chapter 10 – formation and evolution phy6795o – chapitres choisis en astrophysique naines brunes...

Chapter 10 – Formation and Evolution

PHY6795O – Chapitres Choisis en Astrophysique

Naines Brunes et Exoplanètes

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Contents

10.1 Overview10.2 Star formation10.3 Disk formation10.4 Terrestrial planet formation10.5 Size, shape, and internal structure10.6 Giant planet formation10.7 Formation of planetary satellites10.8 Migration10.9 Tidal effects10.10 Population Synthesis

10. Formation and EvolutionPHY6795O – Naines brunes et Exoplanètes

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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.

PHY6795O – Naines brunes et Exoplanètes 10. Formation and Evolution

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10.1 OverviewFraction of stars with a disk as a function of age.


Credit: Erik Mamajek

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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

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.


(10.1)

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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

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 !


(10.2)

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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.

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.


(10.3)

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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)

Sub-mm source No detectable IR emission

Class 0

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YSO Classsification



Flat SED or rising into the mid-IR Protostars with circumstellar disks and envelopes.

Class I

αIR > 0

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YSO Classsification



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



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 diskmust have had (Weidenschilling 1977; Hayashi 1981):

Disk mass between 0.01 -0.07 M

(10.5)

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Accretion rate

PHY6795O – Naines brunes et Exoplanètes 10. Formation and EvolutionMuzerolle et al. 2000

Accretion rate is estimated from (broad) emission-line observations (e.g. Hα, HeI)

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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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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 FormationPlanet 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 FormationPlanet growth rate

For a swarm of planetesimals, the growth rate of the protoplanet is

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.


(10.10)

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10.4 Terrestrial Planet FormationPlanet growth rate

Regime 1: gravitational focussing is weak (FG ~ constant)

with the solution: . The planet radius grows at a linear rate (‘’orderly growth’’).

Regime 2: gravitational focussing is strong (FG >>1, σ=cte )

in a finite time (‘’runaway growth’’). Lead to the formation of >= 100 km-sized bodies at 1 AU in some 104 yr.


(10.11)

(10.12)

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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

Resulting picture: ~100 Moon- to Mars-sized objects + a swarm of 109 1-10 km planetesimals

Runaway growth time scale: 105 – 106 yr


(10.13)

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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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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 gas-rich 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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chapter 10 – formation and evolution phy6795o – chapitres choisis en astrophysique naines brunes...

Documents

formation of disks

formation of systems

byproducts of star formation

star formation10

disk formation10

giant planet formation10

terrestrial planet formation10

molecular clouds of