3. Planet form ation

Frontiers of A stronom y W orkshop/S chool Bibliotheca A lexandrina M arch-A pril 2006 Properties of planetary system s

• all giant planets in the solar system have a > 5 A U w hile extrasolar giant planets have semi-major axes as small as a = 0.02 A U • planetary orbital angular momentum is close to direction of S un’s spin angular momentum (w ithin 7o) • 3 of 4 terrestrial planets and 3 of 4 giant planets have obliquities (angle betw een spin and orbital angular momentum) < 30o • interplanetary space is virtually empty, except for the asteroid belt and the Kuiper belt • planets account for < 0.2% of mass of solar system but > 98% of angular momentum Properties of planetary system s

• orbits of major planets in solar system are nearly circular

(eMercury=0.206, ePluto=0.250); orbits of extrasolar planets are not (emedian=0.28) • probability of finding a planet is proportional to mass of metals in the star Properties of planetary system s

• planets suffer no close encounters and are spaced fairly n regularly (Bode’s law : an=0.4 + 0.3×2 )

planet semimajor axis (A U ) n an (A U ) Mercury 0.39 −∞ 0.4 V enus 0.72 0 0.7 Earth 1.00 1 1.0 Mars 1.52 2 1.6 asteroids 2.77 (Ceres) 3 2.8 Jupiter 5.20 4 5.2 S aturn 9.56 5 10.0 U ranus 19.29 6 19.6 N eptune 30.27 7 38.8 Pluto 39.68 8 77.2 Properties of planetary system s

• planets suffer no close encounters and are spaced fairly n regularly (Bode’s law : an=0.4 + 0.3×2 ) planet semimajor axis (A U ) n an (A U ) Mercury+ 0.39 −∞ 0.4 V enus 0.72 0 0.7 Earth 1.00 1 1.0 *predicted Mars 1.52 2 1.6 +exceptions asteroids* 2.77 (Ceres) 3 2.8 J+ upiter 5.20 4 5.2 S aturn 9.56 5 10.0 U ranus* 19.29 6 19.6 N eptune+ 30.27 7 38.8 Pluto+ 39.68 8 77.2 Properties of planetary system s • O ort cloud: – ~1012 comets of 1 km or larger – radii >104 A U – approximately spherical – source of long-period comets (P > 200 yr) and short- period comets (200 yr > P > 20 yr) • Kuiper belt – ~109 comets – radii > 35 A U – flattened disk – source of Jupiter-family comets (P < 20 yr) Properties of planetary system s

• most planets have satellites

planet number Mmax/Mplanet Earth 1 0.012

Mars 2 1.7×10-8

Jupiter 61 7.8×10-5

S aturn 31 2.4×10-4

U ranus 27 4.1×10-5

N eptune 13 2.1×10-4

Pluto 3 0.15 Properties of planetary system s

• solid planetary and satellite surfaces are heavily cratered; cratering rate must have been far greater in first 109 yr of solar system history than it is now (“late heavy bombardment”) • age of solar system is 4.56 ± 0.02 × 109 yr • “terrestrial” planets (Mercury, V enus, Earth, Mars) are composed of rocky, refractory (high condensation temperature) material • “giant” planets (Jupiter, S aturn) composed mostly of H and H e but are enriched in metals and appear to have rock-ice core of 10-20 Earth masses • “intermediate” or “ice” planets (U ranus and N eptune) also have cores but are only 5-20% H and H e (not “terrestrial”) • gas disks around young stars dissipate in 106 – 107 yr W hat is a planet?

V ersion 1:

– main-sequence stars burn hydrogen (M>0.08 Mú=80 MJupiter) – brow n dw arfs have masses too low to burn hydrogen but

large enough to burn deuterium (80 MJupiter

– planets have masses < 13 MJupiter – Good points: mass is easy to measure; maximum mass of

close companions to stars is around 15 MJupiter (brow n- dw arf desert) – Bad points: deuterium burning has no fundamental relation to the formation or properties of a planet W hat is a planet?

V ersion 2: – planets are objects similar to the planets in our ow n solar system – Bad points: is a Jupiter-mass object at a=0.02 A U a planet? is Pluto a planet? Is our solar system special? V ersion 3: – anything formed in a disk around a star is a planet – Bad points: figuring out how something is formed is really hard, and w hat do w e call them until w e do? B row n et al. (2005) T he encounter hypothesis

• Close encounter w ith a passing star rips material off the S un that spreads into a long filament and condenses into planets (Buffon 1745, Jeans 1928, Jeffreys 1929) • Problems: Prove!

– very rare event: needs impact parameter < 2 Rú so only happens to 1 in 108 stars 1/2 1/2 – specific angular momentum of order (GMúRú) not (GMúaJ) ; factor 30 too small (Russell 1935) (not a problem for some extrasolar planets!)

– 1 Jupiter mass of material requires digging to R ~ 0.1 Rú w here temperature ~5 × 105 K and resulting blob w ill have positive energy, and cooling time ~ 1010 sec. B lob expands adiabatically and disperses (S pitzer 1939) – w here did Jupiter’s deuterium come from? T he brow n-dw arf hypothesis

• extrasolar “planets” are simply very low -mass stars that form from collapse of multiple condensations in protostellar clouds • distribution of eccentricities and periods of extrasolar planets very similar to distributions for binary stars Cumulative distribution functions in period and eccentricity for extrasolar planets and low -mass companions of spectroscopic binaries

period eccentricity

from Z ucker & Mazeh (2001) T he brow n dw arf hypothesis

• extrasolar “planets” are simply very low -mass stars that form from collapse of multiple condensations in protostellar clouds • distribution of eccentricities and periods of extrasolar planets very similar to distributions for binary stars • but: – w hy is there a brow n-dw arf desert? – how did planets in solar system get onto circular, coplanar orbits? – how do you make planets w ith solid cores, or terrestrial planets? T he nebular hypothesis

• the S un and planets formed together out of a rotating cloud of gas (the “solar nebula”) • gravitational instabilities in the gas disk condense into planets (Kant 1755) • Good points: variations might w ork to form Jupiter, S aturn, extrasolar gas giants • Bad points: how do you make U ranus, N eptune, terrestrial planets? T he planetesim al (S afronov) hypothesis

• forming S un is surrounded by a gas disk (like nebular hypothesis) • planets form by multi-stage process: 1. as the disk cools, rock and ice grains condense out and settle to the midplane of the disk – chemistry and gas drag are dominant processes 2. small solid bodies grow from the thin dust layer to form km- sized bodies (“planetesimals”) - gas drag, gravity and chemical bonding are dominant processes 3. planetesimals collide and grow – gravitational scattering and solar gravity are dominant processes. “Molecular chaos” applies and evolution is described by statistical mechanics T he planetesim al (S afronov) hypothesis

planets form by multi-stage process: 1. rock and ice grains condense out and settle 2. formation of km-sized planetesimals 3. planetesimals collide and grow 4. a few planetesimals grow large enough to dominate evolution. O rbits become regular or w eakly chaotic and are described by celestial mechanics rather than statistical mechanics (“planetary embryos”) 5. on much slow er timescales, planetary embryos collide and grow into “planetary cores” 6. cores of intermediate and giant planets accrete gas envelopes

requires grow th by 45 orders of magnitude in mass through ~6 different physical processes! M inim um solar nebula

• add volatile elements to each planet to augment them to solar composition • spread each planet into an annulus reaching halfw ay to the next planet • smooth the resulting surface density: Σ(r) ≈ 3 × 103 g cm -2 (1 A U /r)1.5 Prove! M inim um solar nebula

Σ(r) ≈ 3 × 103 g cm-2 (1 A U /r)1.5

• assume 0.5% metals and divide into r = 0.1 µ dust particles w ith density ρ = 3 g cm-3 • geometric optical depth is Prove! τ ≈ 4 × 105 (1 A U /r)1.5 i.e. disk is opaque to very large distances the “V ega phenomenon” (Z uckerman & S ong 2003)

dust emission at 850 µ from S CU BA on JCMT . From Z uckerman (2001) • destruction mechanisms include radiation pressure, Poynting- Robertson drag, collisions, sublimation • likely destruction times short compared to age • “debris disks” (Z uckerman 2001) O rion nebula PR O toPLanetarY D iskS = “proplyds” Prove! Prove! S tability of the m inim um solar nebula

Consider a disk w ith surface density Σ, angular speed Ω, and sound speed c, and examine a small patch of size L. – mass is M~Σ L2 2 2 3 – gravitational potential energy is EG ~ -GM /L ~ -GΣ L 2 2 4 – energy in rotational motion is ER ~ M(Ω L) ~ ΣΩ L 2 2 2 – internal energy is EP ~ Mc ~ Σ L c

– stable if EG + ER + EP > 0 or -GΣ2L3 + ΣΩ2L4 + Σ L2c2 > 0, or -GΣ L + Ω2L2 + c2 > 0 for all L. T he quadratic function on the left reaches its minimum at L=Gσ/2Ω2, and this is positive if Prove! 2cΩ/GΣ > 1. A ccurate calculations show that gravitational stability requires that T oomre’s parameter T he nebular hypothesis revisited

For standard parameters at 1 A U , Q = 170 Prove! Minimum solar nebula is very stable! T his is a big problem for the nebular hypothesis. H ow to fix it: – increment surface density by factor 10 above minimum solar nebula – consider only formation of giant planets at 10 A U , w here temperature is low er – probably Q ~ 1.5 is sufficient for instability Gravitational instability is just possible for extreme parameters; nebular hypothesis might w ork for Jupiter and S aturn and extrasolar gas giants, but not U ranus, N eptune, terrestrial planets Form ation of planetesim als

D ust condenses out of the cooling gaseous disk (iron, silicates,nickel in inner solar system; ammonia and ice in outer solar system)

Maximum grow th rate of dust is dr/dt ~ α cρg/ρp w here c is sound speed, α is mass fraction of particulate material in gas phase, ρg~ -9 3 3 10 g/cm is gas density, ρp ~ 3 g/cm is particle density. Y ields dr/dt ~ 1 cm/yr D ust settles to the midplane of the disk through competition betw een gravitational force –m dΦ/d z = -m(GM/R3)z = -mΩ2z, and gas drag 2 force F=-π r ρgcvz, so equating these

Prove!

T herefore particles grow to ~10 cm in ~10 yr before settling to the midplane of the disk

Prove! Form ation of planetesim als

T here are tw o competing mechanisms for jumping the meter-size hurdle: 1. G ravitational instability (the G oldreich-W ard m echanism ): • as solids settle to the midplane of the gas disk the particulate disk becomes gravitationally unstable w hen T oomre’s parameter Q =c Ω/πGΣ < 1 • H ere c, Σ are velocity dispersion and surface density of particles. If solid mass fraction is 0.5% , Σ=15 g cm-2 at 1 A U w hich requires c < 15 cm s-1 or thickness h = c/Ω < 800 km Prove! 2 2 9 • For Q << 1 all w avelengths < λc = 4π GΣ/Ω = 1 × 10 cm are 2 19 unstable. Maximum unstable mass is Mc = πΣ(λ/2) = 10 gm, corresponding to radius of 10 km Form ation of planetesim als the Goldreich-W ard mechanism, continued: • gas disk rotates slow er than Keplerian by about 0.2% . T his leads to strong shear at the surface of the particulate disk • shear induces Kelvin-H elmholtz instability w hich leads to 2 3 -1 turbulent velocities of order v – vg ~ c /ΩR ~ 5 × 10 cm s w hich gives Q > 100 and suppresses gravitational instability • possibly K-H instability can be suppressed if solid/gas surface density ratio enhanced by factors of 2-10 (Y oudin & S hu 2002) Form ation of planetesim als

2. S ticky collisions • particle velocities are turbulent (v ~ 5 × 103 cm s-1) but collisions lead to sticking

• characteristic grow th time rρp / ΣpΩ ~ 3 yr Prove! • but: – rocks don’t stick w hen they collide! – icy bodies fracture at these high speeds – largest inclusions in meteorites are a few cm

3. O ther instabilities? • Y oudin & Goodman (2005) Form ation of planets

• once the meter hurdle is jumped, gas drag becomes unimportant • further grow th occurs through collisions. W hat is the collision cross-section betw een a test particle and a body of mass m and radius r? W ithout gravity, σ=π r2 W ith gravity, Prove! 2 2 2 2 σ=π r (1+Θ) Θ = 2Gm/rv = vescape /v here Θ is the S afronov number. T he cross-section is enhanced by 1+Θ through gravitational focusing. W hen Θ>>1 grow th is very fast because • gravitational focusing enhances the cross-sections • collision debris doesn’t have to stick Form ation of planets

Rate of mass grow th is dm/dt = π r2 ρ v(1+Θ) But ρ ~ Σ/h w here h is disk thickness, and h ~ v/Ω: dm/dt ~ π r2ΣΩ (1+Θ) 3 and since m=4πρp r /3, Prove! dr/dt~ ΣΩ/ρp (1+Θ)

1. O rderly grow th: A ll grow ing planetesimals have similar mass and velocity dispersion. T hen w e expect Θ~1 since near-misses are about as common as collisions For minimum solar nebula Prove! dr/dt ~ 20 cm/yr (1 A U /R)3 N eeds 107 yr to form Earth,>109 yr to form Jupiter, even longer for U ranus and N eptune Form ation of planets

2. Runaw ay grow th A few bodies grow much faster than the others. T hen 2 dr/dt~ ΣΩ/ρp (1+Θ) ~ (ΣΩ/ρp)(1+2Gm/rv ) so for the most massive particles dr/dt ~ ΣΩ Gr2/v2 so grow th of massive bodies runs aw ay (formally, they reach infinite mass in finite time) N eeds 107 yr to form Jupiter, longer for U ranus and N eptune Planet migration

T emperature in disk ∝ 1/r1/2. A t r < 0.1 A U no elements condense so planetesimals cannot form. S o w hy are there planets there?

Gravitational interactions betw een a planet and the surrounding gas disk leads to repulsive torques betw een them. T he torque depends only on the surface density of the disk, not viscosity, pressure, self-gravity, etc. Imbalance betw een inner and outer torques leads to: • migration, usually inw ard • gap formation Repulsive torques can “shepherd” narrow rings and open gaps in w ide rings Cordelia and O phelia at U ranus T ypes of m igration

T ype I: low mass planet only w eakly perturbs the disk -1 2 – timescale of order Ω (ΣR /Mú)(Mp/Mú) – very rapid, ~ 104 years for Jupiter in minimum solar nebula – usually inw ard T ype II: bigger planet opens a gap in the disk – planet evolves w ith the disk on the disk’s viscous evolution timescale (acts like a disk particle) – probably ~ 103 - 105 yr timescale – usually inw ard from Masset (2002) M igration

• migration from larger radii offers a plausible w ay to form giant planets at small radii, but: – w hy did the migration stop? – w hy are the planetary semimajor axes distributed over a w ide range? – w hy did migration not occur in the solar system? • outw ard migration by U ranus and N eptune helps to solve the timescale problem Planet form ation can be divided into tw o phases:

Phase 1 Phase 2 • protoplanetary gas disk → • subsequent dynamical dust disk → planetesimals evolution of planets due to → planets gravity • solid bodies grow in mass • lasts 99.99% of lifetime by 45 orders of magnitude through at least 6 • involves very simple different processes physics (only gravity) • lasts 0.01% of lifetime • involves very complicated physics (gas, dust, turbulence, etc.) M odeling phase 2 (M . J uric, Ph.D . thesis)

• distribute N planets randomly betw een a=0.1 A U and 100 A U , uniform in log(a) • choose masses randomly betw een 0.1 and 10 Jupiter masses, uniform in log(m) • choose small eccentricities and inclinations from Maxw ellian distribution w ith specified ¿ e2–, ¿ i2 – • follow for 100 Myr • repeat 1000 times for each parameter set N , ¿ e2–, ¿ i2– • many planets are ejected, collide, or fall into the central star • most systems end up w ith an average of only 2-3 planets

(Juric 2006) • mean eccentricity of surviving planets is correlated w ith number of surviving planets • there are many high- eccentricity systems w ith 1 or 2 planets (the extrasolar planets?) and rare low -eccentricity systems w ith more planets (the solar system?)

(Juric 2006) • a w ide variety of systems converge to a common eccentricity distribution

(Juric 2006) w hich matches the observed eccentricity distribution

(Juric 2006) W hat I’ve left out

• origin of planetary rotation • origin of planetary satellites • origin of planetary atmospheres and oceans • comets and Kuiper belt • formation of gas giant envelopes