Formation of the Solar System and Extrasolar Planets

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How did the Solar System Form?We weren't there. We need a good theory. Check it against other forming solar systems. What must it explain?

- Solar system is very flat.

- Almost all moons and planets orbit and spin in the same direction. Orbits nearly circular.

- Planets are isolated in space.

- Terrestrial - Jovian distinction (esp. mass, density, composition).

- Leftover junk and its basic properties (comets, asteroids, TNOs).

Not the details and oddities – such as Venus’ and Uranus’ retrograde spin. 2

General theory – the Nebular Model• Idea goes back to Descartes (1664), then Kant and LaPlace in late

18th century.

• Interstellar cloud of dust and gas

• Slow rotation, original quasi-spherical shape

• Gravitational collapse, dissipation into a plane due to conservation of angular momentum

• Differing temperature environments

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A cold, relatively dense cloud of interstellar molecular gas

The associated dust blocks starlight. Composition mostly H, He.

a few pc,or about 10,000times bigger thanSolar System

Collisions cause rotational transitions in molecules – emission lines at mm wavelengths. From Doppler shifts, clouds rotate at a few km/s.

Some clumps within clouds collapse under their own weight to form stars or clusters of stars. Clumps spin at about 1 km/s.

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Conservation of Angular Momentum

where L is angular momentum, I is moment of inertia, and Ω isangular rotation rate = 2πν = 2π/P.

For uniform density sphere,

In general

L is conserved if object contracts. R decreases, so Ω increases.

(For orbiting object, is conserved.)

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2MRI

For an isolated spinning object:

2MRL

2MRL

So how can you get a flat, rapidly rotating Solar System?

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L=IΩ

Clump within cloud starts collapsing under its own gravity. It’s pressure cannot support it.

Clump within cloud starts collapsing under its own gravity. It’s pressure cannot support it.

It spins more rapidly as it collapses (conservation of angular momentum). Gravity strong enough at center – forming star is spherical. But rest flattens into a disk.

It spins more rapidly as it collapses (conservation of angular momentum). Gravity strong enough at center – forming star is spherical. But rest flattens into a disk.

We observe these now in star forming regions, using the Hubble.We observe these now in star forming regions, using the Hubble.

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How does the nebular model explain planets and “debris”?

• Solar Nebula composed of 71% H (by mass), 27% He, traces of heavier elements in gas, and dust grains (only about 2% of mass).

• After collapse, now so dense that solid material can grow by collisions and accretion. In warm inner nebula, growth of dust grains.

• Further from Sun, ice mantles on dust grains form readily. Lots of gas to make ice from => much more solid material. But most matter still gas.

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Condensation temperatureTemp (K) Elements Condensate

>2000 K All elements gaseous

1600 K Al, Ti, Ca Mineral oxides

1400 K Fe, Ni Metallic grains

1300 K Si Silicate grains

300 K C Carbonaceous grains

300-100 K H, N Ices (H2O, CO2, NH3, CH4)

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The “snow line"

• Rock and metals forms where T<1300 K

• Ices form where T<170 K

• Inner Solar System is too hot for ices

• In the Outer Solar System ices form beyond the "snow line"

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Temperature distribution in Solar Nebula at time offormation of the planets

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Snow line

The planets formed by the collision and sticking of solid particles, leading to km-scale planetesimals (few 106 yrs). Collisions of planetesimals enhanced by gravity, growth of proto-planets. Larger ones grew faster – end result is a few large ones.

Grains => planetesimals => protoplanets

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Observations of disk around young star with Hubble and ALMA, showing ring structure. Presumably unseen planets sweeping out gaps.

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Terrestrial planets• Only rocky planetesimals inside the frost line• Energy of collisions heats growing protoplanets. Along

with heat from radioactivity, they become molten • Hotter close to the Sun, and lower gravity protoplanets

=> they cannot capture H, He gas and retain thick atmosphere.

• Solar wind also dispersing nebula from the inside, removing H & He

=> Rocky terrestrial planets with few ices

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Jovian planets• Addition of ices increases masses of grains - large proto-

planets of rock and ice result (few to 15 MEarth)

• Larger masses & colder temps: can accrete and retain H & He gas from the solar nebula

Form large Jovian planets with massive cores of rock and ice and heavy H, He atmospheres

• Alternative: formed directly and rapidly by gravitational collapse in disk. Denser material sunk to center. Should take 100’s to 1000’s of years only!

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Moons & AsteroidsSome gas attracted to proto-Jovians formed disks:• “Mini solar nebula” around Jovians• Rocky/icy moons form in these disks (later, more detail

on four Galilean moons of Jupiter as mini “solar” system)• Later moons added by asteroid/comet capture

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Planetary MigrationEssentially friction with remaining gas and dust may havecaused Jovian planets to migrate. Gravitationalinteractions with each other and smaller objects may haveled to exchanges of energy, causing inward or outward migration.

Early Migration

Thought that in first few 100,000 years, Jupiter migrated inwardto 1.5 AU, scattering planetesimals that would have made a largerMars. Then migrated outward, deflecting planetesimals inwardto form Asteroid Belt. Explains why some asteroids are icy.

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Planetary MigrationLate Migration

All Jovians thought to have formed within 20 AU, in order to have enough accreting material. Generally migrated outward due to gravitational interactions with planetesimals over few 108 yrs. Possible that Neptune initially closer to Sun than Uranus, and they switched via an interaction.

Deflection of planetesimals by Jupiter created the large Oort cloud.

Neptune’s outward migration flung out planetesimals to create the TNOs. Also some flung inward to explain “Late Heavy Bombardment” of Terrestrial planets and Moon.

“Nice model”

Icy bodies and comets• Leftover bodies from planet building in Jovian planet

zone. Hence more icy than asteroids.

• Oort Cloud and TNOs are sources of comets. For example, a TNO may encounter Neptune and get sent into inner Solar System, where they start to evaporate, grow a tail, and appear as comets.

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What evidence do we have for the Nebular model?

• Theory is reasonable, but needs to make predictions to compare with observations. Saw some evidence from other forming systems.

• But what about other formed planetary systems?

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Extrasolar Planets

• Test solar system formation process• Possibility of life on other planets

Techniques:• Direct detection (images)• Transit of star by planet• Detection of star’s wobble by spectroscopy• Detection of star’s wobble by imaging• Microlensing

20About 2000 found by Fall 2015 See exoplanet.eu

Idea: a planet and its star both orbit around their common center of mass, staying on opposite sides of this point.

Detecting a star’s wobble

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The massive star is closer to center of mass, and moves more slowly than the planet, but it does move!

Example: ignore planets other than Jupiter. Then Sun and Jupiter orbit their common center of mass every 11.86 years. Jupiter’s orbit has semi-major axis of 7.78 x 108 km, while Sun’s semi-major axis is 742,000 km.

(Compare to Sun’s radius of 696,000 km).

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A wobbling star might be seen by careful observations of its position, called “astrometry”:

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No confirmeddetections this way

More successful method: Use the Doppler shift of star’s spectral lines due to its radial (= back and forth) motion:

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Over 600 foundthis way by Fall 2015

Calculate orbital speed of Sun, assuming Jupiter is only planet:

Moves in nearly circular orbit of radius 742,000 km

How much Doppler shift? Consider H-alpha absorption line, at rest wavelength 656 nm:

This is tiny!

V 2rP

2 (742,000 km)

11.86 years12.5 m/s

V

c0

12.5 m/s

3108 m/s656 nm 2.7 10 5 nm

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51 Pegasi

• Mayor & Quelozat Geneva

Observatory saw observed wobble in star 51Peg in 1995

• Sun-like star ~40 ly distance

• Wobble was 53 m/s, period 4.15 days• Implied a planet with 0.5 Jupiter mass orbiting at

0.05 AU!• First planet found around sun-like star 26

Selection effects• Doppler wobble biased towards massive planets close

to their star (leads to larger velocities and shorter periods). But now detecting Earth-mass planets!

• Inclination of binary orbit unknown (unless transits observed). More likely to be close to edge-on for detection. If not, wobble is larger than measured and so is planet.

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Second technique: detect eclipse of planet. Over 1200 found.

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Kepler mission. Launched March 2009. Several years of data – still being analyzed. Detected eclipses. Yields only radii, not masses.

Third technique: direct imaging of planet.59 found by July 2015.

HR 8799

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Fourth technique: Gravitational microlensing

• If two stars line up, one near and one far, the light from the background star will bend around the foreground star (due to gravity)

• A planet around the foreground star will cause an intense amplification if passing close to the line of sight

• 37 thus detected as of July 2015

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Earth Jupiter

1 Jupiter Mass

10 Jupiter Masses

Most planets found are more massive than Jupiter – many are closer tostar than 1 AU (“hot Jupiters”)! Did they form there or migrate there?

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Most planets have eccentric orbits. Circular might be better for life!

0.01 0.1 1(Earth)35

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Habitable planets

Habitable Exoplanets Catalog

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From statistics of detections, we estimate about 20% of Sun-like stars have habitable planet near Earth-size (1-2 Earth radii)!

Most are probably around the most common kind of star, red dwarf (M class) stars.

Since red dwarfs are dim, planets have small orbits to be in Habitable Zone. Leads to strong tidal forces. Planets probably “tidally locked” to their stars like our Moon. Could make life less likely.

Habitable planets

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Next NASA Mission – TESS (Transiting Exoplanet Survey Satellite)

• Like Kepler, but all-sky• 3 year mission• Launch ready Aug 2017• >500,000 of the nearest and brightest stars, making follow-

up ground-based and JWST observations easier than Kepler• Should find >3000 exoplanets, include 500 Earth-size or

“Super-Earths”

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For a little fun, see:

http://tauceti.sfsu.edu/~chris/SIM/

http://vo.obspm.fr/exoplanetes/encyclo/catalog.php

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Problem 5.31

• The bright star Sirius in the constellation of Canis Major has a radius of 1.67 Rsolar, and a luminosity of 25 Lsolar.

• Use this information to calculate the energy flux at the surface of Sirius.

• Use your answer in part a) to calculate the surface temperature of Sirius.

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Atmosphere composition• 78% N2, 21% O2, 1% everything else

• Initial atmosphere had more H, CH4, NH3

• Composition depends on – Original formation (what gases were trapped)

– Chemical processes (including life)

– Escape speed

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Molecular weights

Hydrogen 2

Helium 4

Methane 16

Ammonia 17

Water 18

Neon 20

Nitrogen 28

Oxygen 32

Argon 40

CO2 44

Air: 29 (Ar, CO2, Ne, He and other rare gases).

Early atmosphere: CO2, steam, NH3 and CH4 (volcanoes). No oxygen.

Steam condensed to water => seas

Photosynthesis: CO2 and H2O to O2. NH3 and CH4 reacted with O2.

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Problem 7.24

a) Find the mass of a hypothetical spherical asteroid 2 km in diameter and composed of rock with average density 2500 kg m-3.

b) Find the speed required to escape from the surface of this asteroid.

c) A typical jogging speed is 3 m/s. What would happen to an astronaut who decided to go for a jog on this asteroid?

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