Astronomy 311: Lecture 2 - Solar System Formation. A theory for the formation of the Solar System must explain:

Transcription

1 Astronomy 311: Lecture 2 - Solar System Formation A theory for the formation of the Solar System must explain: Patterns of Motion. 2 types of planets. High numbers of asteroids, KBO s and Oort Cloud objects. Exceptions (eg. Size of Earth Moon, Uranus tilt. Star-gas-star cycle. Big Bang Theory created just Hydrogen and Helium and maybe small amounts of other elements like Lithium, Deuterium, but nothing like Copper, Iron etc. The first generation of stars made these during nuclear fusion in their cores and in supernovae explosions at the end of their lifetime. These supernovae explosions redistributed this metal enriched material into space and a new generation of stars formed from this new material. This new generation of stars and any subsequent planets were thus richer in metals etc. The Sun has the basic composition typical of this second generation of stars. Universe age is roughly 13 billion years ago. Solar System is roughly 4.6 billion years old. Stars forming today form in interstellar gas clouds eg. Eagle Nebula etc. A spherical gas cloud that is cold and dense consisting of mainly molecular hydrogen starts to collapse under its own self gravity. This collapse can be initiated by external sources eg. the shock wave from a supernova. Because of gravity s inverse square nature, the collapse starts slowly at first and then speeds up. A spherical gas cloud collapsing under its own self gravity will heat up, flatten out and start to spin. Such a collapsing gas cloud heats up because collapsing particles are converting potential energy to kinetic energy and this kinetic energy is converted to random thermal motion by collisions. Random thermal motion is another way of saying that the material gets hot and heats up. 1

2 Highest temperatures/densities are at the center of this gas cloud - thats where the star will form. The cloud starts to spin because of the conservation of angular momentum. Angular momentum is momentum due to circular motion: L = Mvr. L is always conserved so if M is constant, but r decreases because the cloud collapses, the v must increase. The flattening is a consequence of collisions between particles in a spinning cloud - a result borne out by N body calculations. The spinning flattened disk does explain why planest are co-planar and orbit the SUn in the same direction and tend to spin about their own axes in the same direction as they rotate about the Sun. N body calculations are a way of simulating this process on a computer. The main force to consider, at least initially, is gravity. Consider 9 particles, each of mass 1kg, arranged in a 2d grid, each 1m away from the next along and the next one down. The an N body calculation estimates the gravitational force on one particle due to the effect of all the other particles and then uses this to find out how much that particle moves in a certain unit of time due to this gravitational force. Do this for all the particles and then find the position of the particles after a certain length of time. Then repeat. Consider a dense cool gas, say at a temperature of 10K, perhaps 99% gas and 1% dust (ie. solid matter). There are about 2000 such clouds between us and the Milky Way center. Typical densities in the interstellar medium are roughly 10 6 particles per cubic meter whereas in such molecular hydrogen clouds, typical denities are particles per cubic meter. For a given set of conditions (ie. temperature and density) there is a minimum value for the mass of a uniform spherical cloud at which the gravitational force will overcome the force due to the motion of the particles: this is the Jeans mass. For example, at T 30K, ρ 10 9 /m 3, M J = 10M, for T 30K, ρ /M 3, M J = 3M, T 100K, ρ /m 3, M J = 10M. 2

3 The Jeans Mass is M J = 3kTR 2Gm, where k is Boltzmann s constant, T is the temperature, R is the radius of the cloud, G is the gravitational constant and m is the mass of the hydrogen atom. This is a simplification because it neglects things like magnetic fields and rotation. In many cases, the gas cloud fragments into quasi-separate clouds each of which collapse in their own right: fragmentation. Young stars are often seen in clusters eg. open clusters. After a few thousand years of such contraction, the edge of the cloud is K with a protostar in the center. A protostar does shine, though it doesnt use nuclear fusion to create this energy. In contracting, it uses the release of gravitational potential energy to release some radiation. This radiation is hard to see in the visible due to the obscuring gas and dust in the outer part of the nebula: need to observe at longer wavelengths like radio and IR. The protostar is in the center of the nebula. During the initial collapse, the protostar has maybe 20 times the solar diameter with a very high luminosity. It radiates away energy using the energy released by gravitational collapse. The temperature goes up and the size goes down. Because the luminosity is related to size and temperature (Stefan Boltzmann law: L = 4πR 2 T 4 ), the luminosity of the protostar goes down. When the protostar core temperature reaches about 10 million degrees kelvin, nuclear fusion is released but this energy release is insufficient to halt the gravitational contraction but it does slow down. The surface temperature goes up and the luminosity goes up a bit (even though the radius decreases). This phase takes about 10 million years though it depends on the mass of the protostar. Finally the nuclear fusion rate in the protostar increases to match the gravitational force in until hydrostatic equilibrium is reached and the star is born. Hydrostatic equilbrium is the exact macthing of the gravitational force in to the pressure out at every layer in the star. 3

4 On the Hertzsprung - Russell (HR) diagram, a plot of temperature (on the x axis) against luminosity (on the y axis) the path followed by this protostar from the moment it starts to collapse to the point nuclear fusion in the core can halt the contraction is called a Hayashi track. It depends again on the mass of the protostar. Once the nucelar fusion halts the contraction, the protostar is a star and is on the main sequence. An example of these contracting proto-stars are T-Tauri stars: these have a protostar in the center and a flat disk of circumstellar material or accretion disk around it. Material falling into the protostar first falls into the accretion disk and then falls onto the protostar. The accretion disk is about 100 AU with some bi-polar flows: these are flows of outward fllowing gas from the poles at about 50km/s. These T-Tauri stars have masses between solar masses. Note the time sequence described above is not a strict consecutive one: in different parts of the nebula the sequence may be going at slightly different rates. The above was for the protostar at the center of the nebula. Now detail the stages for the nebula. Stage 1: Dense cloud collapse: lasts about years. Stage 2: Disk dissipation: material falling onto accretion disk is transported inwards onto protostar (lasts about years). Stage 3: Proto-Sun to a T-Tauri star phase: planetary accretion begins (lasts about years). Stage 4: Gas dissipation: planetary accretion in inner solar system ends and residual nebula gas is removed by T-Tauri winds (lasts about years). Near Uranus, Neptune, the planetary accretion may have continued for much longer. The observational evidence for this is that disks are often seen around young stars. The conservation of angular momentum explains direction of rotation of Sun and the orbits of most planetary bodies in Solar System. The accretion disk explains why most solar system object orbits are coplanar. 4

5 There is a central bulge aroud the protostar because the disk doesnt flatten too much due to a small r in the L = mrv equation for angular momentum. Above the accretion disk, only gas pressure opposes the collapse of material onto the disk. In the disk, gas pressure and centrifugal force will oppose the collapse of material into the central protostar. Remember collapse implies conversion of gravitational potential energy to kinetic energy which are converted to heat via collisions. As the nebula becomes more dense it becomes more opaque (opacity is the resistance to radiation flow). If radiation flow is impeded its trapped inside and the temperature increases. Temperature increases implies an increase in pressure which again resists gravitational contraction. The Minimum Solar nebula model postulates that the mass of the nebula around the protosun was just equivalent to the total mass of the planets plus some extra H, He and icy compounds to make the overall composition similar to what we see in the Sun today. This needs a nebula mass of around 0.01M. In contrast the massive solar mass model postulates that the mass of the nebula around the protostar was around one solar mass. Note in both the mass of the protosun was around one solar mass or slightly more (to allow for more during the T-Tauri stage. The mass of the planets is currently less than M. The minimum solar nebula model requires that all suitable material is converted to planets. The maximum solar nebula model requires that a large proprotion of the nebula mass is lost. Recall angular momentum problem: Sun has 99% of the solar system s mass but very little of the solar system s current angular momentum. That is its rotating far too slowly too satisfy the conservation of angular momentum. The protosun and Sun somehow would have had to transfer its angular momentum outward to the outer parts of the disk. 5

6 This could not have happened if the gas molecules and dust grains in the nebular material were moving without any interaction ie. in Keplerian orbits. There was interaction that is there was viscous drag between the different elements of the disk. Also turbulence inherited from initial contraction. Outcome of viscous drag: transfer of angular momentum outwards because outer parts speeded up and inner parts slowed down. This can explain the angular momentum problem. This outward flow of material can also account for some of the mass loss that is needed in the massive solar nebula model. Also bipolar flows and transfer of mass from nebula to the protsun can explain mass loss needed by the massive solar nebula model. Also T-Tauri stellar winds. Condenstation of materials Temperatures at the outer parts of stars are usually above about 3000K. Below this, elements will form chemical compounds and these chemical compounds control the evolution of the Solar nebula. Compunds important in the evolution of the Solar Nebula include water (H 2 O), metahne (CH 4 ), iron sulfide or troilite (FeS), corundum (Al 2 O 3 ) and pyroxene (CaMgSi 2 O 6 ). Temperature of the solar nebula highest at the center ie. there was a temperature gradient. Initially as the SN got denser due to gravitational contraction, temperature in the outer parts of the SN increased. Viscous drag also increased this temperature. Temp. near about 4-5AU was about 400K. At about 1AU from protosun, it was about 2000K. At this time (stage 2), everything in the form of atoms, not grains. Most material within about 2-3AU in gaseous state though a few molecules like H 2 or CO existed. As the protosun blew of the excess mass, the Solar Nebula became more transparent to radiation and could thus cool - allowing more compounds to form. Condensation 6

7 Breathe out on a cold day, water vapour in your breath in gaseous form turns into liquid form. That is molecules of H 2 O loose energy in their gaseous state and come together to form the liquid state of water. In conditions of low pressure, as existed in the early SS, substances can condense directly from gas to solid with no interveing liquid phase: volatile condensation. Condensation of atoms into molecules can occur at relatively high temperatures (eg. H to H 2 ). Elements joining together like this to form molecules at relatively high temperatures is known as refractory condensation. Once a tiny grain is formed in this way, its easier to subsequent atoms to attach to this grain - Why? Formation history of SS depends on stability of compounds and rate at which these compounds can form a gas at the prevailing temperature and pressure. SN cooled after it had reached its peak temperature: planet forming process started after SN started to cool. More dust-sized grains forming by condensation within the nebula during Stage 3. As these grains formed, they settle towards the mid-plane of the nebula, producing a sheet rich in dust and larger particles. Settling towards mid-plae occurs due to gravity and collisions. Becomes more rapid as size of grains grew. H and He (98% of the solar nebula) never condense under the conditions present. H compounds (1.4% of the SN): water, methane, ammonia (NH 3 ) can solidify into ices at low temperatures (< 150K under the low Rock (0.4% of the SN): gaseous at high temperatures but condenses into solid bits at temperatures around K. Metal (0.2% of the SN): Fe, Nickel, Al, gaseous at high temperatures but condense into solid form at temperatures in the range K). Innermost regions of SN where temps greater than 1600K, too hot for anything to condense. Inside Mars orbit, temps. low enough for rocks and metals to condense into first grains but H, H compounds remain gaseous. These condensed beyond Mars orbit. Now consider how grains could grow. Gravitational attraction between grains is too small to bring two grains together. Chance encounters, collisions seem to tbe the most important. 7

8 In such a collision, one of three things happen: one or both particles could be fragmented or broken up, or they can bounce of each other or they can stick together. Why could colliding particles stick together? One possibility: grain surfaces were fluffy, with cavities (maybe caused by evaporation of ice that was previously there). Magnetism plus electrical attraction could also play a part. Coagulation: sticking together of grains - see references by S. Simons. Rate at which coagulation proceeds depends on density of materinal in nebula. One model: once settling of dust grains towards the mid-plane has begun, it would take only about 2000 years to produce particles up to 10mm in diameter at 1AU from the Sun, about 5000 years to produce particles upto 15mm in diameter at about 5AU (ie Jupiter) and about years tp produce particles about 0.3mm in diameter about 30AU (Neptune orbit). Note this is initail growth. Many things can happen subsequent to this eg. Neptune and Uranus formed over extended periods of time, but Jupiter formed over a timescale comparable to the formation of the inner planets: otherwise asteroid belt would have formed into a rocky planet. Slow grain growth further from the Sun - why? Column mass (mass per square meter of the SN measured perpendicular to the galactic plane) decreases outwards so grains condense more slowly in the outer parts of the nebula. Lower density means less frequent collisions. Thirdly the nebula is flatter the further out you go, so grains have to fall flatter to reach mid-plane region, taking longer to complet their journeys. Between Mars and Jupiter (about 5AU), the column mass of dust increases sharply due to the condensation of water. Also increases due to condensation of more volatile compounds such as ammonia. This is expected since tmperature here are low enough for water to condense in the form of ice. This ice is more like snow (ie fluffy) and encouraged individual grains to stick together. This is the frost line and explains the difference in composition between the terrestrial and Jovian planets. 8

9 Examination of meteorites reveal refractory materials (eg Ca and Al rich inclusions) and globules of silicate rich materials a few mm across (chondrules). Chondrules are often found embedded in a silicate matrix known as chondrites or chondritic meteorites. Ca/Al rich inclusions and chondrules could represent types of grains that wre available for coagulation. So far have particles a few mm in size. Time for this was only a few thousand years. See references on chondrules from xxx.lanl.gov Planetesimals and embryonic planets Young stars of maybe 1M experience a T-Tauri phase of violent stellar winds when they are about a million years old. The Sun probably went through such a phase. T Tauri type winds can blow out objecta from the SS about 10m across, at least from the inner part of the SS. Not so intense effects from the outer parts - otherwise no gas left to form the outer planets. Thus masses greater than say 10m lump of rock (roughly kg) would have needed to exist before the T Tauri phase. Thus coagulation must have led to bodies 0.1 to 10km across: planetissmals. Grains to planetessimals - how? Planetissmals existed a few hundred thousand years after condensation began - within inner SS, perhaps longer in outer parts. Once a planetissmal has reached 10km across its own gravity can attract other particles and perturn the motion of other planetissmals. This perturbation is gravitational focusing and results in more frequent collisions. That is instead of fragmenting and dispersing, get larger and larger bodies and fewer and fewer bodies. Hard to model. Larger planetesimlas grow more rapidly than smaller bodies: runaway growth - planetary embryo. 9