Download ph507lecnote07

PH507
Astrophysics
Professor Michael Smith
1
Week 4:
Theory: protostars and protoplanetary discs,
evolution
Radiation
Workshop
Week 5:
Radiation
Star & Planet Formation & Theory of Exoplanets
1. Intro: THE SOLAR NEBULA
The Birth of the Solar System
The properties of the Solar System hold important clues to its origin

Orbits of the planets and asteroids.

Rotation of the planets and the Sun.

Composition of the planets, especially the strong distinction between
Terrestrial, Jovian, and Icy planets
 What is the origin of our solar system? Collision with preformed Sun, external cloud…..
 Descartes, Kant, Laplace: vortices, nebular hypothesis:
importance of angular momentum:
PH507
Astrophysics
Professor Michael Smith
2
Major facts for nebula hypothesis in our solar system:

Coplanar orbits of the planets

Planet orbits are nearly circular.








All planets have prograde revolution (orbits)
The revolution of rings and natural moons are all prograde (some moons of the
outer planets are not prograde, but these are believed to be captured satellites)
All planets except Venus and Uranus have prograde rotation
The sun contains essentially all the mass
The planets (especially Jupiter and Saturn) contain most of the angular
momentum in the solar system
Small, dense, iron and silicate rich planets in the inner 2 AU. Slow rotors, few
or no moons, no rings, differentiated (molten interiors)
Large, low density, gaseous planets rich in H, He and volatile elements at >= 5
AU. Rapid rotors, many moons, all have ring systems

Abundance gradient. Inner solar system is poor in light volatile gases such as H,
He, but rich in Fe & Ni. Outer solar system is rich in volatiles H, He, etc.

Sun. Sun rotates in the same direction in the same sense.
PH507

Astrophysics
Professor Michael Smith
3
Jovian moon systems mimic the Solar System.
Star formation is on-going.

In general: Gravity is fast-acting. Galaxy is old. But young stars
are still being born.

Stars don't live forever, they must continue to be "born".
Where?

Born in obscurity….needed infrared/millimeter/radio
wavelengths.
Gas Disks around Young Stars
During star formation, gas accretion occurs through a geometrically thin
disk that is optically thick. The disks are cooler than the young star, and we
thus see an infrared excess superimposed on the black body stellar
spectrum:
PH507
Astrophysics
Professor Michael Smith
4
PH507
Astrophysics
Professor Michael Smith
5
PH507
Astrophysics
Professor Michael Smith
6
Debris Disks
Debris disks are remnant accretion disks with little or no gas left (just
dust & rocks), outflow has stopped, the star is visible.
Theory: Gas disperses, “planetesimals” form (100 km diameter rocks),
collide & stick together due to gravity forming protoplanets).
Protoplanets interact with dust disks: tidal torques cause planets to
migrate inward toward their host stars. Estimated migration time ~ 2 x
105 yrs for Earth-size planet at 5 AU.
Perturbations caused by gas giants may spawn smaller planets:
Start with a stable disk
around central star.
Jupiter-sized planet forms
& clears gap in gas disk.
Planet accretes along spiral Disk fragments into more
arms, arms become unstable. planetary mass objects.
Spiral density waves continuously produced by the gravity of embedded or
external perturber.
Debris Disks – Outer Disk
AB Aurigae outer
debris disk nearly
face on – see
structure &
condensations
(possible protoplanet formation
sites? Very far
from star) .
(Grady et al. 1999)
Debris: not from original nebula but from recent collisions.
PH507
Astrophysics
Professor Michael Smith
7
Beta Pictorisecame a surrounding outer disk of material and an inner "clear"
zone about the size of our solar system.
Strong evidence for the formation of planets. Beta Pictoris is 50 light years
away and any orbiting planets are too small and faint to image at that distance.
Shown here in false color, this ESO near-infrared image was obtained by
blocking the overwhelming direct starlight . The disk's warped bright inner
region is indirect evidence for an orbiting planet.
After a few hundred million years, a planetary system is expected to have assumed its
final configuration and has either set the stage for life, or will probably remain barren
forever. It is difficult to probe this era. Most of its traces have been obliterated in the
solar system. Only a minority of the nearby stars are so young. Even for them, planets—
and particularly those in the terrestrial planet/asteroidal region—are faint and are lost in
the glare of their central stars.
However, when bodies in this zone collide, they initiate cascades of further collisions
among the debris and between it and other members of the system, eventually grinding a
significant amount of material into dust grains distributed in a so-called debris disk.
Because the grains have larger surface area per unit mass compared to larger bodies, they
(re)radiate more energy and therefore are more easily detected in the infrared compared
to their parent bodies. By studying this signal, we can probe the evolution of other
planetary systems through this early, critical stage.
PH507
Astrophysics
Professor Michael Smith
8
Debris disks are found around stars generally older than 10 Myr, with no signs of
gas accretion (as judged from the absence of emission lines or UV excess) . In the
absence of gas drag, a 10 m sized dust grain from the primordial, proto–planetary
nebula cannot survive longer than 1 Myr within 10 AU of a star due to a number of
clearing processes, such as sublimation, radiation pressure, Poynting-Robertson, and
stellar wind drag . Therefore, any main-sequence star older than 10 Myr with an IR
excess is a candidate to have circumstellar material supplied through debris disk
processes.
Formation of the Sun: back to the Primordial Solar Nebula
Stars form out of interstellar gas clouds:

Large cold cloud of H2 molecules and dust gravitationally collapses and
fragments.
Rotating fragments collapse further:

Rapid collapse along the poles, but centrifugal forces slow the collapse
along the equator.

Result is collapse into a spinning disk

Central core collapses into a rotating proto-Sun surrounded by a rotating
"Solar Nebula"
Primordial Solar Nebula
The rotating solar nebula is composed of

~75% Hydrogen & 25% Helium

Traces of metals and dust grains
Starts out at ~2000 K, then cools:

As it cools, various elements condense out of the gas into solid form as
grains or ices.

Which materials condense out when depends on their "condensation
temperature".
Condensation Temperatures
Temp (K)
Elements
>2000 K
Condensate
All elements are gaseous
PH507
Astrophysics
Professor Michael Smith
9
1600 K
Al, Ti, Ca
Mineral Oxides
1400 K
Iron & Nickel
Metallic Grains – Refractory, Rocky
1300 K
Silicon
Silicate Grains - Rocky
300 K
Carbon,
Oxygen
Carbonaceous grains -Volatiles
300-100 K
Hydrogen,
Nitrogen
Ices (H2O, CO2, NH3, CH4)
The "Frost Line"
Rock & Metals can form anywhere it is cooler than about 1300 K.
Carbon grains & ices can only form where the gas is cooler than 300 K.
Inner Solar System:

Too hot for ices & carbon grains.
Outer Solar System:

Carbon grains & ices form beyond the "frost line".
The location of the "frost line" is also a matter of some debate but current
thinking holds that it is probably about 4 AU . A great deal depends on how
much solar radiation can penetrate deep into the outer parts of the primordial
Solar Nebula.
From Grains to Planetesimals to Planets
Grains that have low-velocity collisions can stick together, forming bigger
grains.

Beyond the "frost line", get additional growth by condensing ices onto
the grains.

Grow to where their mutual gravitation assists in the aggregation
process, accelerating the growth rate. Can form km-sized planetesimals
after a few 1000 years of initial growth.

Aggregation of planetesimals into planets
Terrestrial vs. Jovian planet formation.
Terrestrial Planets
Only rocky planetesimals inside the frost line:

Collisions between planetesimals form small rocky bodies.
PH507
Astrophysics
Professor Michael Smith
10

It is hotter closer to the Sun, so the proto-planets cannot capture H and
He gas.

Solar wind is also dispersing the solar nebula from the inside out,
removing H & He.
Result:

Form rocky terrestrial planets with few ices.
Jovian Planets
The addition of ices to the mix greatly augments the masses of the
planetesimals
These collide to form large rock and ice cores:.

Jupiter & Saturn: 10-15 MEarth rock/ice cores.

Uranus & Neptune: 1-2 MEarth rock/ice cores.
As a consequence of their larger masses & lower temperatures:

Can accrete H & He gas from the solar nebula.

Planets with the biggest cores grow rapidly in size, increasing the
amount of gas accretion.
Result:

Form large Jovian planets with massive rock & ice cores and heavy H
and He atmospheres
Moons & Asteroids
Some of the gas attracted to the proto-Jovians forms a rotating disk of material:

Get mini solar nebula around the Jovians

Rocky/icy moons form in these disks.

Later moons added by asteroid/comet capture.
Asteroids:

Gravity of the proto-Jupiter keeps the planetesimals in the main belt
stirred up.

Never get to aggregate into larger bodies.
Icy Bodies & Comets
Outer reaches are the coldest, but also the thinnest parts of the Solar Nebula:

Ices condense very quickly onto rocky cores.
PH507

Astrophysics
Professor Michael Smith
11
Stay small because of a lack of material.
Gravity of the proto-Neptune also plays a role:

Assisted the formation of Pluto-sized bodies in 3:2 resonance orbits
(Pluto and Plutinos)

Disperses the rest into the Kuiper Belt to become Kuiper Belt Objects.
Comets and other Trans-Neptunian objects are the leftover icy planetesimals from the
formation of the Solar System.
Mopping up...
The entire planetary assembly process probably took about 100 Million years.
Followed by a 1 Billion year period during which the planets were subjected to heavy
bombardment by the remaining rocky & icy pieces leftover from planet formation.
Light from the Sun dispersed the remaining gas in the Solar Nebula gas into the
interstellar medium.
Planetary motions reflect the history of their formation.
Planets share the same sense of rotation, but have been perturbed from perfect
alignment by strong collisions during formation.
The Sun "remembers" this original rotation. Rotates in the same direction with its
axis aligned with the plane of the Solar System.
Planetary compositions reflect the formation conditions.
Terrestrial planets are rock & metal:

They formed in the hot inner regions of the Solar Nebula.

Too hot to capture Hydrogen/Helium gas from the Solar Nebula.
Jovian planets contain ice, H & He:

They formed in the cool outer regions of the Solar Nebula.

Grew large enough to accrete lots of H & He.
.
Two obvious differences between the exoplanets and the giant planets in
the Solar System:
• Existence of planets at small orbital radii, where our previous theory
suggested formation was very difficult.
PH507
Astrophysics
Professor Michael Smith
12
• Substantial eccentricity of many of the orbits. No clear answers to
either of these surprises, but lots of ideas...
The Problem. It is very difficult to form planets close to the stars in a standard theory
of planet formation using minimum mass solar nebula, because

it's too hot there for grain condensation and

there's too little solid material in the vicinity to built protoplanet's core of 10 ME
(applies to r~1 AU as well).

problematic to build it quickly enough (< 3 Myr)

there's too little gas to build a massive envelope
Most conservative (accepted) possibility:
• Planet formation in these extrasolar systems was via the core accretion model –
i.e. same as dominant theory for the Solar System
• Subsequent orbital evolution modified the planet orbits to make them closer to
the star and / or more eccentric
We will focus on this option. However, more radical options in which exoplanets form
directly from gravitational instability are also possible.
PH507
Astrophysics
Professor Michael Smith
13
http://hubblesite.org/newscenter/archive/releases/2003/19
PH507
Astrophysics
Professor Michael Smith
14
Initial state: gas+dust discs:
Stage 1:
Settling and growth of dust grains: quite well-coupled to gas, rapid only if
turbulent?
Gas orbits slightly slower than Keplerian, because the gas pressure is higher
nearer the centre, providing an outward force in additional to the centrifugal force
From pebbles to planetesimals (km size): inward drift due to gas drag.
So the pebble must grow quickly to avoid spiraling in.
Stage 2:
Planetesimal to rocky planet/gas-giant core: independent of gas. It is a slow process
– gravitational dynamics (gravity increase the collision cross-section).
Stage 3:
Gas accretion onto core,
Stage 4: Orbital evolution – migration
Giant planets can form at large orbital radii.
Need a migration mechanism that can move giant planets from formation at ~5 AU to a
range of radii from 0.04 AU upwards.
Three theories have been proposed:
• Gas disc migration: planet forms within a protoplanetary disc and is swept
inwards with the gas as the disc evolves and material accretes onto the star. The
most popular theory, as by definition gas must have been present when gas giants
form.
• Planetesimal disc migration: as above, but planet interacts with a disc of rocks
rather than gas. Planet ejects the rocks, loses energy, and moves inwards.
• Planet scattering: several massive planets form – subsequent chaotic orbital
interactions lead to some (most) being ejected with the survivors moving inwards
as above.
Gas disc migration
PH507
Astrophysics
Professor Michael Smith
15
Planet interacts with gas in the disc via gravitational force.
Strong interactions at resonances, e.g. where

disc = nplanet,
with n an integer. For example the 2:1 resonance, where n = 2,
which lies at 2-2/3 rp = 0.63 rp
Resonances at r < rp: Disc gas has greater angular velocity than planet. Loses
angular momentum to planet -> moves inwards
Resonances at r > rp: Disc gas has smaller angular velocity than planet. Gains
angular momentum from planet -> moves outwards.
Migration type I - no gap
If the object has too small a mass to open a gap, it will drift inwards. The
analysis of Type I migration relies on the (near) exact cancelling of the various
torques. The planet, unless more massive than the surrounding disk, follows
the disk's viscous flow.
It is very rapid, and may shift the protoplanetary core to arbitrarily small
distance from the star in the allotted ~3 Myr time frame.
Migration type II - inside an open gap
Interaction tends to clear gas away from location of planet.
Result: planet orbits in a gap largely cleared of gas and dust.
Tidal locking of the planet in the gap.
PH507
Astrophysics
Professor Michael Smith
16
This process occurs for massive planets (~ Jupiter mass) only.
Earth mass planets remain embedded in the gas though gravitational torques can be
very important source of orbital evolution for them too.
How does this lead to migration?
1. Angular momentum transport in the gas (viscosity) tries to close the gap (diffusive
evolution of an accretion disc).
2. Gravitational torques from planet try to open gap wider.
3. Gap edge set by a balance:
-> Internal viscous torque = planetary torque
4. Planet acts as an angular momentum ‘bridge’:
• Inside gap, outward angular momentum flux transported by viscosity within disc
• At gap edge, flux transferred to planet via gravitational torques, then outward
again to outer disc
• Outside gap, viscosity again operative
Typically, gap extends to around the 2:1 resonances interior and exterior to the planet’s
orbit.
PH507
Astrophysics
Professor Michael Smith
17
As disc evolves, planet moves within gap like a fluid element in the disc – i.e. usually
inwards.
Inward migration time ~ few x 105 yr from 5 AU.
Mechanism can bring planets in to the hot Jupiter regime.
This mechanism is quantitatively consistent with the distribution of exoplanets at
different orbital radii – though the error bars are still very large!
Eccentricity generation mechanisms
Substantial eccentricities of many exoplanets orbits do not have completely satisfactory
explanation. The theories can be divided into groups corresponding to different
formation mechanisms:
(A) Direct molecular cloud fragmentation
(B) Protostellar disk fragmentation theories
(C) Companion star-planet interaction (in double star like 16 Cyg)
(D) Classical giant planet formation with planet-planet interaction
(E) Resonant disk-planet interaction
(D) Scattering among several massive planets
Assumption: planet formation often produces a multiple system
which is unstable over long timescales:
• Chaotic evolution of a, e (especially e)
• Orbit crossing
• Eventual close encounters -> ejections
• High eccentricity for survivors
Advantages:
• Given enough planets, close together, definitely works
• Can produce very eccentric planets cf e=0.92 example discovered
• Some (stable) multiple systems are already known
Disadvantages:
• Requires planets to form very close together.
Is it plausible that unstable systems formed in a large fraction of
extrasolar planetary systems?
• Collisions may produce too many low e systems
(E) Disc interactions
Assumption: gravitational interaction with disc generates eccentricity
Advantages:
• Same mechanism as invoked for migration
• Works for just one planet in the system
• Theoretically, interaction is expected to increase eccentricity
if dominated by 3:1 resonance
Disadvantages:
PH507
Astrophysics
Professor Michael Smith
18
• Gap is only expected to reach the 3:1 resonance for brown dwarf type
masses, not massive planets. Smaller gaps definitely tend to circularize the
orbit instead.
• Seems unlikely to give very large eccentricities
(B) Protoplanetary disc itself is eccentric
Assumption: why should discs have circular orbits anyway?
Eccentric disc -> eccentric planet?
Not yet explored in much depth. A possibility, though again seems unlikely to lead to
extreme eccentricities.
Scattering theory is currently most popular, possibly augmented
by interactions with other planets in resonant orbits.
Lecture 9: Radiation processes
Almost all astronomical information from beyond the Solar System comes to us
from some form of electromagnetic radiation (EMR).
We can now detect and study EMR over a range of wavelength or, equivalently,
photon energy, covering a range of at least 1016 - from short wavelength, high
photon energy gamma rays to long wavelength low energy radio photons.
Out of all this vast range of wavelengths, our eyes are sensitive to a tiny slice of
wavelengths- roughly from 4500 to 6500 Å. The range of wavelengths our eyes
are sensitive to is called the visible wavelength range. We will define a
wavelength region reaching somewhat shorter (to about 3200 Å) to somewhat
longer (about 10,000 Å) than the visible as the optical part of the spectrum.
Physicists measure optical wavelengths in nanometers (nm). Astronomers tend
to use Angstroms. 1 Å = 10-10 m = 0.1 nm. Thus, a physicist would say the
optical region extends from 320 to 1000 nm.)
All EMR comes in discrete lumps called photons. A photon has a definite
energy and frequency or wavelength. The relation between photon energy (Eph)
and photon frequency  is given by:
Eph = h
or, since c = 
PH507
Astrophysics
Professor Michael Smith
E ph 
19
hc

where h is Planck’s constant and  is the wavelength, and c is the speed of
light.
The energy of visible photons is around a few eV (electron volts). (An electron
volt is a non- metric unit of energy that is a good size for measuring energies
associated with changes of electron levels in atoms, and also for measuring
energy of visible light photons. 1 eV = 1.602 x 10-19 Joules.) An approximate
value (1 in 104) for the energy of electromagnetic radiation expressed in electron
volts is given by 1234 / λ, where λ is the wavelength in nanometres.
In purely astronomical terms, the optical portion of the spectrum is important
because most stars and galaxies emit a significant fraction of their energy in this
part of the spectrum. (This is not true for objects significantly colder than stars e.g. planets, interstellar dust and molecular clouds, which emit in the infrared
or at longer wavelengths - or significantly hotter- e.g. ionised gas clouds,
neutron stars, which emit in the ultraviolet and x-ray regions of the spectrum.
Another reason the optical region is important is that many molecules and
atoms have electronic transitions in the optical wavelength region.
We will define the regions of the Electromagnetic Spectrum to have wavelengths as
follows:

Gamma-rays: < 0.1Å, highest frequency, shortest wavelength, highest
energy.

X-Rays: 0.1Å -- 100Å

Ultraviolet light: 100Å -- 3000Å

Visible light: 3000Å -- 10000Å = 1µm (micrometer or micron)

Infrared Light: 1µm -- 1mm

Radio waves: >1mm, lowest frequency, longest wavelength, lowest
energy.
Radio
Infrared
Visible
Ultraviolet
X-rays
Gamma rays
Wavelength
Range
wavelength > 10-4 m = 0.1 mm
700 nm < wavelength < 0.1 mm
400 nm < wavelength < 700 nm
20 nm < wavelength < 400 nm
0.1 nm < wavelength < 20 nm
wavelength < 0.1 nm
PH507
Astrophysics
Professor Michael Smith
20
Blackbody Radiation
Where then does a thermal continuous spectrum come from? Such a continuous
spectrum comes from a blackbody whose spectrum depends only upon the absolute
temperature. A blackbody is so named because it absorbs all electromagnetic energy
incident upon it - it is completely black.
To be in perfect thermal equilibrium, however, such a body must radiate energy at
exactly the same rate that it absorbs energy; otherwise, the body will heat up or cool
down (its temperature will change).
Ideally, a blackbody is a perfectly insulated enclosure within which radiation has come
into thermal equilibrium with the walls of the enclosure. Practically, blackbody
radiation may be sampled by observing the enclosure through a tiny
pinhole in one of the walls.
The gases
in
the interior
of a
star are
opaque
(highly
absorbent)
to all radiation (otherwise, we would see the stellar interior at some wavelength!);
hence, the radiation there is blackbody in character. We sample this radiation as it
slowly leaks from the surface of the star - to a rough approximation, the continuum
radiation from some stars is blackbody in nature.
Planck’s Radiation Law
After Maxwell's theory of electromagnetism appeared in 1864, many attempts were
made to understand blackbody radiation theoretically. None succeeded until, in 1900,
Max K. E. L. Planck (1858-1947) postulated that electromagnetic energy can propagate
only in discrete quanta, or photons, each of energy E = hv. He then derived the
spectral intensity relationship, or Planck blackbody radiation law:




2h 3  1

I( )d 
 c 2  hkT 
e  1


where I(v)dv is the intensity (J/m2 . s . sr) of radiation from a blackbody at temperature
T in the frequency range between v and v + dv, h is Planck's constant, c is the
speed of light, and k is Boltzmann's constant. Note the exponential in the denominator.
Because the frequency v and wavelength of electromagnetic radiation are related by
v = c, we may also express Planck's formula in terms of the intensity emitted per
unit wavelength interval:
PH507
Astrophysics
Professor Michael Smith
21
This is illustrated for several values of T:
Note that both I() and I(v) increase as the blackbody temperature increases - the
blackbody becomes brighter. This effect is easily interpreted when we note that I(v)∆v
is directly proportional to the number of photons emitted per second near the energy
hv. The Planck function is special enough so that its given its own symbol, B() or B(v),
for intensity.
Long wavelengths: Rayleigh tail : B( )  1 / 4
Wien’s Law
A blackbody emits at a peak intensity that shifts to shorter wavelengths as its
temperature increases.
PH507

Astrophysics
Professor Michael Smith
22
Wilhelm Wien (1864-1928) expressed the wavelength at which the
maximum intensity of blackbody radiation is emitted - the peak (that
wavelength for which dI()/d = 0) of the Planck curve (found from
taking the first derivative of Planck's law) - by Wien's displacement law:
max = 2.898 x 10-3 / T
where max is in metres when T is in Kelvin. Note that because maxT =
constant, increasing one proportionally decreases the other.
For example, the continuum spectrum from our Sun is approximately
blackbody, peaking at max ≈ 500 nm. Therefore, the surface temperature is
near 5800 K.
PH507
Astrophysics
Professor Michael Smith
23
The Law of Stefan and Boltzmann
The area under the Planck curve (integrating the Planck function) represents the
total energy flux, F (W/m2), emitted by a blackbody when we sum over all
wavelengths and solid angles:
The formula is:

The constant "sigma" is called the Stefan-Boltzmann constant
and is given by:

The temperature in this equation is the surface temperature of
the object! The object might be much hotter deep inside, but this
doesn't matter.
The strong temperature dependence of this formula was first deduced from
thermodynamics in 1879 by Josef Stefan (1835-1893) and was derived from
statistical mechanics in 1884 by Boltzmann. Therefore we call the expression
the Stefan-Boltzmann law. The brightness of a blackbody increases as the
fourth power of its temperature. If we approximate a star by a blackbody, the
total energy output per unit time of the star (its power or luminosity in watts)
is just
L = 4R2T4
since the surface area of a sphere of radius R is 4R2
PH507
Astrophysics
Professor Michael Smith
24
To summarise: A blackbody radiator has a number of special characteristics.
One, a blackbody emits some energy at all wavelengths. Two, a hotter
blackbody emits more energy per unit area and time at all wavelengths than
does a cooler one. Three, a hotter blackbody emits a greater proportion of its
radiation at shorter wavelengths than does a cooler one. Four, the amount of
radiation emitted per second by a unit surface area of a blackbody depends on
the fourth power of its temperature.