Download Observational Constraints The Nebular Hypothesis

The Sun and Planets
Lecture Notes 2.
Spring Semester 2017
Prof Dr Ravit Helled
Lecture 2
Formation of the Solar System
Observational Constraints
Observational Constraints
The following are the observed features of the Solar System that any formation theory has
to reproduce. We call these features “observational constraints” because they constrain
our formation theories.
Age — The age of the Solar System is 4.567 billion years (Gyr).
Orbit shape — The orbits of the planets are ellipses with the Sun at one focus. The
orbits of the planets are all more or less in the same plane.
Orbit direction — The planets orbits are prograde (i.e., in the same direction as the
Sun’s rotation).
Orbit distance — The planets’ orbits lie within 30 AU of the Sun and the spacing
between the planets is large.
Mass distribution — The planets only account for < 0.2% of the Solar System’s total
mass.
The Nebular Hypothesis
Roughly 4.6 billion years ago, a great cloud of gas and dust (i.e., a nebula) began to
collapse when gravitational forces became stronger than the cloud’s internal gas pressure.
The cloud was composed mostly of hydrogen and helium, with smaller fractions of heavier
elements. As the cloud collapsed, three things happened:
1. The cloud begins to rotate faster (conservation of angular momentum),
2. The cloud flattens into a disk,
3. The interior of the cloud heats up.
At the center, the temperature continues to rise until it reaches ∼1 million degrees Kelvin.
This is the temperature required to trigger thermonuclear fusion (i.e., the star “turns on”).
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Protoplanetary Disk
The disk of gas and dust that surrounds a young star is called a “protoplanetary disk”.
This is the disk of material that planets form in. The temperature at any given location
in the disk determines whether certain materials at that location will be solid of gaseous.
The disk is hotter closer to the Sun, so the composition of the disk will change depending
on the distance from the center.
In the inner disk, the gas and dust are strongly heated by the Sun. In this inner region,
ices and gasses cannot condense to form solids. Particles that condense in the inner region
are mainly silicates and iron compounds (i.e., rocks and metals).
In the cold outer disk, ices and gasses are able to condense to form solids. The boundary
that separates the two regions is know as the “snowline”. When we discuss the snowline,
we usually mean the H2 O snowline, however each material has a different condensation
temperature and therefore a different snowline (e.g., iron compounds have a much higher
condensation temperature and therefore their snowline will be much closer to the Sun).
Planet Composition
Metal is found in the cores of planets, mostly in the form of iron (Fe) and nickel (Ni).
Rock: the most common rocks are silicates. Silicates are oxides of silicon (Si), magnesium
(Mg), and Aluminium (Al).
Ices are also referred to as “volatiles”. The most common ices are water (H2 O), carbon
dioxide (CO2 ), methane (CH4 ), and ammonia (NH3 ).
Gas in planets is predominately hydrogen (H) and helium (He). The origin of these gases
is the nebula (i.e., cloud of gas and dust) that the Solar System formed from.
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Planet Formation
Terrestrial planets:
1. Small dust grains grow into larger—but still relatively small—asteroid-like bodies
called planetesimals.
2. Planetesimals repeated crash into each other, resulting in increasingly large planetesimals. Some of these objects grow large enough to be called protoplanets.
3. As the protoplanets grow to their final size, they slowly clear out the Solar System
of most smaller bodies (this process is called disk dispersal).
Giant planets:
There are two suggested models to explain how giant planets are formed: core accretion
and disk instability.
Core accretion: Planet agglomerates from dust and attracts gas envelope. In
this scenario, giant planets should have non-stellar compositions and massive cores.
Core accretion proceeds through the following three steps:
1. Accretion of dust particles and planetesimals results in a core of a few Earth
masses with a low-mass gaseous envelope.
2. Further accretion of gas and solids: the envelope grows faster than the core
until the cross-over mass is reached.
3. Runaway gas accretion with relatively small accretion of solids.
Disk instability: Clump of gas inside the protoplanetary disk collapses to form a
giant planet. In this scenario giant planets should have stellar compositions and no
cores. The time scale for giant planet formation via disk instability is roughly 1000
years. The Toomre parameter, Q, is a way to measure when and where the disk will
become unstable and potentially lead to giant planet formation:
Q=
cs Ω
πGσg
where cs is the sound speed, Ω is the angular velocity, G is the gravitational constant,
and σg is the surface density. For the ideal case of an infinitesimally thin disk, Q > 1
is stable and Q < 1 is unstable. The disk instability process is most efficient as large
radial distances.
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Giant Planets
In the Solar System:
Jupiter, Saturn, Uranus, and Neptune.
In the Solar System we can identify a few trends in physical and orbital characteristics.
1. Giant planets exist at large radial distances (> 5 AU).
2. The mass of the giant planets decreases with orbital distance.
3. Heavy element enrichment increases with decreasing mass.
Outside of the Solar System:
1. While there are many observed extrasolar giant planets, they still appear to be
less common than small (terrestrial) planets. An up-to-date catalogue of observed
extrasolar planets can be found at http://exoplanets.eu/.
2. Giant planets exist at very small orbital distances (e.g., the record for the shortest
orbital period is held by PSR J1719-1438 b, a Jupiter mass planet orbiting its host
star at 0.004 AU).
3. The giant planet occurrence rate is ∼5–20%. The occurrence rate is a measure of
how many stars host giant planets (e.g., if we look at 100 stars and find giant planets
orbiting 20 of them, the occurrence rate is 20%). The variation between 5% and 20%
reflects the fact that the occurrence rate varies with stellar mass and metallicity.
4. Observations of protoplanetary disks around other stars suggest that the typical
disk lifetime is < 10 million years and the typical disk mass is 0.01–0.1 M . This
tells us that giant planets have to form in less than 10 Myr and from a disk of
material that is 1% to 10% the mass of the Sun).
5. Transiting giant planets contain 0–100 M⊕ of heavy elements.
6. Giant planets exist at very large radial distances. We know this thanks to a technique called direct imaging, whereby astronomers are able take pictures of planets
around other stars.
7. Giant planets have been observed around M dwarf stars (< 0.6 M ) and metal-poor
stars.
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Stellar Composition & Metallicity
Stellar composition, as determined by spectroscopy, is usually defined by the parameters
X, Y, and Z. In this system, X is the fractional percentage of hydrogen, Y is the fractional
percentage of helium, and Z is the fractional percentage of all remaining elements (i.e.,
the “metals”). X, Y, and Z must add up to exactly one:
X + Y + Z = 1.0
The overall stellar metallicity is defined using the total iron (Fe) content of the star relative
to its hydrogen (H) content. Stellar metallicity is denoted as [Fe/H]. Note that iron is
not the most abundant heavy element—oxygen is—but it is the easiest for astronomers
to measure using spectroscopy. The metallicity is commonly defined as the logarithm of
the ratio of a star’s iron abundance compared to that of the Sun:
[Fe/H] = log10
NF e
NH
− log10
star
NF e
NH
Sun
where NF e and NH are the number of iron and hydrogen atoms per unit of volume,
respectively. These values we can determine from spectroscopy.
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