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SPM inclusions Speck-ulations on Big Dust Alyssa A. Goodman Harvard University Astronomy Department Essential Physical Properties of Dust Size Distribution – MRN: N(a) ~ a-3.5... how often applicable? Composition – effects emissivity, Q » QFIR~λ−β β=0 for pure blackbody; β~1 for amorphous, layerlattice material; β~2 for metals & crystalline dielectrics Shape (“Fluffiness”, “Compactness”) – effects surface area & sticking properties Size: Which Grains Matter Most? 2 a F = N 2 Q B (T ) D Q x=2πa/λ ISM: N(a)~a-3.5 Grain Size Distribution in the ISM –N(a)~a-3.5 (Mathis, Rumpl & Nordseick 1977) –BUT both slope and upper & lower size cutoffs can effect RV observed –RV is observed to vary substantially in ISM!! (recall: AV=RV E(B-V)) Cardelli, Clayton & Mathis 1989. Size Distributions: What’s In-Between? 20 10 ISM Dust (MRN) 15 Relative Number 10 10 10 5 10 0 ? 10 -5 10 -10 10 -15 10 Kuiper Belt Objects (Jewitt & Luu) -6 10 -4 10 -2 10 0 10 2 10 4 10 6 10 8 10 Particle Size [cm] ? Asteroids, Interplanetary Dust, “Big” Interstellar Dust SEDs & Mass Determination Flux at for N particles of size a: a F = N 2 Q B (T ) D 2 B (T ) = 2 2 hc 5 1 exp (hc kT ) − 1 QFIR ∝ − =0 blackbodies lattice =1 amorphous, layer materials & crystalline =2 metals dielectrics Flux at for a distribution with Na particles of each size a: a2 (Note: same flux can be achieved using different F (obs) = Na 2 Q , a B (T ) ∑ combinations of size distribution and emissivity law!) D grain distribution Mass determination: 4sF D2 a Mdust = 3B (Tdust ) Q Using "appropriate average" of a/Q . "Wien's Law": peak 5 −1 ≈ 3000 T + 5 Peak flux moves to longer λ for smaller β. Mdust (true ) = ∑ grain & temperature distribution 4 sF D2 a 3B (Tdust ) Q ,a N = number of grains a = "typical" grain size D = distance from observer Tdust = dust temperature Q = emissivity s = density of grain material Composition: Changes Wavelength [cm] 2 1 10 -8 10 0 10 -1 10 -2 10 -3 10 Maximum emissivity is for pure blackbody, =0 SED peaks move to longer for smaller Decreasing gives you more flux at any so... 10 -10 10 -12 10 -14 10 -16 10 Pure Blackbodies -18 10 Emissivity-Weighted, =1.5 14 arbitrarily normalized at 10 Hz -20 10 8 10 9 10 10 10 11 10 12 10 Frequency [Hz] 13 10 14 10 – overestimating will mean more mass required to produce observed flux WARNING: In theory, is only a property of individual grains, but in “practice” it has come to include size distribution Essential Physical Properties of Dust Size Distribution – MRN: N(a) ~ a-3.5... how often applicable? Composition – effects emissivity, Q » QFIR~λ−β β=0 for pure blackbody; β~1 for amorphous, layerlattice material; β~2 for metals & crystalline dielectrics Shape (“Fluffiness”, “Compactness”) – effects surface area & sticking properties Evidence for Grain Growth in Cirucumstellar Environments Modification of “ ”, a.k.a. “dust opacity index” – opacity ~ ~ ~ – ISM: ~ 2 – Disks around Young Stars: << 2 » more opacity at longer wavelengths in disks than ISM » (e.g. TTS Disks ~ 0.6; Mannings & Emerson 1994, see also Beckwith & Sargent 1991) – Low ’s are easily Inconsistent with N(a)~a-3.5 Flux Density [MJy] The Data: Low-β and Free-Free ν2.1, β=0.1 free-free ν-0.1 Frequency (GHz) Chen, Zhao & Ohashi, 1995 Disk Masses from SEDs Uncertain by ~ x100 Plots show χ2 for disk masses derived from fits of Mannings & Emerson (1994) Axes: Mass vs. β Typical β~0.6 How (Big) Solids are Formed More Obvious Scenario: Direct Coagulation of Material, in-situ (Goldreich & Ward 1973; Cameron 1975, etc.) Less Obvious Scenarios: Mixtures of Materials formed in Hot/Cold Environments, on Varying Timescales – e.g. as accomplished through star/disk-formation/ outflow process (see F. Shu et al.) or... some of both? Making Big Dust(balls) by Coagulation Requirements – substantial rate of low-speed collisions – “sticky” material (ices good) – melting & other exotic possiblities Dangers – equilibrium established short of “big” dust – evaporation & destruction by high T & h » within several A.U. of forming stars – destruction by high-speed collisions » e.g. infall, supersonic turbulence, etc. Single Particle: Aggregate of Similar Particles Recall: cm/s 100 1000 10000 100000 Ice km/s 0.001 0.01 0.1 1 Single Particle :Aggregate of Similar Particles Quartz Single Particle: Aggregate of MRN-like Particles Ice Aggregate:Aggregate (Each made of like particles) Ice Grain Growth in Cores? Some, but not too much. Weidenschilling & Ruzmaikina (1994) find “...weak turbulence results in few collisions and preserves [original particle size distribution, while] strong turbulence tends to produce net destruction, rather than ...growth]” For a Proper Model of Big Dust around YSOs... We’d need, all as functions of 3D position (and time)... – “Initial” Size Distribution – Velocity Distributions (of dust and gas) » including effects of binaries & shocks – Temperature Distribution » including effects of “cloud surface” heating, transient grain heating & shocks – Composition Distribution » e.g. more ices in colder regions? – Serious Dedication & Brilliance Observations to Constrain a Model Total Flux at a given wavelength Integrated (unresolved) SED Spatially resolved SED Spatially resolved multi-λ polarimetry Spatially resolved maps of ice features Record in meteorites, comets & asteroids Questions to Consider How to make big dust? – How long does it last in a given environment? How to best detect big dust? How much big dust makes how much of a difference in: – – – – SEDs mass calculations chemistry ISM