Interstellar Dust Flashcards Preview

PHYS3281 Star and Planet Formation > Interstellar Dust > Flashcards

Flashcards in Interstellar Dust Deck (41)
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1
Q

Temperature Gradients in Dust Clouds

A
  • there is a clear temperature gradient
  • further to the edges of the cloud, dust is more exposed to the radiation field of the interstellar medium so it is warmer
2
Q

Flux of Radiation for a Blackbody

A

-the amount of energy emitted from an objects surface per unit area per unit time is called the flux, F
-flux is measured in units of Wm^(-2)
-for a blackbody, the Stefan-Boltzmann law applies:
F = σ T^4
-where σ=5.67*10^(-8) is the Stefan-Boltzmann constant and T is the object’s temperature

3
Q

Luminosity

A

-multiplying flux by the surface area of the emitting surface we obtain luminosity, L
Lstar = 4π(Rstar)² σ T^4

4
Q

Apparent Magnitude

A

m_λ = -2.5logFλ(d) + m_λ0

-where F_λ(d) is the flux at wavelength λand distance d in units of parsec and m_λ0 is the magnitude at some reference wavelength

5
Q

Absolute Magnitude

A

M_λ = -2.5logFλ(10pc) + m_λ0

-where F_λ(10pc) is the flux at wavelength λand distance 10pc and m_λ0 is the magnitude at some reference wavelength

6
Q

Relationship Between Apparent and Absolute Magnitude

A

m_λ = M_λ + 5log(d/10pc)
-a difference of 1 magnitude corresponds to a difference in brightness by a factor of 2.5 i.e. it is measured on a log scale

7
Q

Extinction Along the Line of Sight

A

-if there is dust present along the line of sight
m_λ = M_λ + 5log(d/10pc) + A_λ
-where A_λ is the extinction at a wavelength λ
-EXTINCTION IS DEPENDENT ON WAVELENGTH

8
Q

Extinction at Two Wavelengths

A

-consider two different wavelength λ1 and λ2, subtract the extinction along the line of sight equations for each wavelength:
(m_λ1 - m_λ2) = (M_λ1 - M_λ2) + (A_λ1 - A_λ2)
-where:
m_λ1-m_λ2 = C_12, observed colour index
M_λ1-M_λ2 = C^0_12, intrinsic colour index
A_λ1-A_λ2 = C_12-C^0_12 = E_12, colour excess

9
Q

Extinction, Colour Excess and Density of Dust Grains

A

-extinction and colour excess are proportional to the column density of dust grains along the line of sight

10
Q

Extinction at Three Wavelengths

A

-consider another wavelength, λ3, the ratios A_λ3/E_12 and E_32/E_12 depend only on intrinsic grain properties
-let the the third wavelength have some arbitrary value:
E_(λ-V)/E_(B-V) = A_λ/E_(B-V) - A_v/E_(B-V)
= A_λ/E_(B-V) - R_v
-in the diffuse interstellar medium, Rv=3.1, this quantity is the ratio of total to selective extinction
-Rv is determined by the properties of the dust grains, not how many grains there are

11
Q

The Interstellar Extinction Curve

A

-objects become redder when there is more dust along the line of sight

12
Q

Transfer of Radiation

Description

A
  • assume that the radiation field travels along a small distance Δs
  • the radiation can be:
  • -absorbed, transformed into internal morion of the grain lattice
  • -scattered, a photon is absorbed and then some or all of it is reemitted
  • radiation can be added to the beam by:
  • -thermal emission, grains in the lattice radiate aas blackbodys
  • -scattering into the beam from outside sources
13
Q

Transfer of Radiation

Change in Intensity Dues to Absorption and Scattering

A

ΔIν1 = - ρκνIν*Δs

-where ρis the mass density, κν is the opacity which is dependent on ν, Iν is the beam’s original specific intensity and Δs is the path length

14
Q

Transfer of Radiation

Photon Mean Free Path

A

1/ρ*κν

15
Q

Transfer of Radiation

Optical Depth Definition

A

Δτν = ρκνΔs

16
Q

Transfer of Radiation

Transfer of Radiation Due to Thermal Emission

A

ΔIν2 = + jν*Δs

-where jν is the emissivity such that jνΔνΔΩ is the energy per unit volume per unit time emitted into the direction n_

17
Q

Transfer of Radiation

Total Transfer of Radiation Equation

A

ΔIν = ΔIν1 + ΔIν2 = - ρκνΔs + jνΔs

18
Q

Transfer of Radiation

The Equation of Radiative Transfer

A

dIν/ds = - ρκνIν + jν
-changing variable to optical depth:
dIν/dτν = - Iν + Sν
-where Sν is the source function

19
Q

Transfer of Radiation

Source Function Definition

A

-the ratio of efficiency of emission vs absorption along the line of sight
Sν = jν/ρ*κν

20
Q

Transfer of Radiation

Source Function in the Case of Thermal Emission

A

Sν = Bν
=>
jν = ρκνBν(Tdust)

21
Q

Transfer of Radiation

General Solution to the Radiative Transfer Equation

A

Iν(r) = Iν(Rstar)e^(τν) + Sνe^(-τν’) dτν’

22
Q

Transfer of Radiation
Solutions to the Radiative Transfer Equation
Case 1: Zero Absorption & Zero Emission

A

-zero absorption => τν=0
-zero emission => jν=0
=>
Iν(r) = Iν(Rstar)

23
Q

Transfer of Radiation
Solutions to the Radiative Transfer Equation
Case 2: Zero Emission & Non-Zero Absorption

A

-zero absorption => τν=0
-non-zero emission => jν≠0
=>
Iν(r) = Iν(Rstar)*e^(-τν)

24
Q

Transfer of Radiation
Solutions to the Radiative Transfer Equation
Case 3: Zero Absorption & Non-Zero Emissivity

A

-zero absorption => jν=0
-non-zero emission => τν≠0
=>
Iν(r) = Iν(Rstar) - ∫ jν ds
-integral from 0 to r

25
Q

Transfer or Radiation
Solutions to the Radiative Transfer Equation
Case 4: The Optically Thin Case

A

-we see all photons that are emitted but still have the some absorption of the background radiation field:
Iν(r) ≈ Iν(Rstar) + τνSν

26
Q

Transfer of Radiation

Flux at Point P Distance r from Star for a Purely Absorbing Medium

A

Fν(r) = π * Iν(Rstar) * (Rstar/r)² * exp(-Δτν)

27
Q

Transfer of Radiation

Flux at Point P Distance r from Star With Nothing Along the Line of Sight

A

-no extinction or absorption

Fν*(r0) = π * Iν(Rstar) * (Rstar/r)²

28
Q

Relationship Between Extinction and Optical Depth

A
Aλ = 2.5 log(e) Δτν
Aλ = 1.086 Δτν
29
Q

Opacity

Definition

A

-the opacity, κν, represents the total extinction cross section per mass of interstellar material:
ρκν = ndσd*Qν
-where:
nd = number density of dust grains
σd = cross sectional area of a typical dust grain
Qv = extinction efficiency factor = Qvabs + Qvscat

30
Q

Equation of Radiative Transfer in Terms of Opacity

A

dIv/ds = -ρκνIv + jv

31
Q

What is Mie theory?

A

-a complete analytical solution of Maxwell’s equations for the scattering of electromagnetic radiation off of spherical particles
-Mie demonstrated that when the wavelength of the light is of the order of the size (diameter) of the dust grain, then:
Qλ ∝ ad/λ
–if λ»ad, then Qλ->0
–if λ<2, i.e. constant, independent of λ
-Mie theory works well for all wavelengths between infrared and visible
-there are significant deviations at ultraviolet

32
Q

Relationship Between Efficiency of Extinction, Extinction and Column Density

A

Qv ∝ Av/Nd

-where Nd=nd*Δs is the column density of dust grains

33
Q

Efficiency and Relative Extinctions

A

Qλ/Qλo = Aλ/Aλo

-where λo is ant reference wavelength

34
Q

Efficiency of Extinction in the Optical Regime

A

-in the optical regime:

Qλ ∝ 1/λ

35
Q

How does the efficiency change with wavelength?

A

-at long wavelengths (FIR and millimetre), the ISM is generally transparent (no absorption) so one needs to observe the emission from heated dust clouds to determine Aλ and Qλ
-recall
Qλ ∝ Av ∝ Δτλ
-thus knowledge of Av and Td give information on the wavelength dependence of Qλ

36
Q

Qλ and β

A
  • typically, Qλ ∝ λ^(-β), with β≈1-2 for 30m ≤ λ ≤ 1mm
  • in the densest clouds and circumstellar disks β tends towards the lower end of this range: it lies closer to 2 in more diffuse environments
  • once the grain size is larger than wavelength, the opacity and efficiency no longer depend on λ
37
Q

List the Mechanisms That Can Lead Dust to Polarise Light

A
  • dichroic extinction
  • scattering
  • thermal emission
38
Q

Dichroic Extinction

A

-there is a correlation between polarisation and extinction:
% polarisation ∝ Aλ
-this is because the grains are elongated and aligned and also they are para-magnetic and spinning in a magnetic field
-the grains tend to rotate about their shortest axis, they have a small electric charge and hence acquire magnetic moment M along the axis of rotation
-interaction with the ambient magnetic field then creates a torque MxB which gradually forces the grains short axis to align with the field
-thus grains tend to line up such that their time-averaged projected lengths are longer in the direction perpendicular to B
-the electric field is most effective in driving charge down the grain’s long axis, this direction becomes the one of maximum absorption of the impinging radiation
-the electric vector of the transmitted radiation lies along the ambient B

39
Q

Polarisation of Scattered Light

A
  • prior to scattering, the incident electric field E oscillates randomly within the plane normal to propagation direction n^
  • for the radiation scattered in direction 90’ from n^, the scattered field E only oscillates along the line that is the projections of the new plane and the radiation is linearly polarised
  • scattering in other directions results in partial polarisation, E oscillates along two orthogonal lines but with unequal amplitude
40
Q

Polarised Thermal Emission

A
  • light emitted by a star behind a dust cloud is absorbed along the main axis of the dust grains
  • the polarisation in the optical is then orthogonal to the grain and parallel to B
  • in the sub-mm domain, the dominant component of the radiation is along the main axis of the grain and the radiation is thus polarised orthogonal to the optical polarisation and is perpendicular to B
41
Q

The Zeeman Effect

A
  • atoms have magnetic moments which are proportional to their total angular momentum J
  • when a B field is present, it exerts a force on the atom and because the angular momentum is quantised, so are the associated energy levels
  • the result is line splitting, the magnitude of which is proportional to the magnetic field