Download Collapse: Method 2

PH507
Astrophysics
Professor Michael Smith
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PH712: Star Formation & Molecular Clouds
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.
Major facts for nebula hypothesis:
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Coplanar orbits of the planets
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 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
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Astrophysics
Professor Michael Smith
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
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.
Abundances similar to that of the sun.
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In general: Gravity is fast-acting. Galaxy is old. But young stars
are still being born.
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Stars don't live forever, they must continue to be "born".
Where?
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Born in obscurity….needed infrared/millimeter/radio
wavelengths.
2. Molecular clouds: ingredients
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Young stars are located in or near molecular clouds (the stellar
factories/nurseries).
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Stars mainly form in clusters in giant molecular clouds.
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Over 90% of atoms tied up in molecules. 99.99% is molecular hydrogen:
H2
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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
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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).
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Cosmic rays, magnetic field.
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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).
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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.
Molecular clouds are cold: 8<= Tkin<=20 K Typical value ~10 K
PH507
Astrophysics
Professor Michael Smith
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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: Diameters ~ 325 ly
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
1019 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
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
Clumps/Globules
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
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The Horsehead (optical – dark cloud)
Summary: clouds are turbulent, possibly fractal
3. Molecular clouds: their origin
Agglomeration: collisions and merging/coalescence of smaller
clouds – not sufficient small clouds. Spiral arm density-wave
focusing.
Gravitational instability followed by fragmentation
Condensation: out of atomic clouds.
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Astrophysics
Professor Michael Smith
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Accumulation: gas swept up into supershells, focused in turbulent
interstellar medium.
Answer: combination of these.
4. Molecular cloud evolution
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Astrophysics
Professor Michael Smith
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Observed: Giants, clumps, cores, eggs
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Gravitational Collapse: When a fragment of a molecular cloud reaches a
critical mass – the Jeans mass (after Sir James Jeanss (1877-1946) - it
collapses to form a star. Gas and dust are then pulled together by gravity
until a star is formed.
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Balance forces: gravity and pressure: GMJ2/R ~ MJcs2
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
Astrophysics
Professor Michael Smith
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Eliminate R in favour of the density, yields the Jeans Mass, which more
precisely calculated is
MJ 
  
 
6 G
3/ 2
c s3  1 / 2
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Fragmentation: The molecular cloud does not collapse into a single star.
It fragments [through the Jeans instability - into many clumps.
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As the density rises, the Jeans mass falls. This means the cloud
continues to fragment into smaller clumps.
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What makes it reach/exceed the critical mass?
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Mechanisms: sequential, spontaneous, turbulence, triggers
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.
PH507
Astrophysics
Professor Michael Smith
9
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.
By ionization of the gas around a molecular clump: radiatively-driven
implosion.
Collapses
Methods
Collapse: Method 1
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Accretion- coalescence:
Build up of small clouds of gas and dust into
clumps.
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Clumps "stick" together and grow.
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Very slow - due to low interstellar densities
Collapse: Method 2
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Gravity and Radiation Pressure
Collapse: Method 3: sequential, triggered
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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
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trapped in chondrules within meteorites).
The Difficult
Path
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Gravity makes parts of a the cloud collapse.
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to Collapse
Astrophysics

Professor Michael Smith
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Hindrances to collapse which favour expansion:
1. Internal heating
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Causes pressure build-up
2. Angular momentum
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Causes high rotation speeds
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(exemplified by a figure skater)
3. Magnetic support
Internal
Heating
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Cloud fragments collapse
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Potential energy => Kinetic Energy
o
Angular
Momentum
Gas particles speed up and collide.
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The temperature increases.
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This causes a pressure build-up which slows (or
stops) the collapse.
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Solution: Energy is radiated away.
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Angular momentum
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o
A = mass x vel. of rotation x radius
o
A=mvr
Conservation of angular momentum.
o
A = constant for a closed system.
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As the cloud fragment shrinks due to gravity, it
spins faster.
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Collapse occurs preferentially along path of least
rotation.
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The cloud fragment collapses into a central core
surrounded by a disk of material.
PH507
Magnetic
support
Astrophysics
Professor Michael Smith
12
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Further collapse: magnetic braking – winding
and twisting of magnetic field lines connected to
external gas.
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There is a critical mass, for which gravity is held up by
magnetic pressure.
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A cloud can be super-critical – free to collapse
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The field diffuses out: ambipolar diffusion –
since the magnetic field is only tied to the ions,
and the ions slip through the molecules.
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 slightly. Dust grains provide efficient cooling. The hydrogen
is molecular.
Stage 2. An isothermal collapse all the way from densities of 10 4 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 re-radiate 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 300microns. 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 cm-3.
Stage 6. The temperature reaches 2000 K. Hydrogen molecules dissociate at
such a high temperature if held sufficiently long. The resulting atoms hold less
PH507
Astrophysics
Professor Michael Smith
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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 cm-3 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.
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.
Further Collapse with Angular Momentum into a Disk
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All astronomical objects spin, even if very slowly.
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The original collapsing cloud will have some small amount of spin.
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During a collapse, angular momentum is conserved.
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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
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If angular momentum is conserved then
Wfinal = W0 x (R0/Rfinal)2
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Since R0/Rfinal is much larger than 1
Final angular velocity can be very high, even if the initial angular velocity is
very low.
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Centrifugal force and gravity approach equilibrium
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A very rapidly rotating cloud will get flattened into a disk.
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This disk can then fragment into protoplanets.
Disk
Formation
PH507
Making the
Stars
Visible
THE END
Astrophysics
Professor Michael Smith
Making the Stars Visible
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After a star is born it heats the gas and dust
around it.
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Jets of gas are ejected: bipolar outflows are
observed.
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Eventually the gas and dust are accreted or
dispersed.
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The star is then "visible."
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