Download Planet Formation

Planet Formation
Phil Armitage, University of Colorado
XIII Ciclo de Cursos Especiais
Theory
Initial conditions?
Very detailed:
only one system
Solar System
observations
How do
planets
form?
Many systems:
limited individual
information
Extrasolar planet
observations
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Historically: observation that the planets orbit the Sun
in (approximately) the same orbital plane
Nebula Hypothesis: planets formed from a
rotating disk of gas and dust orbiting the
proto-Sun (Kant, Laplace in the 18th century)
…fundamentally correct concept
Quantitatively:
Terrestrial planet formation: Victor Safronov - “Evolution
of the Protoplanetary Cloud and Formation of the Earth
and the Planets” (1969)
Giant planet formation: Hiroshi Mizuno (~1980) building
on many earlier ideas
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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 point
to the unexpected importance of planetary system
evolution and reveal a great diversity of planetary
systems
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Outline
1.
2.
3.
4.
5.
Observations of planetary systems
Protoplanetary disks
Formation of planetesimals (km-scale bodies)
Formation of terrestrial and giant planets
Evolution and stability of planetary systems
Today: mostly introductory
Generally, mix of basic ideas + open questions
Feel free to ask questions at any time!
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Solar System Observations
Terrestrial planets
Low mass (up to 1 Earth mass = 6 x 1027 g), mostly rocky
objects.
Found in the inner Solar System (Mercury 0.39 AU,
Mars 1.52 AU)
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Giant planets - found only in the outer Solar System
Gas giants: primarily gaseous objects but not
made 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…
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Comparison of the multipoles
of gravity field (J2 - J6) with
internal structure models
High density EOS for H /
He (c.f. Militzer & Hubbard
2008 work)
Could do much better
on the observations:
JUNO mission
Tristan Guillot
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Integrated properties
Mass: planets are ~0.2% of the mass of the Sun
Sun is ~2% “metals” (not H / He) - most of the
heavier elements are also in the Sun… planet
formation need not be 100% efficient
Angular momentum:
50
2 -1
Jupiter’s orbit LJ = M J GM sun aJ " 2 #10 g cm s
2
Solar rotation Lsun = k 2 M sun Rsun
"sun ~ 3 #10 48 g cm2 s-1
!
..segregation
of mass from angular momentum
during the formation of the Solar System
!
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Minimum mass Solar Nebula
How much mass was needed to form the planets?
1. Take mass of heavy elements in each planet
2. Augment the mass with enough H / He to restore
Solar composition
3. Spread the mass into an annulus around each orbit
Jupiter’s orbit
spread Jupiter’s augmented
mass (~3 x real mass)
across this annulus to
yield a surface density
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Minimum mass Solar Nebula
(Weidenschilling 1977)
*3 2
$
'
r
-2
" gas (r) = 1.7 #10 3 &
) g cm
%1 AU (
!
Integrated mass out to
30 AU = 0.01 Msun
Comparable to the masses
of disks measured around
other stars
BUT… this is at best a lower limit - could have been more
gas / could have been a different radial profile…
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Minor bodies in the Solar System
Asteroids, Kuiper Belt objects, comets…
Dynamical clues as to
the early evolution of
the Solar System
Most stable orbits
in the Solar System
are populated with
minor bodies
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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 i
=
P2 j
…with i, j integers. “Plutinos”, include
Pluto itself. Who ordered that!?
2. Apparent edge at ~47 AU (not just selection function)
!
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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
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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…
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Chemical evidence:
Ratio of deuterium to hydrogen:
Earth’s water: 153 parts per million
Meteorites known as carbonaceous chondrites: 159 ppm
Comets: 309 ppm
These meteorites appear to originate
from the outer asteroid belt (beyond
about 2.7 AU)
Evidence for radial transport - mass
dynamically negligible but critical
for life
How common is water on planets in the “habitable zone”?
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Extrasolar Planets
Difficult to directly image extrasolar planets
Contrast ratio in reflected light:
# "R p2 &
*10
f =%
A
~
1.4
)10
(
2
4
"
a
$
'
…for Earth
Astronomical units: 24-25 magnitudes
!
Contrast at the peak of the planet’s thermal emission is
less: about f ~ 10-6 at 20 µm for the Earth
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Tinetti et al. (2006)
Imaging planets would allow measurement of atmospheric
spectra - biomarkers such as oxygen / ozone…
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Tinnetti et al. (2006)
Future goal: NASA’s
Terrestrial Planet
Finder / ESA’s
Darwin proposals
All detections of
extrasolar planets
to date are via
indirect methods
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Radial velocity searches
Observable: time dependent
radial velocity of star (via
Doppler shift of spectral
lines), due to perturbation
from orbiting planet
For planet on circular orbit: v K =
GM*
a
Linear momentum conservation: M*v* = M p v K
!
M
Observable: K = v* sini = p
M*
GM*
sini
a
!
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!
Mp
K = v* sini =
M*
GM*
sini
a
Observable quantity:
! is ~ m s-1
best precision
Usually unknown:
derive lower limit
on mass
Massive planets are
easier to detect
Planets at small a
easier to detect
Jupiter: 12.5 m s-1
Earth: 9 cm s-1
very challenging observationally,
but achievable…
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High resolution astronomical spectrographs: R ~ 105 (3 km s-1)
How can we detect m s-1 shifts? Consider limit to radial
velocity measurement from a single pixel, assuming perfect
calibration:
"N ph =
dN ph
dv
"v # "v min $
N 1ph2
dN ph /dv
Can detect small RV shift if (a) high S/N and (b) spectrum
has plenty!of structure (limited by thermal broadening)
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Estimate S/N = 100, thermal broadening means lines have
width of ~10 km s-1
Then spectrum with Npix “effective” pixels yields an RV
measurement that could be as good as:
"v shot
100 m s -1
~
N 1pix2
Can measure very small RV shifts against shot noise if
calibration 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
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Mp
K = v* sini =
M*
GM*
sini
a
If a survey could detect K > Kmin for some sample of stars:
log Mp sin i
!
P = Psurvey
Detectable
Undetectable
log a
In fact no survey is anything like this simple…
but basic selection function is of this form with
Kmin ~ 20 m s-1 for complete samples…
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Example of real data, measure:
• orbital period
• MP sin i (with stellar mass)
• orbital eccentricity e
…all that is known for
most extrasolar planets
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Multiple planet system
Interesting degeneracies and statistical questions concerning
survey biases - be careful!
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Results #1: eccentricity vs semi-major axis
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Results #2: mass vs semi-major axis
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Results #3: eccentricity vs mass
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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 distribution
increases to large orbital radius
Note: only very limited information
on planet population with M and a
similar to that of Jupiter…
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Fischer & Valenti (2005)
Abundance of (detected) planets is a strongly increasing
function of the metallicity of the host star measured from
the spectrum
Giant planet formation process “knows” about the trace
abundance of heavy elements (~1-2%)
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Transits
Detection of planet via
photometric monitoring
of host star
" Rp %2
Fractional decrement f = $ ' ( 0.01 (Jupiter)
# R* &
during transit
Probability of
!
observing a transit
OK from ground
= 8.4 )10*5 (Earth) space only
Ptransit
R* + R p
=
a
About 10% for hot
Jupiters, 0.5% for
Earth in Earth’s orbit
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Ground based data quality
(TrES project)
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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 to
planets with Earth radius
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Also possible to observe the secondary eclipse / phase
modulation in the infra-red (Spitzer):
Measure of temperature
on the day / night side
of the planet
Harrington et al. (2006)
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A radius mystery
Measured Rp are not a
one parameter family with
planet mass
What is the additional
physics at work in setting
the radius?
Torres et al. (2008)
• planetary structure?
• dynamics (heating
due to tides)?
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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?
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