Astronomy 340 Fall 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 ▫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, ▫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 ▫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, ▫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

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 ▫Same abundance as the star ▫Spins in the same direction as the star ▫Temperature/density gradient (T(r) ~ r -0.5 ) ▫Other characteristics  Size: AU observed  Total mass ~ 0.04 M Earth  R ~ 150 AU  Lifetime: years

1 st Phase - Condensation Grains can survive in ISM conditions Condensation ▫Nebula/disk cools  solids condense ▫“refractory” elements go 1 st  Fe, silicates condense at K ▫Meteoritic ages  condensation ~4.5 Gyr ago  Meteorites sample asteroid belt

2 nd Phase – Collisional Accretion Sticky collisions ▫V i = (V 2 + V e 2 ) 1/2 = impact velocity ▫V e = [2G(M 1 +M 2 )/(R 1 +R 2 )] 1/2 ▫If V i < V e  bodies remain bound  accretion Growth rate ▫dM/dt = ρvπR 2 F g or R 2 ΣΩF g /(2π) ▫F g = cross-section = 1+(V e /V) 2 ▫dR/dt = (ρ d v/ρ p )(1+[8πGρ p R p 2 ]/3v 2 )  ρ d = mass density in disk  ρ p = mass density of planetesimals  V = average relative velocity  R p = radius of planetesimals

Collisional Accretion continued If V e >> V, then dR/dt goes as R 2  big things grow rapidly Can evaluate growth rate using R 1 =R 2 (same assumption for V) Formation of rocky/solid cores  next step is accretion ▫R accretion = GM p /c 2 (c = speed of sound)

Collisional Accretion III Predicted timescales ▫Accretion of dust  1 km sized bodies (10 4 yrs) ▫“runaway growth”  1 km to planetesimals (10 5 yrs) ▫Impacts finalize terrestrial planets (~10 8 yrs) Lifetimes ▫Disk lifetimes: yrs so process must be complete by then! ▫Earth timescales ~ 10 8 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(R 4 Ω 2 )) ▫Timescales ~ freefall time ▫One simulation with M d ~ 0.1 Earth masses, T~100K, R d ~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?