G4 - dust emission

emission is well described by black body radiation
this can be quantified by establishing an equilibrium between the incident and reradiated radiation

E_{i n} = \frac{L}{4 π d^{2}} σ_{g} = \frac{L}{4 π d^{2}} π r_{g}^{2} Q_{λ}

where, $r_{g}$ is the grain radius, and $Q_{λ}$ is the absorptoion coefficient

taking an O star, with $L \sim 10^{6} L_{⊙}$ mostly in UV, so $Q_{λ} \approx 1 :$

E_{i n} = \frac{L_{U V}}{4 d^{2}} r_{g}^{2}

E_{o u t} = 4 π r_{g}^{2} σ T_{g}^{4}

T_{g} = {(\frac{L}{16 π d^{2} σ})}^{1 / 4}

for typical values, $L = 10^{6} L_{⊙}$ and $d = 1$ pc, $T_{g} \approx 15$ K
note that $T_{g}$ does not depend on $r_{g}$
typically, for galaxies with high star formation rates, $T_{g} \approx 15 - 30$ K
using Wien's law, the peak emission would be at $100 - 200 μ$ m, which is the far infrared region (FIR)
thus, galaxies with intense star formation rates should be luminous in the FIR
the spectra of such galaxies in detail have more structure to recognise and multiple peaks

image: H Cegla, lecture notes

at the longest wavelengths, the black body peak of cold dust, ie. similar to those derived above, with a slight shift due to a C vs Si composition
a warm dust component, peaking around $40 - 50 μ$ m, describes the grains closer to the new born stars
a complex spectrum at $λ < 10 μ$ m arises from Polycyclic Aromatic Hydrocarbons (PAHs),
PAHs are chains of $60 - 100$ C-H rings
they are the main reservoir of C in dust and have a prominent role in complex organic molecule formation in space

types of dusty galaxies

dusty star-forming galaxies (DSFGs) peak at $10 - 30 μ$ m, meaning that the dust is headed heavily by very young stars
ultra-luminous infrared galaxies (ULIRGs) peak at $100 - 200 μ$ m, and are further subdivided according to their FIR luminosities, integrated between $15 μ$ m $- 1$ mm
- ULIRGs with $L_{F I R} \sim 10^{12} L_{⊙}$
- LIRGs with $L_{F I R} \sim 10^{11} L_{⊙}$
- (Hyper) HyLIRGs with $L_{F I R} \sim 10^{13} L_{⊙}$
Sub-mm galaxies (SMGs) peak at $\sim 0.85$ mm

image: H Cegla, lecture notes

Hubble flow means that recession speeds of galaxies are proportional to their distances, hence they have progressively higher redshifts
flux from a galaxy should scale as the inverse square of the distance, $F \propto 1 / d^{2}$
for dusty galaxies with high IR luminosities, the flux is observed to be constant in a band around $850 μ$ m
but this is only an apparent effect
dusty galaxies at large distances will have red-shifted peaks of their emissions