Formations of Planetary Systems Test 1

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  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 1
    • 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 2

    Image Upload 3


    Image Upload 4


    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 5
  5. MMSN Standard Form
    Image Upload 6


    Image Upload 7

    where Image Upload 8


    • - Most of the mass is in outer disk
    • - different Image Upload 9 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 10

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

    • Separating Planet from from Star:
    • - dust, atmosphere, telescope size, diffraction = limitations
    • - Diffraction Limit: Image Upload 11 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 12

    • - 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 13

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

    • Observables:
    • - Depth of Transit Image Upload 14

    - Period of Orbit Image Upload 15

    - Stellar Parameters (a, Image Upload 16)
  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 17
    • Orbital Speed of Star: Image Upload 18

    • For an observer at inclination i:
    • Image Upload 19
    • - k=amplitude
    • - gives lower limit for Image Upload 20

    • Observables:
    • 1.) Period -> a, knowing Image Upload 21
    • 2.) k -> Image Upload 22 = minimum mass of planet
    • 3.) eccentricity from shape of time dep (skewed sine curve = e > 0)
    • 4.) when i~Image Upload 23, 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 24 (depends only on Image Upload 25 of cloud)(typically 3 - 5 Myr)
    • - Specific Angular Momentum of Disk:
    • Image Upload 26
    • for a disk with scale Image Upload 27 and rotation speed Image Upload 28:
    • Image Upload 29
    • Specific L at distance r from a protostar of mass Image Upload 30:
    • Image Upload 31
    • - Characteristic Disk Size: Image Upload 32
    •      - 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 33
    •      - implies:
    •      - L transport within disk
    •      - OR L loss (wind)
    •      - low loss = disks stable for Image Upload 34 (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 35

    • - less than 10 Myr to form gas giants
    • - final formation of terrestrial planets must have occured in a gas-free environment
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Formations of Planetary Systems Test 1
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Formations and Dynamics of Planetary Systems Test 1
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