8. Observed Properties of Molecular Clouds

Question 1

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

Answer 1

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

Rearrange and m = µm_H

Question 2

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

Answer 2

Δv ~ c_s

where cs is the sound speed

Question 3

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

Answer 3

Use cloud mass and radius [virial equation]

Question 4

Derive cs^2 ~ GM_c / 5R_c

Answer 4

See notes

Question 5

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

Answer 5

T ~ 10K, µ ~ 2.4

delta v ~ 0.2 km/s

Question 6

Why do we see emission over a range of velocities?

Answer 6

Doppler shifting due to gas moving across the line of sight

Question 7

What shape is the emission line of projected velocities?

Answer 7

Gaussian

Question 8

What is the FWHM?

Answer 8

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

Question 9

What is sigma in terms of a Gaussian?

Answer 9

Dispersion - another measure of line widths

Question 10

How are dispersion (sigma) and FWHM related?

Answer 10

FWHM ~ 2.3 * sigma

Question 11

Why does FWHM matter?

Answer 11

FWHM = delta v

Question 12

How are dispersion (sigma) and velocity dispersion related?

Answer 12

sigma = delta v / sqrt(8ln2)

Question 13

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

Answer 13

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

Question 14

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

Answer 14

When they are very small

Question 15

What do Larsons observations tell us about larger clouds?

Answer 15

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

Question 16

What does larger FWHM mean for delta v?

Answer 16

Velocity of the gas is increased

Question 17

What is the equation for observed velocity widths?

Answer 17

Δv^2 = Δv^2_th + Δv^2_NT

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

Question 18

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

Answer 18

Non-thermal velocities

Question 19

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

Answer 19

Velocity approaches the ambient thermal velocity

Question 20

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

Answer 20

Yes

Question 21

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

Answer 21

Yes - observed whether or not protostar is present

Question 22

What is Larson’s empirical relationship?

Answer 22

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

where

sigma = line width
L = cloud (core) size

Question 23

For what L is Larson’s empirical relationship valid?

Answer 23

0.1 pc < L < 100 pc

Question 24

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

Answer 24

τ ~ L / σ

τ ~ 2 x tff

Question 25

What is tau with relation to Larson's law?

Answer 25

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

Question 26

What is crossing time tau?

Answer 26

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

Question 27

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

Answer 27

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

Question 28

What happens within a crossing time?

Answer 28

Dissipation of turbulent motions will occur, and star formation will probably occur Cloud can be dispersed or restructured

Question 29

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

Answer 29

Crossing time

Question 30

What might disperse / restructure clouds within a crossing time?

Answer 30

Stellar winds, HII regions etc.

Question 31

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

Answer 31

tau ~ 10e5-7 year

Question 32

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

Answer 32

Don't expect molecular clouds to stick around long - transient Dispersed / restructured after ~10M yr

Question 33

As cloud size increases, how does crossing time vary?

Answer 33

L increases, crossing time increases

Question 34

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

Answer 34

There is lots of jeans mass to reach the MJ threshold So we are seeing a lot less star formation than expected

Question 35

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

Answer 35

Theoretical 200-400 solar masses worth of stars Only see ~ 3 solar masses of stars

Question 36

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

Answer 36

Molecular clouds cannot be supported by thermal pressure alone

Question 37

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

Answer 37

Molecular clouds cannot be supported by thermal pressure alone

Question 38

Why do we retain tff?

Answer 38

Useful lower limit to the cloud collapse time

Question 39

What are potential other sources of cloud support?

Answer 39

M fields and turbulence

Question 40

Is rotation a source of cloud support?

Answer 40

No - rotational energies are generally small compared to gravitational energies

Question 41

Where does rotational input come from for molecular clouds?

Answer 41

Galactic rotation or cloud-cloud collisions

Question 42

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

Answer 42

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

Question 43

What can perturbations in magnetised cloud give rise to?

Answer 43

Magnetohydrodynamic (MHD) waves called Alfven waves

Question 44

What do Alfvén waves show?

Answer 44

Magnetic fields can support clouds if magnetic field is sufficiently high

Question 45

Is turbulence a source of support for molecular clouds?

Answer 45

Yes - supersonic line widths are evidence

Question 46

How important is turbulence?

Answer 46

Initially thought to be cloud support mechanism Now know it is much more - fundamental ingredient for cloud properties

Question 47

What cloud properties does turbulence determine?

Answer 47

Lifetime, morphology, star formation rate

Question 48

What happens during turbulence?

Answer 48

KE cascades from large scales to small

Question 49

What is the issue with turbulence?

Answer 49

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

Question 50

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

Answer 50

Δv_th ~ c_s = sqrt(kT/µm_H)

Question 51

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

Answer 51

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