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Star and Planet Formation > 9. Rotation and Magnetic Fields > Flashcards

9. Rotation and Magnetic Fields Flashcards

1
Q

Equation for angular momentum L of a cloud?

A

L = mvr = mΩr^2

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2
Q

What forces act in the equatorial plane of the collapsing object?

A

Centrifugal and gravitational force

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3
Q

What happens to the balance of centrifugal and gravitational forces for a rotating cloud?

A

Centrifugal force eventually wins and halts collapse / accretion of material along equatorial plane

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4
Q

What is the centrifugal radius?

A

The radius at which Fc = FG

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5
Q

Typical value of Rc for a typical Jeans critical molecular cloud?

A

100 - 1000 au

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6
Q

For a rotating molecular cloud, what happens to rotational velocity with decreasing latitude?

A

Decreases with increasing latitude

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7
Q

For a rotating molecular cloud, what happens to centrifugal force with latitude?

A

Fc decreases with increasing latitude and only acts perp. to the rotational axis

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8
Q

What is centrifugal force in the polar regions of a molecular cloud?

A

0

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9
Q

What does a graph of infalling material show?

A

A pile up of material at rc the centrifugal radius

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10
Q

What is the radius of the disc like structure?

A

r_disk = 2 * Rc

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11
Q

What is the angular momentum problem?

A

As cloud collapses, rotation freq must increase to conserve angular momentum

But final frequency would have to be relativistic

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12
Q

Show the angular momentum problem

A

See notes

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13
Q

Effect of collapsing cloud on rotational velocity?

A

Even slowly collapsing clouds result in massive amplification of rotational velocity

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14
Q

Why must there be a way for collapsing clouds to lose angular momentum?

A

Otherwise rotational velocity will be near relativistic speeds and cause cloud to break down

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15
Q

How might the system lose angular momentum when the cloud collapses to form a star?

A

Fragmentation/fission

Cloud-cloud interactions

Magnetic braking

Mass loss through outflows

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16
Q

How does fragmentation/fission help a star lose angular momentum?

A

Transfer of angular momentum to a cluster, a binary, or planets

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17
Q

How do cloud-cloud interactions help a star lose angular momentum?

A

Transfers angular momentum

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18
Q

How does magnetic braking of a star help lose angular momentum?

A

Charged particles coupled with the m field and resist angular motion

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19
Q

How does mass loss through outflows help a star lose angular momentum?

A

The mass lost carries with it angular momentum

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20
Q

What is magnetic breaking?

A

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

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21
Q

Derive the centrifugal radius and evaluate for a typical molecular cloud.

A

See notes

22
Q

How can angular momentum be transferred locally?

A

Via a force linking rapidly rotating inner cloud to slowly rotating outer cloud

(Turbulent viscosity or M fields)

23
Q

What does the Keplerian profile of the disk mean for the velocity of the material within?

A

Material closest to the centre moves fastest

24
Q

Generally, how are annuli in a disk brought into co-rotation?

A

Friction between neighbouring annuli create torques

Outer annuli will try to gain angular momentum: so angular momentum is transferred outwards

25
Q

How does turbulent viscosity help to transfer angular momentum to the outer region of a disk?

A

Exchange of particles bringing differing angular momenta to the annuli to which they are transferred

26
Q

How do magnetic fields help to transfer angular momentum to the outer region of a disk?

A

Tethered annuli become stretched due to shear, creating a restoring force

(similar to magnetic braking)

27
Q

Why do we have weak magnetic fields in molecular clouds?

A

Cosmic rays ionise particles so full of charged particles

28
Q

What is the force due to magnetic fields?

A

F_B prop to R^2B^2

where R is distance from magnetic field

29
Q

What generates internal magnetic force in the gas?

A

Charged particles couple and move along field lines

30
Q

What is the force due to magnetic field analogous to?

A

Force on a wire

F_B = Il x B

I prop to lB

31
Q

Why are magnetic fields effectively frozen into the material of a molecular cloud?

A

Charged particles spiral around the field lines in the material

32
Q

What is the implication that magnetic fields are ‘frozen into’ the material?

A

Provide support mechanism for collapse

33
Q

Why do we expect molecular clouds to have flattened structure?

A

If magnetic field is strong and uniform, particles cannot cross field lines only along them

34
Q

How does magnetic force depend on radius?

A

FB prop to R^-2

35
Q

How does a cloud supported by magnetic force differ to that of thermal pressure?

A

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)

36
Q

What is the implication that both F_G and F_B are proportional to R^-2?

A

M force cannot overcome gravitational force once collapse has started

37
Q

What is the magnetic flux problem?

A

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

38
Q

Show Force due to Magnetic support is proportional to 1/R^2

A

See notes

39
Q

What would the magnetic field for a relatively massive star be if magnetic flux was conserved?

A

~ 10^3 T

Whereas observed is around 0.3 T

40
Q

Show how the magnetic flux problem arises

A

When magnetic flux is conserved

See notes

41
Q

How do we know the collapsing system must lose magnetic flux?

A

Evaluated values when flux is conserved are much higher than observed

42
Q

How is magnetic flux lost from the system?

A

Ambipolar diffusion

43
Q

What is ambipolar diffusion?

A

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

44
Q

When does ambipolar diffusion occur?

A

In a weak plasma

45
Q

What opposes the neutrals in ambipolar diffusion?

A

Only collisions with ions

46
Q

What is the timescale for ambipolar diffusion?

A

Longer than free-fall time scale

47
Q

What needs to occur for magnetised clouds to collapse?

A

Ambipolar diffusion

48
Q

What implication does the timescale for ambipolar diffusion > free fall time scale have?

A

Ambipolar diffusion must occur before collapse

49
Q

Why do molecular clouds posses a small amount of angular momentum?

A

Rotation

50
Q

What assumptions are made in the magnetic flux problem?

A

Flux freezing and conservation of magnetic flux

51
Q
A

Star and Planet Formation (14 decks)

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