3. Radiation and the ISM Flashcards
What are the basic concepts of radiation we cover?
Intensity
Planck Fn
Rayleigh-Jeans Law
Wien’s Displacement Law
What are the basic properties of the ISM we cover?
NIR/FIR emission
21cm line of H
2.6 mm rotational line of CO
Molecular clouds / cores / GMCs
What is solid angle in 2D and 3D?
theta = l / r radians
omega, w = A / r^2 steradians
What is Iv?
Specific intensity
What is the energy dEv in a frequency range v to v + dv entering a solid angle dw in time dt, with radiation passing through a SA element dA?
dEv = Iv cosø dA dv dw dt
What are the cgs units of Iv?
erg s^-1 cm^-2 Hz^-1 st^-1
What are the metric units of Iv?
W m^-2 Hz^-1 st^-1
What is total intensity?
Specific intensity integrated over all frequencies (0 to infinity)
Why is intensity dependent of distance?
As once inside the beam, radiation stays within it i.e., conserved
What is flux fv of radiation?
Amount of energy crossing a unit area per unit time per unit frequency interval
Does flux depend on distance?
Yes
Units of flux in cgs units?
erg cm^-2 s^-1 Hz^-1
Units of flux in SI units?
J m^-2 s^-1 Hz^-1
Relationship between flux and intensity?
See notes
Is the atmosphere only transparent to radiation in specific wavelength ranges?
Yes
e.g., radio, optical
In thermodynamic equilibrium, what is specific intensity equal to?
Iv = Bv (Planck fn)
How to calculate total intensity in thermodynamic equilibrium?
Integrate Planck fn between 0 and infinity wrt frequency
What is total intensity when in thermodynamic equilibrium?
B = σ T^4 / π Wm^-2
Where σ is the Stefan-Boltzmann constant
(Integrate Planck fn over all frequencies)
Value for Stefan-Boltzmann constant?
5.67 e -8 Wm^-2K^-4
What is total flux for a surface radiating in all outwards directions?
F = πB
How to find flux for a surface radiating in all outwards directions?
Integrate over a solid angle equal to half a sphere
Describe a Bv vs Frequency graph of a black body.
Straight line at lower temperatures (Rayleigh-Jeans approx.)
Reaches a peak temp then quickly decreases
Peak temperature increases at higher temperatures
When does the linear portion of the Planck fn occur?
Low freqs and high temps (hv «_space;kT)
Derive Rayleigh-Jeans Law
See notes
What is the equation for the Rayleigh-Jean approximation in the low freq / high temp limit?
Bv = 2kTv^2 / c^2
Why does Rayleigh-Jean’s approx. form a straight line?
Bv = 2kTv^2 / c^2
Take logs of both sides
log(Bv) = 2log(v) + log(T) + c
Compare with y = mx + c
How NOT to calculate peak wavelength of Planck fn?
Can’t use direct relation between freq and wavelength
How to find the peak frequency in the Planck fn?
Take the derivative of Bv and set this to 0
Solved using numerical methods
What is the equation for the peak frequency of the Planck fn?
v_max / T = 2.82k / h = 5.88e10 Hz/K
Show how to get from max frequency (Wien’s displacement law) and max λ of Bv are related
See notes
What is Wien’s displacement law?
v_max / T = 2.82k / h
Does Bv = Bλ? Why?
No, freq and λ are fns of each other also
What is max λ of Planck fn equal to?
Bλ = -c/λ^2 * Bv
Does vmax*λmax = c of the Planck fn? Why?
No
Since Bλ does not equal Bv
But Bvdv = Bλdλ (total intensity)
How is body heat radiated away and why?
In the form of IR
T = 310K, λmax = ~9 µm
Is the intensity of radiation from a source conserved?
Yes
Which radiation is the atmosphere of earth transparent to?
Radio and optical wavelengths
What is the Rayleigh-Jeans law?
Approx. of the Planck fn in the limit of low freq and / or high temp
What is Wein’s displacement law?
Describes location of the peak frequency (or wavelength) for an object emitting as a black body
Historically, how have dense molecular clouds become to be understood?
First identified as dark nebulae in 1785
Photos in 1920s - these objects were discrete, optically opaque interstellar clouds
1950s - discovery of atomic HI 21cm line meant dust absorption linked to [HI] emission
1955 - Bok said gas is molecular hydrogen
1970s - Cold molecular component of ISM discovered via CO obs
What are dark clouds (nebulae)?
Molecular clouds consisting of entirely molecular H, mixed with trace amounts of other molecules (n <10^-3) and small amounts (<1% mass) interstellar dust
What are the dark lines obscuring light from background stars in the Milky Way?
Filled with gas and dust, where stars are forming
What temperatures are dust grains warmed to in molecular clouds?
T = 10 - 100 K
What wavelength does dust emit from a molecular cloud?
λ ~ 30 - 300 µm
Using Wien’s Law λmaxT = 0.29 cm K
What range does dust emit from molecular clouds?
Far IR (FIR)
30 - 300 µm
What radiates most strongly in FIR?
Interstellar dust
What is a FIR view of the sky a view of the location of interstellar dust?
Interstellar dust radiates more strongly than stars in the FIR range
What telescope operated at FIR?
Herschel
Is there currently an observatory at FIR?
No (used to be Herschel)
What is interstellar extinction roughly inversely proportional to?
Wavelength
How can we best see into the plane of the Milky Way?
Visible wavelengths - light suffers a lot of extinction through absorption by dust so galactic nucleus obscured from view
IR - can see further into plane of Milky Way
Radio - traverse galaxy unimpeded
Is NIR or FIR higher wavelength?
FIR
How did we get a detailed understanding of the structure of the galactic disc?
Radio astronomy
Which wavelength can penetrate the ISM most easily?
Radio
What radiation does atomic hydrogen emit (that is useful)?
Radio waves
(Even in relatively cold clouds)
What wavelength do electronic transitions in atomic hydrogen usually emit? Why?
NIR
High energy since distance between energy levels is large
Why can atomic hydrogen emit radio waves?
Spin
Flipping spin emits a lot smaller energy than electronic transitions
How can spin be arranged in a hydrogen atom?
The spin of the proton and electron can either be parallel or anti-parallel
(slightly different energies for each)
What wavelength of radiation is emitted during the spin flip in atomic hydrogen?
21 cm
What is the implication that spin flip is very low energy in atomic hydrogen?
Easily excited in interstellar clouds
How do we see the 21cm line?
When spin flip occurs in an electron in atomic hydrogen from a higher to lower energy state configuration, a photon is emitted
How does the energy transition in H between the spin configurations compare to electron transitions?
Spin ~10e-6 times the magnitude of electronic
How do radio waves from gas cloud help to map the morphology of the Milky Way?
The waves undergo different doppler shifts, so take shifts at different lines of sight
Frequency lines are narrow so can see shift
When is an object red-shifted?
When it is moving away from us (increased wavelength)
When is an object blue-shifted?
When it is moving towards us (decreased wavelength)
If part of an image is neither blue or red-shifted what might we assume?
This part of the object is moving at the same speed as us
Why is there a blank spot in the map of the Milky Way using 21 cm emission?
Objects immediately behind galactic centre moving perp. to our line of sight so cannot see Doppler shift
Why can’t we see molecular hydrogen?
Homonuclear molecule means we don’t have electric moment transitions
What can we use instead of molecular H to detect molecular gas?
CO
Why can we use CO to identify molecular gas?
Non-zero dipole moment (polar)
When it rotates in space it changes energy between rotational states
Compute quantised rotational energy states of CO
See Notes
Why is the first excited rotational state of CO easy to populate in dark, cold molecular clouds?
J=1 only 0.48 meV / 5.5K above the ground state
(remember av. molecular cloud is ~10K so state will be populated)
How does excitation of CO primarily occur?
Through collisions with ambient H2
What is J in terms of CO transitions?
Rotational quantum number
What is B in terms of CO transitions?
Rotational constant
What is I in terms of CO transitions?
Moment of inertia
How to convert Energy levels to wavelengths?
E = hc / λ
In thermodynamic equilibrium, what models the energy level population?
Boltzmann distribution
What is the Boltzmann distribution equation?
ni/n0 = gi exp (-Ei / kT)
where
ni = no. density in state I
n0 = no. density in ground state
gi = 2J + 1 is the degeneracy of the energy level
Can you calculate gas temperature using 1 transition?
No, you need a range of transitions along with Boltzmann distribution
How does the amount of molecular and atomic gas compare in the Milky Way?
~ the same
2-4 e 9 solar masses
Where is most molecular gas concentrated in the Milky Way?
Giant Molecular Clouds GMCs in the spiral arms
~ > 10e5 solar masses
How much mass is contained in small clouds and complexes in our galaxy?
~ 10e4 solar masses
Example of a dense gas tracer?
NH3
What are dense gas tracers used for?
Detect cores - find largest concentration of molecular material (where stars are forming primarily)
What are Bok globules?
Small, dense, almost spherical clouds
4 types of gas tracers we can use?
CO, C18O, NH3, N2H+
What can Bok globules also be known as?
Isolated clouds
Typical values for Bok globules?
T ~ 10K
n > 10e10 m^-3
M ~ 10-50 solar masses
L ~ 1 pc
What type of clouds are most likely to collapse to form a single low-mass star?
Small isolated clouds / Bok globes
What are the sites of star formation in galaxies?
Cold (~10K) and dense (n~ 10e3-5 cm^-3) molecular clodus
Which wavelength do dust grains in molecular clouds primarily radiate at?
FIR (30-300 microns)
What percentage by mass do dust grains make up molecular clouds?
1%
How is atomic gas throughout galaxies detectable?
Via spin-flip transition of atomic hydrogen HI at wavelength 21 cm
How is molecular gas throughout galaxies detectable?
Low-lying rotational energy levels of CO
(Easily detected in cold gas)
Where is most of the molecular gas in the Milky Way?
Giant molecular clouds (GMC) confined in the spiral arms
What are the masses of GMCs?
M ~> 10e5 solar masses
What is the mass range of smaller clouds throughout the galaxy?
10e2-5 solar masses
What is the mass range of isolated clouds throughout the galaxy?
10-50 solar masses
How are isolated clouds also known?
Bok globules
