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Naines Brunes et Exoplanètes
Chapter 10 – Formation and Evolution
Contents
10.1 Overview
10.2 Star formation
10.3 Disk formation
10.4 Terrestrial planet formation
10.5 Size, shape, and internal structure
10.6 Giant planet formation
10.7 Formation of planetary satellites
10.8 Migration
10.9 Tidal effects
10.10 Population Synthesis
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10.1 Overview
 Planets are the by-products of star formation.
 Stars and brown are formed through gravitational collapse of
molecular clouds cores.
 Cloud collapse inevitably involves the formation of a disk made of gas
and dust. Canonical dust/gas ratio: 0.01.
 Terrestrial planets are formed within the disk through the
progressive agglomeration of material, denoted, as it grows in size, as
dust, rocks, planetesimals and protoplanets.
 Similar process occurs further out in the disk results in the cores of
giant planets followed by accretion of ice and/or gas.
 Gas provides a viscous medium that is partially responsible for
migration. Migration also possible through gravitational scattering
between proto-planets and planetesimals.
 Phase of planet-planet configuration that leads to either partial
destruction or stabilisation of the planetary system.
 Key observation: the disk is cleared in only a few Myr.
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10.1 Overview
Fraction of stars with a disk as a function of age.
Credit: Erik Mamajek
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Contents
10.1 Overview
10.2 Star formation
10.3 Disk formation
10.4 Terrestrial planet formation
10.5 Size, shape, and internal structure
10.6 Giant planet formation
10.7 Formation of planetary satellites
10.8 Migration
10.9 Tidal effects
10.10 Population Synthesis
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10.2 Star formation (1)
 Star formation involves two levels physics:
 Macrophysics leading to the formation of systems of stars to
clusters of galaxies.
 Microphysics leading to the formation of disks and planets
• How protostars acquire their mass via gravitational collapse
• How the in-falling gas loses its magnetic flux and angular
momentum.
• How the resulting stellar properties are determined by the medium
from which they form.
 Accepted paradigm for star formation (M< 8 M)
 Gravitational instabilities in molecular clouds of gas and dust
grains lead to gravitational collapse (Shu et al. 1987) for low mass
stars.
 Formation of more massive stars is more uncertain
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10.2 Star formation (2)
 Molecular clouds are complex structures in scale, density
and composition.
 Dominated by H2 and He with numerous other molecules (CO,
CO2, CH4, H2O, NH3 …
 H2 molecule are very difficult to detect spectroscopically (no dipole
moment). In practice, H2 content inferred by trace gas (usually
CO) with some assumption of the H2/CO ratio.
 Density of hydrogen in the interstellar medium: ~10 /cm3
 Density of H2 in molecular cores: 104 – 106 /cm3
 Dust grains
 Two types of sub-micron amorphous carbon and solid solution
crystalline silicates: olivine (Mg2SiO4 – Fe2SiO4) and pyroxene
(MgSiO3 – FeSiO3).
 At low temperature, volatile molecular gas condense onto dust
grains as icy mantles.
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10.2 Star formation (3)
 Protostars and protostellar collapse are likely triggered by turbulent
gas, e.g. a shock wave hitting a molecular cloud or highly supersonic
turbulent flow within molecular clouds.
 Local density enhancements due to compression becomes
gravitationally unstable if larger than the Jeans length λ
(10.1)
with
, the isothermal sound speed, μ the mean molecular
weigth (~2 mH for gas dominated by H2), T~10 K the gas temperature
and ρ the density. The corresponding Jeans Mass is
 For λ >λJ, thermal pressure cannot resist self-gravity, and runaway
collapse follows.
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10.2 Star formation (4)
 In more useful unit, the Jeans length and mass are
 Thus, any dense molecular core more containing more than a few
tens of M og gas is unstable, and will collase in roughly a free-fall
time
(10.2)
 As the gas collapses, density rises but temperature remains roughly
constant because gas is optically then and cools down radiatively. As
a result, the Jeans’ mass steadily decreases as the collapse proceeds,
and the collapsing cloud fragments into lower and lower mass pieces,
each on its own free-fall time. A star cluster is born !
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Contents
10.1 Overview
10.2 Star formation
10.3 Disk formation
10.4 Terrestrial planet formation
10.5 Size, shape, and internal structure
10.6 Giant planet formation
10.7 Formation of planetary satellites
10.8 Migration
10.9 Tidal effects
10.10 Population Synthesis
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The Toomere instability criteria
 Collapse does not proceed radially but through a flat disk since the
material must collapse while conserving angular momentum.
 Depending of angular momentum, the fraction of dust and gas falling
onto the disk may exceed 90%.
 For high disk/protostar mass ratios, the disk is gravitationally
unstable, spiral waves develop and rapid mass accretion onto the
stars continues until the mass ratio falls below the Toomre
instability limit. A disk is gravitationally unstable if Q < 1, i.e.
(10.3)
where
is the sound speed, Ω the angular velocity and
Σ the disk surface density.
 Disk evolution, proceeding from the massive accretion disks to more
tenuous protoplanetery disks, is determined by viscosity, stellar
accretion rate, grain coagulation and photoevaporation.
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Young stellar objects (YSO)
 Very early stage of star formation.
 YSOs characterized by
 infrared excess due to hot disks
 Possibly a UV excess attributed to accretion hot spots.
 Evidence of strong stellar winds and outflows (Herbig- Haro objects).
HH-30
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SED classification scheme
 YSOs are assigned to one of four classes according to their spectral
index over the region 2.5 – 10 μm.
(10.4)
Armitage 2007
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YSO Classsification
Figures from Greene (2002) and Armitage (2010)
Class 0
 Sub-mm source
 No detectable IR emission
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YSO Classsification
Figures from Greene (2002) and Armitage (2010)
Class I
αIR > 0
 Flat SED or rising into the mid-IR
 Protostars with circumstellar disks and envelopes.
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YSO Classsification
Figures from Greene (2002) and Armitage (2010)
Class II
-1.5 < αIR < 0
 Source with an SED declining into the mid-IR
 Pre-main sequence stars with observable accretion disks (T Tauri stars)
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YSO Classsification
Figures from Greene (2002) and Armitage (2010)
Class III
αIR < -1.5
 Source with little or no IR excess
 Pre-main sequence stars without detectable accretion. Initial disk has
been largely cleared (weak-lined T Tauri stars)
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Planet formation chronology
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Planet formation chronology
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Observations of protoplanetary disks
Gas
Dust
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Minimum Mass Solar Nebula
 Common concept in planet formation
 The minimum mass solar nebula
is the current distribution of mass
(solid and gas) restored to solar
composition, which is the minimum the
Sun’s proto-planetary disk
must have had (Weidenschilling 1977;
Hayashi 1981):
(10.5)
 Disk mass between 0.01 -0.07 M
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Accretion rate
Accretion rate is estimated from (broad) emission-line observations (e.g. Hα, HeI)
Muzerolle et al. 2000
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Debris disk
 Circumstellar dust rings were first identified by the IRAS
(Infrared Astronomical Satellite (Aumann et al. 1984) as
IR excess.
 Vega (AOV), Fomalhaut (A4V), εEri (K2V), τCeti (G9V), βPic
(A6V).
 All except Vega and τCeti have a confirmed planet/companion.
 Disk shape likely the result of a planet.
 Many others (.e.g. HR8799)
 Wide range of age: 10-20 Myr for βPic, 2-4x108 yr for
Vega and Fomalhaut and up to ~1 Gyr.
 Disk origin for old stars: gas-poor debris arising from
collisions of planetesimals. Those are referred to as
secondary disk.
 For βPic, a combination of a secondary disk and the remnant
protostellar disk.
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Debris disk
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Observational properties of disks
 Size: tens to hundreds of AU
 Debris disks can be much larger: 500 – 1000 AU
 Mass range: from ~0.1 M to < 0.001 M
 Accretion rate range: 10-10 - 10-7 M/yr
 Disk lifetime: ~Myr (gas and dust), witn significant
scatter
 Cessation of gas accretion roughly simultaneous with
dust disk clearing.
 Disk lifetimes set a limit on the timescale for giant planet
formation.
 Disk observations tell us the typical conditions for planet
formation.
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Contents
10.1 Overview
10.2 Star formation
10.3 Disk formation
10.4 Terrestrial planet formation
10.5 Size, shape, and internal structure
10.6 Giant planet formation
10.7 Formation of planetary satellites
10.8 Migration
10.9 Tidal effects
10.10 Population Synthesis
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10.4 Terrestrial Planet Formation
 Present paradigm: ‘bottom-up’ process, with bodies of
ever-increasing size being produced.
 Main references: Lissauer (1993), Pollack et al. (1996),
Morbidelli et al. (2012)
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10.4 Terrestrial Planet Formation
Planet formation stages
1. Dust to rocks: sub-micron to 10m.




Dust settles into the mid-plane of the disk through a combination of
electrostatic forces and collisional impacts, growing as they collide.
Detailed process still very uncertain.
This phase corroborated by observational evidence of mm-size
particules in disks (Herbst et al. 2008).
Dust grains subject to gas drag -> inward drift.
2. Rocks to planetesimals: 10m to 10km
 Planetesimals = solid objects whose internal strength is dominated by
self-gravity and whose orbital dynamics are not significantly affected by
gas drag.
 Growth through pairwise collisions.
 Once formed, planetesimals decoupled from gas.
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10.4 Terrestrial Planet Formation
Planet growth rate
 For a swarm of planetesimals, the growth rate of the protoplanet is
(10.10)
where M is the embryo mass, Σp the disk surface density, Rc the
embryo radius, Ω the angular velocity, vesc the escape velocity of the
embryo and σ is the velocity dispersion of the planetesimal swarm.
Last term is the gravitational focusing term FG.
 For plausible models of disk mass of order 0.1 M, total formation
times estimated from such models would be of the order



4 x 106 yr for the Earth (r=1 AU, Σ~103 kg/m2)
5 x 108 yr for a 10 ME Jupiter core (Σ~200 kg/m2)
3 x 1010 yr for Neptune (Σ~30 kg/m2)
 Process clearly too slow compared to disk clearing time scale of a
few 106 yr. Larger Σ and/or smaller σ required to reduce the
formation time scales to plausible values.
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10.4 Terrestrial Planet Formation
Planet growth rate
 Regime 1: gravitational focussing is weak (FG ~ constant)
(10.11)
with the solution:
. The planet radius grows at a linear rate
(‘’orderly growth’’).
 Regime 2: gravitational focussing is strong (FG >>1, σ=cte )
(10.12)

in a finite time (‘’runaway growth’’). Lead to the formation
of >= 100 km-sized bodies at 1 AU in some 104 yr.
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10.4 Terrestrial Planet Formation
Planet formation stages
3. Oligarchic growth: 100 km to 1000 km
 The size of a growing planet’s feeding zone is set by the maximum distance
over which its gravity is able to perturb other orbits sufficiently to allow
collisions. The feeding zone itself scales with the Hill radius.
 Leads to a slowdown in the accretion rate once a certain isolation mass is
reached, and runaway growth gives way to a phase of slower oligarchic
growth.
 Feeding zone scales with the Hill radius.
 The isolation mass is
(10.13)
 Resulting picture: ~100 Moon- to Mars-sized objects + a swarm of 109 1-10
km planetesimals
 Runaway growth time scale: 105 – 106 yr
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10.4 Terrestrial Planet Formation
Planet formation stages
4. Post-oligarchic growth: 1000 km to 10 000 km







Phase characterized by planet-planet interactions, chaotic collisions and
mergers.
Final phase of terrestrial planet formation
Embryos above ~3000 km characterized by internal meting and
differentiated interiors (denser elements like Fe sinking in the core,
silicate flaoting above).
Head-on collisions lead to merge with little mass loss. Large impacts
causing extensive heating and formation of magma oceans.
Mergers procdeed until orbit spacing becomes large enough to converge
towards a quasi-stable configuration.
Final planet assembly takes ~10 – 100 Myr.
Numerical simulations for the Solar system: Earth reached half of its
mass in 10-30 Myr and its present mass in ~100 Myr.
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Contents
10.1 Overview
10.2 Star formation
10.3 Disk formation
10.4 Terrestrial planet formation
10.5 Size, shape, and internal structure
10.6 Giant planet formation
10.7 Formation of planetary satellites
10.8 Migration
10.9 Tidal effects
10.10 Population Synthesis
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10.6 Giant planet formation
Formation by core accretion
 Applies to objects within 10-50 AU.
 Two stage process:
1. Formation of a rocky/icy core required to be between 5 and 20 ME.
2. Rapid accretion of gas onto the resulting core along with planetesimals
 Core formation process and gas dispersal operate on similar time
scales of order 5-10 Myr.
 If gas dispersal is faster than core formation, ice giants rather than gasrich giants may results.
 This model could account for the relative amounts of high- low-Z
materials in the giant planets.
 Massive core easier in the outer disk beyond the snow line.
 Insufficient solids in the inner disk and no ice.
 Lower gravitational influence of the host star eases core growth
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10.6 Giant planet formation
Formation by core accretion
 Applies to objects within 10-50 AU.
 Two stage process:
1. Formation of a rocky/icy core required to be between 5 and 20 ME.
2. Rapid accretion of gas onto the resulting core along with planetesimals
 Core formation process and gas dispersal operate on similar time scales
of order 5-10 Myr.
 If gas dispersal is faster than core cormation, ice giants rather than gas-rich
finats may results.
 Such a scenario broadly accounts for the enhancement of some high-Z
elements in the atmospheres of the solar system giants, and for their
progressive enrichment from Jupiter to Saturn to Uranus/Neptune.
 Massive core easier in the outer disk beyond the snow line
 Insufficient solids in the inner disk and no ice.
 Lower gravitational influence of the host star eases core growth
 Accretion process ends when the planetesimal and gas supplies
terminate either through the opening of a disk gap or because gas disk
dissipates.
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10.6 Giant planet formation
Simulations for Solar system
For Saturn, phase 1 lasts four times longer, while the overall duration of phase 2 is
similar. For Uranus, phase 1 is a further factor of eight longer, while the overall
duration is a factor 2–3 longer than for Jupiter.
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Contents (suite sur PDF annoté)
10.1 Overview
10.2 Star formation
10.3 Disk formation
10.4 Terrestrial planet formation
10.5 Size, shape, and internal structure
10.6 Giant planet formation
10.7 Formation of planetary satellites
10.8 Migration
10.9 Tidal effects
10.10 Population Synthesis
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