Download Collapse: Method 2

PH507
Astrophysics
Professor Michael Smith
1
Final exam: Important Revision Topics
Exoplanet: finding techniques
Exolanet formation processes, debris disks
Distances – luminosity – magnitudes - temperatures
Radiation processes - multiwavelength
Kepler’s laws
Hertzsprung-Russell tracks
Exolanets; brown dwarfs
Stellar lifetimes
Protostars & Young stars: classes.and evolution.
Lectures Week 8: Star Formation
1. Intro: Star formation is on-going.
 What is the origin of our solar system? Descartes, Kant,
Laplace: vortices, nebular hypothesis: importance of angular
momentum.
 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.
2. Molecular clouds: ingredients

Young stars are located in or near molecular clouds (the
stellar factories/nurseries).

Stars mainly form in clusters in giant molecular clouds.

Over 90% of atoms are tied up in molecules. 99.99% is
molecular hydrogen: H2
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Astrophysics
Professor Michael Smith
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
Over 120 other molecules discovered, including water, carbon
monoxide CO, formaldehyde H2CO, ammonia NH3, hydrogen
cyanide HCN, formic acid HCOOH and methanol CH3CO

Admixture of dust: 1% by mass– tiny grains (less than 1
micron in size) of silicates/graphite with ice coatingss, or soot
(polycyclic aromatic hydrocarbons or PAHs).

Cosmic rays, magnetic field.

The large amount of gas and dust in the cloud shields the
molecules from UV radiation from stars in our galaxy. The
molecules can then cool the gas down to 10-30K. Dense cold
cores can form (eggs?) in which gravity rules).

The H2 molecules cannot form by H-H collisions (excess
energy needs an outlet). H2 forms on dust, atoms stick,
migrate, bind, ejected. Other molecules form through
collisions (ion-chemistry).
3. Molecular clouds: anatomy
Opaque at UV and visible wavelengths.
Bright and luminous at millimetre wavelengths: dust
continuum.
Bright rotational and vibrational molecular emission lines at
radio and infrared wavelengths e.g. CO lines
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Astrophysics
Professor Michael Smith
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Molecular clouds are cold: 8<= Tkin<=20 K Typical value
~10 K
Low ionization: fe =ne/n ~10-6 - 10-7 => very neutral!
High density: n(H2) >= 100 cm-3
Giant molecular clouds are very massive: M~ 104 to 106
solar masses
Giant molecular clouds are large: size ~ 100 parsecs
They are clumpy
Supersonic gas motions are found in almost all clouds
Line widths ~ 0.5 to 2 km s-1; sound speed ~ 0.2 km s-1
indicative of nonthermal motions such as rotation,
turbulence, shocks, contraction or expansion, stellar
bipolar outflows, etc.
Measures:
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Astrophysics
Professor Michael Smith
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Atmospheric cloud:
A comparison of scales between typical molecular and
atmospheric clouds.
Molecular Cloud
Size
1014 km
Mass
1036 gm
Particle density
103 cm-3
Temperature
20
K
Mol/atomic weight
2.3
Speed of sound
0.3 km/s
Turbulent speed
3
km/s
Dynamical time
Million years
Atmospheric Cloud
1
km
11
10
gm
19
10
cm-3
260
K
29
0.3
km/s
0.003 km/s
Five minutes
Scales & Types:
Estimated properties of individual molecular aggregates in the
Galaxy:
Phase
GMCs
Clumps/Globules
Mass
(Msun)
6x104 - 2x106
Size
(parsecs)
20 - 100
Density (cm-3)
100 - 300
Temperature (K)
15 - 40
Magn. Field(G)
1 - 10
Line width (km/s)
6 - 15
Dynamic life (years)
3 x 106
102
0.2 - 4
103 - 104
7 - 15
3 - 30
0.5 - 4
106
Cores
1 - 10
0.1 - 0.4
104 - 105
10
10 - 50
0.2 - 0.4
6 x 105
Note: dynamical life defined as Size/(Line width), true lifetimes
would be considerably longer if clouds were static.
Example: Orion millimeter dust emission – clumps and cores
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Astrophysics
Professor Michael Smith
The Horsehead (optical – dark cloud)
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Astrophysics
Professor Michael Smith
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Summary: clouds are turbulent, possibly fractal
4. Molecular clouds: their origin
Agglomeration: collisions and merging/coalescence of smaller
clouds – not sufficient number of small clouds. Spiral arm
density-wave focusing.
Gravitational instability followed by fragmentation
Condensation: out of atomic clouds.
Accumulation: gas swept up into supershells, focused in
turbulent interstellar medium.
Answer: combination of these.
5. Molecular cloud evolution
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Astrophysics
Professor Michael Smith
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
Observed: Giants, clumps, cores, eggs

Gravitational Collapse: When a fragment of a molecular
cloud reaches a critical mass – the Jeans mass (after Sir
James Jeans (1877-1946) - it collapses to form a star. Gas
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Astrophysics
Professor Michael Smith
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and dust are then pulled together by gravity until a star is
formed.

Balance forces: gravity and pressure: GM J2/R ~ MJcs2

Eliminate R in favour of the density, yields the Jeans Mass,
which more precisely calculated is
MJ 
 T 
M J  1

 10 K 
3/ 2
  
 
6 G


n


 4 3 
 10 cm 
1/ 2
 T 
RJ  0.19

10
K


3/ 2
c s3  1 / 2
1 / 2


n


 4 3 
 10 cm 
M sun
1 / 2
par sec s

Fragmentation: The molecular cloud does not collapse into a
single star. It fragments through the Jeans instability - into
many clumps.

As the density rises, the Jeans mass falls. This means the
cloud continues to fragment into smaller clumps.

What makes it reach/exceed the critical mass in the first
instance?

Mechanisms: sequential, spontaneous, turbulence,
triggers
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Astrophysics
Professor Michael Smith
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What are the conditions that favour the initiation of star
formation?
Decrease internal pressure: By decreasing the temperature or
the density or both
Increasing the mean mass per particle by transforming from
an atomic gas to a molecular gas.
Decrease the ionization fraction, fe = ne/n to < 10-7 => gas
decouples from any magnetic field present so that magnetic
pressure cannot support the cloud.
Increase the external pressure: By partially focused shocks.
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Astrophysics
Professor Michael Smith
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By ionization of the gas around a molecular clump: radiativelydriven implosion.
Collapse: Method 1

Accretion- coalescence:
Build up of small clouds of gas and dust into clumps.

Clumps "stick" together and grow.

Very slow - due to low interstellar densities
Collapse: Method 2

Gravity and Radiation Pressure

Collapse: Method 3: sequential, triggered

Compression by supernova blast waves
Evidence that the Solar System/Sun was triggered by a supernova – (radioactive
isotopes so short-lived that they no longer exist were trapped in chondrules within
meteorites).
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Collapses
Methods
Astrophysics
Professor Michael Smith
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Collapse: Method 1

Accretion- coalescence:
Build up of small clouds of gas and dust into
clumps.

Clumps "stick" together and grow.

Very slow - due to low interstellar densities
Collapse: Method 2

Gravity and Radiation Pressure
Collapse: Method 3: sequential, triggered

Compression by supernova blast waves
Evidence that the Solar System/Sun was triggered by a supernova –
(radioactive isotopes so short-lived that they no longer exist were
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Astrophysics
Professor Michael Smith
trapped in
chondrules within meteorites).
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Astrophysics
Professor Michael Smith
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6. Why clouds can’t collapse
The Difficult
Path
to Collapse

Gravity makes parts of a the cloud collapse.

Hindrances to collapse which favour expansion:
1. Internal heating

Causes pressure build-up
2. Angular momentum

Causes high rotation speeds

(exemplified by a figure skater)
3. Magnetic support
Internal
Heating

Cloud fragments collapse

Potential energy => Kinetic Energy
o
Gas particles speed up and collide.

The temperature increases.

This causes a pressure build-up which slows (or
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Astrophysics
Professor Michael Smith
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stops) the collapse.
Angular
Momentum

Solution: Energy is radiated away.

Angular momentum

o
A = mass x velocity. of rotation x radius
o
A=mvr
Conservation of angular momentum.
o
Magnetic
support
A = constant for a closed system.

As the cloud fragment shrinks due to gravity, it
spins faster.

Collapse occurs preferentially along path of
least rotation.

The cloud fragment collapses into a central core
surrounded by a disk of material.

Further collapse: magnetic braking – winding
and twisting of magnetic field lines connected to
external gas.

There is a critical mass, for which gravity is held up by
magnetic pressure.

A cloud can be super-critical – free to
collapse

Otherwise, the field diffuses out slowly:
ambipolar diffusion – since the magnetic field
is only tied to the ions, and the ions slip through
the molecules.
PH507
Astrophysics
Professor Michael Smith
15
7 The Final Collapse: approaching birth
Final adjustments. The thermodynamics now take on supreme
importance. Much of what occurs is still theory:
Stage 1. The density shields the core from external radiation,
allowing the temperature to drop. Dust grains provide efficient
cooling. The hydrogen is molecular.
Stage 2. An isothermal collapse all the way from densities of 104
cm-3 then proceeds. The gravitational energy released goes via
compression into heating the molecules. The energy is rapidly
passed on to the dust grains via collisions. The dust grains reradiate the energy in the millimeter range, which escapes the
core. So long as the radiation can escape, the collapse remains
unhindered.
Stage 3. At densities of 1011 cm-3 and within a radius of 1014 cm
the gas becomes opaque to the dust radiation even at 300 microns.
The energy released is trapped and the temperature rises. As the
temperature ascends, the opacity also ascends. The core
suddenly switches from isothermal to adiabatic.
Stage 4. The high thermal pressure resists gravity and this ends
the first collapse, forming what is traditionally called the first core at
a density of 1013 cm-3 - 1014 cm-3 and temperature of 100-200 K.
Stage 5. A shock wave forms at the outer edge of the first core.
The first core accretes from the envelope through this shock.
The temperature continues to rise until the density reaches 1017 cm3
.
Stage 6. The temperature reaches 2000 K. Hydrogen molecules
dissociate at such a high temperature if held sufficiently long. The
resulting atoms hold less energy than the molecules did (the
dissociation is endothermic), tempering the pressure rise. The
consequence is the second collapse.
Stage 7. The molecules become exhausted and the cooling stops at
the centre of the first core. Protostellar densities of order 1023 cm3
are reachedand with temperatures of 10,000 K, thermal pressure
brakes the collapse. This brings a second and final protostellar
core into existence. The mass of this core may only be one per cent
of the final stellar mass.
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Astrophysics
Professor Michael Smith
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Stage 8. The first shock from Stage 5 disappears while a second
inner shock now mediates the accretion onto the protostellar
core. A star is born.
Stage 9: Further Collapse with Angular Momentum into a Disk

All astronomical objects spin, even if very slowly.

The original collapsing cloud will have some small amount
of spin.

During a collapse, angular momentum is conserved.

Angular momentum is J = a x W R2
o
a = a constant whose value we aren't interested in
o
W = Angular velocity = 2 pi/P
o
P = Spin Period
o
R = Radius of the star cloud

If angular momentum is conserved then
Wfinal = W0 x (R0/Rfinal)2

Since R0/Rfinal is much larger than 1
Final angular velocity can be very high, even if the initial
angular velocity is very low.

Centrifugal acceleration (GMv2/R) is proportional to W2R)
and gravity (GM/R2) approach equilibrium

A very rapidly rotating cloud will get flattened into a disk.

This disk can then fragment into protoplanets.
Disk
Forms
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Planet
Formation
Astrophysics
Professor Michael Smith
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
The disk around the central core will
fragment further, producing rings of
material.

The particles in these rings can accrete
together to form planetesimals and
planets!
PH507
Making the
Stars
Visible
Astrophysics
Professor Michael Smith
18
Making the Stars Visible

After a star is born it heats the gas
and dust around it.

Jets of gas are ejected: bipolar
outflows are observed.

Eventually the gas and dust are
accreted or dispersed.

The star is then "visible."

Prior to this it could be seen only in
the radio and the infrared.
Spectral energy distributions define the classes of protostars
and Young Stellar Objects……
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Astrophysics
Professor Michael Smith
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PH507
Astrophysics
Professor Michael Smith
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Processes in Young Star Evolution
accretion, contraction, jets and outflow
Proplyds – protoplanetary disks:
Accretion through disc: bolometric luminosity of protostar is
.
GM M
L
R
Where M*dot* is the mass accretion rate and GM/R is the energy released
per unit mass onto the protostar of (accumulating) mass M and radius R.
Star accumulates gas from envelope through the disc, releases some
through jets back into cloud. The jets are thought to be the channels
for the extraction of angular momentum.
PH507
Astrophysics
Professor Michael Smith
21
Jets: extend parsecs from source. They are seen through their impact with
cloud: shock wave heating: Herbig-Haro Objects. They create large
reservoirs of outpouring and swept-up gas: bipolar outflows or molecules
outflows
HH46/47:
Optical: HST
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Astrophysics
Professor Michael Smith
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Infrared: Spitzer
Massive Stars & Clusters:
Massive stars should not form: hydrogen burning begins while
accreting: radiation pressure should resist the infall.
Accretion must be high and through a disk: to suffocate the
feedback.
Massive stars create hot molecular cores, masers,
compact/extended H II regions:
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Astrophysics
Professor Michael Smith
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Most stars are in multiple bound systems.
Frequency of occurrence:
Single:binary:triple:quadruple is 58:33:7:1
Multiplicity theory covers: capture, fission,
core/collapse/disk fragmentation
Capture: extremely unlikely
Fission: splitting leads only to close binaries
Fragmentation is plausible.
90% of stars are born in clusters.
Cluster: over 35 stars, at least 1 Msun/pc3
Embedded clusters: 1000 Msun with a density
10,000 Msun/pc3
Segregation: Massive stars tend to form in centre (form in
situ, don’t migrate)
Relaxation: Cloud evolves and cluster disperses in a few
million years.
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Astrophysics
Professor Michael Smith
24
Clusters dissolve: most stars are NOT in clusters, they
become field stars.
All suggests: Hierarchical fragmentation within a
turbulent medium
.
Star formation efficiency, the amount of cloud gas
transformed into stars, is only 3%-20%.
The initial mass function (the IMF: initial mass function):
most star are of low mass.
Question: Power law?
Salpeter IMF: N proportional to M-1.3
Scale-free hierarchy. Jeans mass?
Is there a brown dwarf desert? Planets form in disks, stars
in collapse.
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Astrophysics
Turbulence v. Gravity
Professor Michael Smith
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Astrophysics
Professor Michael Smith
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PH507
Astrophysics
Professor Michael Smith
The Sun: A Model Star
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
Astrophysics
Professor Michael Smith
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Our Sun is the nearest star. The fascinating properties and phenomena of
the solar surface layers are easily observed and have been studied
intensely. Unfortunately, models for understanding solar phenomena have
not kept pace with such detailed data. Because the Sun is a fairly typical
star and because it is the only star that spans a large angular diameter as
seen from the Earth, the discussion here serves as the physical basis to
investigate the other stars.
Sun
Earth
Mass (1024 kg)
1,989,100.
GM (x 106 km3/s2)
132,712.
Volume (1012 km3)
1,412,000.
Volumetric mean radius (km) 696,000.
Mean density (kg/m3)
1408.
Surface gravity (eq.) (m/s2)
274.
Escape velocity (km/s)
617.7
Ellipticity
0.00005
2
Moment of inertia (I/MR )
0.059
Visual magnitude V
-26.74
Absolute magnitude
+4.83
24
Luminosity (10 J/s)
384.6
Mass conversion rate (106 kg/s)
4300.
Mean energy production (10-3 J/kg)
0.1937
6
2
Surface emission (10 J/m s)
63.29
Spectral type
G2 V
Model values at center of Sun:
Central pressure:
Central temperature:
Central density:
(Sun/Earth)
5.9736
333,000.
0.3986
333,000.
1.083 1,304,000.
6371.
109.2
5515.
0.255
9.78
28.0
11.2
55.2
0.0034
0.015
0.3308
0.178
-3.86
2.477 x 1011 bar
1.571 x 107 K
1.622 x 105 kg/m3
The Structure of the Sun

The average density of the Sun is only 1400 kg/m 3 - consistent with a
composition of mostly gaseous hydrogen and helium.

From its angular size of about 0.5° and its distance of almost 150 million
kilometres, we determine that its diameter is 1,392,000 kilometres (109
Earth diameters and almost 10 times the size of the largest planet, Jupiter).

All of the planets orbit the Sun because of its enormous gravity. It has about
333,000 times the Earth's mass and is over 1,000 times as massive as
Jupiter.

The Sun is made of 94% Hydrogen, 6% Helium, - the other elements make
up just 0.13% (the three most abundant ‘metals’ Oxygen, Carbon, and
Nitrogen make up 0.11%).
PH507

Astrophysics
Professor Michael Smith
29
The Sun’s atmosphere has the following layers (from innermost to
outermost):
o
The photosphere is about 300 km thick. Most of the Sun's visible
light that we see originates from this region.
o
The chromosphere is about 2000 km thick. We only see this layer
and the other outer layers during an eclipse.
o
The corona extends outwards for more than a solar radius.
The Photosphere
An image of the Sun's Photosphere shows:

Limb Darkening. Limb darkening is evidence that the temperature of the
Sun's photosphere decreases outwards.

Sunspots
The Sun's Spectrum is an Absorption Spectrum

Since the photosphere is cooler and less dense than the interior region it
allows the continuous blackbody spectrum to flow through it.

Only at the wavelengths at which atoms in the photosphere can absorb
light will photons be impeded in their outward travel.
Sunspots:

Sunspots are regions with high magnetic fields (1000 x higher magnetic
field than average)

Typical size of spots is similar to the size of the Earth.

These regions are cooler (redder) than average, so they look darker than
the surrounding hotter region.

Sunspots are related to X-ray flares, mass ejections and the aurora seen
on earth
PH507
Astrophysics
Professor Michael Smith
30
.
Close-up Picture of a group of Sunspots

The darkest regions (umbra) have the largest magnetic fields and the
coolest temperatures. The outer brighter region is the penumbra.

Sunspots come in pairs: each member of the pair has opposite polarity.
(I.e. one is a north magnetic pole, the other is south.)

Each sunspot region lasts for a few days to a few weeks.

The filaments in the penumbra are due to the magnetic lines of force.
Movement of Sunspots

Movements of spots reveal that the Sun rotates with a period close to
one month.
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Astrophysics
Professor Michael Smith
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
Equator rotates faster than the higher lattitudes. Differential Rotation

You can find photos of the Sun in many different wavelengths (updated
daily) at the website: http://umbra.nascom.nasa.gov/images/latest.html
http://science.nasa.gov/ssl/pad/solar/surface.htm
Granules
Close-up Picture of the Photosphere

Granules are the cell-like features seen on the Sun's photosphere that
cover the entire solar surface, except for the sunspot regions..

The granules are the tops of convective cells which lie in the
convective zone just below the photosphere.

Each cell ranges in size from 100 km to 1000 km across and may last up
to half an hour.

The bright regions are zones where hot gas rises. They are the tops of
deep gas columns where energy is transported by convection. Spectra of
the centers of the granules shows these regions to be a few hundred
Kelvin hotter than the surrounding darker lanes.

The dark borders are the places where the cool gas sinks.

The gas moves outwards or inwards at speeds up to 7 km/s. (Measured
through Doppler shifts.).
The Sun's Chromosphere
A Solar Eclipse

The photosphere is much brighter than the outer parts of the Sun's
atmosphere (the chromosphere and the corona), so regular photos of
the Sun do not show the outer atmosphere.
PH507

Astrophysics
Professor Michael Smith
32
During a solar eclipse the Moon blocks out the light from the
photosphere and we can only see the light coming from the
chromosphere and corona.
The Chromosphere with a close-up of the spicules.

The Chromosphere is not exactly a sphere: there are many spicules and
prominences which jut outwards.

Magnetic fields help support the spicules and the prominences.

The red colour results from the emission of Balmer-alpha photons:
electrons jumping from the n=3 level to the n=2 level.
The emission lines can only occur if the gas in the chromosphere is very hot
and the density is very low. The chromosphere is hotter (but less dense) than
the photosphere.
In the spicules, which are best observed in H , gas is rising at about 20 to 25
km/s. Although spicules occupy less than 1% of the Sun’s surface area and
have lifetimes of 15 minutes or less, they probably play a significant role in the
mass balance of the chromosphere, corona, and solar wind, and occur in
regions of enhanced magnetic fields
Solar spicules, short-lived narrow jets of gas that typically last mere minutes,
can be seen sprouting up from the solar chromosphere in this H alpha image of
the Sun. The spicules are the thin, dark, spikelike regions. They appear dark
against the face of the Sun because they are cooler than the solar photosphere
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Astrophysics
Professor Michael Smith
33
Prominences

Close-up picture of the chromosphere showing a prominence.
The prominences are loops of gas which arch over sunspot regions.
The quiescent prominences are very stable and can last weeks or months.
Eruptive Prominences

Some of the prominences will erupt, causing gas to be flung outwards.

The gas travels outwards about 70,000 km in the course of a few hours.

Prominences are more likely to erupt when the magnetic fields near the
sunspots are changing.
Variation of Temperature in the Sun's Atmosphere:

Photosphere: Temperature decreases outwards.
o
At bottom: T = 6400 K
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Astrophysics
o

Professor Michael Smith
34
At top: T = 4000 K
Chromosphere: Temperature increases outwards.
o
At top: T = 10,000 K

Transition Zone: Temperature shoots up to near 1 million K

Corona: Temperatures increase to about 2 million K

The source of this heat is not well understood. Current theories suggest
that magnetic waves might transport energy from the convective zone
to the corona.
The Transition Zone

The next picture shows the transition zone as seen through a filter which
only sees the light coming from an electronic transition of Sulfur VI at
temperatures of about 200,000ºC. Instead of hydrogen, the light emitted
by the transition region is dominated by such ions as C IV, O IV, and Si
IV (carbon, oxygen, and silicon each with three electrons stripped off).
These ions emit light in the ultraviolet region of the solar spectrum that is
only accessible from space.
PH507
Astrophysics
Professor Michael Smith
35

These emission lines are Ultra-violet. which are only possible when the
gas is very hot, near 100,000 K.

The structures seen here are similar to those seen in the chromosphere.
The Corona

A visible light photograph of the Corona during a solar eclipse.
Photograph of the solar corona during the July, 1991 eclipse, at the peak of the
sunspot cycle. At these times, the corona is much less regular and much more
extended than at sunspot minimum. Astronomers believe that coronal heating
is caused by surface activity on the Sun. The changing shape and size of the
corona are the direct result of variations in prominence and flare activity over
the course of the solar cycle.
PH507
Astrophysics
Professor Michael Smith
36

The Corona emits X-rays.

This image corresponds to an electronic transition of highly ionized iron.
(Iron stripped of 11 of its electrons.)

Iron can only lose 11 electrons and emit this X-ray light if the
temperature is more than one million K.

The dark regions are coronal holes which are lower density than
average.
PH507

Astrophysics
Professor Michael Smith
37
The solar wind originates from the coronal holes.
Coronal Loops
Huge numbers of small, closely intertwined magnetic loops continuously
emerge from the Sun's visible surface, clash with one another and dissolve
within 40 hours.
The loops seem to form a tight pattern that form a magnetic carpet. Their
interaction generates electrical and magnetic short-circuits
(magnetic
reconnection) and releases enough energy to heat the corona to temperatures
hundreds of times higher than those of the solar surface.
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Astrophysics
Professor Michael Smith
38
Coronal loops come in a variety of shapes and sizes, but most are enormous,
capable of spanning several Earth's. (Photo: NASA and the TRACE team)
Solar Flares

Solar flares are large outbursts similar to eruptive prominences, but
larger and more energetic.

Solar flares increase the amount of particles which escape into the solar
wind.

If the particles ejected from the flare hit the Earth, then we get intense
auroral displays.
A negative effect is that the solar wind particles can disrupt radio transmissions.
Coronal Mass Ejection

When an eruptive prominence or a solar flare occurs, a coronal mass
ejection (CME) can also take place.
A CME is a stream of plasma (charged particles) ejected from the corona.
PH507
Astrophysics
Professor Michael Smith
39
The Solar Wind

UV images show the flow of gas from the Sun.

The solar wind is a stream of charged particles (protons and electrons)
which flow outwards from the coronal holes.
PH507
Astrophysics
Professor Michael Smith
40

The wind speed is high (800 km/s) over coronal holes and low (300
km/s) over streamers. These high and low speed streams interact with
each other and alternately pass by the Earth as the Sun rotates.

The solar wind particles flow throughout the solar system. The variations
buffet the Earth's magnetic field and can produce storms in the Earth's
magnetosphere
THE END