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Star and Planet Formation > 3. Radiation and the ISM > Flashcards

3. Radiation and the ISM Flashcards

1
Q

What are the basic concepts of radiation we cover?

A

Intensity

Planck Fn

Rayleigh-Jeans Law

Wien’s Displacement Law

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2
Q

What are the basic properties of the ISM we cover?

A

NIR/FIR emission

21cm line of H

2.6 mm rotational line of CO

Molecular clouds / cores / GMCs

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3
Q

What is solid angle in 2D and 3D?

A

theta = l / r radians

omega, w = A / r^2 steradians

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4
Q

What is Iv?

A

Specific intensity

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5
Q

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?

A

dEv = Iv cosø dA dv dw dt

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6
Q

What are the cgs units of Iv?

A

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

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7
Q

What are the metric units of Iv?

A

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

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8
Q

What is total intensity?

A

Specific intensity integrated over all frequencies (0 to infinity)

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9
Q

Why is intensity dependent of distance?

A

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

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10
Q

What is flux fv of radiation?

A

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

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11
Q

Does flux depend on distance?

A

Yes

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12
Q

Units of flux in cgs units?

A

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

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13
Q

Units of flux in SI units?

A

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

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14
Q

Relationship between flux and intensity?

A

See notes

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15
Q

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

A

Yes

e.g., radio, optical

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16
Q

In thermodynamic equilibrium, what is specific intensity equal to?

A

Iv = Bv (Planck fn)

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17
Q

How to calculate total intensity in thermodynamic equilibrium?

A

Integrate Planck fn between 0 and infinity wrt frequency

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18
Q

What is total intensity when in thermodynamic equilibrium?

A

B = σ T^4 / π Wm^-2

Where σ is the Stefan-Boltzmann constant

(Integrate Planck fn over all frequencies)

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19
Q

Value for Stefan-Boltzmann constant?

A

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

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20
Q

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

A

F = πB

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21
Q

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

A

Integrate over a solid angle equal to half a sphere

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22
Q

Describe a Bv vs Frequency graph of a black body.

A

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

Reaches a peak temp then quickly decreases

Peak temperature increases at higher temperatures

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23
Q

When does the linear portion of the Planck fn occur?

A

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

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24
Q

Derive Rayleigh-Jeans Law

A

See notes

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25
Q

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

A

Bv = 2kTv^2 / c^2

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26
Q

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

A

Bv = 2kTv^2 / c^2

Take logs of both sides

log(Bv) = 2log(v) + log(T) + c

Compare with y = mx + c

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27
Q

How NOT to calculate peak wavelength of Planck fn?

A

Can’t use direct relation between freq and wavelength

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28
Q

How to find the peak frequency in the Planck fn?

A

Take the derivative of Bv and set this to 0

Solved using numerical methods

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29
Q

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

A

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

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30
Q

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

A

See notes

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31
Q

What is Wien’s displacement law?

A

v_max / T = 2.82k / h

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32
Q

Does Bv = Bλ? Why?

A

No, freq and λ are fns of each other also

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33
Q

What is max λ of Planck fn equal to?

A

Bλ = -c/λ^2 * Bv

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34
Q

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

A

No

Since Bλ does not equal Bv

But Bvdv = Bλdλ (total intensity)

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35
Q

How is body heat radiated away and why?

A

In the form of IR

T = 310K, λmax = ~9 µm

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36
Q

Is the intensity of radiation from a source conserved?

A

Yes

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37
Q

Which radiation is the atmosphere of earth transparent to?

A

Radio and optical wavelengths

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38
Q

What is the Rayleigh-Jeans law?

A

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

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39
Q

What is Wein’s displacement law?

A

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

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40
Q

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

A

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

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41
Q

What are dark clouds (nebulae)?

A

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

42
Q

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

A

Filled with gas and dust, where stars are forming

43
Q

What temperatures are dust grains warmed to in molecular clouds?

A

T = 10 - 100 K

44
Q

What wavelength does dust emit from a molecular cloud?

A

λ ~ 30 - 300 µm

Using Wien’s Law λmaxT = 0.29 cm K

45
Q

What range does dust emit from molecular clouds?

A

Far IR (FIR)

30 - 300 µm

46
Q

What radiates most strongly in FIR?

A

Interstellar dust

47
Q

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

A

Interstellar dust radiates more strongly than stars in the FIR range

48
Q

What telescope operated at FIR?

A

Herschel

49
Q

Is there currently an observatory at FIR?

A

No (used to be Herschel)

50
Q

What is interstellar extinction roughly inversely proportional to?

A

Wavelength

51
Q

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

A

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

52
Q

Is NIR or FIR higher wavelength?

A

FIR

53
Q

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

A

Radio astronomy

54
Q

Which wavelength can penetrate the ISM most easily?

A

Radio

55
Q

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

A

Radio waves

(Even in relatively cold clouds)

56
Q

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

A

NIR

High energy since distance between energy levels is large

57
Q

Why can atomic hydrogen emit radio waves?

A

Spin

Flipping spin emits a lot smaller energy than electronic transitions

58
Q

How can spin be arranged in a hydrogen atom?

A

The spin of the proton and electron can either be parallel or anti-parallel

(slightly different energies for each)

59
Q

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

A

21 cm

60
Q

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

A

Easily excited in interstellar clouds

61
Q

How do we see the 21cm line?

A

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

62
Q

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

A

Spin ~10e-6 times the magnitude of electronic

63
Q

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

A

The waves undergo different doppler shifts, so take shifts at different lines of sight

Frequency lines are narrow so can see shift

64
Q

When is an object red-shifted?

A

When it is moving away from us (increased wavelength)

65
Q

When is an object blue-shifted?

A

When it is moving towards us (decreased wavelength)

66
Q

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

A

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

67
Q

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

A

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

68
Q

Why can’t we see molecular hydrogen?

A

Homonuclear molecule means we don’t have electric moment transitions

69
Q

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

A

CO

70
Q

Why can we use CO to identify molecular gas?

A

Non-zero dipole moment (polar)

When it rotates in space it changes energy between rotational states

71
Q

Compute quantised rotational energy states of CO

A

See Notes

72
Q

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

A

J=1 only 0.48 meV / 5.5K above the ground state

(remember av. molecular cloud is ~10K so state will be populated)

73
Q

How does excitation of CO primarily occur?

A

Through collisions with ambient H2

74
Q

What is J in terms of CO transitions?

A

Rotational quantum number

75
Q

What is B in terms of CO transitions?

A

Rotational constant

76
Q

What is I in terms of CO transitions?

A

Moment of inertia

77
Q

How to convert Energy levels to wavelengths?

A

E = hc / λ

78
Q

In thermodynamic equilibrium, what models the energy level population?

A

Boltzmann distribution

79
Q

What is the Boltzmann distribution equation?

A

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

80
Q

Can you calculate gas temperature using 1 transition?

A

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

81
Q

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

A

~ the same

2-4 e 9 solar masses

82
Q

Where is most molecular gas concentrated in the Milky Way?

A

Giant Molecular Clouds GMCs in the spiral arms

~ > 10e5 solar masses

83
Q

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

A

~ 10e4 solar masses

84
Q

Example of a dense gas tracer?

A

NH3

85
Q

What are dense gas tracers used for?

A

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

86
Q

What are Bok globules?

A

Small, dense, almost spherical clouds

87
Q

4 types of gas tracers we can use?

A

CO, C18O, NH3, N2H+

88
Q

What can Bok globules also be known as?

A

Isolated clouds

89
Q

Typical values for Bok globules?

A

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

90
Q

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

A

Small isolated clouds / Bok globes

91
Q

What are the sites of star formation in galaxies?

A

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

92
Q

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

A

FIR (30-300 microns)

93
Q

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

A

1%

94
Q

How is atomic gas throughout galaxies detectable?

A

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

95
Q

How is molecular gas throughout galaxies detectable?

A

Low-lying rotational energy levels of CO

(Easily detected in cold gas)

96
Q

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

A

Giant molecular clouds (GMC) confined in the spiral arms

97
Q

What are the masses of GMCs?

A

M ~> 10e5 solar masses

98
Q

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

A

10e2-5 solar masses

99
Q

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

A

10-50 solar masses

100
Q

How are isolated clouds also known?

A

Bok globules

Star and Planet Formation (14 decks)

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