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Table 1

Parameters of the dark dust model for the diffuse ISM using the Draine (2003) optical constants for amorphous silicate grains.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Model Mass ratio (%) abundances (ppm) Sizes Derived quantities




(μm) χ2 N (χ2 < 1) mDark mSi mvSi maC mVSG mPAH q (nm) (nm) (nm) (nm) δ0(Si) (µm) RV τV
0 (‡) 0.5 46 23 25 4 3 3.0 243 203 80 166 0.5 5.2 125 3.09 1.01
0 15 7 92 15 10
0.75 (†) 0.7 7 43 20 24 4 2 3.0 228 201 84 166 0.5 5.5 138 3.16 1.42
0 15 7 96 15 8

1 0.6 6 44 21 23 4 2 3.0 217 207 76 143 1.0 5.0 131 3.09 1.37
5 15 7 88 15 8
5 0.6 7 41 22 23 3 3 2.9 220 208 80 166 0.5 5.2 124 3.11 1.30
3 15 8 95 13 11
10 0.7 6 49 17 22 3 2 3.1 239 222 88 183 0.5 4.6 124 3.18 1.36
3 15 6 91 14 8

Notes. In Col. 1 the upper radius of the dark dust agglomerates is specified, in Col. 2 the goodness χ2 of the best-fit model, and below the number N of models that are consistent with the observational constraints and fit the reddening and Serkowski curve at χ2 < 1. Corresponding parameters of the specific mass in percent per gram dust (Cols. 3–8) of dark dust as lower limit mDark, and for large silicates mSi, nano-sized silicates mvSi, large amorphous carbon maC, very small graphite mVSG, and PAHs mPAH. Below, in the second row of Cols. 4–8, exemplified dust abundances [X]/[H] (ppm) are given by adopting [Si]/[H] = 15 ppm in large silicates. Column 9 gives the exponent of the dust size distribution q. The upper radius of large silicates (Col. 10) and amorphous carbon (Col. 11), their lower alignment radii and (Cols. 12 and 13), respectively, and the alignment efficiency (Col. 14) of large silicates δ0(Si) is given. Derived quantities of the dust models are given for the dust abundance ratio [C]/[Si] (Col. 15), the gas-to-dust mass ratio Mgas/Mdust (Col. 16), the total-to-selective extinction RV (Eq. (5), Col. 17), and the optical depth (Col. 18) that matches the optical-to-submm polarisation ratio of p850µm/(pV/τV) = 4.31 (Eq. (8)) by Planck Collaboration XII (2020). (†) The model violates the abundance constraint (Eq. (1)). (‡) Models without dark dust do not fit the Planck Collaboration XXI (2015); Planck Collaboration XII (2020) data at ≳0.8 mm.

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