3. Radiation and the ISM

Question 1

What are the basic concepts of radiation we cover?

Answer 1

Intensity

Planck Fn

Rayleigh-Jeans Law

Wien’s Displacement Law

Question 2

What are the basic properties of the ISM we cover?

Answer 2

NIR/FIR emission

21cm line of H

2.6 mm rotational line of CO

Molecular clouds / cores / GMCs

Question 3

What is solid angle in 2D and 3D?

Answer 3

theta = l / r radians

omega, w = A / r^2 steradians

Question 4

What is Iv?

Answer 4

Specific intensity

Question 5

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?

Answer 5

dEv = Iv cosø dA dv dw dt

Question 6

What are the cgs units of Iv?

Answer 6

erg s^-1 cm^-2 Hz^-1 st^-1

Question 7

What are the metric units of Iv?

Answer 7

W m^-2 Hz^-1 st^-1

Question 8

What is total intensity?

Answer 8

Specific intensity integrated over all frequencies (0 to infinity)

Question 9

Why is intensity dependent of distance?

Answer 9

As once inside the beam, radiation stays within it i.e., conserved

Question 10

What is flux fv of radiation?

Answer 10

Amount of energy crossing a unit area per unit time per unit frequency interval

Question 11

Does flux depend on distance?

Answer 11

Yes

Question 12

Units of flux in cgs units?

Answer 12

erg cm^-2 s^-1 Hz^-1

Question 13

Units of flux in SI units?

Answer 13

J m^-2 s^-1 Hz^-1

Question 14

Relationship between flux and intensity?

Answer 14

See notes

Question 15

Is the atmosphere only transparent to radiation in specific wavelength ranges?

Answer 15

Yes

e.g., radio, optical

Question 16

In thermodynamic equilibrium, what is specific intensity equal to?

Answer 16

Iv = Bv (Planck fn)

Question 17

How to calculate total intensity in thermodynamic equilibrium?

Answer 17

Integrate Planck fn between 0 and infinity wrt frequency

Question 18

What is total intensity when in thermodynamic equilibrium?

Answer 18

B = σ T^4 / π Wm^-2

Where σ is the Stefan-Boltzmann constant

(Integrate Planck fn over all frequencies)

Question 19

Value for Stefan-Boltzmann constant?

Answer 19

5.67 e -8 Wm^-2K^-4

Question 20

What is total flux for a surface radiating in all outwards directions?

Answer 20

F = πB

Question 21

How to find flux for a surface radiating in all outwards directions?

Answer 21

Integrate over a solid angle equal to half a sphere

Question 22

Describe a Bv vs Frequency graph of a black body.

Answer 22

Straight line at lower temperatures (Rayleigh-Jeans approx.)

Reaches a peak temp then quickly decreases

Peak temperature increases at higher temperatures

Question 23

When does the linear portion of the Planck fn occur?

Answer 23

Low freqs and high temps (hv &laquo_space;kT)

Question 24

Derive Rayleigh-Jeans Law

Answer 24

See notes

Question 25

What is the equation for the Rayleigh-Jean approximation in the low freq / high temp limit?

Answer 25

Bv = 2kTv^2 / c^2

Question 26

Why does Rayleigh-Jean's approx. form a straight line?

Answer 26

Bv = 2kTv^2 / c^2 Take logs of both sides log(Bv) = 2log(v) + log(T) + c Compare with y = mx + c

Question 27

How NOT to calculate peak wavelength of Planck fn?

Answer 27

Can't use direct relation between freq and wavelength

Question 28

How to find the peak frequency in the Planck fn?

Answer 28

Take the derivative of Bv and set this to 0 Solved using numerical methods

Question 29

What is the equation for the peak frequency of the Planck fn?

Answer 29

v_max / T = 2.82k / h = 5.88e10 Hz/K

Question 30

Show how to get from max frequency (Wien's displacement law) and max λ of Bv are related

Answer 30

See notes

Question 31

What is Wien's displacement law?

Answer 31

v_max / T = 2.82k / h

Question 32

Does Bv = Bλ? Why?

Answer 32

No, freq and λ are fns of each other also

Question 33

What is max λ of Planck fn equal to?

Answer 33

Bλ = -c/λ^2 * Bv

Question 34

Does vmax*λmax = c of the Planck fn? Why?

Answer 34

No Since Bλ does not equal Bv But Bvdv = Bλdλ (total intensity)

Question 35

How is body heat radiated away and why?

Answer 35

In the form of IR T = 310K, λmax = ~9 µm

Question 36

Is the intensity of radiation from a source conserved?

Answer 36

Yes

Question 37

Which radiation is the atmosphere of earth transparent to?

Answer 37

Radio and optical wavelengths

Question 38

What is the Rayleigh-Jeans law?

Answer 38

Approx. of the Planck fn in the limit of low freq and / or high temp

Question 39

What is Wein's displacement law?

Answer 39

Describes location of the peak frequency (or wavelength) for an object emitting as a black body

Question 40

Historically, how have dense molecular clouds become to be understood?

Answer 40

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

Question 41

What are dark clouds (nebulae)?

Answer 41

Molecular clouds consisting of entirely molecular H, mixed with trace amounts of other molecules (n <10^-3) and small amounts (<1% mass) interstellar dust

Question 42

What are the dark lines obscuring light from background stars in the Milky Way?

Answer 42

Filled with gas and dust, where stars are forming

Question 43

What temperatures are dust grains warmed to in molecular clouds?

Answer 43

T = 10 - 100 K

Question 44

What wavelength does dust emit from a molecular cloud?

Answer 44

λ ~ 30 - 300 µm Using Wien's Law λmaxT = 0.29 cm K

Question 45

What range does dust emit from molecular clouds?

Answer 45

Far IR (FIR) 30 - 300 µm

Question 46

What radiates most strongly in FIR?

Answer 46

Interstellar dust

Question 47

What is a FIR view of the sky a view of the location of interstellar dust?

Answer 47

Interstellar dust radiates more strongly than stars in the FIR range

Question 48

What telescope operated at FIR?

Answer 48

Herschel

Question 49

Is there currently an observatory at FIR?

Answer 49

No (used to be Herschel)

Question 50

What is interstellar extinction roughly inversely proportional to?

Answer 50

Wavelength

Question 51

How can we best see into the plane of the Milky Way?

Answer 51

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

Question 52

Is NIR or FIR higher wavelength?

Answer 52

FIR

Question 53

How did we get a detailed understanding of the structure of the galactic disc?

Answer 53

Radio astronomy

Question 54

Which wavelength can penetrate the ISM most easily?

Answer 54

Radio

Question 55

What radiation does atomic hydrogen emit (that is useful)?

Answer 55

Radio waves (Even in relatively cold clouds)

Question 56

What wavelength do electronic transitions in atomic hydrogen usually emit? Why?

Answer 56

NIR High energy since distance between energy levels is large

Question 57

Why can atomic hydrogen emit radio waves?

Answer 57

Spin Flipping spin emits a lot smaller energy than electronic transitions

Question 58

How can spin be arranged in a hydrogen atom?

Answer 58

The spin of the proton and electron can either be parallel or anti-parallel (slightly different energies for each)

Question 59

What wavelength of radiation is emitted during the spin flip in atomic hydrogen?

Answer 59

21 cm

Question 60

What is the implication that spin flip is very low energy in atomic hydrogen?

Answer 60

Easily excited in interstellar clouds

Question 61

How do we see the 21cm line?

Answer 61

When spin flip occurs in an electron in atomic hydrogen from a higher to lower energy state configuration, a photon is emitted

Question 62

How does the energy transition in H between the spin configurations compare to electron transitions?

Answer 62

Spin ~10e-6 times the magnitude of electronic

Question 63

How do radio waves from gas cloud help to map the morphology of the Milky Way?

Answer 63

The waves undergo different doppler shifts, so take shifts at different lines of sight Frequency lines are narrow so can see shift

Question 64

When is an object red-shifted?

Answer 64

When it is moving away from us (increased wavelength)

Question 65

When is an object blue-shifted?

Answer 65

When it is moving towards us (decreased wavelength)

Question 66

If part of an image is neither blue or red-shifted what might we assume?

Answer 66

This part of the object is moving at the same speed as us

Question 67

Why is there a blank spot in the map of the Milky Way using 21 cm emission?

Answer 67

Objects immediately behind galactic centre moving perp. to our line of sight so cannot see Doppler shift

Question 68

Why can't we see molecular hydrogen?

Answer 68

Homonuclear molecule means we don't have electric moment transitions

Question 69

What can we use instead of molecular H to detect molecular gas?

Answer 69

CO

Question 70

Why can we use CO to identify molecular gas?

Answer 70

Non-zero dipole moment (polar) When it rotates in space it changes energy between rotational states

Question 71

Compute quantised rotational energy states of CO

Answer 71

See Notes

Question 72

Why is the first excited rotational state of CO easy to populate in dark, cold molecular clouds?

Answer 72

J=1 only 0.48 meV / 5.5K above the ground state (remember av. molecular cloud is ~10K so state will be populated)

Question 73

How does excitation of CO primarily occur?

Answer 73

Through collisions with ambient H2

Question 74

What is J in terms of CO transitions?

Answer 74

Rotational quantum number

Question 75

What is B in terms of CO transitions?

Answer 75

Rotational constant

Question 76

What is I in terms of CO transitions?

Answer 76

Moment of inertia

Question 77

How to convert Energy levels to wavelengths?

Answer 77

E = hc / λ

Question 78

In thermodynamic equilibrium, what models the energy level population?

Answer 78

Boltzmann distribution

Question 79

What is the Boltzmann distribution equation?

Answer 79

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

Question 80

Can you calculate gas temperature using 1 transition?

Answer 80

No, you need a range of transitions along with Boltzmann distribution

Question 81

How does the amount of molecular and atomic gas compare in the Milky Way?

Answer 81

~ the same 2-4 e 9 solar masses

Question 82

Where is most molecular gas concentrated in the Milky Way?

Answer 82

Giant Molecular Clouds GMCs in the spiral arms ~ > 10e5 solar masses

Question 83

How much mass is contained in small clouds and complexes in our galaxy?

Answer 83

~ 10e4 solar masses

Question 84

Example of a dense gas tracer?

Answer 84

NH3

Question 85

What are dense gas tracers used for?

Answer 85

Detect cores - find largest concentration of molecular material (where stars are forming primarily)

Question 86

What are Bok globules?

Answer 86

Small, dense, almost spherical clouds

Question 87

4 types of gas tracers we can use?

Answer 87

CO, C18O, NH3, N2H+

Question 88

What can Bok globules also be known as?

Answer 88

Isolated clouds

Question 89

Typical values for Bok globules?

Answer 89

T ~ 10K n > 10e10 m^-3 M ~ 10-50 solar masses L ~ 1 pc

Question 90

What type of clouds are most likely to collapse to form a single low-mass star?

Answer 90

Small isolated clouds / Bok globes

Question 91

What are the sites of star formation in galaxies?

Answer 91

Cold (~10K) and dense (n~ 10e3-5 cm^-3) molecular clodus

Question 92

Which wavelength do dust grains in molecular clouds primarily radiate at?

Answer 92

FIR (30-300 microns)

Question 93

What percentage by mass do dust grains make up molecular clouds?

Answer 93

1%

Question 94

How is atomic gas throughout galaxies detectable?

Answer 94

Via spin-flip transition of atomic hydrogen HI at wavelength 21 cm

Question 95

How is molecular gas throughout galaxies detectable?

Answer 95

Low-lying rotational energy levels of CO (Easily detected in cold gas)

Question 96

Where is most of the molecular gas in the Milky Way?

Answer 96

Giant molecular clouds (GMC) confined in the spiral arms

Question 97

What are the masses of GMCs?

Answer 97

M ~> 10e5 solar masses

Question 98

What is the mass range of smaller clouds throughout the galaxy?

Answer 98

10e2-5 solar masses

Question 99

What is the mass range of isolated clouds throughout the galaxy?

Answer 99

10-50 solar masses

Question 100

How are isolated clouds also known?

Answer 100

Bok globules