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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