Download Lecture 19: Planet Formation I. Clues from the Solar System

Lecture 19: Planet Formation I.
Clues from the Solar System
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Outline
• The Solar System:
! Terrestrial planets
! Jovian planets
! Asteroid belt, Kuiper belt, Oort cloud
• Condensation and growth of solid bodies
• The minimum mass solar nebula
The Solar System
Planets and most of the
other bodies of the
solar system do orbit
the Sun in about the
same plane, called the
ecliptic plane.
Not to scale!
The Solar System: content
e
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The Solar System:
the terrestrial planets
•
•
•
Mercury, Venus, Earth, and
Mars share many similar
features.
Small compared with the
huge planets beyond them,
these inner planets also
have rocky surfaces
surrounded by relatively thin
and transparent
atmospheres.
Together, we call these four
the terrestrial planets (from
the Latin “terra,” meaning
earth).
Mars
R=3397 km
M=0.11 ME
Earth
R=6378 km
ME=6.0×1024 kg
Venus
R=6052 km
M=0.82 ME
Mercury
R=2440 km
M=0.06 ME
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The Solar System:
the Jovian planets
• Jupiter, Saturn,
Uranus, and Neptune
are giant planets;
they are also called
the jovian planets.
• They are much bigger,
more massive, and
less dense than the
inner, terrestrial
planets.
• Their internal structure
is entirely different
from that of the four
inner planets.
D = 5.2 AU
R = 71,492 km = 11.2 Rearth
M = 317.8 Mearth
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T = 165 K (cloudtops)
The Solar System:
the Jovian planets
The Solar System
The Solar System:
Other constituents
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http://www.telegraph.co.uk/science/space/
8052528/Water-carried-on-asteroids-are-common.html
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http://www.sciencedaily.com/releases/2010/10/101007114114.htm
Herschel makes a splash and fuels the
controversy of the origin of Earth's water.
H 2O
HDO
Hartogh et al. 2011, Nature,12 478, 218
HDO/H2O in Jupiter family comet = HDO/H2O in oceans !
The Solar System:
Other constituents
The Solar System:
Other constituents
The Solar System:
Formation scenario
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The Formation of the solar system:
Condensation and growth of solid bodies
The mechanical and chemical
processes related to grain
agglomeration are poorly understood.
Loosely packed fractal structures which
are held together by Van der Waals
forces may be formed.
IDP
Interplanetary
Dust
Particle
Dominik et al. 2006, PPV
The Formation of the solar system:
Condensation and growth of solid bodies
The motions of small grains in a protoplanetary disk are
strongly coupled to the gas.
For solid particles smaller than 1 cm, the dust-gas coupling
is well described by Epstein’s drag law:
FD = − A ρ g vc s
A ≡projected surface area of the body
ρg≡gas density
v≡velocity of the body with respect to the gas
cs≡mean thermal velocity of the gas
€
The Formation of the solar system:
Condensation and growth of solid bodies
When grains condense, the vertical component of the star’s gravity causes
the dust to sediment out towards the midplane of the disk.
Current models (appropriate for the solar nebula) suggest that the bulk of
solid material was able to agglomerate into bodies of macroscopic size
within ≤ 104 yr at 1 AU. Most of the bodies confined to a thin region.
The Formation of the solar system:
Condensation and growth of solid bodies
Growth from cm-size particles to km-sized planetesimals depends on the
relative motions between the various bodies. The motions of (sub-)cm-sized
material are coupled with the gas.
The gas is partially supported against stellar gravity by a pressure gradient in
the radial direction " gas circles the star slightly less rapidly than the
keplerian rate. The “effective” gravity felt by the gas is:
geff =
GM* 1 dP
+
r2
ρ g dr
acceleration due to
pressure gradient
For circular orbits, the effective gravity must be balanced by centrifugal
acceleration. Considering that the pressure is much smaller than gravity,
one finds that the gas rotates ~0.5% slower than the keplerian speed.
€
In the next slides we will demonstrate 20
this.
The Formation of the solar system:
Condensation and growth of solid bodies
Let P be the gas pressure, ρ its density and r the distance from the nebular
axis. The central gravity g and the circular Keplerian orbital velocity VK are
related by
GM! VK2
g= 2 =
.
r
r
In a reference frame rotating with the gas, the residual gravity is
Δg =
€
1 dP
,
ρ g dr
which is the condition for hydrostatic equilibrium.
[see Weidenschilling (1977, MNRAS)]
€
The Formation of the solar system:
Condensation and growth of solid bodies
If Vg is the rotational velocity of the gas,
geff
Vg2 VK2
=
=
+ Δg.
r
r
Therefore, the deviation of the gas velocity from the circular orbital velocity is:
ΔV = VK − Vg ,
€
with
Vg = VK2 + rΔg
VK2
Δg
= V + Δg
= VK 1+
g
g
€
2
K
€
€
The Formation of the solar system:
Condensation and growth of solid bodies
If Δg/g << 1:
1+
and
€
Δg
1 Δg
~ 1+
,
g
2 g
$ Δg '
$ Δg '
ΔV = VK − Vg ~ VK − VK &1+
) = −VK & ).
2g
%
(
% 2g (
Over some range of r, the pressure can always be approximated by a powerlaw: P = P0(r / r0)-a. Therefore, for an ideal gas:
€
Δg =
1 dP
a nk B T
ak T
=−
=− B
ρ g dr
ρg r
µm H r
€
The Formation of the solar system:
Condensation and growth of solid bodies
Example: assuming M = 1 M!, a = 2, T = 300 K and r = 5 AU:
Δg
= −5.8 × 10−3
2g
Therefore, the gas rotates ~0.5% slower than the keplerian speed.
€
The Formation of the solar system:
Condensation and growth of solid bodies
Large particles thus encounter a headwind which removes angular
momentum and causes them to spiral inward toward the star. Small grains
drift less. A meter-sized body at 1 AU would approach the Sun in ~ 100 yr!
As a consequence of the difference in velocities, small (sub-)cm sized grains
can be swept up by the larger bodies, while gas drag on the meter-sized
planetesimals induces considerable radial motions.
!
The material that survives to form planets must complete the
transition from cm- to km- size rather quickly!
…unless the material is confined to a thin dust-dominated subdisk in
which the gas is dragged along at the same Keplerian velocity.
Two alternative hypotheses describe the growth through this size range:
The Formation of the solar system:
Condensation and growth of solid bodies
1. If the nebula is quiescent, the dust and small particles settle into a layer
thin enough to be gravitationally unstable to clumping, and planetesimals are
formed. The planetesimals produced have sizes of the order ~ 1 km.
2. In a turbulent nebula, growth continues via simple two-body collisions.
The growth of solid bodies from mm to km size must occur very quickly, but
the related physics is poorly understood.
Molecular forces can lead to ~1 km-sized planetesimals by coagulation (van
der Waals binding energies [~103 erg g-1] ~ gravitational binding energy of a
1 km body). Then, when size ≥ 1 km, gravity takes over and mutual
gravitational perturbations become important.
The Solar System:
Formation scenario
-Material within the disk condenses into
several large chunks of material called
planetesimals.
-These collide with other planetesimals and
coalesce into larger bodies, eventually
forming planets.
-Since the Sun and planets all form from
the same cloud →all rotate in the same
direction as initial cloud.
-Planets rotate counter-clockwise around
the Sun.
-Also planets and Sun rotate counterclockwise about their axes,
-with the exception of Venus which
rotates clockwise (retrograde motion)
The Solar System:
Formation scenario
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The Solar System:
Formation scenario
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The Solar System:
Formation scenario
The snowline
rsnow
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The Solar System:
Formation scenario
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The Solar System:
Formation scenario
TC material, further away both
lecture 9
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The Solar System:
Formation scenario
[1 Pa = 1 N/m2 = 10−5 bar = 9.8692×10−6 atm]
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The Solar System:
Formation scenario
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The Solar System:
Formation scenario
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The Solar System:
Formation scenario
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The Solar System:
Formation scenario
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The Solar System:
Formation scenario
Summary
•The Solar System: Terrestrial planets, Jovian planets, Asteroid belt, Kuiper
belt, Oort cloud.
•Problems with the condensation and growth of solid bodies from cm- to kmsize (headwind on large particles)
•Minimum Mass Solar Nebula
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