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star and planet formation > 8. Observed Properties of Molecular Clouds > Flashcards

8. Observed Properties of Molecular Clouds Flashcards

1
Q

How to get the velocity dispersion for particles moving along the line of sight?

A

Assume core is supported by thermal pressure only, in one coordinate (along line of sight)

Rearrange and m = µm_H

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2
Q

What is velocity dispersion for particles moving along the line of sight equal to?

A

Δv ~ c_s

where cs is the sound speed

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3
Q

How to quickly work out the sound speed cs in a cloud?

A

Use cloud mass and radius [virial equation]

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4
Q

Derive cs^2 ~ GM_c / 5R_c

A

See notes

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5
Q

Sound speed in a typical molecular cloud due to thermal motions alone?

A

T ~ 10K, µ ~ 2.4

delta v ~ 0.2 km/s

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6
Q

Why do we see emission over a range of velocities?

A

Doppler shifting due to gas moving across the line of sight

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7
Q

What shape is the emission line of projected velocities?

A

Gaussian

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8
Q

What is the FWHM?

A

The full width at half the maximum on the y-axis

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9
Q

What is sigma in terms of a Gaussian?

A

Dispersion - another measure of line widths

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10
Q

How are dispersion (sigma) and FWHM related?

A

FWHM ~ 2.3 * sigma

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11
Q

Why does FWHM matter?

A

FWHM = delta v

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12
Q

How are dispersion (sigma) and velocity dispersion related?

A

sigma = delta v / sqrt(8ln2)

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13
Q

What does measuring line widths over a range of cloud sizes show?

A

As molecular cloud increases in size, measured velocity dispersion increases linearly in log-log space

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14
Q

When do clouds reach thermal velocity dispersion according to Larson’s observations?

A

When they are very small

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15
Q

What do Larsons observations tell us about larger clouds?

A

They have larger FWHM than what we would expect than if we had thermal motion only, some other mechanism causing them to move in this way to speed up gas

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16
Q

What does larger FWHM mean for delta v?

A

Velocity of the gas is increased

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17
Q

What is the equation for observed velocity widths?

A

Δv^2 = Δv^2_th + Δv^2_NT

[Total observed velocity widths are a sum of the thermal and non-thermal components]

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18
Q

In the equation for total observed velocity widths, which velocities dominate?

A

Non-thermal velocities

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19
Q

What happens as smaller clouds are considered in Larson’s dataset?

A

Velocity approaches the ambient thermal velocity

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20
Q

Is the trend between velocity dispersion and line width true for cloud complexes?

A

Yes

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21
Q

Is the trend between velocity dispersion and line width true if a protostar is not present?

A

Yes - observed whether or not protostar is present

22
Q

What is Larson’s empirical relationship?

A

sigma (km/s) = 1.1 x [L(pc)]^-.38

where

sigma = line width
L = cloud (core) size

23
Q

For what L is Larson’s empirical relationship valid?

A

0.1 pc < L < 100 pc

24
Q

What is the timescale that large scale disturbances can propagate through the cloud?

A

τ ~ L / σ

τ ~ 2 x tff

25
Q

What is tau with relation to Larson’s law?

A

The time at which the pressure wave can propagate through the cloud (and disrupt any star formation taking place)

26
Q

What is crossing time tau?

A

The time at which the pressure wave can propagate through the cloud

27
Q

What does it mean, that free fall time is faster than crossing time?

A

Potential of disturbance for star formation takes longer than time for star formation itself

28
Q

What happens within a crossing time?

A

Dissipation of turbulent motions will occur, and star formation will probably occur

Cloud can be dispersed or restructured

29
Q

What is the timescale associated with the observed internal motions in the structure of a molecular cloud called?

A

Crossing time

30
Q

What might disperse / restructure clouds within a crossing time?

A

Stellar winds, HII regions etc.

31
Q

What is the rough crossing time for clouds between 0.1 - 100 pc?

A

tau ~ 10e5-7 year

32
Q

What are the implications that crossing time is 10e5-10e7 years?

A

Don’t expect molecular clouds to stick around long - transient

Dispersed / restructured after ~10M yr

33
Q

As cloud size increases, how does crossing time vary?

A

L increases, crossing time increases

34
Q

What is a contrasting argument that clouds don’t stay around long enough to form stars?

A

There is lots of jeans mass to reach the MJ threshold

So we are seeing a lot less star formation than expected

35
Q

Using MJ, how does theoretical star formation rate compare to the observed rate?

A

Theoretical 200-400 solar masses worth of stars

Only see ~ 3 solar masses of stars

36
Q

What can we say since actual star formation is much less than what we expect?

A

Molecular clouds cannot be supported by thermal pressure alone

37
Q

What fact implies cloud collapse times cannot be gauged by tff?

A

Molecular clouds cannot be supported by thermal pressure alone

38
Q

Why do we retain tff?

A

Useful lower limit to the cloud collapse time

39
Q

What are potential other sources of cloud support?

A

M fields and turbulence

40
Q

Is rotation a source of cloud support?

A

No - rotational energies are generally small compared to gravitational energies

41
Q

Where does rotational input come from for molecular clouds?

A

Galactic rotation or cloud-cloud collisions

42
Q

How would you show rotational energies are not a source of support?

A

Calculated delta v = R omega, compare to thermal support 3/2kT

43
Q

What can perturbations in magnetised cloud give rise to?

A

Magnetohydrodynamic (MHD) waves called Alfven waves

44
Q

What do Alfvén waves show?

A

Magnetic fields can support clouds if magnetic field is sufficiently high

45
Q

Is turbulence a source of support for molecular clouds?

A

Yes - supersonic line widths are evidence

46
Q

How important is turbulence?

A

Initially thought to be cloud support mechanism

Now know it is much more - fundamental ingredient for cloud properties

47
Q

What cloud properties does turbulence determine?

A

Lifetime, morphology, star formation rate

48
Q

What happens during turbulence?

A

KE cascades from large scales to small

49
Q

What is the issue with turbulence?

A

Decays quickly (in a crossing time) having implications for formation and lifetimes of GMCs

50
Q

What equation gives the expected molecular line width of a typical molecular cloud from thermal motions alone?

A

Δv_th ~ c_s = sqrt(kT/µm_H)

51
Q

What tells us that clouds cannot be supported by thermal pressure alone?

A

Timescale for dispersion / short crossing time, long observed life-time of clouds, low observed star formation rate in the galaxy

star and planet formation (14 decks)

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