Jupiter, being ejected
from the solar system, or getting destroyed in collisions. What currently remains is in a stable
orbit and will likely stay that way. It is worth noting that the asteroid belt isn’t homogeneous –
there is a density gradient in it. The spread in chemical properties in the belt implies that this
material formed there – that it wasn’t formed elsewhere. So odds are there was more material
here, but likely not enough to make anything substantial, like a planet.
Notes 3 - 14
What about the comets? These objects could have formed at distances anywhere from between
3-30 AU. After they formed they were ejected by the gas/ice giants into the outer solar system.
This redistribution of masses would have affected mainly Jupiter (the one most guilty of all these
gravitational interactions). A result of the gravitational tossing of all of these cometary cores is
the migration of Jupiter closer to the Sun (remember – Newton’s laws of equal and opposite,
when something is thrown out, something else is thrown “in”). In a rather unusual move, the
other giants would have been more likely to send many small objects towards Jupiter, and this
would have caused those object to migrate outwards (further from the Sun).
What about the satellites? These would have formed in a manner analogous to the formation of
the solar system – at least in part. Satellites with orbits that are close to the equator of their host
would/should have formed with the planet. These are often called regular satellites. Other
satellites were likely captured by the gravitational influence of the planet and these tend to have
highly inclined, and/or retrograde orbits. These are irregular satellites. The birthplace of
irregulars could be surmised based on their composition, specifically their rock/ice ratios. If they
have more ice than rock they likely formed further from the Sun. Also the type of ice varies
with distance (H2O, CO2, methane, etc). Another source of satellites is formation through
collisions, or “a chip off the old block” method. This is thought to be the source of the Moon,
and objects like Pluto, and satellites around asteroids.
And last but not least, we have the rings. These are likely not primordial, since ring material is
not in a long term stable orbit. Saturn’s rings are much cleaner ice than the others, so that
doesn’t jive with a composition gradient within the solar system. Ring material can be created
through tidal destruction of small satellites, or through material ejected from the surfaces of
satellites through impacts or eruptions, such as the ring that is fed by the satellite Enceladus. So
technically rings are not part of the formation of planets – at least not the rings seen today.
Notes 3 - 15