Formations of Planetary Systems Final

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DrGirlfriend
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253188
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Formations of Planetary Systems Final
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2013-12-15 21:41:57
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Astronomy Planetary Dynamics Final
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Astronomy
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Astro Final
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  1. Direct Imaging
    • - 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)
  2. Transits
    • - 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, )
  3. 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:
    • 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
  4. Protoplanetary Disk Structure
    1.) Radial Dist. of gas measured of col. dens. (r)

    • 2.) Vertical Distribution (above/below plane)
    • - <<
    • - vert (z) dist set by hydrostatic equilibrium (pressure grad. vs. gravity --> balanced against each other)
    • -Pressure gradient in vertical (?), horizontal L is conserved

              

    • When z<<d:

    Balance Against Pressure Gradient:    (balance pressure and density)

    where

    • Disk Thickness:
    • Thickness depends on T via sounds speed


    Balance:

                 

    • Density:
    • very low in disk, aero forces negligible
  5. What Sets Temp?
    • 1.) Stellar Irradiation
    • - Flat disk absorbs 1/4 stellar irrad.
    • - flared disk absorbs more

    2.) Potential E due to accretion

    • Accretion Rate onto Star:
    •      

    •    only 1/2 of E -->heat, other 1/2 --> KE
    • - moves faster as it gets closer
    • - late stages: irradiation dominates
  6. Protoplanetary Disk
    • Stars form in mlclr cloud cores
    • - most gas in solar system mlclr
    • - Scale:     
    • - Collapse time only depends on density of cloud
    • - disk size>>star's radius
  7. Tides
    Perturber exerts force on body - creates two bulges

      = bulge closest to perturber



    • tidal force is proportional to 1/a^3

    Tidal Disruption: how close can body get before tides disrupt the planet?



    • Distance where tidal gravitational force overwhelms self gravity of M1:

    • Tidal Bulges:
    • 1.) Static Situation
    • - planet not rotating
    • - fluid planet, adjusts to hydrostatic equilibrium
    • - symmetry about line joining centers of bodies = no uneven forces
    • - no torque on planet
    • - when perturber orbits, planet takes time to respond to changing grav. (bulge lags)

    • 2.) Rotating Planet = gravitational torque
    • - each bulge exerts gravitational force on moon

    • When Rotation of planet < Orbital P of moon --> bulge lags
    • - lagging bulge exerts backward force on moon --> moon slows down, spirals in
    • - tidal lag --> torque on moon --> orbital decay
    • - torque on planet --> rotation rate increases
    • - torque is also a tidal effect
    • Rate of change of L: very rapid fall-off

    • When Rotation of planet > orbital P of moon --> bulge leads
    • - tides lead to increase in L of moon = recession of moon = decrease in planet's rotation
    • - bulge exerts forward force on moon, accelerating it, causing it to move outward, which causes rotation of planet to decrease


    • Tides are more complex than this because:
    • - solar and lunar tides
    • - tides have different periods due to orbital motion of moon
  8. Puzzles of Outer Solar System Evolution

    Possible solutions to puzzels
    • 2 Puzzles
    • 1.) Pluto
    • - 3:2 resonance with Neptune
    • - pericenter within Neptune's orbit
    • 2.) Predicted formation timescale of Neptune too large
    • - too large
    • - so, if bodies come close to Neptune, they get a big boost in velocity
    • - Neptune stirs up bodies in its vicinity
    • - evidence that outer solar system has evolved

    • Possible Solutions:
    • - Planetesimal Scattering
    • - Resonant Capture
    • - Nice Model
  9. Planetesimal Scattering
    Planet and closely orbiting planetesimal disrupt each other's orbits

    • 1.) Planet scatters planetesimal from outer orbit onto interior orbit
    • - m's L increases, moves in
    • - M's L decreases, moves out

    • 2.) Planet scatters m from interior orbit to exterior
    • - m's L increases, moves out
    • - M's L decreases, moves in

    Expect change in orbit:

    If there's an equal abundance of planetesimals on inner orbit and outer orbit --> no change in M's orbit

    • Apply to Solar System:
    • Planetesimal in outer solar system scattered by Neptune --> m moves in, N moves out
    • m then scattered by U --> U moves out, m moves in
    • ... so on, to J... J ejects m, J moves in

    • - m altered planet's orbits
    • - ejection process = formation of KB

    • For significant orbital evolution:
    • Need 30 - 50 to move Neptune
  10. Resonant Capture
    • Two planets on converging orbits captured into mean motion resonance if migration is slow enough
    • Once in resonance --> eccentricities increase

    valid for j : j+1 resonance

    Supported by discovery of KBO's with same orbital properties as Pluto and also 2:1 resonance

    --> Neptune moved out during early solar system evolution
  11. Nice Model
    Extension of other theories

    • "Proposes migration of giant planets from an initial compact configutation to their present positions."
    • - happened after dissipation of proto gas disk

    • Saturn crossed 2:1 resonance with Jupiter
    • - res. crossing --> eccentricity of outer planets --> sudden depletion of outer planetesimal belt due to scattering
    • - cause of late heavy bombardment on moon ~7Myrs after solar system formed
    • - eccentricities of planets suggest they started close together

    • Supports:
    • - late heavy bombardment
    • - oort cloud formation
    • - existence of small bodies in solar system
    • - Nep/Jup torjans
    • - numerous resonant trans Nep objects
    • Limits:
    • - can't reproduce KB in sims?
  12. Factors of Habitability
    • atmosphere (composition, density, etc...)
    • liquid H2O / Temperature / rotation rate
    • magnetic fields (to keep H2O from escaping)
    • gravity (techtonics, high M = no tech, low m = no atmosphere)
    • location in galaxy (plances with high numner of SN? older stars, newer stars, and metallicity)
    • Moon (Planet's stability, tides)
    • Planet's composition
  13. Estimating Surface Temperature of Planet (naive version)
    • Radiation striking planet:

    • Radiation leaving planet:

    • Incoming = Outgoing, so:

    • But must also account for Albedo:

    In reality, GHG's (like H20) in atmosphere absorb IR light --> GH Effect (higher surface Temp)
  14. Habitable Zone
    Range of orbital separation for which a planet can sustain liquid H2O on its surface

    • Inner Edge:
    • --> Runaway GH
    • - ocean evaporates
    • - H2O vapor in atmosphere dissociates
    • - H2 vapor escapes

    • T > 340K at 1 atm --> Moist GH
    • @ 0.95 AU
    • - H2O in stratosphere = escape (of H2O)

    Venus:

    - Seff is ratio of flux hitting upper atmosphere compared to that of Earth

    • Outer Edge:
    • Assumption: substantial amount of Carbon in rocks, volcanism releases Carbon into atmosphere, CO2 builds up but is reduced by weathering processes and sediments deposited on sea floor (which is slower with less rain)
    • - Outer edge defined by "maximum greenhouse"
    • - Warming by CO2 maximal
    • - Higher CO2 --> less warming b/c higher albedo

    • Mars:
    • Seff = 0.36 @ 1.67 AU
    • Seff = 0.32 @ 1.77 AU

    Puzzle: Sun expected to be fainter in pas --> habitable zone closer to sun
  15. Stability
    Planets orbiting star --> How close can they be and still be stable?

    • RH = radius of influence that a planet has in disk:
    • - Hill Radius depends on and is linearly dependent on a
    • - Annulus with within which planet perterbation > stellar radial grav
    • - large RH = stable
  16. Terrestrial Planet Formation
    • 1.) Dust coalesces, forms planetesimals
    • 2.) Direct collisions of planetesimals --> grav focusing when m is large enough
    • - runaway growth phase: a few grow rapidly, leaving behind many small bodies
    • 3.) Runaway --> large bodies that stir up surroundings --> oligarchic growth (smaller than runaway)
    • 4.) Final Assembly
    • - 100 Myrs or more
    • - more collisions = more evolution
    • - giant planets perturb orbits of smaller planets = crossing orbits
    • - final body varies depending on existence/nonexistence of giant planets and surface density
  17. Giant Planet Formation
    Core Accretion
    • - Planets have 5 - 10 Mearth cores
    • - Hydrostatic Phase (core + "small" envelope)
    • - Runaway accretion phase takes ~M yrs

    • 1.) Core Formation (accretion/collisions)
    • 2.) Core + Significant gas envelope in hydrostable balance
    • 3.) Exceed core mass, runaway gas accretion

    • 1.) Core Formation:
    • Isolation Mass - mass at which growing planet has consumed all of its nearby planetesimal supply (mass can be found through )





    • Miso higher in outer disk
    • LIMIT:
    • increases with a
    • - prevents rapid growth of M>Mearth cores beyond critical distance (20 AU)
    • - why there are small bodies in KB

    • 2.)Envelope Accretion (atmosphere)
    • - depends on ratio:
    • - If cs>vesc, atmosphere is unbound "hydrodynamic unbound" (which requires low m, m<0.1Mearth..... currently, giant planet envelope accretion requires a few Mearth core in Jupiter region)

    • Critical Core Mass: max m of gas envelope that exists in hydrostatic equilibrium
    • - envelope unstable to collapse when Menv>Mcore
    • - once core reaches critical mass, hydrostatic equilibrium no longer possible, phase of rapid gas accretion occurs
    • Problems: planetesimals may move inward very quickly when they reach a certain mass, so the core would probably migrate inwards too
    • J's upper limit core mass < mcore theorized
  18. Gas Giant Formation
    Gravitational Collapse/Gravitational Instability
    • - Requires disk to have high mass and early formation
    • - Produces massive planets/brown dwarfs
    • - No initial core


    • Gas disk unstable to fragmentation, gas disk collapses
    • - solids play no role, possible far out
    • Depends on Q parameter
    • - unstable if

    • - is ang. velocity
    • - Q is unitless
    • - csOmega opposes collapse
    • - piGSigma is gravity
  19. Hot Jupiters
    • Giants planets @ a<~0.1 AU (really close to star) on nearly circular orbits b/c of tidal effects
    • PUZZLE: no solids at 0.1 AU --> how'd they form?
    • - MIGRATION
    • - form planets at larger radii, lose L and migrate in
    • Possible reasons for migration:
    • - interactions with gas disk (small particles gain L and move out, planet loses L and moves in)
    • - planet-planet interactions due to highly eccentric orbits
    • - binary stars
    • - interactions with small bodies

    • Formation:
    • 1.) Core accretion = planet formation
    • 2.) Open gap (gas in exterior orbit gains L, moves out; gas in interior orbit loses L, moves in -->planet "repels" gas)
    • 3.) disk evolves, planet spirals towards star b/c of gravitational torque from gas

    • KNOWN: Gas giants form where gas is present (so interactions MUST take place)
    • UNKNOWN: Unclear how to stop migration, Unclear how to make orbits inclined, gas in outer disk can't accrete on planet unless planet also moves inwards (?)
  20. Dynamical Routes for Forming Hot Jupiters
    • 1.) Planet-Planet Scattering
    • - must form unstable system of mult. planets, until orbits cross = close encounters = ejections and eccentric orbits
    • - for tides to matter: a<0.1 AU (tides can circularize orbit)
    • - Get enough planets with high eccentricities if there's a large reservoir of unstable systems at a few AU (unstable = close together/small RHill)

    • 2.) Secular Chaos
    • - No close encounters
    • - Angular Momentum Deficit
    • - when i = 0, e = 0, AMD = 0
    • - when e = 0, i = 0, AMD depends on ek
    • - circular orbit = most L (AMD measures how noncircular orbit is)

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