Astronomy 340 Fall 2007 11 December 2007 Class

Astronomy 340 Fall 2007 11 December 2007 Class #29

Announcements • Final Exam - Tues Dec 18 at 10: 50 am 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, 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 ▫ ▫ ▫ 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. 5 Gyr • 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: 25 -500 AU observed �Total mass ~ 0. 04 MEarth �R ~ 150 AU �Lifetime: 105 -107 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 1400 -1700 K ▫ Meteoritic ages condensation ~4. 5 Gyr ago �Meteorites sample asteroid belt

2 nd Phase – Collisional Accretion • Sticky collisions ▫ Vi = (V 2 + Ve 2)1/2 = impact velocity ▫ Ve = [2 G(M 1+M 2)/(R 1+R 2)]1/2 ▫ If Vi < Ve bodies remain bound accretion • Growth rate ▫ d. M/dt = ρvπR 2 Fg or R 2ΣΩFg/(2π) ▫ Fg = cross-section = 1+(Ve/V)2 ▫ d. R/dt = (ρdv/ρp)(1+[8πGρp. Rp 2]/3 v 2) �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 d. R/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 ▫ Raccretion = GMp/c 2 (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(R 4Ω 2)) ▫ Timescales ~ freefall time ▫ One simulation with Md ~ 0. 1 Earth masses, T~100 K, Rd~20 AU make J in 6 Myr ▫ 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?