Stability of Molecular Clouds
Recap
Star and Planet Formation:
Structure and distribution of molecular material
Lecture 9
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Disks
Effect of Rotation and Magnetic Fields
majority within GMCs primarily associated with spiral arms
hierarchical structure: clouds ! clumps ! cores
looked at the different observations techniques used
Gravitational collapse
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Lectures 1-9 available at www.ast.leeds.ac.uk/~jsu/
star_and_planet_formation
Jeans criterion
fragmentation
formation of protostar
cloud stability
Disks
Dr James Urquhart
email: jsu@ast.leeds.ac.uk
Office: EC Stoner 9.82
Office Hour: Wednesday 4-5
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effects of rotation and magnetic fields
accretion disks
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Effects of Rotation and Magnetic Fields
Outline
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Rotation
Magnetic field
Ambipolar diffusion
Angular momentum loss
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Effects of Rotation and Magnetic Fields
Effects of Rotation and Magnetic Fields
Cloud Rotation
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Cloud Rotation
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If initial cloud of radius
R has a uniform rotation
rate "
remembering that angular
momentum is given by
The centrifugal force is
!
r
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since
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and the Gravitational force is
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the centrifugal force will eventually win out
R
then conservation of specific
angular momentum along equator
means
"r2=!R2
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Effects of Rotation and Magnetic Fields
Effects of Rotation and Magnetic Fields
Cloud Rotation
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Cloud Rotation
We can determine the radius where FC = FG
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this is referred to as the centrifugal radius
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From observations " = 10-14 rad s-1 and using our typical Jeans critical
molecular cloud with MJ = 8 Mo and RJ = 0.2 pc
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We have only considered how rotation at the equator might impede the inward
motion of gas. How might rotation affect the rest of the cloud?
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Cloud can still contract parallel to rotation axis ! flattened structure
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Effects of Rotation and Magnetic Fields
Effects of Rotation and Magnetic Fields
Cloud Rotation
Cloud Rotation: The Angular momentum problem
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Effects of Rotation and Magnetic Fields
Magnetic Fields
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even slowly rotating cloud will be amplified to very fast rotation
Not seen! Need to lose angular momentum
Any ideas?
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Magnetic Fields
B-field
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if a 0.1 pc cloud collapses to the size of the sun the radius changes by a
factor ~ 4 x 106 ! the rotation frequency must increase ~ 1013
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Effects of Rotation and Magnetic Fields
B-field
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Taking into account the angular momentum what is going to happen to a
rotating cloud as it collapse?
in order to conserve the angular momentum the rotation frequency must
increase, but by how much?
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Charged particles
- Force due to a magnetic field FB
R2B2
# c.f. force on a wire FB=Il x B and I
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lB
- If magnetic field is important and uniform ! flattened clouds
Charged particles spiral around field lines effectively freezing in the
magnetic field into the material
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Effects of Rotation and Magnetic Fields
Magnetic Fields
Effects of Rotation and Magnetic Fields
Magnetic Fields
B Field
- Can use conservation of magnetic flux to estimate stellar surface
magnetic field:
- Taking a 30 M
o
Jeans cloud with RJ = 0.3 pc and BC ~ 1 nT to form a single
star R! = 10 Ro gives B! ~ 103 T
- This is much higher than observed for stars so need to lose some
magnetic flux during collapse
- Since magnetic field frozen into material expect magnetic flux #
be conserved so FB
BR2 to
R
-2
- and since gravitational force FG
R-2 as well, magnetic force cannot
overcome the gravitational one once collapse has started
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Effects of Rotation and Magnetic Fields
Effects of Rotation and Magnetic Fields
Ambipolar Diffusion
Ambipolar Diffusion
B Field
- Magnetic field can only act on the ions and electrons - not the neutrals
- Neutrals can drift relative to the magnetic field opposed by only collisions
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with ions - friction slows neutrals
Timescale for this process is typically longer than tff so must occur
before collapse
B Field
- Slowly a cloud (supported by B-field) will expel the field, and contract
- Eventually it will no longer able support itself ! Core collapse
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Effects of Rotation and Magnetic Fields
Effects of Rotation and Magnetic Fields
Angular Momentum Problem
Cloud Rotation
- Need to lose a large amount of angular momentum if cloud is to collapse
to a star
- Can do this by
- fragmentation/fission
- transfer J to star cluster or binary or planet
- angular momentum transfer
- transfer J to surrounding cloud
magnetic
braking
- charged particles couple with magnetic field and resist motion
in the disk
- gas friction
- in the dense parts of the disk
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Effects of Rotation and Magnetic Fields
Stability of Molecular Clouds
Summary
Angular Momentum Loss
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- Need a force linking inner (rapidly rotating) core to outer (slowly rotating)
cloud?
- magnetic field
- turbulent viscosity
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Magnetic field requires a significant ionised fraction in the cloud so that
the field is then ‘frozen’ into the material
Rotation can halt collapse perpendicular to rotation axis
Leads to formation of a disk
Need to lose angular momentum
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Magnetic fields
turbulent viscosity
Magnetic field can not halt collapse, does lead to flattened structure
Need to lose magnetic flux
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ambipolar diffusion
Next
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How material in the disk is accreted onto the protostar
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