Estimate of the dust absorption in the accretion flow. (a) Minimum dust opacity at H α, f_d/g κ_{∙, H α} (per unit gasmass; contour labels), needed to have τ_{dust, H α} ≈ 1 in the accretion flow onto a growing gas giant (Eq. (21)) in the Polar (solid lines) and SpherAcc (dashed lines) cases. We take the cold-population radii and fix T_dest = 1500 K. Grey dotted lines show where R_dest∕R_p = 1.5 and 5 (Eq. (19)). (b) Material opacity κ_{∙, H α}. We show the ISM fits of Cardelli et al. (1989) for R_V = 3.1 (dotted black) and 5.5 (dotted grey), with the absolute scale from Güver & Özel (2009); Wang & Chen (2019) (solid black); and Chiar & Tielens (2006) (dotted grey, up to 8 μm). Red and blue curves are for size distributions set by the slope q and minimum size (see legend). Curves for each model are for 20 or 80 % carbon (bottom to top), with silicate completing. At the bottom, hydrogen lines, two HST filters, and NACO IR filters are shown. The grey area is a BT-Settl model with T_eff = 1200 K and log g = 4. (c) Estimate of the dust opacity κ_{dust, H α} = f_d/gκ_{∙, H α} in the accretion flow. Pale dotted lines are for a_max = 1 mm instead of 0.1 mm. Red curves represent recent simulation results (see text), with a low dust abundance f_d/g ~10⁻⁵–10⁻⁴, implying κ_{dust, H α} ~ 0.3 cm² g⁻¹ with a half-spread σ = 1.5 dex (grey shaded region). The opacity of Flock et al. (2016, “F+16”), Rab et al. (2019, “R+19”), and Sanchis et al. (2020, “ISM”) is shown for f_d/g = 0.01 (grey symbols, shifted left) and the pure-graphite, “mixture”, and pure-silicate opacity of Szulágyi & Ercolano (2020, “SzE20”) is shown (green circles; top to bottom). All but Flock et al. (2016) assume f_d/g = 0.01 in their work.