Lecture on Cosmic Dust Takaya Nozawa (IPMU, University of Tokyo) 2011/12/19 Today’s Contents: 1) Composition of dust 2) Extinction of stellar lights by dust 3) Thermal radiation from dust

○ Cosmic dust ： solid particle with size of a few Å to 1 mm Dust grains absorb UV/optical photons and reemit by thermal radiation at IR wavelengths! Milky Way (optical) Milky Way (infrared) interplanetary dust, interstellar dust, intergalactic dust Introduction

1-1. Hints as to composition of cosmic dust Dust particles are composed of metals (N > 5) ➔ what are abundances of metals in space? ElementLog10(n)Ratio to H H He x10-2 O x10-4 C x10-4 Ne x10-5 N x10-5 Mg x10-5 Si x10-5 Fe x10-5 S x10-5 Solar elemental abundances (Asplund+2009, ARAA, 47, 481) depletion of elements (Sakurai 1993) More than 90 % of Si, Mg, Fe, Al, and Ca are depleted in the ISM

○ Major candidates of cosmic dust ・ carbonaceous grains (C-based) － graphite － amorphous carbon － diamond, C 60 (fullerene) ・ silicate grains (SiO based) － Mg x Fe (1-x) SiO 3 (pyroxene): MgSiO 3 (enstatite) FeSiO 3 (ferrosilite) － Mg 2x Fe 2(1-x) SiO 4 (olivine): Mg 2 SiO 4 (forsterite) Fe 2 SiO 4 (fayalite) － SiO 2 (silica, quartz) － astronomical silicate (MgFeSiO 4 ) 1-2. Expected composition of dust (1) IR spectral feature extinction curve 2175 A bump ・ small graphite ・ PAH

○ Minor candidates of dust composition ・ Iron-bearing dust (Fe-based) ?? Fe (iron), FeO (wustite), Fe 2 O 3 (hematite), Fe 3 O 4 (magnetite), FeS (troilite), FeS 2 (pyrite) ・ Other carbides and oxides SiC (silicon carbide), Al 2 O 3 (corundum), MgO, TiC, … ・ Ices ( appeared in MCs and YSOs ) H 2 O, CO, CO 2, NH 3, CH 4, CH 3 OH, HCN, C 2 H 2, … ・ large molecules PAH (Polycyclic Aromatic Hydrocarbon): C 24 H 12 (coronene), etc. HAC (Hydrogenated Amorphous Carbon) 1-3. Expected composition of dust (2)

○ Extinction = absorption + scattering albedo = scattering / extinction : w = τ sca / τ ext ・ extinction curve optically thin, slab-like geometry bright point source (OB stars, QSOs, GRB afterglow) ・ attenuation curve effective extinction including effects of radiative transfer (Calzetti law for galaxies, Calzetti+1994, 2000) 2-1. Extinction by dust I0I0 I 0 (1-exp[-τ ext ]) I 0 exp[-τ ext ]

○ Optical depth produced by dust with a radius “a” τ ext (a,λ) = ∫ dr n dust (a,r) C ext (a,λ) C ext (a,λ) : cross section of dust extinction τ ext (a,λ) = ∫ dr n dust (a,r) πa 2 Q ext (a,λ) Q ext (a,λ) = C ext (a,λ) / πa 2 : extinction coefficient Q ext (a,λ) = Q abs (a.λ) + Q sca (a,λ), w = Q sca (a,λ) / Q ext (a,λ) ○ Total optical depth produced by dust τ ext,λ = ∫ da ∫ dr f dust (a,r) πa 2 Q ext (a,λ) f dust (a) = dn dust (a)/da : size distribution of dust (= number density of dust with radii between a and a+da) A λ = -2.5 log 10 (exp[-τ ext,λ ]) = τ ext,λ 2-2. Optical depth by dust

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 index m(λ) = n(λ) + i k(λ) n, k: optical constant dielectric permeability ε = ε 1 + i ε 2 ε 1 = n 2 – k 2 ε 2 = 2nk

size parameter : x = 2 π a / λ － x ~ 3-4 (a ~ λ) ➔ Q sca has a peak with Q sca > ~2 － x >> 1 (a >> λ) ➔ Q ext = Q sca + Q abs ~ 2 － x << 1 (a << λ, Rayleigh limit) ➔ Q sca ∝ x 4 ∝ a 4 Q abs ∝ x ∝ a 2-4. Behaviors of Q factors ➔ Q ext = Q abs ∝ 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 (MgFeSiO 4 ) & graphite (C) ・ size distribution : power-law distribution n(a) ∝ a^{-q} with q=3.5, μm ≤ a ≤ 0.25 μm optical constants : Draine & Lee (1984)

2-8. Dependence of extinction on grain size 〇 R V provides a rough estimate of grain size ・ smaller R V ➔ steeper curve ➔ smaller grain radius ・ larger R V ➔ flatter curve ➔ larger grain radius

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) 2-9. Extinction curves in Magellanic Clouds no 2175 A bump steep far-UV rise Gordon+03 for SMC and LMC SMC extinction curve can be explained by the MRN model without graphite (Pei 1992)

○ Luminosity density emitted by dust grains L λ (a) = 4 N dust (a) C emi (a,λ) πB λ (T dust [a]) = 4πa 2 N dust (a) Q abs (a,λ) πB λ (T dust [a]) C emi (a,λ) = πa 2 Q abs (a,λ) ## Kirchhoff law: Q emi (a,λ) = Q abs (a,λ) ○ at IR wavelengths (Q abs ∝ a for a << λ) L λ (a) = 4 N dust (a) (4πρa 3 /3) (3Q abs [a,λ]/4ρa) πB λ (T dust [a]) = 4 M dust κ abs (λ) πB λ (T dust [a]) κ abs (a,λ) = 3Q abs /4ρa : mass absorption coefficient ➔ IR emission is derived given M dust, κ abs, and T dust 3-1. Thermal emission from dust grains

3-2. Dependence of Q/a on wavelengths Q abs /a ~ Q abs, 0 /a (λ / λ 0 ) -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. Q abs /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 (Q abs ∝ a for a << λ) L λ (a) = 4 M dust κ abs (λ) πB λ (T dust [a]) ➔ IR emission is derived given M dust, κ abs, and T dust

○ energy reemitted by dust = energy absorbed by dust time during which dust is thermalized extremely short < s 3-4. Reemission of stellar light by dust I 0 exp[-τ ext ] L = 4πR star 2 σT star 4 L λ = 4πR star 2 πB λ (T star ) How is dust temperature determined? ➔ approaching from conservation of energy

○ Luminosity emitted by a dust grain L emi = ∫ dλ 4πa 2 Q abs (a,λ) πB λ (T dust [a]) = 4πa 2 σT dust 4 : plank-mean absorption coefficient = ∫ Q abs (a,λ) πB λ (T dust [a]) dλ / ∫ πB λ (T dust [a]) dλ ○ Stellar luminosity absorbed by a dust grain L abs = ∫ dλ πa 2 Q abs (a,λ) F λ (T star ) = (R star /D) 2 πa 2 σT star 4 = L star /4πD 2 πa 2 a star is assumed to be a blackbody: F λ (T star ) = L λ /4πD 2 = (R star /D) 2 πB λ (T star ) 3-5. Luminosity of dust emission

○ L abs = L emi (dust is assumed to be in thermal equilibrium) (R star /D) 2 T star 4 = 4T dust 4 or L star /4πD 2 = 4σT dust 4 ○ analytical solutions, assuming = 1 and Q abs = Q abs,0 (λ / λ 0 ) -β ➔ = Q abs,0 λ 0 β (15/π 4 ) (kT dust /hc) β ζ(β+4)Γ(β+4) (β=0) L star /4πD 2 = 4Q abs,0 σT dust 4 (β=1) L star /4πD 2 = 4Q abs,0 (kλ 0 /hc) σT dust 5 (373.3/π 4 ) (β=2) L star /4πD 2 = 4Q abs,0 (kλ 0 /hc) 2 σT dust 6 (π 2 /63) 3-6. Temperature of dust grains (1)

○ Dust temperatures as functions of D (distance) and β for L star = L sun = 3.85x10 33 erg s -1, Q abs,0 = 1, λ 0 = 1.0 µm 3-7. Temperature of dust grains (2) Dust temperature is higher for higher β ➔ Higher β causes lower efficiency of radiative cooling