Lecture on Cosmic Dust
Takaya Nozawa(IPMU, University of Tokyo)

Today’s Contents:
1) Composition of dust2) Extinction of stellar lights by dust3) Thermal radiation from dust
2011/12/19

Introduction○ Cosmic dust： solid particle with size of a few Å to 1 mm

interplanetary dust, interstellar dust, intergalactic dust
Milky Way (optical)

Milky Way (infrared)

Dust grains absorb UV/optical photons andreemit by thermal radiation at IR wavelengths!

1-1. Hints as to composition of cosmic dust
Dust particles are composed of metals (N > 5)
➔ what are abundances of metals in space?
Solar elemental abundances(Asplund+2009, ARAA, 47, 481)

Element Log10(n)Ratio to H

H

12.00

1.00

He

10.93

8.51x10-2O

8.69

4.90x10-4C

8.43

2.69x10-4

Ne

7.93

8.51x10-5N

7.83

6.76x10-5

Mg

7.60

3.98x10-5More than 90 % of Si, Si
Mg, Fe, Al, and Ca are Fe
depleted in the ISM

7.51

3.24x10-5

7.50

3.16x10-57.12

1.32x10-5

depletion of elements(Sakurai 1993)

S1-2. Expected composition of dust (1)○ Major candidates of cosmic dust・ carbonaceous grains (C-based)－ graphite－ amorphous carbon－ diamond, C60 (fullerene)・ silicate grains (SiO42--based)－ MgxFe(1-x)SiO3 (pyroxene):
MgSiO3 (enstatite)
FeSiO3 (ferrosilite)－ Mg2xFe2(1-x)SiO4 (olivine):
Mg2SiO4 (forsterite)
Fe2SiO4 (fayalite)－ SiO2 (silica, quartz)－ astronomical silicate (MgFeSiO4)

extinction curve

2175 A bump・ small graphite
・ PAH

IR spectral feature1-3. Expected composition of dust (2)○ Minor candidates of dust composition

・ Iron-bearing dust (Fe-based) ??
Fe (iron), FeO (wustite), Fe2O3 (hematite),
Fe3O4 (magnetite), FeS (troilite), FeS2 (pyrite)
・ Other carbides and oxides
SiC (silicon carbide), Al2O3 (corundum), MgO, TiC, …
・ Ices (appeared in MCs and YSOs)
H2O, CO, CO2, NH3, CH4, CH3OH, HCN, C2H2, …

・ large molecules
PAH (Polycyclic Aromatic Hydrocarbon):
C24H12 (coronene), etc.
HAC (Hydrogenated Amorphous Carbon)

2-1. Extinction by dust
I0

I0 exp[-τext]

I0(1-exp[-τext])○ Extinction = absorption + scatteringalbedo = scattering / extinction : w = τsca / τext
・ extinction curve
optically thin, slab-like geometry
bright point source (OB stars, QSOs, GRB afterglow)
・ attenuation curve
effective extinction including effects of radiativetransfer (Calzetti law for galaxies, Calzetti+1994, 2000)

2-2. Optical depth by dust
○ Optical depth produced by dust with a radius “a”

τext(a,λ) = ∫ dr ndust(a,r) Cext(a,λ)
Cext(a,λ) : cross section of dust extinctionτext(a,λ) = ∫ dr ndust(a,r) πa2 Qext(a,λ)
Qext(a,λ) = Cext(a,λ) / πa2: extinction coefficient
Qext(a,λ) = Qabs(a.λ) + Qsca(a,λ), w = Qsca(a,λ) / Qext(a,λ)○ Total optical depth produced by dust

τext,λ = ∫ da ∫ dr fdust(a,r) πa2 Qext(a,λ)
fdust(a) = dndust(a)/da : size distribution of dust(= number density of dust with radii between a and a+da)Aλ = -2.5 log10(exp[-τext,λ]) = 1.068 τext,λ2-3. Evaluation of Q factors
How are Q-factors determined?
➔ using the Mie (scattering) theory○ Mie solution (Bohren & Huffmann 1983)

describes the scattering of electromagnetic radiation
by a sphere (solving Maxwell equations)refractive indexm(λ) = n(λ) + i k(λ)
n, k: optical constantdielectric permeability
ε = ε1 + i ε2ε1 = n2 – k2
ε2 = 2nk2-4. Behaviors of Q factors

size parameter : x = 2 π a / λ－ x ~ 3-4 (a ~ λ) ➔ Qsca has a peak with Qsca > ~2－ x >> 1 (a >> λ) ➔ Qext = Qsca + Qabs ~ 2－ x << 1 (a << λ, Rayleigh limit)➔ Qsca ∝ x4 ∝ a4
➔ Qext = Qabs ∝ aQabs ∝ x ∝ a

2-5. Q factors as a function of wavelengths

2-6. Dependence of albedo on grain radius

2-7. Classical interstellar dust model in MW〇 MRN dust model (Mathis, Rumpl, & Nordsieck 1977)
・ dust composition : silicate (MgFeSiO4) & graphite (C)・ size distribution : power-law distributionn(a) ∝ a^{-q} with q=3.5, 0.005 μm ≤ a ≤ 0.25 μm

optical constants :Draine & Lee (1984)

2-8. Dependence of extinction on grain size

〇 RV provides a rough estimate of grain size

・ smaller RV ➔ steeper curve ➔ smaller grain radius・ larger RV ➔ flatter curve ➔ larger grain radius

2-9. Extinction curves in Magellanic Clouds
no 2175 A bumpsteep far-UV rise

SMC extinction curve can be
explained by the MRN model
without graphite (Pei 1992)

Gordon+03 for SMC and LMC〇 SMC extinction curve
・ implying different properties of dust than those in the MW・ being used as an ideal analog of metal-poor galaxies
cf. extinction curves of reddened quasars (Hopkins et al. 2004)

3-1. Thermal emission from dust grains○ Luminosity density emitted by dust grains

Lλ(a) = 4 Ndust(a) Cemi(a,λ) πBλ(Tdust[a])= 4πa2 Ndust(a) Qabs(a,λ) πBλ(Tdust[a])Cemi(a,λ) = πa2Qabs(a,λ)## Kirchhoff law: Qemi(a,λ) = Qabs(a,λ)○ at IR wavelengths (Qabs ∝ a for a << λ)Lλ(a) = 4 Ndust(a) (4πρa3/3) (3Qabs[a,λ]/4ρa)πBλ(Tdust[a])= 4 Mdust κabs(λ) πBλ(Tdust[a])κabs(a,λ) = 3Qabs/4ρa : mass absorption coefficient➔ IR emission is derived given Mdust, κabs, and Tdust3-2. Dependence of Q/a on wavelengths

Qabs/a ~ Qabs,0/a (λ / λ0)-β in FIR region－ β ~ 1.0 for amorphous carbon－ β ~ 2.0 for graphite, silicate grains－ β = 1.5 for mixture of silicate and am.car➔ e.g. Qabs /a ~ (1/a)(λ / 1.0 μm)-β (β = 1-2)
for graphite and am.car with a = 0.1 μm

3-3. Example of thermal emission from dust

○ at IR wavelengths (Qabs ∝ a for a << λ)Lλ(a) = 4 Mdust κabs(λ) πBλ(Tdust[a])➔ IR emission is derived given Mdust, κabs, and Tdust3-4. Reemission of stellar light by dust
I0 exp[-τext]

L = 4πRstar2σTstar4
Lλ = 4πRstar2πBλ(Tstar)

How is dust temperature determined?
➔ approaching from conservation of energy○ energy reemitted by dust = energy absorbed by dust
time during which dust is thermalized
extremely short < 10-5 s

3-5. Luminosity of dust emission○ Luminosity emitted by a dust grainLemi = ∫ dλ 4πa2 Qabs(a,λ) πBλ(Tdust[a])= 4πa2 σTdust4 <Qabs(Tdust)><Qabs(Tdust)> : plank-mean absorption coefficient= ∫ Qabs(a,λ) πBλ(Tdust[a]) dλ / ∫ πBλ(Tdust[a]) dλ○ Stellar luminosity absorbed by a dust grain

Labs = ∫ dλ πa2 Qabs(a,λ) Fλ(Tstar)= (Rstar/D)2 πa2 σTstar4 <Qabs(Tstar)>= Lstar/4πD2 πa2 <Qabs(Tstar)>a star is assumed to be a blackbody:Fλ(Tstar) = Lλ/4πD2 = (Rstar/D)2 πBλ(Tstar)3-6. Temperature of dust grains (1)○ Labs = Lemi (dust is assumed to be in thermal equilibrium)(Rstar/D)2 Tstar4 <Qabs(Tstar)> = 4Tdust4 <Qabs(Tdust)>
or
Lstar/4πD2 <Qabs(Tstar)> = 4σTdust4 <Qabs(Tdust)>○ analytical solutions, assuming <Qabs(Tstar)> = 1 andQabs = Qabs,0 (λ / λ0)-β➔ <Qabs(Tdust)> = Qabs,0λ0β (15/π4) (kTdust/hc)β ζ(β+4)Γ(β+4)(β=0) Lstar/4πD2 = 4Qabs,0 σTdust4(β=1) Lstar/4πD2 = 4Qabs,0 (kλ0/hc) σTdust5 (373.3/π4)(β=2) Lstar/4πD2 = 4Qabs,0 (kλ0/hc)2 σTdust6 (π2/63)

3-7. Temperature of dust grains (2)○ Dust temperatures as functions of D (distance) and βfor Lstar = Lsun = 3.85x1033 erg s-1, Qabs,0 = 1, λ0 = 1.0 µm

Dust temperature is higher for higher β➔ Higher β causes lower efficiency of radiative cooling