Formations of Planetary Systems 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)

    Image Upload 1

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

    • Separating Planet from from Star:
    • - dust, atmosphere, telescope size, diffraction = limitations

    - Diffraction Limit:Image Upload 2 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
    • Image Upload 3

    • - 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 4

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

    • Observables:
    • - Depth of Transit  Image Upload 5
    • - Period of Orbit  Image Upload 6
    • - Stellar Parameters (a, Image Upload 7)
  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: Image Upload 8
    • Orbital Speed of Star: Image Upload 9

    • For an observer at inclination i:
    • Image Upload 10
    • - k=amplitude
    • - gives lower limit for Image Upload 11

    • Observables:
    • 1.) Period -> a, knowing Image Upload 12
    • 2.) k -> Image Upload 13 = minimum mass of planet
    • 3.) eccentricity from shape of time dep (skewed sine curve = e > 0)
    • 4.) when i~Image Upload 14, get true mass
  4. Protoplanetary Disk Structure
    1.) Radial Dist. of gas measured of col. dens. Image Upload 15(r)

    • 2.) Vertical Distribution (above/below plane)
    • - Image Upload 16<<Image Upload 17
    • - vert (z) dist set by hydrostatic equilibrium (pressure grad. vs. gravity --> balanced against each other)
    • -Pressure gradient in vertical (?), horizontal L is conserved

    Image Upload 18         Image Upload 19  Image Upload 20

    • When z<<d:
    • Image Upload 21

    Balance Against Pressure Gradient: Image Upload 22   (balance pressure and density)

    Image Upload 23 where Image Upload 24

    • Disk Thickness: Image Upload 25
    • Thickness depends on T via sounds speed


    Balance: Image Upload 26

    Image Upload 27       Image Upload 28       Image Upload 29

    • Density: Image Upload 30
    • 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: Image Upload 31
    • Image Upload 32     

    • Image Upload 33   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: Image Upload 34     Image Upload 35
    • - Collapse time only depends on density of cloud
    • Image Upload 36
    • - disk size>>star's radius
    • Image Upload 37
  7. Tides
    Perturber exerts force on body - creates two bulges

     Image Upload 38 = bulge closest to perturber

    Image Upload 39

    • Image Upload 40
    • tidal force is proportional to 1/a^3

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

    Image Upload 41

    • Distance where tidal gravitational force overwhelms self gravity of M1:
    • Image Upload 42

    • 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
    • Image Upload 43
    • - torque is also a tidal effect
    • Rate of change of L: Image Upload 44 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
    • - Image Upload 45 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: Image Upload 46

    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:
    • Image Upload 47
    • Need 30 - 50 Image Upload 48 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

    Image Upload 49 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:
    • Image Upload 50

    • Radiation leaving planet:
    • Image Upload 51

    • Incoming = Outgoing, so:
    • Image Upload 52

    • But must also account for Albedo:
    • Image Upload 53

    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:
    • Image Upload 54 --> Runaway GH
    • Image Upload 55
    • - ocean evaporates
    • - H2O vapor in atmosphere dissociates
    • - H2 vapor escapes

    • T > 340K at 1 atm --> Moist GH
    • Image Upload 56 @ 0.95 AU
    • - H2O in stratosphere = escape (of H2O)

    Venus: Image Upload 57

    - 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:
    • Image Upload 58
    • - Hill Radius depends on Image Upload 59 and is linearly dependent on a
    • - Annulus with Image Upload 60 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 Image Upload 61)

    Image Upload 62

    Image Upload 63

    • Miso higher in outer disk
    • LIMIT:
    • Image Upload 64 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: Image Upload 65
    • - 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 Image Upload 66

    • Image Upload 67
    • - Image Upload 68 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
    • Image Upload 69
    • - 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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253188
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Formations of Planetary Systems Final
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Astro Final
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