Formation of the Solar System Overview
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Formation of the Solar System Overview Observations of trends in our solar system, plus observations of young stars, yield a coherent picture of the formation of planetary systems • The major distinction between terrestrial and Jovian planets comes from where in the solar nebula they formed • “exceptions” arise from collisions and other interactions • We know the age of our solar system by studying radioactive isotopes in meteorites and rocks. Two models 1. Close Encounter – tidal stream (Buffon 1745) Physics • Hot gas will expand due to high pressure, rather than collapsing • Gas pressure ∼ nT – n is gas density – T is the gas temperature • If the pressure exceeds that of the interplanetary medium, it will expand Two models 2. Nebular Hypothesis (Kant 1755; LaPlace 1790) The Physics • Large, cold cloud of gas (D ~ few ly) • Collapse begins • Gravity pulls cloud together • Cloud heats (why?) • Cloud rotates (why?) • Disk forms (why?) • Sun forms at hot center How do we know this happened? • We see disks around young stars Proplyd : Protoplanetary Disk Edge-on Disks HL Tau: Environs and ALMA image b Pictoris Debris Disks The Jeans Mass – or – What Collapses? Consider an interstellar cloud of mass M and radius R The cloud is in equilibrium with a mean temperature T • cs, the sound speed of particles, is given by the mean of the Maxwell-Boltzmann distribution: 2 3/2 2 N(v)=4pv (m/2pkBT) exp(-mv / 2kBT) The Jeans Length 1/2 • Free fall timescale: tff = [3p/(32Gr)] • Sound crossing time: ts = R/cs 1/2 • cs = (kBT/m) where m is the mean mass • For tff < ts , the cloud will collapse • This is the Jeans length, lJ = cs tff • The Jeans radius RJ = lJ /2 The Jeans Mass The Jeans mass is the mass contained within a Jeans radius 3 • MJ = 4/3 p rRJ , where r is the mean density 3 3 • MJ = 4/3 p rRJ = 4/3 p r [cs/ tff] -1/2 ( 3/2 • MJ ~ r cs/G) -3 -24 -3 • Let n = 1000 cm , r~3x10 g cm (H2), T=30K – RJ ~ 1.5 pc; MJ ~ 18 M¤ You can also derive this by setting setting the net energy, K+U, of the cloud to zero. 2 • K = ½ Mcs • U = GM2/R Planet Formation Planet formation in flattened disks, dictated by conservation of angular momentum, explains the shape of our Solar System Fraction of Stars with Disks Hernandez et al. 2007, ApJ 662, 1067 Towards a Hypothesis: • Disks are ubiquitous • Disks are a by-product of star formation • Disks are planar • Disks rotate differentially • Disk compositions = stellar compositions To Be Explained: • 4 terrestrial (rocky) planets – Poor in volatiles – 0.4 < d/au < 1.5 • Asteroid belt • 4 gas giants – Outside the ice line – 5.5 < d/au < 40 – Uranus, Neptune less volatile-rich • Debris Elemental Abundances Sun Mass Fraction Earth Mass Fraction H 0.74 Fe 0.32 He 0.24 O 0.30 O 0.010 Si 0.15 C 0.0046 Mg 0.14 Ne 0.0013 S 0.029 Fe 0.0011 Ni 0.018 N 0.00096 Ca 0.015 Si 0.00065 Al 0.014 Mg 0.00058 Cr 0.005 Planet Formation in a Disk: Condensation Sequence •Solar nebula had uniform composition •Temperature decreases outwards •Different materials condense at different T •H and He never condense Condensation Sequence Temperature (K) Condensate 1500 Fe2O3, FeO, Al2O3 1300 Fe, Ni 1200 Silicates 1000 MgSiO3 680 FeS 175 H2O 150 NH3 120 CH4 65 Noble gases Solar Composition at Low Temperature Competing Models • Accretion • Gas collapse Debris Disk HD 135344B = SAO 206462 F8V Age: 8(+8,-4) Myr Sco-Cen assoc StolKer et al. 2016, A&A 595, A113 How Big Should a Disk Be? • Accreting material has angular momentum – Specific angular momentum l/m = vr – W = v/r • v=(GM/r)½ (Keplerian rotation) • At the outer edge of the disk RD ½ – l = vRD = (GMRD) 2 – R = cst; l=W(cst) (cs is sound speed) 2 4 4 3 – RD = W cs t /GM where M = ṁt ; ṁ =cs /G • Let t= M¤/ ṁ 2 3 3 8 -15 -1 • RD =W G M¤ /cs ~ 100 au for W = 5x10 s Disk Geometry • Kraus et al., 2008, ApJ, 676, 490 Disk Evolution Williams & Cieza Disk Evolution • Transition disk: – planet formation sweeps out gaps • Debris disk: – Planet formation completed – Small particles fall into star due to Poynting-Robertson drag; timescale < 105 yrs @ 1au – Gas swept out by stellar wind Stages of Planet Formation 1. Accumulation of dust into planetesimals 2. Growth of planetesimals into embryos 3. Growth of the oligarchs 4. Gas accretion 5. Dynamics • Formation of Planetesimals • Dust particles are coupled to gas in disk • Particles grow by sticking together – Atomic/molecular forces > gravity – Ice is sticky • Interplanetary dust as analogs? – Silicate/carbonate cores with icy mantles From Grains to Planetesimals • Disk plane shielded (cold) • Particle sedimentation • Collisions result in – Sticking – bouncing – fragmentation • Models produce steady-state particle size distribution. • Gravitational instabilities -> dense filaments Dominating the Orbit 1/3 Hill radius: rH=a (mp/3M⊙) • a: distance from planet to Sun • mp: mass of planet • M⊙: mass of Sun Planet will sweep up mass within rH of its orbit The Rings of Saturn • The Rings of Saturn The Rings of Saturn HL Tau Disk (ALMA) • Embryos to Planets • Planetesimals: ~ 1 km; rocky • Embryos: ~ 100 km; rocks, ice • Planets: 1000 km +; rocks, ice, gas Terrestrial Planets • Inside frost line: rock/metal condenses • Small size reflects limited material • Seed grow via accretion to make planetesimals • Planetesimals grow via gravity to 102 to 103 km • Only the largest planetesimals survive fragmentation • This idea is supported by meteorites—metal grains embedded in rock Birth of the Earth • Small dust grains collide and stick • Once grain becomes large enough, gravity takes over • Runaway accretion ensues. Chondrite Jovian Planets • Beyond frost line—H compounds can condense (ices: CH4, NH3, H2O) • Lots of ice—planetesimals grow large • Can gravitationally capture H and He • Grow very large • Moons form in accretion disks of Jovian planets • Sub-nebula also has temperature gradient Jupiter as a Miniature Solar System End of Planet Formation • Solar wind / radiation pressure blows disk away • Gaseous phase ~ 10 million yr • Strong magnetic field transfers angular momentum outward • Supported by observations of young stars Resulting Solar System Inside Frost Line: small rocky planets Outside Frost Line: large gaseous planets Age of the Solar System • Radiometric dating: measure solidification age – Look at proportions of isotopes and atoms • Radioactive decay: – Breaking apart or change (p+ into no) of nucleus – E.g. 40K becomes 40Ar – Parent isotope: 40K – Daughter isotope: 40Ar • Half-life: time it takes for ½ of parent nuclei to decay Radiometric Dating Useful radioisotopes 14 14 C → N: t1/2 = 5730 years 26 26 Al → Mg: t1/2 = 717,000 years 40 40 K → Ar: t1/2 =1.25 billion years 238 206 U → Pb: t1/2 = 4.47 billion years 87 87 Rb → Sr: t1/2 = 49.4 billion years Radiometric Dating. II Other useful radioisotopes 3 3 H → He: t1/2 = 12.4 years 81 81 Kr → Br: t1/2 = 210,000 years 36 36 Cl → Ar: t1/2 = 301,000 years 129 129 I → Xe: t1/2 =15.7 Myr 235 207 U → Pb: t1/2 = 0.7 Gyr 232 208 Th → Pb: t1/2 = 14.4 Gyr Radiometric Dating • Rock forms with 40K but no 40Ar • Any 40Ar you find in the rock is due to radioactive decay • Remains trapped in the rock unless heated • Ratio è age • Moon rock dating uses U and Pb (note: different chemical properties + understanding minerals) Result: lunar rocks ~ 4.4 billion years old Radiometric Dating. II Consider rock samples A,B,C containing 86Sr, 87Sr, 87Rb • Sr is stable, 87Rb decays to 87Sr • Initially (then) 87Sr/ 86Sr is constant • 87Rb to 87Sr moves along 45o slope to (now) line • Angle q increases with time • tan q = t/t1/2 The Age of the Solar System • Radiometric dating ≈ solidification age • Earth rock age < SS age (surface reshaping) • Moon rock age < SS age (impact) • Meteorite ages: – Have not melted or vaporized since SS formation – Age ~ 4.55 billion years • Age consistent with solar evolution theory The Debris • Solar wind removed gas – Small planetesimals remained • Asteroids: remaining rocky planetesimals – Planet formation inhibited between Mars and Jupiter – Initially lots of planetesimals – Most crashed into inner planets or were ejected • Comets: remaining icy planetesimals – Initially all throughout outer solar system • KBOs – accreted too slowly 4 Vesta Mean diameter: 525 Km 4 Vesta • Brightest asteroid. – Distance = 2.4au • Second most massive asteroid (after Ceres) – 9% of mass of asteroid belt • Second largest asteroid (after Ceres) – Oblate spheroid (<r>=260 km) • Rocky: r = 3.4 g/cm3 • Differentiated with metallic core – Surface composition matches 1200 “Vestan achondrite” meteorites – Evidence for chondritic material, hydrated minerals • Last remaining rocky protoplanet? History of Vesta Pluto/Charon P=248 Years Arrakoth (2014 MU69) P = 298 years Farout (2018 VG18) D = 120au; P>1000 years Titius-Bode Law A mathematical relation published by J.E. Bode in 1772 a = (2n x 3 + 4) / 10 • a is the semimajor axis of the orbit in au • n is an index: – Mercury: -1 (define 2-1 = 0) – Venus: 0 – Earth: 1 – Mars: 2 – Jupiter: 4 – Saturn: 5 a matches observation to within a Few %. The Titius-Bode law is empirical: there is no physical reason why it should hold, but it has proven oF some use as a predictor. Titius-Bode Law. II a = (2n x 3 + 4) / 10 “Missing” values of n: • 3: corresponds to the distance of Ceres, discovered in 1801 by Piazzi. • 6: corresponds to Uranus • 7: a=40 au.