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Star and Planet Formation > 4. Interstellar Dust > Flashcards

4. Interstellar Dust Flashcards

1
Q

What happens to light from a star when it reaches a dust cloud?

A

Blue - reflected

OR absorbed and reradiated at longer (redder) wavelengths

Red - transmitted more efficiently

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2
Q

What is reddening?

A

In absorption when red light is transmitted more efficiently than blue

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3
Q

Which type of light is less likely to be scattered: red or blue?

A

Red

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4
Q

In an image of B68 at visible (red) wavelengths, what do we see?

A

Black, whereas at IR can see emission

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5
Q

How would you create a temperature map of a dense core?

A

Treat grains as black bodies, and having multiple wavelengths of emission, can reconstruct the Planck fn

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6
Q

What is Flux F?

A

The amount of energy emitted from an object’s surface per unit area per unit time

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7
Q

What is flux measured in (metric and cgs)?

A

W/m^2 or erg cm^-2 s^-1

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8
Q

Which rule applies for a black body regarding flux?

A

F = σT^4

Where σ constant

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9
Q

In a telescope, what is measured at the aperture: flux or intensity?

A

Flux

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10
Q

How is luminosity L obtained?

A

Flux * surface area of the emitting surface

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11
Q

Equation for luminosity?

A

L* = 4π R*^2 σ T^4

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12
Q

Units of Luminosity L*?

A

W (metric)

erg s^-1 (cgs)

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13
Q

What are the ways of measuring brightness of a star at wavelength λ?

A

Apparent or absolute magnitude

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14
Q

Symbol for apparent magnitude?

A

m_λ

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15
Q

Symbol for absolute magnitude?

A

M_λ

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16
Q

In the absolute and apparent magnitude equations, what do Fλ(d), d and mλ0 represent?

A

Fλ(d) = flux at wavelength λ

d = distance d in pc

mλ0 = magnitude at some reference wavelength

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17
Q

Derive the relation between apparent and absolute magnitude

A

See notes

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18
Q

If there is dust along the line of sight, what is the equation for apparent magnitude?

A

mλ = Mλ + 5log(d/10pc) + Aλ

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19
Q

What is A_λ?

A

Extinction at wavelength λ

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20
Q

Is extinction wavelength-dependent?

A

Yes

(longer λ light, more likely to pass through cloud)

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21
Q

How do we measure apparent magnitude of an object at two different wavelengths?

A

Observed colour index

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22
Q

What is observed colour index?

A

The difference in brightness of an object at two different wavelengths (that we see)

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23
Q

What is intrinsic colour index?

A

The difference in brightness of an object at two different wavelengths (not affected by scattering)

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24
Q

What is colour excess?

A

Difference in extinction of an object at two different wavelengths

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25
Q

What is the apparent magnitude of an object when measured at two different wavelengths?

A

(mλ1 - mλ2) = (Mλ1 - Mλ2) + (Aλ1 - Aλ2)

[Observed colour index = Intrinsic colour index + Colour excess]

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26
Q

What are extinction and colour excess proportional to?

A

The column density of dust grains along the line of sight

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27
Q

What is Rv in extinction?

A

Extinction in the visible Av / Colour Excess in B-V

i.e. the ratio of total to selective extinction

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28
Q

What is the value of Rv in the Milky Way / diffuse interstellar medium?

A

3.1

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29
Q

What do Aλ3/E12 and E32/E12 depend on?

A

Only on intrinsic grain properties

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30
Q

How would you use colour excess at 3 different λs?

A

Infer extinction another wavelength

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31
Q

Why is Vega an important star?

A

It’s our reference star for our magnitude system

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32
Q

Calculate the extinction of Vega in the visible when colour excess = 1

A

See notes

E_(B-V) =1

ANS: Av = 3.1

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33
Q

Calculate the extinction of Vega in the blue wavelengths when colour excess = 1

A

See notes

ANS: A_B = 4.1 (magnitudes of extinction)

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34
Q

What are the axes for the interstellar extinction curve?

A

x = inverse wavelength (wavelength decreases as x increases)

y = Aλ/Av ratio of extinction at this λ over in the visible

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35
Q

What wavelength range is 100 nm?

A

~ UV

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36
Q

What wavelength range is 500 nm?

A

Visible

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37
Q

Describe interstellar extinction curve

A

(Log scale)

Decreasing fro visible to UV:

Approx linear increase of extinction through visible wavelengths

Bump at far UV

Towards shorter wavelengths, steep extinction

(Shorter λ of light, more affected by extinction)

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38
Q

How can interstellar extinction curve be changed?

A

Changing Rv i.e., changing the properties of the dust grains

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39
Q

What happens to extinction as Rv increases?

A

The higher Rv is above 1, the more effective the dust grains are at scattering and absorbing radiation at short λs vs visible (less extinction)

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40
Q

How can radiation be transferred?

A

Absorbed (transformed into internal motion of the grain lattice) and

Scattered (a photon with the same energy is reemitted in a different direction)

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41
Q

What is the equation for change in intensity due to absorption and scattering?

A

ΔIv1 = -ρ * κv * Iv * Δs

where

ρ = gas mass density
κv = opacity (dependent on freq)
ρκv = absorption coefficient (sometimes Xv)
1/ρκv = photon mfp

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42
Q

Equation for optical depth?

A

Δτv = -ρ * κv * Δs

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43
Q

Which change in intensity equation does optical depth appear?

A

Due to absorption and scattering

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44
Q

What is the equation for change in intensity due to thermal emission from the dust?

A

ΔIv2 = + jv * Δs

jv = emissivity

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45
Q

How does emissivity link to energy per unit volume emitted in a certain direction?

A

E = jv * Δv * ΔQ

46
Q

Derive dIv/dτv = Iv - Sv

A

See notes

47
Q
A
48
Q
A
49
Q
A
50
Q

What is the equation for the source function Sv?

A

Sv = jv / ρκv

51
Q

What does the source function become in the case of local thermodynamic equilibrium?

A

Sv = Bv

52
Q

If LTE applies, what does emissivity equal?

A

jv = ρ * κv * Bv(T_dust)

53
Q

Derive the formal solution of the radiative transfer equation

A

See notes

54
Q

What are the 3 conditions to solve the radiative transfer equation?

A

Absorption only

Emission only

Optically thin emission

55
Q

How is the solution to the radiative transfer equation calculated for absorption only?

A

Zero emission: jv = 0, Sv = 0, τv ≠ 0

56
Q

Derive the solutions to the radiative transfer equation for absorption / emission only, and optically thin emission

A

See notes

57
Q

How is the solution to the radiative transfer equation calculated for emission only?

A

τv = 0, jv ≠ 0, Sv ≠ 0

58
Q

How is the solution to the radiative transfer equation calculated for optically thin emission?

A

τv goes to 0, jv ≠ 0, Sv ≠ 0

59
Q

In what case could you
simplify the radiative transfer equation using emission only conditions?

A

If you have no background source i.e., Iv(0) = 0

so just add up light emitted from gas and dust

60
Q

How much light can pass through an optically thin object?

A

Most light passes through

61
Q

Derive the relationship between extinction and optical depth

A

See notes

62
Q

What is the relationship between extinction and optical depth?

A

Aλ = 1.086Δτλ

63
Q

Why is radiation at short wavelengths more strongly scattered and absorbed than that at longer wavelengths?

A

Extinction

64
Q

What must be assumed for Luminosity L = 4πR^2σT^4?

A

Stars radiate as a black body

65
Q

What scale is apparent / absolute magnitude measured on?

A

Log

66
Q

How are apparent and absolute magnitude related?

A

mλ = Mλ + 5log(d/10pc) + Aλ

67
Q

What does the equation of radiative transfer describe?

A

The change in intensity of radiation along a path due to absorption, scattering and emission

68
Q

What is the equation of radiative transfer?

A

dIv / dτv = Iv - jv/Xv

where

jv = emissivity
Xv = ρκv (absorption coefficient)

69
Q

For the case of zero emissivity and scattering, what is the formal solution of the radiative transfer equation?

A

Iv(r) = Iv(R*)exp(-Δτv)

where

Δτv = ρκvΔs (optical depth)f

70
Q

What is the opacity κv?

A

Total extinction cross section per mass of interstellar material

71
Q

Absorption coefficient ρκv equation?

A

ρκv = nd * σd * Qv

nd = no. density of dust grains
σd = πa_d^2 = cross-sectional area of a typical dust grain
Qv = extinction efficiency factor = Q_v, abs + Q_v, sca

72
Q

When does Mie theory apply?

A

Spherical particles

73
Q

What are the two limiting factors in Mie theory?

A

λ&raquo_space; a_d then Qλ goes to 0

λ &laquo_space;a_d then Qλ goes to 2

74
Q

What is Mie theory?

A

A complete analytical solution of Maxwell’s equations for the scattering of EM radiation by spherical particles

75
Q

According to Mie theory, what is Qλ proportional to?

A

Qλ prop. to a_d / λ

76
Q

Which wavelength range does Mie theory work well?

A

Between IR and visible

77
Q

Where does Mie theory deviate from reality?

A

UV

78
Q

Show that extinction efficiency factor Qv ∝ Av/Nd

A

See notes

79
Q

In Qv ∝ Av/Nd, what is Nd?

A

Column density of the dust grains (cm^-2)

[Nd = nd * Δs]

80
Q

What is Qλ / Qλ0 equal to?

A

Qλ / Qλ0 = Aλ / Aλ0

81
Q

How does extinction efficiency change with wavelength?

A

Long λ (FIR & mm) - ISM transparent, no absorption

Need to observe emission from heated dust clouds

82
Q

How does Qλ vary with wavelength in the optical regime?

A

Qλ ∝ λ^-1

83
Q

How does Qλ vary with wavelength at longer λs?

A

Qλ ∝ λ^-B

where B = 1-2 for 30µm<λ<1mm

84
Q

What happens to efficiency and opacity when grain size is larger than λ?

A

No longer depend on λ

85
Q

Show how extinction efficiency varies with λ^-B at longer wavelengths

A

See notes

86
Q

Which mechanisms can lead dust to polarise light?

A

Dichroic extinction

Scattering

Thermal emission

87
Q

What is the correlation between polarisation and extinction?

A

% extinction ∝ Aλ

87
Q

Why do dust grains polarise light?

A

They are elongated and aligned (due to a magnetic field)

88
Q

What does it mean, that grains are elongated and aligned?

A

They are paramagnetic and spinning in a magnetic field

89
Q

How are grains polarised through dichroic extinction?

A

Grains have a small electric charge and are paramagnetic

So acquire magnetic moment M that points along the axis of rotation

Interaction with ambient M field creates a torque MxB

Torque gradually forces grain’s short axis to align with field

90
Q
A
91
Q

Why do grains undergo dichroic extinction?

A

Grains are irregular structures that tend to rotate about their shortest axis

91
Q

How does dichroic extinction allow the grains to see a time-independent magnetic field as they spin?

A

The torque on the grains forces the short axes to align with the field

92
Q

For dichroic extinction, in which direction do the grains line up?

A

So that their time-averaged projected lengths are longer in the direction perpendicular to B

93
Q

In dichroic extinction, in which direction is the electric field most effective in driving charge? What implication does this have on absorption?

A

Down the grain’s long axis

This direction is the one of max. absorption of incoming radiation (highest extinction)

94
Q

In dichroic extinction, which light is let through?

A

Light which is parallel to the magnetic field

95
Q

In dichroic extinction, which light is strongly extincted?

A

Perpendicular to the direction of the magnetic field

(Long grains block the light in this direction)

96
Q

How does polarised light link to star forming regions

A

Star forming regions have higher polarisation as this is where dust is concentrated

97
Q

Why do further away stars appear more polarised?

A

Have to travel through more material to reach us so are more extinct

98
Q

What happens if a dust grain scatters light forwards?

A

No polarisation

99
Q

For radiation scattered 90º from the normal, what polarisation occurs?

A

Linearly polarised: Scattered field E only oscillates along the line that is the projections of the new plane

100
Q

For radiation scattered in non-90º directions, what polarisation occurs?

A

Partial polarisation: E oscillates along two orthogonal lines but with unequal amplitude

101
Q

How does polarised thermal emission occur?

A

Grains are elongated and aligned to m field

Light is absorbed by dust grains

Sub-mm domain, dominant component of radiation is along main axis of the grain

So IR / sub-mm radiation is polarised orthogonal to optical polarisation and perp to B

102
Q

How does polarisation in optical vs sub-mm differ?

A

Polarisation in optical is orthogonal to grain and parallel to B (transmitted)

Polarisation in sub-mm / IR is polarised perpendicular to B and in the direction of the main axis of the grain

103
Q

What is self-scattering?

A

When large amounts of dust are emitting at long wavelengths, light from dust grains is scattered by other dust grains in the vicinity

104
Q

Why might polarisation vectors change direction?

A

Self scattering

105
Q

What is the Zeeman effect?

A

Magnetic field exerts force on atom

Atoms have magnetic moments proportional to their total angular momentum J

Since J is quantised, so are associated energy levels

Results in line splitting

106
Q

In the Zeeman effect, what is the line-splitting proportional to?

A

The magnitude of line splitting is proportional to the magnetic field

107
Q

What can give us information on magnetic field?

A

Dust (polarisation)

and Gas emission lines (Zeeman effect)

108
Q

What is flux-freezing?

A

Magnetic field strength increases with density, so an indication that field lines can be compressed along with the gas

[not a general rule]

109
Q

What theory describes the scattering behaviour of spherical particles?

A

Mie theory

110
Q

At sub-mm wavelengths, which direction do grains emit radiation? Why effect does this have on polarisation?

A

Emit radiation along longer grain axis,

Thus radiation polarised orthogonal to direction of magnetic field

Star and Planet Formation (14 decks)

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