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Appendix A: Supplementary figure

	Fig. A.1 Spitzer IRS spectrum of GoHam (continuous black line) and fit (diamonds) using the PAHTAT model. The mid-IR optical depth derived with the model is shown in red. The positions and bandwidths of the VISIR PAH1 and PAH2 filters are indicated. This spectrum includes GoHam a and b, the absorption is dominated by the disk mid-plane.
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Appendix B: Model

Appendix B.1: Model description

We modeled GoHam b as a spherical clump of constant density n_b and radius r_b. The presence of this clump results in a localized excess of column density with a profile along the cut as a function of position p (Fig. 3) of parabolic form: (B.1)where p_b is the position of GoHam b in the cross cut, that is, 4.25′′. The resulting mid-IR optical depth τ_b due to GoHam b is then (B.2)where C_ext is the dust cross-section per unit of H atom. The mid-IR emission along the cut, corrected for the extinction by GoHam b, can then be recovered by (B.3)where I_IR(p) is the observed mid-IR emission profile shown in Fig. 3. In addition, we computed the emission in the ¹³CO(2−1) line as a function of p: (B.4)where Δv is the width of the line measured to be 1.7 km s^-1, Ω_ff is the beam-filling factor equal to , where a and b are the minor and major axis of the beam, that is, a = 1.14′′ and b = 1.52′′. K is a Gaussian kernel of width equal to b, which is the angular resolution along the cut shown in Fig. 3 (since the major axis of the beam is almost aligned north-south, see Bujarrabal et al. 2009, as is our cross cut). is the brightness temperature of the ¹³CO(2−1) line that is equal to zero for p<p_b − r_b and p>p_b + r_b. For the other values of p, the brightness is equal to (optically thick line) (B.5)where T_ex is the excitation temperature, which we fixed at 16 K, that is, the temperature of the disk midplane derived by Bujarrabal et al. (2009). T_ex could be higher than this value in the internal parts of the clump, but this is not critical in the estimation of r_b , which is a function of the square root of T_ex. Overall, the parameters of the model are the density of GoHam b n_b, the radius of GoHam b r_b, and the dust cross-section C_ext. For interstellar dust, the cross section is typically C_ext = 2.5 × 10^-23 cm² per H atom at 8.6 and 11.2 μm (Weingartner & Draine 2001). In disks, however, this value is expected to decrease significantly due to grain growth, typically by a factor of 10 in the mid-IR (Andrews et al. 2009; D’Alessio et al. 2001). We therefore considered these two extreme cases and their effects on the parameters derived by the model.

Appendix B.2: Adjustment of the parameters n_b and r_b

First, r_b was adjusted so as to reproduce the observed emission profile of I_CO as shown in Fig. 3. Once the value of r_b is adjusted, the following step consists of adjusting the parameter n_b so as to obtain a symmetric profile, which is what is expected in a disk without any clump. The result of this procedure is shown in Fig. 3. From the adjusted values of n_b and r_b, we can derive the clump mass, (B.6)where μ is the mean molecular weight and m_H the proton mass. The parameters used in the model and those derived from the fit for the two values of C_ext are summarized in Table B.2.

© ESO, 2015