Specialist Topics in Astrophysics: Lecture 2

Formation and Evolution of Planetary Systems

Ken Rice ([email protected]) FormationFormation ofof PlanetaryPlanetary SystemsSystems

Lecture 2: Main topics

• Solar System characteristics

• Origin of the Solar System

• Building the planets

Most theories of planet formation have been carried out in the context of explaining our Solar System

• Any theory must first explain the data/observables OriginOrigin ofof ourour SolarSolar SystemSystem

To have a successful theory we must explain the following:

• Planets revolve in mostly circular orbits in same direction as the Sun spins OriginOrigin ofof ourour SolarSolar SystemSystem

• Planetary orbits nearly lie in a single plane (except Pluto [no longer a planet!!] and Mercury), close to the Sun’s equator

• Planets are well spaced, and their orbits do not cross or come close to crossing (except Neptune/Pluto) OriginOrigin ofof ourour SolarSolar SystemSystem

• All planets (probably) formed at roughly the same time

• Meteorites suggest inner portions of the Solar System were heated to ~1500 K during meteorite/planet formation period OriginOrigin ofof ourour SolarSolar SystemSystem

• Planet composition varies in a systematic way throughout the Solar System Terrestrial planets are rocky Outer planets are gaseous OriginOrigin ofof ourour SolarSolar SystemSystem

• Jupiter/Saturn are dominated by H and He; Neptune/ Uranus have much less H and He (mainly ices, methane, carbon dioxide and ammonia) OriginOrigin ofof OurOur SolarSolar SystemSystem

• Planetary satellites are common and generally orbit in the same direction and in the same plane

E.g. Galilean Satellites of Jupiter OriginOrigin ofof OurOur SolarSolar SystemSystem

• Cloud of comets (Oort Cloud) extends to about 50,000 AU with random orbits

• Second cloud of comet-like objects (Kuiper Belt) at 30-100 AU with orbits similar to the planets OriginOrigin ofof OurOur SolarSolar SystemSystem

• Planets contain about 0.1% of the mass of the Solar System PlanetPlanet FormationFormation TheoriesTheories

(1) Formed by debris dragged out of the Sun by a close stellar encounter

(2) Spun-off material from a rapidly rotating Sun

(3) Formed by the collapse of a protostellar gas/dust cloud (“Solar Nebular” hypotheses)

Lissauer, In: Annual review of astronomy and astrophysics. Vol. 31 (A94-12726 02-90), p. 129-174

Astronomers like to believe the last one since there is observational evidence to back it up ☺ SitesSites ofof StarStar FormationFormation

• High densities and cold temperatures are required to form stars

• Molecular clouds tend to be located in spiral arms, where most stars are formed

• Compression in spiral arms can cause gas to collect, and the clouds there can be compressed

~30 light years SolarSolar NebularNebular HypothesisHypothesis

• The solar nebula most likely started off as a near spherical cloud a few light years in diameter it was very cold! rotating slightly…

• It received a shock wave, possibly from a nearby supernova • This caused the nebula to collapse as gravity increased

• As the nebula falls inwards, gravitational potential energy is converted to heat Conservation of energy • As the nebula’s radius decreases, it rotates faster Conservation of angular momentum InitialInitial ConditionsConditions forfor CollapseCollapse

≥ ≈ • For collapse Egrav Esupport Ethermal

3 GM 2 – Gravitational energy – sphere E = grav 5 R 3 M 3 – Thermal energy E = NkT = kT thermal µ 2 mH 2 3 GM 2 3 kT • For collapse ≥ M × µ 5 R 2 mH 1 M 5 kT  3 M 3 ⇒ ≥ , with R = µ  π ρ  R 2 G mH 4 

3 −1 5 kT  2 4π  2 M ≥ M = ρ • Jeans mass J  µ    2 G mH   3  StarStar FormationFormation TheoryTheory

Class 0 Class I Class II

5 6 T ~10 4 years T ~10 years T ~10 years 3 R ~ 10 4 AU R ~ 10 AU R ~ 100 AU -6 -8 -5 dM/dt ~ 10 M
/yr dM/dt ~ 10 M
/yr dM/dt ~ 10 M
/yr StarStar formationformation :: ObservationsObservations

BHR 71 IRAS 04302+2247 TW Hydrae

Padgett et al. 1999 Bourke 2001 Krist et al. 2000 DiscDisc FormationFormation

• Cloud contains some angular momentum. – Conserved during collapse. r r r • Specific angular momentum J = r ×v ≈ rv • Centrifugal (rotational) barrier – At some point v increases sufficiently to halt collapse J v2 GM J 2 v = ⇒ ≈ ⇒ r = r r r 2 cent GM – Collapse halted perpendicular to J : disc formation.

Protostellar Sun Protoplanetary disk DiscDisc SizesSizes

• Consider a sphere of radius 0.1 pc and

mass 1 MSun . • Angular velocity Ω = 5 x 10 -15 rad/sec – Solid body rotation

J = vr = Ωr 2

• The centrifugal radius is then J 2 Ω2 R 4 = = cloud ≈ × 13 ≈ rcent 7.1 10 m 114 AU GM GM cloud

• Disc sizes : ~ hundreds of AU • Certainly large enough to account for the size of the Solar System DiscDisc PropertiesProperties

• The existence of a disc can be inferred from the infrared (IR) excess • From assumed dust to gas ratios can infer disc masses −3 < < 10 MSun M disc 1.0 MSun • Observations suggest that discs have lifetimes of about 5 million years. • Only a small fraction of stars in star forming regions older than 5 Myr have IR excesses (discs) • Almost 90 % of stars in star forming regions younger than 1 Myr have IR excesses (discs). MinimumMinimum MassMass SolarSolar NebulaNebula

• About 105 Earth masses of solid material in Solar System bodies between about 1 and 40 AU ⇒ 10500 Earth masses of gas in presolar disc. • Distributed roughly as a power law with surface density Σ ∝ r − 5.1

− 40 AU 40 AU 5.1 40 AU  r  − = π Σ = π Σ   = πΣ 5.1 5.0 M ∫2 r dr ∫2 r o   dr 2 oro ∫ r dr AU 1 AU 1 AU  ro  1 AU

40 AU × × 24 = πΣ 5.1 5.0 10500 97.5 10 kg 2 o 2r r o 1 AU 27.6 ×10 28 kg ⇒ Σ = = 42000 kg m 2- ()with r =1 AU o 4πr 5.1 []()()40 AU 5.0 − 1 AU 5.0 o o

−  r  5.1 • The MMSN is then Σ = 42000   kg m 2- ⇒ 3800 kg m 2- at r = 5 AU MMSN 1 AU  DiscDisc EvolutionEvolution

• Most of the star’s mass initially has too much angular momentum to be part of the star – Needs to be processed through the disc ⇒ Accretion disc • Disc evolution is often assumed to be driven by a turbulent viscosity ν = α cs H • • Mass accretion rate onto the star M = 3πνΣ

• Viscous timescale R2 R2 1  R 2 c t = = ≈   since H ≈ s v ν α αΩ Ω cs H  H 

2 3 01.0  R   R 2 ⇒ t =10 7     years v α  25 H  100 AU  SolarSolar NebularNebular HypothesisHypothesis

• Collapsing gas and dust form a disk and central star

• Planets formed in the disk plane

• Once the Sun was dense and hot enough in the core it began fusing hydrogen

• The subsequent solar wind blew all the remaining dust and gas out of the Solar System revealing the planets PlanetesimalPlanetesimal HypothesisHypothesis

(a) Solar nebula contracts to form a spinning disk

(b) Interstellar dust grains act as condensation nuclei allowing accretion of planetesimals

(c) Solar winds push gas out, outer planets already formed

(d) Inner planets start to form from collisions of planetesimals

(e) Collisions continue over time making the 4 inner planets DustDust GrainsGrains

Dust grains are formed in the Solar Nebula! • Evidence for this comes from observations of other star forming regions

• Grains grow through two primary processes

Condensation: adding matter one atom (or molecule) at a time (bit like water condensing on cold pipes on a humid day…)

In the hot, inner Solar System the temperatures were so high that only metals could take part in this fundamental process

Accretion: sticking together of solid particles as they collide (electrostatic forces, stickiness of hydrocarbon compounds ) MoreMore aboutabout accretionaccretion

• Accretion - the slow build up of matter around dust grains

• Runaway growth – larger objects grow much more rapidly than smaller ones

• Oligarchic growth – the largest objects then dominate their surroundings and grow by accreting their neighbours. NebulaNebula hypothesishypothesis andand thethe SolarSolar SystemSystem

• The Sun formed in the very centre of the nebula temperature and density were high enough for nuclear fusion

• The planets formed in the rest of the disk

Such a scenario would explain why:

All planets lie along one plane (in the disk) All planets orbit in one direction The Sun rotates in the same direction The planets tend to rotate in the same direction Most moons orbit in this direction Most planetary orbits are nearly circular SupportingSupporting ObservationsObservations

• Discs of Solar System dimension around nearby stars SupportingSupporting ObservationsObservations

• Spectral signatures expected for accretion disks (mainly from IR observations)

• Millimetre-wave observations allow disk masses to be determined – similar to our Solar System

• Dopper analysis of gas motions reveal gas accreting onto central star and winds emanating from the star or inner disk

• Optical and IR images reveal jets emanating from the star-disk system GravitationalGravitational focussingfocussing

• Geometrical cross section of an accreting body is simply πR2. • Gravitational cross section

• Consider a test particle at velocity Vo approaching a grain of radius R • Test particle starts at S >> R so its potential energy is initially zero.

= Conservation of angular VR VoS momentum. 2 2 mV mV GmM Conservation of o = − 2 2 R energy. 1 2 2 V V GM  2GM 2 = o + ⇒V = V 2 +  2 2 R  o R 

1 1 1  2GM 2 R  2GM 2  V 2 2 = 2 + ⇒ = 2 + =  + esc  Vo S Vo  R S Vo  R1 2   R  Vo  R   Vo  GrowthGrowth raterate ofof planetsplanets

• Let the sum of planetary radii be R1 + R2 = Rs ρ • Let the density of the planetesimal swarm by sw ( << density of individual bodies)

• Collisional growth occurs at a rate

2 dm  V   p = ρ π 2 +  esc  = ρ π 2 sw Vo Rs 1    sw Vo Rs Fg dt   Vo   • Can relate the volume density of the planetesimal swarm to its surface density, σ, using σ σ  3 σΩ  dm  3  ρ ≈ ≈ ≈    ⇒ p =  σΩπ 2 sw   Rs Fg 2asin i 2H  2  Vo  dt  2 

We have assumed that the velocity dispersion, Vo, is isotropic. Density is inversely proportional to Vo – higher velocity means a thicker disc. SnowlineSnowline

• Angular velocity : Ω ~ a-3/2 • Surface density of planetesimals : σ ~ a-3/2 – Growth rate ~ a-3

• When temperature in disc drops below ~ 170 K – ices can condense onto grains – Snowline – surface density increases by about a factor of 3.

• Easiest to form planets just beyond snowline.

• Very difficult to form planets at large radii > 10 AU. HillHill RadiusRadius

• Consider a rigid spherical body of radius r and mass m orbiting a star of mass

M* at a distance a. • From Kepler’s third law 4π 2a3 2πa GM v GM 2 = ⇒ = = * ⇒ ω = = * P v 3 GM * P a a a

• The centripetal acceleration of the outer/inner edge of the body must be balanced by the gravitational force from the star plus that from the body. GM Gm GM * − pl = ω 2 ()a − r = * ()a − r ()a − r 2 r 2 a3

m 2 M 3 M − pl ()a − r = * ()a − r * r 2 a3 a 2 a r r 2 r 3 ⇒ M − m + 2m − m = M − 3M + 3M − M * pl r 2 pl r pl * * a * a 2 * a3 1 a3  m 3 m = 3M ⇒ r = a pl  The radius of the body must be less than rH (Hill radius) pl 3 * H   or else it will be tidally distrupted. r  3M *  IsolationIsolation massmass

1  m  3 • Critical radius – Hill radius =  p  RH a   3M *  • All planetesimals swept up inside the Hill sphere

1 3  m  3 ()4πa2σ 2 = π σ = π 2σ  isolation  ⇒ = misolation 2 a 2RH 4 a   misolation 1 3M ()2  *  3M *

• Around a solar mass star 3 3 σ 2 =  a    m .0 014     M⊕ isolation 1 AU  100 kg m 2-  SubsequentSubsequent growthgrowth

• Once the isolation mass is reached, runaway/oligarchic growth ceases and further growth is slow – Further growth through collisional mergers of fewer large bodies – Perturbed from their orbits by gravitational interactions

• Expected formation times – Terrestrial planets ~ 100 Myr – Core of Jupiter ~ 1 – 10 Myr

• These timescales are reasonable – what is unclear is how one forms Uranus and Neptune in the outer solar system – Formation timescale becomes extremely long in the outer solar system. EvidenceEvidence forfor PlanetesimalPlanetesimal BuildingBuilding

• Earth-like planets are believed to be built via planetesimal collisions produces larger bodies produces dust grains as a by-product of collisions

• In the Solar System evidence of collisions comes from the cratering history and also inclination of the planet rotation axes

• Outside the Solar System, evidence of collisions comes from light scattered towards us from small dust grains and thermal emission from heated grains

• Exoplanets preferentially found around metal-rich host stars – Star formed from metal-rich cloud – Metal-rich protostellar disc has an enhanced abundance of dust grains – Enhanced collision and growth rate. GasGas giantgiant planetsplanets

• The atmosphere of a forming planet cannot be static once the mass exceed ~ 10 Earth masses – For lower core masses, static envelope can be sustained by accretion of planetesimals • Envelope fills Hill sphere – no room for more – Not true for higher mass cores • Need additional energy source – gravitational contraction of envelope • Can accrete more gas in Hill sphere – further accretion of gas – Calculations suggest several Myr are required to accrete the mass of Jupiter in this way. – Gas disc could have dispersed before Uranus and Neptune finished accreting • Accounts for their lower envelope masses. – Final mass can also be calculated using an isolation mass

3 3  σ  2 =  a  gas σ ≈ σ m .0 014     M ⊕ 100 isolation 1 AU  100 kg m 2-  gas planetesim als