2006ApJ...636.1114D

Solid particles with the composition of interstellar dust and power-law size distribution dn/da∝a^–p (for a≤a_maxwith a_max≳3λ and 3<p<4) will have submillimeter opacity spectral index β(λ)≡dlnκ/dlnν~(p-3)β_ISM, where β_ISM~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 a_max≳3λ.