On the Submillimeter Opacity of Protoplanetary Disks

Solid particles with the composition of interstellar dust and power-law size distribution dn/da ∝ a-p (for a ≤ amax with amax ≳ 3λ and 3 < p < 4) will have submillimeter opacity spectral index β(λ) ≡ d ln κ/d ln ν ≈ (p - 3)βISM, where βISM ≈ 1.7 is the opacity spectral index of interstellar dust material in the Rayleigh limit. For the power-law index p ≈ 3.5, which characterizes interstellar dust and may apply for particles growing by agglomeration in protoplanetary disks, grain growth to sizes a ≳ 3 mm will result in β(1 mm) ≲ 1. Grain growth can naturally account for β ≈ 1 observed for protoplanetary disks, provided that amax ≳ 3λ.

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