14. Formation of Planetary Systems Flashcards
Difference between asteroid and Kuiper Belt?
Asteroid: mainly rocky
Kuiper: mainly icy
How many planets do we have?
8
What are the 4 terrestrial planets?
Mercury, Venus, Earth, and Mars
What defines terrestrial planets?
Metallic cores, rocky exteriors, some have atmospheres
What are the 4 gas giant / Jovian planets?
Jupiter, Saturn, Uranus, Neptune
What defines Jovian planets?
Metallic, rocky cores, huge gaseous atmospheres (H/He)
Why does Pluto not fit in to the solar system of planets?
Different orbit
How does the atmosphere of Mars compare to Earth?
More tenuous
Which planet has visible rings?
Saturn
Do all the Jovian planets have rings?
Yes - just can’t see them
Why can’t we see the rings around the other planets?
They do not have such a large component of ice
How big must the rocky cores be in Jovian planets? Why?
> 10 earth masses
Mass threshold you are able to accrete gas from surrounding PP disk
What is metallic hydrogen?
Nucleus embedded in sea of electrons (high pressure)
What are the other constituents of the solar system, apart from planets?
Asteroids, Kuiper Belt, Oort Cloud, Comets
Where do most asteroids orbit?
Near ecliptic plane (asteroid belt)
Largest asteroid?
Ceres
What is the Kuiper Belt?
Collection of cometary nuclei located roughly in the plane of the ecliptic
Where is Kuiper Belt located?
Beyond the orbit of Neptune (> 30 au from the Sun)
What is the source of ‘short-period’ comets?
Kuiper belt
What is the Oort Cloud?
An approximately spherically symmetric cloud of cometary nuclei with orbital radii
between ~ 3,000 - 10,000 au
What is the source of all ‘long-period’ comets?
Oort cloud
What are comets?
Ancient remnants of the formation of the solar system (“pristine” material)
What did Oort Cloud form?
Thought that 4 massive planets were closer, had an energetic encounter and passed L to sea of smaller planetesimals
What are interstellar visitors?
Objects that have come in from another solar system - hyperbolic orbit
What is the minimum mass solar nebula (MMSN)?
Minimum amount of mass that is required
to build all the bodies orbiting the Sun
What is the snow line?
Beyond which, T low enough that ice coatings on dust grains increase the mass of solids available for building planetesimals
How is the radius of the snow line determined?
Spectral type of host star
What phase is everything before the snow like?
Gas and dust
What are ices made of?
Mainly H2O, some other molecules e.g., PAHs, CO2/CO etc.
What is F_snow in equation for MMSN?
Solid mass enhancement due to freeze out (sticking) of water onto dust grains beyond snow line
What does a graph of MMSN look like (∑ vs R)?
As R increases ∑ (mass dist) decreases
Bump in middle indicates snow line due to more available material and stickiness
Work out total mass in minimum mass disk
See notes
[ ∑gas = 1700(r/au)^-3/2 with ∑ ∝ R^-3/2 so M_D(R) ∝ R^1/2
Get M_D(R) to get surface density ∑(R)
Subs in values]
How are grains agglomerated?
Loosely packed fractal
structures that are held together by van der Waals forces may be
formed
When do dust grains in planet formation begin to feel the gravity of the star?
~ mm
How does the vertical component of the star’s gravity affect growth of solid bodies?
Causes the dust to settle towards the mid plane of the disk
What happens to dust grains when they grow massive enough?
As they to cm-sized they become less well mixed with the gas
(Due to settling towards mid plane and gas pressure gradient)
What is the gas pressure gradient?
When gas is partially supported against stellar gravity by a pressure gradient in the radial direction
Show why gas orbits slower than dust during growth of solid bodies
See notes
(There is an effective gravity felt by the gas
Calculate F=PA
Use F=ma to find a)
How much slower does gas orbit due to effective gravity?
0.5% slower than Keplerian
Consequence of difference in velocities of dust and gas during condensation?
Small grains can be swept up by larger bodies, while gas drag on the meter-sized planetesimals and can make them fall into star
What are the 2 hypotheses to explain how grains grow past the > cm size range without falling into the star?
1 - If quiescent nebula: the dust and small particles settle into a layer thin enough to be gravitationally unstable to clumping
2 - If turbulent nebula: growth continues via simple two-body collisions. The growth of solid bodies from mm to km size must occur very quickly (physics poorly understood)
During growth of solid bodies, what happens when size > 1km?
Gravity takes over and mutual gravitational
perturbations become important
How does the acceleration due to the pressure gradient affect the gas in the growth of solid bodies?
It decreases further away from the star
What is the effect of effective gravity on gas?
Causes it to orbit sub-Keplerian
What is radial drift?
When dust grains growing to form planets get dragged slower by the gas and fall inwards to gain angular momentum
Summary of formation scenario of our solar system (up to km sizes)?
Dust settles gravitationally to the midplane
Dust composition changes with distance to the proto-Sun (snow lines)
Close to the Sun, only high Tc materials (silicates, oxides) further away, there are both (+ H2O, CO2, NH3 etc)
H and He are mostly in gas form
Disk temp profile T ∝ r^-0.4
Hierarchical grain growth (mm - cm - m - km):
Occurs as the disk becomes thinner and thinner
Collisions and sticking: dust agglomerates, creates meteor-type
bodies
Collisions and gravitational attraction: planetesimals, creates km-sized bodies
How do we go from km-sized bodies to terrestrial planets?
Runaway coagulation of
planetesimals to Earth masses (<100Myr to form)
Giant impacts
Ends with depletion of
available material
Steady, slow accretion of remaining gas, if present
How do we go from km-sized bodies to Jovian planets?
Outer disk: lower temperatures therefore slower moving grains
Increase in mass of solids available (snow line)
Allows more rapid core growth
When core mass ≥ 10 solar masses, gravitational accretion of the gaseous
envelope (runaway process)
Accretion stops when there is no more material available
Combination of accretion and tidal forces create a gap in the disk
Leading theory for moon formation?
100 Myr after the birth of the Solar System, the proto-Earth was hit by a
Mars-sized object: the heavy cores of both formed the new Earth
and the light silicate crusts formed the moon
Why must conversion to cm to km sizes must be fast to form planet?
To stop radial drift
Main planet detection methods?
Radial velocity
Imaging
Transit method
Planet’s source of emission?
Reflected light
Gravitational contraction
What albedo do we assume for planets?
1
Equation for reflected light from a planet?
Lp / L* = Rp^2 / 4a^2
Where a is the semi-major axis of the orbit of the planet
since light from star is L*/4πa^2 and reflected light is πRp^2
Can we see planets via just reflected light?
Very difficult / impossible with current technology
Why do some planets via direct imaging show 100 x brightness compared to reflection alone?
Young planets have gravitational contraction as a source of energy
What age planets still have gravitational contraction as an energy source?
100 - 300 Myr old
Why can we see some planets via direct imaging?
Young planets have gravitational contraction as their energy source
Approx. temperature of a young planet undergoing gravitational contraction?
1000 K
Planet luminosity considering gravitational contraction?
Lp / L* = (Rp/R)^2 (Tp/T)^4
What is the definition of a planet?
They’re not sufficiently massive for fusion to ever consume a majority of their
deuterium, ≤ 13 MJ.
What is a brown dwarf?
Brown dwarfs, 13 MJ ≤ M ≤ 75 MJ, are large enough for deuterium
fusion but not massive enough to sustain hydrogen fusion
What is the major source of energy radiated by giant planets and brown dwarfs?
Gravitational contraction
What implication does the cooling and shrinkage of brown dwarfs and giant planets have?
The is no unique relationship between luminosity and mass (a young planet can look the same as an old brown dwarf)
How was the first planet orbiting a main sequence star (other than the sun) discovered?
Radial velocity technique
What is the radial velocity technique?
Doppler-shifting of spectral lines
due to orbital motion
about centre of mass
What is the radial velocity technique particularly sensitive to?
Short-period massive planets
How does a planet affect the spectral lines in the radial velocity technique?
Planet causes phase shift that can be seen in the spectra
Which is the most successful method of detecting planets?
Transit method
What is the transit method particularly sensitive to?
Massive planets
orbiting cool stars in short-period orbits
How do exoplanets differ to those seen in our solar system?
Masses considerably larger than Jupiter
Planets moving on highly eccentric orbits
Planets orbiting closer than ~ 10 R★
Planets orbiting components of stellar binaries
Short-period tightly-packed inner (rocky) planetary systems
(STIPS)
What type of planets is direct imaging most sensitive to?
Longer period, more massive planets that are more luminous
What is the most commonly sized exoplanet?
Between Earth and Neptune sized
(Super-Earths / Sub-Neptunes)
How does exoplanet distribution differ from what we see in our solar system?
Hot Jupiters - close to star, snow line?
Super-Earths most common - why don’t we have one?
Larger radii - orbits aren’t as circular
Planet mass function declines towards larger masses - measure more smaller mass planets
Multiple planet systems
Planets more likely to be found around stars with higher metallicity
What are selection effects for planets?
Effects that prevent detection of low mass / long orbital period planets
How do eccentricities compare in the solar system and for exoplanets?
Solar system = 0
Exoplanets = 0 to 1
How do location of gas giants compare in the solar system and for exoplanets?
Solar system > 5au
Exoplanets = few solar radii to ~5au
How does mass distribution compare in the solar system and for exoplanets?
Solar system < 1Mj
Exoplanets < 10Mj
How does metallicity (Fe/H) compare in the solar system and for exoplanets?
Solar system ~ 0.15
Exoplanets > 0.20
What are the two gas exoplanet formation models?
- Gravitational instability in disk for direct formation of gas-giant planets
- Core accretion scenario with coalescence of solid particles - then big rocky planets accrete gas and form gas giant planets
Why is self-gravity important in the gravitational instability mechanism for gas exoplanet formation?
The self-gravity of the disk can form denser clumps
What influences clump formation in gravitational instability mechanism for gas exoplanet formation?
Self-gravity for denser clumps
Opposed by pressure forces and shear
How to estimate the effect of self-gravity for the gravitational instability mechanism for gas exoplanet formation?
For self-gravity to win over pressure forces and shear, require that time scale for collapse < time scale that sound waves can cross a clump / shear forces destroy it
Derive planet formation via gravitational instability
See notes
(Consider a clump with mass m that would collapse with tff timescale
Take timescale for sound wave to cross, and shear timescale
Set 3 timescale constants
To derive condition for instability)
What shear timescale in planet formation?
Time scale required for a clump to be sheared azimuthally by amount delta r
What is timescale for pressure disruption of a clump equal to?
Timescale for sound wave to cross a clump
According to the gravitational instability mechanism, when will a disk collapse?
At a given radius, i.e., at fixed Ω, the disk will be unstable if it is massive (large Σ) and /or cool (small cs)
What is the Toomre Q parameter?
Stability of a disk of either gas or stars is controlled by this
[QT = c_s*𝜅/πG∑ <1
𝜅 = Radial frequency at which a fluid element
oscillates when perturbed from circular motion
In a Keplerian disk, 𝜅 ~ Ω, the rotational angular speed
Σ = Surface mass density of the disk
For axisymmetric disturbances, disks are stable when QT > 1
When does gravitational instability arise in a real disk?
The formation of a massive disk during protostellar core collapse
Clumpy infall onto a disk
Cooling of a disk from a stable to an unstable state
Slow accretion of mass
Perturbation by a binary companion
Close encounters with other other star/disk systems
Accumulation of mass in a magnetically dead zone
Problems with gravitational instability to explain gas planet formation?
Hard to explain the enhanced abundance of heavy species in giant
planets
Too massive disks are required (?)
Hard to account for presence of small bodies
Problems with differentiation in planet composition
Most likely planet formation mechanism?
Core accretion (same as discussed for solar system formation)
Core accretion scenario for planet formation?
(Same as discussed for solar system formation)
- Coalescence of solid particles
- Big rocky planets (≥ 10 M㊏) accrete gas and form gas planets
What are the stages in core accretion to form planets?
Core formation
Hydrostatic growth
Runaway growth
Termination of accretion
What is the core formation stage in the core accretion mode of planet formation?
A solid protoplanet (“core”) grows via a succession of two-body collisions until it becomes massive enough to retain a
significant gaseous atmosphere (similar to terrestrial planet formation)
What is the hydrostatic growth stage in the core accretion mode of planet formation?
Initially the envelope surrounding the solid core is in hydrostatic equilibrium. Over time, both the core and envelope grow until the core exceeds a critical mass
What is the runaway growth stage in the core accretion mode of planet formation?
Once the critical mass is exceeded, a runaway
phase of gas accretion ensues.
The rate of growth is “supply-limited” and defined by the hydrodynamic interaction between the
growing planet and the disk
What is the termination of accretion stage in the core accretion mode of planet formation?
Supply of gas is exhausted (either as a consequence of the dissipation of the entire
protoplanetary disks or of the disk opening up a local gap in the disk)
Accretion tails off and the planet commences a long phase of cooling and quasi-hydrostatic
contraction
How can we account for hot Jupiters (before the snow line)?
Could be formed by gravitational instability
Or planetary migration
Why does planetary migration occur?
Planet in disk modifies gas distribution in planet vicinity
Grav. interaction between planet and non-uniform gas generates torques (through angular momentum exchange) and alters planet’ orbit
Migration of planet towards or away from star
What does direction and rate of planet migration depend on?
Mass of planet and local properties of gas disk
Most likely direction of planet migration?
Towards star
What is type I planetary migration?
Perturbation the planet causes is small enough that it does not alter the
background striation of the gas disk
What type of planets does Type I migration affect?
Earth-mass
What is type I planet migration rate proportional to?
Mass of planet and surface density of the disk
How does type I migration of a planet affect the surrounding disk?
Induces a linear perturbation
Timescale of inward Type I migration (solar mass star)?
~ 10^5 yr
What is type II planetary migration?
Starts to modify
the disk structure in the neighbourhood of
the planet
Why does Type II planetary migration modify disk structure in the vicinity of the planet?
Planet more massive, so Type I they exert on the disk increases
What is the overall effect of Type II planetary migration, and why?
A strong torque repels gas from the vicinity of the planet orbit, creating a gap
Since the interaction adds angular momentum to the planet, and removes it from the interior gas
What size planets does Type II migration affect?
Jupiter-mass
What are disk-planet interactions?
Explanation for planetary migration
How does disk-planet interaction work?
Gap forms in the disk due to tidal interaction
Prevents material flowing to inner disk
Inner disk shrinks
Angular momentum transferred from inner disk to planet and from
planet to outer disk
Planet and gap move inwards
If viscous, outer disk also move inwards
Continues until either inner disk has disappeared, or
tidal interaction with (rapidly) spinning star stabilises orbit
Comparison of planet formation models?
Core accretion:
Slow - difficult for giant planets for gain enough mass before dissipation of the protoplanetary disk
Favours high metallicity - can form core quickly
Gravitational instability:
Fast
Planets formed in situ -invoking migration is unnecessary
Form giant planets equally well around both high- and low-
metallicity stars
What is the probability of finding planets a strong function of?
Metallicity
Most successful methods of finding exoplanets?
Radial velocity and transit method
What does it mean, that the planetary mass function declines towards large masses?
Low mass planets are more common than higher mass planets
Where are planets more likely to be found, in terms of metallicity?
Around higher metallicity stars
When will disks fragment to form planets via gravitational instability?
If they are massive and cool
What are tidal interactions?
Exchange of mass and angular momentum
What can tidal interactions cause for planets?
Migration through the PP disk
