9. Rotation and Magnetic Fields Flashcards
Equation for angular momentum L of a cloud?
L = mvr = mΩr^2
What forces act in the equatorial plane of the collapsing object?
Centrifugal and gravitational force
What happens to the balance of centrifugal and gravitational forces for a rotating cloud?
Centrifugal force eventually wins and halts collapse / accretion of material along equatorial plane
What is the centrifugal radius?
The radius at which Fc = FG
Typical value of Rc for a typical Jeans critical molecular cloud?
100 - 1000 au
For a rotating molecular cloud, what happens to rotational velocity with decreasing latitude?
Decreases with increasing latitude
For a rotating molecular cloud, what happens to centrifugal force with latitude?
Fc decreases with increasing latitude and only acts perp. to the rotational axis
What is centrifugal force in the polar regions of a molecular cloud?
0
What does a graph of infalling material show?
A pile up of material at rc the centrifugal radius
What is the radius of the disc like structure?
r_disk = 2 * Rc
What is the angular momentum problem?
As cloud collapses, rotation freq must increase to conserve angular momentum
But final frequency would have to be relativistic
Show the angular momentum problem
See notes
Effect of collapsing cloud on rotational velocity?
Even slowly collapsing clouds result in massive amplification of rotational velocity
Why must there be a way for collapsing clouds to lose angular momentum?
Otherwise rotational velocity will be near relativistic speeds and cause cloud to break down
How might the system lose angular momentum when the cloud collapses to form a star?
Fragmentation/fission
Cloud-cloud interactions
Magnetic braking
Mass loss through outflows
How does fragmentation/fission help a star lose angular momentum?
Transfer of angular momentum to a cluster, a binary, or planets
How do cloud-cloud interactions help a star lose angular momentum?
Transfers angular momentum
How does magnetic braking of a star help lose angular momentum?
Charged particles coupled with the m field and resist angular motion
How does mass loss through outflows help a star lose angular momentum?
The mass lost carries with it angular momentum
What is magnetic breaking?
Gas full of charged particles couples with B from star
Results in resistant tension force opposite to direction of motion of fluid particle
In turn, spin up during collapse twists field lines, increasing local m. tension
This creates braking torque on gas parcel that counteracts spin up
Lowering specific angular momentum
Derive the centrifugal radius and evaluate for a typical molecular cloud.
See notes
How can angular momentum be transferred locally?
Via a force linking rapidly rotating inner cloud to slowly rotating outer cloud
(Turbulent viscosity or M fields)
What does the Keplerian profile of the disk mean for the velocity of the material within?
Material closest to the centre moves fastest
Generally, how are annuli in a disk brought into co-rotation?
Friction between neighbouring annuli create torques
Outer annuli will try to gain angular momentum: so angular momentum is transferred outwards
How does turbulent viscosity help to transfer angular momentum to the outer region of a disk?
Exchange of particles bringing differing angular momenta to the annuli to which they are transferred
How do magnetic fields help to transfer angular momentum to the outer region of a disk?
Tethered annuli become stretched due to shear, creating a restoring force
(similar to magnetic braking)
Why do we have weak magnetic fields in molecular clouds?
Cosmic rays ionise particles so full of charged particles
What is the force due to magnetic fields?
F_B prop to R^2B^2
where R is distance from magnetic field
What generates internal magnetic force in the gas?
Charged particles couple and move along field lines
What is the force due to magnetic field analogous to?
Force on a wire
F_B = Il x B
I prop to lB
Why are magnetic fields effectively frozen into the material of a molecular cloud?
Charged particles spiral around the field lines in the material
What is the implication that magnetic fields are ‘frozen into’ the material?
Provide support mechanism for collapse
Why do we expect molecular clouds to have flattened structure?
If magnetic field is strong and uniform, particles cannot cross field lines only along them
How does magnetic force depend on radius?
FB prop to R^-2
How does a cloud supported by magnetic force differ to that of thermal pressure?
Thermal pressure prop. to R^-3 - so as cloud contracted this became negligible
Whereas magnetic force and gravitational force increase at the same rate during collapse (both prop to R^-2)
What is the implication that both F_G and F_B are proportional to R^-2?
M force cannot overcome gravitational force once collapse has started
What is the magnetic flux problem?
FB and FG depend similarly on radius
So as star collapses magnetic force will increase at same rate as gravitational force
So magnetic flux cannot be conserved
Show Force due to Magnetic support is proportional to 1/R^2
See notes
What would the magnetic field for a relatively massive star be if magnetic flux was conserved?
~ 10^3 T
Whereas observed is around 0.3 T
Show how the magnetic flux problem arises
When magnetic flux is conserved
See notes
How do we know the collapsing system must lose magnetic flux?
Evaluated values when flux is conserved are much higher than observed
How is magnetic flux lost from the system?
Ambipolar diffusion
What is ambipolar diffusion?
Relative drift of neutrals (not coupled to field) and ions (well coupled to field) allows neutrals to condense, magnetic flux to be lost, and collapse to occur
When does ambipolar diffusion occur?
In a weak plasma
What opposes the neutrals in ambipolar diffusion?
Only collisions with ions
What is the timescale for ambipolar diffusion?
Longer than free-fall time scale
What needs to occur for magnetised clouds to collapse?
Ambipolar diffusion
What implication does the timescale for ambipolar diffusion > free fall time scale have?
Ambipolar diffusion must occur before collapse
Why do molecular clouds posses a small amount of angular momentum?
Rotation
What assumptions are made in the magnetic flux problem?
Flux freezing and conservation of magnetic flux
