G2 - dust-radiation interaction

a photon entering a dust cloud undergoes a sequence of scattering events until it is fully absorbed and remitted as a longer wavelength black body raditation
defining the cross section for a spherical grain of dust:

σ_{g} = π r_{g}^{2} Q_{λ}

where, $r_{g}$ is the grain radius, and $Q_{λ}$ is the absorption coefficient (wavelength dependent)

the change in flux after travelling a length $d s$ is:

d F = - σ_{g} n (s) F d s

where, $n (s)$ is the number density of dust grains at the coordinate $s$

assuming a constant density $n :$

\int_{F_{0}}^{F_{e}} \frac{d F}{F} = - \int_{0}^{s} σ_{g} n d s F_{e} = F_{o} \exp (- σ_{g} n s) = F_{0} \exp (- τ_{λ})

where, $F_{0}$ and $F_{e}$ are the initial and emergent fluxes, respectively

applying the definition of magnitude, and defining the extinction $A_{λ}$ as the difference between the measured magnitude (affected by dust) and the magnitude it would have in the absence of dust:

A_{λ} = Δ m = - 2.5 \log F_{e} + 2.5 \log F_{0} = 2.5 τ_{λ} \log e = 1.086 τ_{λ}

extinction affects distance estimates
it increases the apparent magnitude, thus $Δ m$ making the objects appear further away
thus, extinction must be accounted for to obtain unbiased distances

scattering

scattering mostly depends on grain size
small grains $r_{g} ≪ λ$ is the Rayliegh scattering regime

σ_{g} \propto λ^{- 4}

this causes blue/UV photons to scatter more efficiently than red/IR
due to fragmentation, small grains always out number large grains
intermediate grains $r_{g} \approx λ$ is the Mie scattering region

σ_{g} \propto λ^{- 1}

big grains $r_{g} ≫ 1$ is the macroscopic regime, where dust does not behave differently according to the wavelength of the incident photon

σ_{g} \sim cosntant

in nearly all regimes, the cross section decreases with the wavelength
hence, IR wavelengths are used to 'see through' dust

absorption

absorption mostly on composition