Astronomy 340
Fall 2007
11 December 2007
Class #29
Announcements
• Final Exam - Tues Dec 18 at 10:50am in 6515
• HW#6 due Thursday in class
▫ You will not be penalized for not doing the HW
(though I do recommend you try them!) – points
will be award after dealing with the class curve
• Project due on Thurs Dec 13
Second Half Review
• Atmospheres of giant planets – know the basic
compositions and we’ve figured that out
• Interiors of the giant planets
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Chapter 6.1 (eqn 6.27)
Figure from page 24 of Lecture 18 (Fig 6.23)
What are the J terms all about?
What is the underlying physics behind the
derivation of the maximum size of a planet
• Satellites of the outer planets
▫ Figure 6.21
Second Half Review – cont’d
• Satellites of the outer planets
▫ Chapters 5.5.5, 5.5.6, 5.5.7, 5.5.8, 5.5.9
▫ Know why Io, Europa, Titan, Encelaedus, Triton are
interesting – what’s the role of tidal forces in all this?
▫ Lecture 20 & 21!!!
• Rings – what accounts for the variation in structure?
▫ Chapter 11 (through 11.4)
• Comets – equation 10.5
▫ Chapter 10.3, 10.6, 10.7
Second Half Review – cont’d
• Dwarf Planets and KBOs
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You should be able to summarize the results of your project
How do you estimate the mass/size of a KBO?
Why is Pluto considered a dwarf planet?
What are the advantages of near-IR spectroscopy?
Recreate the HW question on why asteroids are brighter in the mid-IR
than in the optical – do you think the same is true for KBOs?
• Extrasolar Planets
▫ Detection techniques (how do they work and what are the limitations?)
▫ Chapter 13
• Star/Planet Formation
▫ Chapter 12
▫ Eqn 12.7, 12.22
▫ What are the effects of planetary migration and why do people think it
happens?
Review
• What are the primary techniques for detecting
extrasolar planets and how do they work?
• Given the radial velocity curve for a star would
you be able to identify the period, mass, orbital
eccentricity of the orbiting planet?
• How do you detect atmospheres around
exoplanets?
Fraction of Stars with Planets
Lineweather & Grether
Star Formation
Star Formation
Feigelson & Montmerle
Star Formation
Key Observations of the Solar System
• Coplanar/prograde
orbits – angular
momentum
• Orbital spacing
• Comets
• 0.2% of mass in
planets, 98% of the
angular momentum
• composition
• Asteroid belt  power
law size distribution
• Age  4.5Gyr
• Consistent isotopic
ratios
• Rapid heating/cooling
• Cratering record 
bombardment
Key Physical Characteristics
• Angular momentum  disk formation a must
• Key properties of disk
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Same abundance as the star
Spins in the same direction as the star
Temperature/density gradient (T(r) ~ r-0.5)
Other characteristics
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Size: 25-500 AU observed
Total mass ~ 0.04 MEarth
R ~ 150 AU
Lifetime: 105-107 years
1st Phase - Condensation
• Grains can survive in ISM conditions
• Condensation
▫ Nebula/disk cools  solids condense
▫ “refractory” elements go 1st
 Fe, silicates condense at 1400-1700 K
▫ Meteoritic ages  condensation ~4.5 Gyr ago
 Meteorites sample asteroid belt
2nd Phase – Collisional Accretion
• Sticky collisions
▫ Vi = (V2 + Ve2)1/2 = impact velocity
▫ Ve = [2G(M1+M2)/(R1+R2)]1/2
▫ If Vi < Ve  bodies remain bound  accretion
• Growth rate
▫ dM/dt = ρvπR2Fg or R2ΣΩFg/(2π)
▫ Fg = cross-section = 1+(Ve/V)2
▫ dR/dt = (ρdv/ρp)(1+[8πGρpRp2]/3v2)
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ρd = mass density in disk
ρp = mass density of planetesimals
V = average relative velocity
Rp = radius of planetesimals
Collisional Accretion continued
• If Ve >> V, then dR/dt goes as R2  big things
grow rapidly
• Can evaluate growth rate using R1=R2 (same
assumption for V)
• Formation of rocky/solid cores  next step is
accretion
▫ Raccretion = GMp/c2 (c = speed of sound)
Collisional Accretion III
• Predicted timescales
▫ Accretion of dust  1 km sized bodies (104 yrs)
▫ “runaway growth”  1 km to planetesimals (105
yrs)
▫ Impacts finalize terrestrial planets (~108 yrs)
• Lifetimes
▫ Disk lifetimes: 105-107 yrs so process must be
complete by then!
▫ Earth timescales ~ 108 yrs
▫ Much larger for Neptune
Formation Scenarios
• Core Accretion vs Gravitational Collapse
▫ Q = κc/πGΣ  gravity vs thermal pressure
 Surface mass density
 Local velocity (dispersion, sound speed)
 Κ = R-3(d/dr(R4Ω2))
▫ Timescales ~ freefall time
▫ One simulation with Md ~ 0.1 Earth masses, T~100K,
Rd~20 AU  make J in 6Myr
▫ Benefit
 Can make planets on eccentric orbits
 Timescales are short
▫ Minuses
 Hard to explain rocky cores
Core Accretion
Alibert, Mordasini, Benz 2004
Formation Issues
• Minimum Mass  r—1.5
• Core-Accretion
▫ Timescales too long for Uranus, Neptune
▫ What makes cm-size things stick?
▫ How come things don’t spiral into Sun?
• Gravitational Collapse
▫ Faster, but is it plausible?