phil armitage, university of colorado
Post on 06-Dec-2021
1 Views
Preview:
TRANSCRIPT
XIII Ciclo de Cursos Especiais
Planet FormationPlanet FormationPhil Armitage, University of Colorado
XIII Ciclo de Cursos Especiais
How doplanetsform?
Theory
Solar Systemobservations
Extrasolar planetobservations
Initial conditions?
Very detailed:only one system
Many systems:limited individualinformation
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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!
XIII Ciclo de Cursos Especiais
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)
XIII Ciclo de Cursos Especiais
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…
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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…
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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)
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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…
XIII Ciclo de Cursos Especiais
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”?
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
Imaging planets would allow measurement of atmosphericspectra - biomarkers such as oxygen / ozone…
Tinetti et al. (2006)
XIII Ciclo de Cursos Especiais
Tinnetti et al. (2006)Future goal: NASA’sTerrestrial Planet Finder / ESA’s Darwin proposals
All detections of extrasolar planetsto date are viaindirect methods
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
!
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…
XIII Ciclo de Cursos Especiais
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)
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
!
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…
XIII Ciclo de Cursos Especiais
Example of real data, measure:
• orbital period• MP sin i (with stellar mass)• orbital eccentricity e
…all that is known formost extrasolar planets
XIII Ciclo de Cursos Especiais
Multiple planet system
Interesting degeneracies and statistical questions concerningsurvey biases - be careful!
XIII Ciclo de Cursos Especiais
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…
XIII Ciclo de Cursos Especiais
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%)
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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
XIII Ciclo de Cursos Especiais
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)?
XIII Ciclo de Cursos Especiais
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?
top related