Formations of Planetary Systems Test 1

  1. What is so special about the Solar System?
    • - Sun has no companion
    • - Planets are non-resonate (resonance observed in other star systems)
    • - Packed (no space to add extra planets)
  2. Properties of the Solar System
    • 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
    • Image Upload 2
    • 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)
  3. Angular Momentum
    Image Upload 4

    Image Upload 6


    Image Upload 8


    Dominated by planets
  4. Minimum Mass Solar Nebula Procedure
    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.) Image Upload 10
  5. MMSN Standard Form
    Image Upload 12


    Image Upload 14

    where Image Upload 16


    • - Most of the mass is in outer disk
    • - different Image Upload 18 for each planet
  6. Detection Techniques
    • - Doppler shifts
    • - Transits
    • - Microlensing
    • - Direct imaging
    • - Astrometry
    • - Pulsar timing
  7. Direct Imaging
    • - gives info about composition
    • - resolve light from planet as separate source (fraction of starlight reflected by planet)

    Image Upload 20

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

    • Separating Planet from from Star:
    • - dust, atmosphere, telescope size, diffraction = limitations
    • - Diffraction Limit: Image Upload 22 D = diam of tele

    - light that planet absorbs is re-radiated as Thermal radiation (T~300K for Earth)
  8. Transits
    - drop in stellar flux is observed Image Upload 24

    • - 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:
    • Image Upload 26

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

    • Observables:
    • - Depth of Transit Image Upload 28

    - Period of Orbit Image Upload 30

    - Stellar Parameters (a, Image Upload 32)
  9. Radial Velocity (Doppler Shifts)
    • - 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: Image Upload 34
    • Orbital Speed of Star: Image Upload 36

    • For an observer at inclination i:
    • Image Upload 38
    • - k=amplitude
    • - gives lower limit for Image Upload 40

    • Observables:
    • 1.) Period -> a, knowing Image Upload 42
    • 2.) k -> Image Upload 44 = minimum mass of planet
    • 3.) eccentricity from shape of time dep (skewed sine curve = e > 0)
    • 4.) when i~Image Upload 46, get true mass
  10. Protoplanetary Disks
    • - 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: Image Upload 48 (depends only on Image Upload 50 of cloud)(typically 3 - 5 Myr)
    • - Specific Angular Momentum of Disk:
    • Image Upload 52
    • for a disk with scale Image Upload 54 and rotation speed Image Upload 56:
    • Image Upload 58
    • Specific L at distance r from a protostar of mass Image Upload 60:
    • Image Upload 62
    • - Characteristic Disk Size: Image Upload 64
    •      - 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: Image Upload 66
    •      - implies:
    •      - L transport within disk
    •      - OR L loss (wind)
    •      - low loss = disks stable for Image Upload 68 (outlive collapse)
  11. Star Formation
    • - 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 Image Upload 70

    • - less than 10 Myr to form gas giants
    • - final formation of terrestrial planets must have occured in a gas-free environment
Author
DrGirlfriend
ID
238907
Card Set
Formations of Planetary Systems Test 1
Description
Formations and Dynamics of Planetary Systems Test 1
Updated