Formation of the 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 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 ( 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. (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?) • forms at hot center How do we know this happened?

• We see disks around young stars Proplyd : 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- 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 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 • 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 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 )

• 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 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

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

• 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 • form in accretion disks of Jovian planets • Sub-nebula also has temperature gradient as a Miniature Solar System

End of Planet Formation

• / 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

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 • 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 • : remaining rocky planetesimals – Planet formation inhibited between and Jupiter – Initially lots of planetesimals – Most crashed into inner planets or were ejected • : remaining icy planetesimals – Initially all throughout outer solar system • KBOs – accreted too slowly

4 Vesta

Mean diameter: 525 km • Brightest . – Distance = 2.4au • Second most massive asteroid (after ) – 9% of mass of • Second largest asteroid (after Ceres) – Oblate spheroid (=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 /

P=248 Years Arrakoth (2014 MU69)

P = 298 years Farout (2018 VG18)

D = 120au; P>1000 years Titius- 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: – : -1 (define 2-1 = 0) – : 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 • 7: a=40 au. is at 30 au

Why does the Titius-Bode Law appear to work? Simulations show planets cannot be too close together. Simulated stable planetary separations can often be approximated as a geometric series (Luna) Luna is too large to have been captured by Earth • Composition different than Earth – Moon has lower density (less iron/nickel) – Could not have formed in same place/time as Earth • Giant Impact – Many large planetesimals leftover during SS formation – Collision between proto-Earth and Mars-sized object • Possible outcomes – Change in axial tilt – Change in rotation rate – Complete destruction – outer layers of Earth blown off From Theia to Luna

Source: New York Times, 5/1/19

Support for Collisional Lunar Origin

• Moon's composition matches outer layers of Earth • Moon has deficit of volatiles: all were vaporized • Other large impacts: – Pluto/Charon ? – Mercury – Uranus – Venus? (perhaps more complicated)

Craters

Comparison of ~ 30 km craters on different bodies.

Names and locations : • Golubkhina (Venus), 60.30N, 286.40E; • Kepler (Moon), 8.10N, 38.10W; • (Mars), 20.80S, 53.60E; • (), 29.80S, 136.00W.

Image Credit: Image of Ganymede Crater contributed by Paul Schenk (Lunar and Planetary Institute). Image of Mars crater obtained from the Mars Multi-Scale Map, Calvin Hamilton (Los Alamos National Laboratory). Images of lunar and venusian craters from Robert Herrick (Lunar and Planetary Institute). Crater, Arizona

Diameter: 1.2 km. Depth: 170m. Rim: 45m. Age: 50,000 years. Impactor: 50m Fe-Ni meteor The Series of papers in in 2005 • Solar system: Sun, planets, debris disk of planetesimals – Planets accrete or scatter planetesimals – Angular momentum exchange causes • Jupiter moves inward, Saturn, Uranus, and Neptune move outward • 1:2 between Jupiter and Saturn reached – Kick in eccentricities, destabilization of – Uranus and Neptune scattered outward, switch positions • Small bodies move inward • Interactions explain current orbital radii and eccentricities • 1:2 resonance explains late heavy bombardment period – Initial geometry can give resonance (and hence scattering) at right time. – Asteroids will also be perturbed at this time. What is a Resonance? The Asteroid Belt • Why not another terrestrial planet? • Total mass ~ 1 lunar mass • Perturbations by Jupiter

Kirkwood Gaps What is Wrong with this Picture?