8. Observed Properties of Molecular Clouds Flashcards
How to get the velocity dispersion for particles moving along the line of sight?
Assume core is supported by thermal pressure only, in one coordinate (along line of sight)
Rearrange and m = µm_H
What is velocity dispersion for particles moving along the line of sight equal to?
Δv ~ c_s
where cs is the sound speed
How to quickly work out the sound speed cs in a cloud?
Use cloud mass and radius [virial equation]
Derive cs^2 ~ GM_c / 5R_c
See notes
Sound speed in a typical molecular cloud due to thermal motions alone?
T ~ 10K, µ ~ 2.4
delta v ~ 0.2 km/s
Why do we see emission over a range of velocities?
Doppler shifting due to gas moving across the line of sight
What shape is the emission line of projected velocities?
Gaussian
What is the FWHM?
The full width at half the maximum on the y-axis
What is sigma in terms of a Gaussian?
Dispersion - another measure of line widths
How are dispersion (sigma) and FWHM related?
FWHM ~ 2.3 * sigma
Why does FWHM matter?
FWHM = delta v
How are dispersion (sigma) and velocity dispersion related?
sigma = delta v / sqrt(8ln2)
What does measuring line widths over a range of cloud sizes show?
As molecular cloud increases in size, measured velocity dispersion increases linearly in log-log space
When do clouds reach thermal velocity dispersion according to Larson’s observations?
When they are very small
What do Larsons observations tell us about larger clouds?
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
What does larger FWHM mean for delta v?
Velocity of the gas is increased
What is the equation for observed velocity widths?
Δv^2 = Δv^2_th + Δv^2_NT
[Total observed velocity widths are a sum of the thermal and non-thermal components]
In the equation for total observed velocity widths, which velocities dominate?
Non-thermal velocities
What happens as smaller clouds are considered in Larson’s dataset?
Velocity approaches the ambient thermal velocity
Is the trend between velocity dispersion and line width true for cloud complexes?
Yes
Is the trend between velocity dispersion and line width true if a protostar is not present?
Yes - observed whether or not protostar is present
What is Larson’s empirical relationship?
sigma (km/s) = 1.1 x [L(pc)]^-.38
where
sigma = line width
L = cloud (core) size
For what L is Larson’s empirical relationship valid?
0.1 pc < L < 100 pc
What is the timescale that large scale disturbances can propagate through the cloud?
τ ~ L / σ
τ ~ 2 x tff
What is tau with relation to Larson’s law?
The time at which the pressure wave can propagate through the cloud (and disrupt any star formation taking place)
What is crossing time tau?
The time at which the pressure wave can propagate through the cloud
What does it mean, that free fall time is faster than crossing time?
Potential of disturbance for star formation takes longer than time for star formation itself
What happens within a crossing time?
Dissipation of turbulent motions will occur, and star formation will probably occur
Cloud can be dispersed or restructured
What is the timescale associated with the observed internal motions in the structure of a molecular cloud called?
Crossing time
What might disperse / restructure clouds within a crossing time?
Stellar winds, HII regions etc.
What is the rough crossing time for clouds between 0.1 - 100 pc?
tau ~ 10e5-7 year
What are the implications that crossing time is 10e5-10e7 years?
Don’t expect molecular clouds to stick around long - transient
Dispersed / restructured after ~10M yr
As cloud size increases, how does crossing time vary?
L increases, crossing time increases
What is a contrasting argument that clouds don’t stay around long enough to form stars?
There is lots of jeans mass to reach the MJ threshold
So we are seeing a lot less star formation than expected
Using MJ, how does theoretical star formation rate compare to the observed rate?
Theoretical 200-400 solar masses worth of stars
Only see ~ 3 solar masses of stars
What can we say since actual star formation is much less than what we expect?
Molecular clouds cannot be supported by thermal pressure alone
What fact implies cloud collapse times cannot be gauged by tff?
Molecular clouds cannot be supported by thermal pressure alone
Why do we retain tff?
Useful lower limit to the cloud collapse time
What are potential other sources of cloud support?
M fields and turbulence
Is rotation a source of cloud support?
No - rotational energies are generally small compared to gravitational energies
Where does rotational input come from for molecular clouds?
Galactic rotation or cloud-cloud collisions
How would you show rotational energies are not a source of support?
Calculated delta v = R omega, compare to thermal support 3/2kT
What can perturbations in magnetised cloud give rise to?
Magnetohydrodynamic (MHD) waves called Alfven waves
What do Alfvén waves show?
Magnetic fields can support clouds if magnetic field is sufficiently high
Is turbulence a source of support for molecular clouds?
Yes - supersonic line widths are evidence
How important is turbulence?
Initially thought to be cloud support mechanism
Now know it is much more - fundamental ingredient for cloud properties
What cloud properties does turbulence determine?
Lifetime, morphology, star formation rate
What happens during turbulence?
KE cascades from large scales to small
What is the issue with turbulence?
Decays quickly (in a crossing time) having implications for formation and lifetimes of GMCs
What equation gives the expected molecular line width of a typical molecular cloud from thermal motions alone?
Δv_th ~ c_s = sqrt(kT/µm_H)
What tells us that clouds cannot be supported by thermal pressure alone?
Timescale for dispersion / short crossing time, long observed life-time of clouds, low observed star formation rate in the galaxy
