Formations of Planetary Systems Test 1

• - Sun has no companion
• - Planets are non-resonate (resonance observed in other star systems)
• - Packed (no space to add extra planets)

• Sun:
• - typical mass, typical metal content (not H/He)
• - mass dominates solar system
• - heavy elements mostly in sun
• - no companion

• Gas Giants:
• - mostly H/He
• - not solar composition
• - more heavy elements than sun

• Resonance
• - planets not resonate
• 
• where i, j are integers

• Packed
• - between planets, bodies exist where orbits are stable
• - no room to add extra planets

• Asteroid Belt
• - Kirkwood Gaps (resonance with Jupiter)

Dominated by planets

Estimates minimum gas needed to form planets

1.) Estimate heavy elements (Fe) to get mass

2.) Calculate area of disk (annulus extending halfway to neighboring planets)

3.)

where

• - Most of the mass is in outer disk
• - different for each planet

• - Doppler shifts
• - Transits
• - Microlensing
• - Direct imaging
• - Astrometry
• - Pulsar timing

• - gives info about composition
• - resolve light from planet as separate source (fraction of starlight reflected by planet)

-gives planet's brightness (very faint compared to star)

• Separating Planet from from Star:
• - dust, atmosphere, telescope size, diffraction = limitations
• - Diffraction Limit: D = diam of tele

- light that planet absorbs is re-radiated as Thermal radiation (T~300K for Earth)

- drop in stellar flux is observed

• - look for periodic dips due to planet transits (f = 0.01 for J-like planets)(f = 1-0.99)
• - on ground, precision sufficient to find gas giants, but atmosphere prevents detection of terrestrial planets

• Probability of Observation:
• 

- lower a = higher P (good way to find planets close to star)

• Observables:
• - Depth of Transit

- Period of Orbit

- Stellar Parameters (a, )

• - star orbits center of mass (moves b/c of planet)
• - detect line of sight (radial) variation in stellar velocity to reflex motion
• - high precision spectra -> measure v via dopp. effect

• Conservation of Momentum:
• Orbital Speed of Star:

• For an observer at inclination i:
• 
• - k=amplitude
• - gives lower limit for

• Observables:
• 1.) Period -> a, knowing
• 2.) k -> = minimum mass of planet
• 3.) eccentricity from shape of time dep (skewed sine curve = e > 0)
• 4.) when i~, get true mass

• - stars form in molecular cloud cores
•      - most gas in solar system not molecular
•      - Scale: r~0.1 pc, M~M(sun) - a few M(sun)

• - Collapse time: (depends only on of cloud)(typically 3 - 5 Myr)
  
• - Specific Angular Momentum of Disk:
• 
• for a disk with scale and rotation speed :
• 
• Specific L at distance r from a protostar of mass :
• 
• - Characteristic Disk Size:
•      - even a very small rot. vel. on cloud core = gas formation
•      - disk MUCH bigger than star (unless binary)
•      - Binary: L of cloud core lost in L of orbiting binary
•      - B-fields slow down rot. as cloud collapses = nonexistent/small cloud

• - Once star and disk form:
•      - implies:
•      - L transport within disk
•      - OR L loss (wind)
•      - low loss = disks stable for (outlive collapse)

• - Class O:
•      - collapse and formation of protostar
•      - protostar shrouded by surrounding dust

• - Class I:
•      - star and disk have formed (possibly jet)
•      - continued in-fall (cloud & core still accreting)

• - Class II:
•      - star and disk only

• - Class III:
•      - disk has dispersed
•      - pre-main-sequence star
•      - weak-lined T-Tauri star

• - Disk Lifetime:
• 1.) Measure disk fraction in young stars
• 2.) Date stars in clusters
•      - usually

• - less than 10 Myr to form gas giants
• - final formation of terrestrial planets must have occured in a gas-free environment