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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
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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
Over 120 other molecules discovered, including water, carbon
monoxide CO, formaldehyde H2CO, ammonia NH3, hydrogen
cyanide HCN, formic acid HCOOH and methanol CH3CO, and ions,
isotopes (i.e. D)
Admixture of dust: 1% by mass– tiny grains (less than 1 micron in
size) of silicates/graphite with ice coatings, 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).
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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
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 non-thermal motions such as rotation, turbulence, shocks,
contraction or expansion, stellar bipolar outflows, etc.
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Measures:
Molecular cloud:
Atmospheric cloud:
A comparison of scales between typical molecular and atmospheric
clouds:
Molecular Cloud
Size
1014 km
Mass
1036 g
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
1011 g
1019 cm-3
260 K
29
0.3
km/s
0.003 km/s
Five minutes
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Scales & Types:
Estimated properties of individual molecular aggregates in the Galaxy:
Phase
GMCs
Mass
(Msun) 6x104 - 2x106
Size
(parsecs)
20 - 100
-3
Density (cm )
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 Cores
102
0.2 - 4
103 - 104
7 - 15
3 - 30
0.5 - 4
106
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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The Horsehead (optical – dark cloud)
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.
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5. Molecular cloud evolution
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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 Jeans (18771946) - it collapses to form a star. Gas and dust are then pulled
together by gravity until a star is formed.
Balance forces: gravity and thermal gradient:
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GMJ2/R ~ MJcs2
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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
1/ 2
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3/ 2
ç ÷
6 èGø


n


 4 3 
 10 cm 
 T 
RJ  0.19

 10 K 

p æp ö
c s3 r -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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What are the conditions that favour the initiation of star formation?
Decrease internal pressure: By decreasing the temperature or increase 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.
By ionization of the gas around a molecular clump: radiatively-driven
implosion.
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Collapse: Method 1
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AccretionBuild up of small clouds of gas and dust into clumps.
Clumps "stick" together and grow.
Very slow - due to low interstellar densities
coalescence:
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 trapped
in chondrules within meteorites).
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6. Why clouds can’t collapse
The Difficult
Path
to Collapse
Internal
Heating
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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
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
stops) the collapse.
Solution: Energy is radiated away.
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Angular
Momentum
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Magnetic
support
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Angular momentum
o A = mass x velocity of rotation x radius
o A=mvr
Conservation of angular momentum.
o 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.
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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 104cm-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 1011cm-3 and within a radius of 1014cm 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
1013cm-3 - 1014cm-3 and temperature of 100-200K.
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 1017cm-3.
Stage 6. The temperature reaches 2000K. 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 1023cm-3 are reached
and with temperatures of 10,000K, 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 (about 10 Jupiter
masses).
Stage 8. The first shock from Stage 5 disappears while a second inner
shock now mediates the accretion onto the protostellar core. A protostar
is born.
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Stage 9: Further Collapse with Angular Momentum into a
Disk
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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.
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Angular momentum is J = a 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
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 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
Planet
Formation
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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!
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Making
the
Stars
Visible
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Making the Stars Visible
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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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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.
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
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HH46/47:
Optical: HST
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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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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.
2/3…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.
Clusters dissolve: most stars are NOT in clusters, they become field stars.
All suggests: Hierarchical fragmentation within a turbulent medium
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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 stars 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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Turbulence v. Gravity
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Brown Dwarfs: Failed Stars
• “Stars” between 13 and 80 times the mass of Jupiter may be able to
burn deuterium into helium for a short time, but cannot sustain
nuclear reactions. Such “failed” stars are called brown dwarfs. They
are similar in size to Jupiter.
• The Lithium Test. At a temperature of 2 million K, a lithium atom can
combine with a proton to form two He atoms. In a star that can sustain the
P-P chain, the core is hot enough to have burned all the Li to He. If Li does
appear in the spectrum, the center of the star must be cooler than 2 million
K, and/or the object is very young. In addition to Li, brown dwarfs show
methane and water absorption in their spectra.