Phil Armitage, University of Colorado

XIII Ciclo de Cursos Especiais

Planet FormationPlanet FormationPhil Armitage, University of Colorado


How doplanetsform?

Theory

Solar Systemobservations

Extrasolar planetobservations

Initial conditions?

Very detailed:only one system

Many systems:limited individualinformation


Historically: observation that the planets orbit the Sunin (approximately) the same orbital plane

Nebula Hypothesis: planets formed from arotating disk of gas and dust orbiting the proto-Sun (Kant, Laplace in the 18th century)

…fundamentally correct concept

Quantitatively:Terrestrial planet formation: Victor Safronov - “Evolutionof the Protoplanetary Cloud and Formation of the Earth and the Planets” (1969)

Giant planet formation: Hiroshi Mizuno (~1980) buildingon many earlier ideas


New developments

1. Observations of protoplanetary disks (initial conditions)

2. Discovery of the Solar System’s Kuiper Belt

3. Discovery of extrasolar planetary systems

…partially confirm earlier ideas, but also pointto the unexpected importance of planetary systemevolution and reveal a great diversity of planetary systems


Outline

1. Observations of planetary systems2. Protoplanetary disks3. Formation of planetesimals (km-scale bodies)4. Formation of terrestrial and giant planets5. Evolution and stability of planetary systems

Today: mostly introductoryGenerally, mix of basic ideas + open questions

Feel free to ask questions at any time!


Solar System Observations

Terrestrial planets

Low mass (up to 1 Earth mass = 6 x 1027 g), mostly rockyobjects.

Found in the inner Solar System (Mercury 0.39 AU, Mars 1.52 AU)


Giant planets - found only in the outer Solar System

Gas giants: primarily gaseous objects but notmade of the same composition as the Sun…enriched in heavy elements

Jupiter: ~10-3 Msun, ~300 MEarth

Ice giants: ~10 Mearth of rock and ice, plus large(several Earth masses) contributions from gas

2 (or maybe 3) classes of planet that need to be explained…


Tristan Guillot

Comparison of the multipolesof gravity field (J2 - J6) withinternal structure models

High density EOS for H /He (c.f. Militzer & Hubbard 2008 work)

Could do much better on the observations:JUNO mission


Integrated properties

Mass: planets are ~0.2% of the mass of the Sun

Sun is ~2% “metals” (not H / He) - most of theheavier elements are also in the Sun… planetformation need not be 100% efficient

Angular momentum:

Jupiter’s orbit

!

LJ

= MJGM

sunaJ" 2 #1050 g cm2s-1

Solar rotation

!

Lsun

= k2M

sunRsun

2"

sun~ 3#10

48 g cm

2 s

-1

..segregation of mass from angular momentum during the formation of the Solar System


Minimum mass Solar Nebula

How much mass was needed to form the planets?

1. Take mass of heavy elements in each planet2. Augment the mass with enough H / He to restore

Solar composition3. Spread the mass into an annulus around each orbit

Jupiter’s orbit

spread Jupiter’s augmentedmass (~3 x real mass) across this annulus toyield a surface density


Minimum mass Solar Nebula(Weidenschilling 1977)

!

"gas(r) =1.7 #103 r

1 AU

$

% &

'

( )

*3 2

g cm-2

Integrated mass out to30 AU = 0.01 Msun

Comparable to the massesof disks measured aroundother stars

BUT… this is at best a lower limit - could have been moregas / could have been a different radial profile…


Minor bodies in the Solar SystemAsteroids, Kuiper Belt objects, comets…

Dynamical clues as tothe early evolution of the Solar System

Most stable orbitsin the Solar Systemare populated withminor bodies


a

!

rperi = a(1" e)

rapo = a(1+ e)

Distribution of Kuiper Belt Objects beyond Neptune:

1. Population in 3:2 resonance with Neptune

!

P1

P2

=i

j…with i, j integers. “Plutinos”, includePluto itself. Who ordered that!?

2. Apparent edge at ~47 AU (not just selection function)


The puzzle of Earth’s water…

Liquid water is stable on the Earth today because the temperature at atmospheric pressure is 0 C < T < 100 C


BUT - when minerals that later formed the Earth condensed, pressure in the disk was very low. Water would be vapor, would not form water-rich rocks…


Chemical evidence:

Ratio of deuterium to hydrogen:

Earth’s water: 153 parts per millionMeteorites known as carbonaceous chondrites: 159 ppmComets: 309 ppm

These meteorites appear to originatefrom the outer asteroid belt (beyondabout 2.7 AU)

Evidence for radial transport - massdynamically negligible but critical for life

How common is water on planets in the “habitable zone”?


Extrasolar Planets

Difficult to directly image extrasolar planets

Contrast ratio in reflected light:

!

f ="Rp

2

4"a2#

$ %

&

' ( A ~ 1.4 )10*10 …for Earth

Astronomical units: 24-25 magnitudes

Contrast at the peak of the planet’s thermal emission isless: about f ~ 10-6 at 20 µm for the Earth


Imaging planets would allow measurement of atmosphericspectra - biomarkers such as oxygen / ozone…

Tinetti et al. (2006)


Tinnetti et al. (2006)Future goal: NASA’sTerrestrial Planet Finder / ESA’s Darwin proposals

All detections of extrasolar planetsto date are viaindirect methods


Radial velocity searches

Observable: time dependentradial velocity of star (viaDoppler shift of spectral lines), due to perturbationfrom orbiting planet

For planet on circular orbit:

!

vK

=GM

*

a

Linear momentum conservation:

!

M*v*

= MpvK

Observable:

!

K = v*sini =

Mp

M*

GM*

asini


!

K = v*sini =

Mp

M*

GM*

asini

Observable quantity:best precision is ~ m s-1

Massive planets areeasier to detect

Planets at small aeasier to detect

Usually unknown:derive lower limiton mass

Jupiter: 12.5 m s-1

Earth: 9 cm s-1very challenging observationally,but achievable…


High resolution astronomical spectrographs: R ~ 105 (3 km s-1)

How can we detect m s-1 shifts? Consider limit to radialvelocity measurement from a single pixel, assuming perfectcalibration:

!

"Nph =dNph

dv"v#"v

min$

Nph

1 2

dNph /dv

Can detect small RV shift if (a) high S/N and (b) spectrum has plenty of structure (limited by thermal broadening)


Estimate S/N = 100, thermal broadening means lines havewidth of ~10 km s-1

Then spectrum with Npix “effective” pixels yields an RVmeasurement that could be as good as:

!

"vshot ~100 m s

-1

Npix

1 2

Can measure very small RV shifts against shot noise ifcalibration is stable - need only resolve the lines…

Actual noise sources include:• stellar activity• stellar oscillations (the signal for helioseismology)

Sub-m s-1 very challenging


!

K = v*sini =

Mp

M*

GM*

asini

If a survey could detect K > Kmin for some sample of stars:

Detectable

Undetectable

P = Psurvey

log

Mp

sin

i

log a

In fact no survey is anything like this simple…but basic selection function is of this form withKmin ~ 20 m s-1 for complete samples…


Example of real data, measure:

• orbital period• MP sin i (with stellar mass)• orbital eccentricity e

…all that is known formost extrasolar planets


Multiple planet system

Interesting degeneracies and statistical questions concerningsurvey biases - be careful!


Results #1: eccentricity vs semi-major axis


Results #2: mass vs semi-major axis


Results #3: eccentricity vs mass


Summary of radial velocity findings

1. Planet frequency among “Solar type” stars is at least 7%

2. “Hot Jupiters” - massive planets at a < 0.1 AU

3. Typical planet is eccentric: <e> = 0.27#2, #3 are different from Solar System expectations

4. Mass function favors low mass planets, radial distributionincreases to large orbital radius

Note: only very limited informationon planet population with M and asimilar to that of Jupiter…


Fischer & Valenti (2005)

Abundance of (detected) planets is a strongly increasingfunction of the metallicity of the host star measured fromthe spectrum Giant planet formation process “knows” about the traceabundance of heavy elements (~1-2%)


Transits

Detection of planet viaphotometric monitoringof host star

!

f =Rp

R*

"

# $

%

& '

2

( 0.01 (Jupiter)

= 8.4 )10*5 (Earth)

Fractional decrementduring transit

OK from ground

space only

Probability of observing a transit

!

Ptransit =R*

+ Rp

a

About 10% for hotJupiters, 0.5% forEarth in Earth’s orbit


Ground based data quality(TrES project)


Space based data quality (COROT mission results)

Giant planets: direct measurement of planetary radius- confirms that these are gas giant planets- limited information on structure

Terrestrial planets: Kepler mission should be sensitive toplanets with Earth radius


Also possible to observe the secondary eclipse / phase modulation in the infra-red (Spitzer):

Harrington et al. (2006)

Measure of temperatureon the day / night sideof the planet


Torres et al. (2008)

A radius mystery

Measured Rp are not a one parameter family withplanet mass

What is the additional physics at work in settingthe radius?

• planetary structure?• dynamics (heating

due to tides)?


What we need to explain

How do terrestrial and gas giant planets form?

How can we understand their orbits:

• in the Solar System?• in extrasolar planetary systems?

Hope is that this will inform questions such as:

• how typical is the Solar System?• how common are habitable planets?

Phil Armitage, University of Colorado

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