7. Dust Grains & Interstellar Extinction. James R. Graham University of California, Berkeley
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1 7. Dust Grains & Interstellar Extinction James R. Graham University of California, Berkeley
2 Visual Extinction Presence of interstellar gas or nebulae has a long history Existence of absorbing interstellar dust remained controversial Star counts show few stars in some directions (W. Herschel ) No stars or something hiding them? No consensus until the 1930 s R. Trümpler (1930 PASP ) conclusively demonstrated existence of interstellar absorption Compare luminosity distances & angular diameter distances for open clusters Angular diameter distances are systematically smaller Discrepancy grows with distance Distant clusters are redder Extimated ~ 2 mag/kpc absorption Attributed to Rayleigh scattering by very tiny grains ~ 25 Å radius
3 Evidence for Interstellar Dust Extinction, reddening and polarization of starlight Dark clouds Reflection nebulae Diffuse Galactic light X-ray halos Continuum IR emission Diffuse emission from the Galaxy Correlated with HI and CO Stars with IR excesses Depletion of refactory elements (e.g., Si, Fe, Ca) from interstellar gas
4 Barnard 68 B,V & I B, I & K Extincted stars appear red
5 Scattered Light in the Pleiades
6 A Dark Nebula B 33
7 Nature of the Absorbers Before Trumpler it was known that Rayleigh scattering by gas cannot account for the magnitude of extinction too much mass is required Small solid particles absorb and scatter very efficiently The advent of photoelectric photometry ( ) lead to the discovery and quantification of interstellar reddening Precise comparison of colors of stars of the same spectral type (temperature) A λ ~ λ -1.5 between µm Expected for dust with 2!a/λ ~ 1, i.e., a ~ 0.1 µm Star light is polarized in regions of high extinction One polarization state is selectively removed Scattering by small conducting or dielectric particles Not spheres, but elongated and aligned (by the Galactic B-field)
8 Interstellar Extinction Continuum opacity Uniform shape General λ -1.5 trend in the visible/near- IR Steep UV rise Peak at ~ 800 Å Strong features λ = 220 nm λ = 47 nm λ = 9.7 µm λ ~ 2-3 µm UV Vis IR
9 Reddening & Extinction Extinction law is deduced from observations of reddened stars of known spectral type (M λ ) and distance (d) m λ = M λ + 5 log d A λ The color excess, e.g., E(B-V) = (B-V) - (B-V) 0 = A(B)-A(V) where the intrinsic color is (B-V) 0 Selective extinction, R λ, measures steepness of the extinction curve R V = A(V) / [A(B)-A(V)] = A(V) / E(B-V) Steep in diffuse ISM: R V = 3.1±0.2 Shallow in dark clouds: R V 5 If R λ is known (or assumed) then the observed color of a star of known spectral type can be converted to A λ
10 The Reddening Vector Cluster at 100 pc A V = 5 mag. A K = 0.54 mag. A V - A K = 4.46 A V - A K A V
11 Standard Interstellar Extinction
12 Gas-to-Dust Ratio For a constant gas-to-dust ratio, Z E(B-V) and A (V) are correlated with distance and with H column, N H In the plane of the Milky Way the average reddening, E(B-V) = 0.61 mag. per kpc A V = 1.9 mag. kpc -1 for R V = 3.1 For uniform size grains, radius a A V = 2.5log 10 (e)τ V =1.086πa 2 Q ext N d = Q Z m ext H N H 4aρ d 1 Z 0.3Q ext a 5 2.5gcm 3 N H,21 mag. ρ d
13 Compare E(B-V) measurements with N(HI) & N(H 2 ) A (V) N H / 1.87 x mag cm -2 for R V = 3.1 Gas-to-Dust Ratio
14 Scattering & Absorption Definitions Efficiency is given in terms of Q ext, Q sca, & Q abs Q ext = Q sca + Q abs σ abs = Q abs πa 2 σ sca = Q sca πa 2 σ ext = Q ext πa 2 = (Q abs + Q sca )πa 2 albedo = σ sca σ ext = Q sca Q ext 1 In general Q = Q(a, λ)
15 Scattering & Absorption Definitions Optical depth and extinction efficiency τ λ ext = n dust σ ext λ ds = σ λ ext n dust = πa 2 Q ext (λ) N dust Optical depth and extinction [ ] I(λ) = I 0 (λ) exp τ λ ext A λ = 2.5log 10 [ I(λ) /I 0 (λ)] ext ext = 2.5log 10 (e)τ λ =1.086τ λ
16 Scattering & Absorption Definitions Scattering efficiency is a function of the angle, θ, between the incident and scattered wave Quantified by the phase function, g g = cosθ = π 0 I(θ)cosθ dω π 0 I(θ)dΩ θ Isotropic scattering cosθ = 0 Forward scattering cosθ = 1 Back scattering cosθ = -1
17 Scattering & Radiation Pressure Light carries momentum as well as energy Of the incident radiation I 0 the absorbed part I 0 $a 2 Q abs is entirely lost A fraction, g, of the scattered energy is returned to the forward beam The total flux removed from the forward beam is I 0 $a 2 (Q abs + Q sca - gq sca ) Q ext - gq sca Q pr is the efficiency factor for radiation pressure Forward momentum removed from the beam is I 0 $a 2 Q pr /c and this is the radiation pressure on the grain
18 Mie Scattering and Q s General theory of scattering by uniform spheres Radius a Refractive index m = n - i k In general m = m (λ) Solution to Maxwell s equations found in closed form Analytic solution for spheres due to A. N. Mie (1908, Ann. Phys., 25, 377) Scattered wave is expressed in terms of spherical harmonics (angular part) and Bessel functions (radial) Boundary conditions on E and B yield the solution for all space For small x = 2!a/λ retain only a few terms Simple asymptotic forms for small grains/long wavelength For large x need to sum many terms
19 Asymptotic Mie Scattering Formula For small x = 2!a/λ Q abs = 4 x Im m2 1 λ 1 m cf. Rayleigh scattering Note: for small x Q sca = 8 3 x m Re m absorption by grains depends only on total mass in grains 2 λ 4 σ abs = Q abs πa 2 a 3 m dust
20 Scattering From a Raindrop m = i Q ext 4 at x 6 x, Q ext = 2 Q abs = 0 In general m depends on wavelength x is a size parameter!
21 Angular Distribution (m=1.33)
22 m = 1.33 a = 100 µm λ = 600 nm What s This?
23 Here s a Hint
24 Pure vs. Dirty Dielectrics Q ext =Q sca Q ext Q sca
25 Nature of Interstellar Dust Gas-to-dust ratio Elemental composition Spectral features Grain size distribution Grain heating and cooling Carbon in the ISM
26 How much interstellar dust? The Purcell Limit From the Kramer-Kronig relation (Purcell 1969 ApJ ) Q ext dλ = 4π 2 a m2 1 0 m τ ext = Q ext πa 2 N d, N d = ρ d L /m d m 2 1 τ ext dλ = 4π 3 a 3 N 0 d m for spherical grains. Lower limit on grain volume for other shapes Extinction, A λ, is related to the dust column, N d A λ =1.086τ λ =1.086Q ext πa 2 N d
27 Gas to Dust Ratio Convert from τ λ to A λ Standard extinction curve A λ (lower limit to integral) A V /L mean dust density N H /A V gas-to-dust ratio Silicate dust m = 1.5-0i ρ gr = 2.5 g cm -3 0 A λ dλ = 3π m2 1 n L m 2 d V gr + 2 n d V gr = n d m gr m gr /V gr = ρ d ρ gr = average dust density density of solid gas - to - dust ratio = ρ d ρ gas 0.006
28 Implications of the Purcell Limit Significant fraction of heavy elements in interstellar grains Unless grains are very non-spherical and conducting Mass fraction of heavy elements, Z = ~ 40% of metals are in grains Typical model: Silicate grains Mg, Si, Fe and O (20-95%) in (Mg,Fe) 2 SiO 4 Carbonaceous material (graphite & organics) C (60%) Some SiC
29 Interstellar Dust Composition Element C Abundance 0.6 x A 12 M/M H Mg Fe Si O Total
30 Clues in the Extinction Curve 220 nm 9.6 µm
31 Interstellar Extinction Curve The shape of the interstellar extinction curve reveals the makeup of dust Overall smoothness of A λ implies multi-component Size distribution of grain General variation of extinction with wavelength Composition Discrete features in the extinction curve 220 nm bump 9.7 & 18 µm
32 Vibrational Modes of Silicate Minerals Species MgSiO 3 Si-O stretch 9.7 O-Si-O bend 19.0 Mg 2 SiO 4 Si-O stretch 10.0 O-Si-O bend 19.5 FeSiO 3 Si-O stretch 9.5 O-Si-O bend 20.0 Fe 2 SiO 4 Si-O stretch 9.8 SiC Mode O-Si-O bend SiC stretch Wavelength (µm)
33 Silicate Minerals Silicate minerals generally have strong absorption resonances near 10 µm due to the Si-O bond stretch Virtually certain that the interstellar 9.7 µm feature is due to absorption by interstellar silicate material 10 µm emission feature is observed in outflows from cool O-rich stars Expected to condense silicate dust Absent in the outflows from C-rich stars where silicates do not form because all of the O is locked up in CO Broad feature at 18 µm is presumed to be the O-Si-O bending mode in silicates
34 The 220 nm Feature The 220 nm feature is ubiquitous in the Milky Way ± 0.5 nm Variation in the width (10%) and strength Graphite has a strong UV resonance due to $-orbital valence electrons Why is the feature so uniform? 220 nm bump is weak in the Small Magellanic Cloud Weakness correlated with C/O Mg 2 SiO 4 grains contaminated by OH -
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