Star Formation

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Star Formation

• Gravitational collapse of molecular cloud
• Evolution of protostars onto main sequence
• Gravitational contraction
• Luminosity versus temperature and radius

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Star formation

• Watch for
• Collapse of cloud
• Rotation of cloud
• Formation of disk near protostar
• Show animation

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Gravitational collapse
Which configuration has more potential energy?
A
B
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Potential energy due to gravity
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Gravitational collapse
Which configuration has more potential energy?
A
B
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Potential energy due to gravity
Sphere of mass M and radius R
Gravitational potential energy is released as
sphere shrinks
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Gravitational collapse

• How much energy is released when 1 M? of material
  collapses from a radius of 10 R ? to 1 R ??

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Evolution of stars

• Stars change over their lifetimes (from formation
  to death).
• We can track these changes via motion of the star
  in the HR diagram.

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Protostars on HR diagram
Where would a collapsing gas cloud appear on an
HR diagram?
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Gravitational collapse

• About 2?1041 J of energy is released when 1 M? of
  material collapses from a radius of 10 R ? to 1 R
  ?. This collapse takes about 10-20 million
  years. The luminosity is

Where would such an object appear on the HR
diagram?
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Protostars evolve into main-sequence stars

• Protostar collapses under gravity.
• The collapse releases energy.
• The star is relatively transparent, so the
  energy is radiated away, temperature doesnt
  change much.
• The star gets smaller so it get dimmer.

Brighter
Hotter
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Cloud collapse to main-sequence star
evolutionary track on HR diagram
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Protostars on the HR diagram
Hotter
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Luminosity versus radius and temperature
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R RSun T TSun
R 2 RSun T TSun
Which star is more luminous?
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Luminosity versus radius and temperature
2
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R RSun T TSun
R 2 RSun T TSun

• Each cm2 of each surface emits the same amount
  of radiation.
• The larger stars emits more radiation because it
  has a larger surface. It emits 4 times as much
  radiation.

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Luminosity of a Black Body Radiator

• For the spherical object, the total power
  radiated the total luminosity is
• L 4?R2?T4
• T temperature
• ? Stephan-Boltzman constant
• 5.67?10-8 W/m2 K4
• R radius

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Protostars evolve into main-sequence stars

• The star gets smaller so it get dimmer.
• Next the protostar becomes opaque, light no
  longer escapes easily.
• Heat is trapped and the protostar gets hotter.

Brighter
Hotter
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Why does temperature increase as star contracts?

• Note that luminosity remains constant.
• To produce constant luminosity as radius
  decreases, need increase in temperature

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More massive stars form faster
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As gas is pulled in towards a protostar which
does not occur

• the gas starts to rotate more rapidly
• some of the gas is ejected in jets
• some of the gas forms a disk around the protostar
• some of the gas undergoes nuclear fusion

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Which clouds will collapse?

• Gravitational force causes objects to collapse.
• What keeps objects from collapsing?
• In the solar system, the motion of the planets
  keeps them from falling in to the Sun.
• In a gas, the random motions of the gas atoms can
  support the gas against gravity.

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Temperature
lower T
higher T

• Temperature is proportional to the average
  kinetic energy per molecule

k Boltzmann constant 1.38?10-23 J/K
8.62?10-5 eV/K
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Energy of gas cloud
Gravitational potential energy Sphere of mass M
and radius R Kinetic energy of N atoms
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Energy of gas cloud
If E lt 0 then gas cloud collapses If E gt 0 then
gas cloud can support itself Density of gas
cloud is n
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Critical size of gas cloud
By increasing the mass, we can always cause the
gravity to dominate so that the gas cloud
collapses. Critical size and mass are called the
Jeans length and mass
T in Kelvin, n in atoms/cm3
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Critical size of gas cloud
If we have a cloud at T 30 K and n 300 cm-3,
how large pieces does it fragment into?
Therefore, such clouds will typically form a
group of stars rather than a single star. Stars
are generally found in groups, called star
clusters or OB associations, depending on the
type of stars.
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Star cluster
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An OB association is a group of O and B class
stars which are producing ionizing radiation,
causing an HII nebula glow (example Trapezium in
Orion Nebula)
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Critical size of gas cloud
The dense cores can reach n 300,000 cm-3, how
large pieces do they fragment into?
Therefore, the dense cores fragment into
individual stars.
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Review Questions

• What is a protostars source of energy?
• How does a protostars radius and luminosity
  change as it contracts?
• What is the relation between luminosity, radius,
  and temperature.
• How does a protostars mass influence its speed
  of formation?
• What is the Jeans mass?