Appendix A: The grain properties of our models

A.1. The submillimetre opacities

	Fig. A.1 Comparison of the grain properties of our two models. The top panels show the opacity of the two mixtures. The grey dash lines show long wavelength fits of these opacities, with empirical laws  ∝ νβ. The bottom panel compares the SEDs of the two grain mixtures illuminated by the ISRF of the diffuse Galactic ISM (U = 1).
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The top panel of Fig. A.1 compares the absorption opacities of the grain mixtures of our two models. These opacities are the sum of PAHs, carbon grains and silicates. The effective submillimeter emissivity index β is defined by the logarithmic index of the opacity: (A.1)It is β ≃ 2 for the “standard model” and β ≃ 1.7 for the “AC model”, although β for amorphous carbons alone is even lower. Table A.1 gives the submilimeter properties of our two models approximated by Eq. (A.1).

The bottom panel compares the infrared emission of the compositions, for the same starlight intensity. It demonstrates that the “AC model” has more emissivity, especially in the submm. It therefore allows us to fit the same observed SED with less mass, and slightly hotter grains.

Fitting the COBE/FIRAS high latitude Galactic cirrus, Li & Draine (2001) had to modify the imaginary part of the dielectric function of their silicate grains, at wavelengths greater than 250 μm. This modification would have a very limited effect on our conclusion, since our constraints go up to 350 μm only, where this increase is very limited (it is  ± 12% in the 250 μm ≤ λ ≤ 1000 μm range). This modification actually lowers the emissivity between 250 and 850  μm, and increases it, at λ > 850 μm. For our dust mixture, the amplitude of this modification is even lower, since the contribution of silicates to the far-IR is lower than for the Li & Draine (2001) model. The difference between the “standard model” and the one using the modified silicate of Li & Draine (2001) is invisible in Fig. A.1. The physical origin of this excess may be similar to the one we find here. However, its amplitude is much larger in the LMC, and manifests at shorter wavelengths (λ ≳ 100 μm).

A.2. Size distribution considerations

It is important to note that the size distribution used here does not include grains larger than 0.35 μm, and the contribution to the emission of grains larger than a ≳ 0.1 μm is negligible. Large grains tend to have a flat UV-visible opacity, and therefore, to have a lower equilibrium temperature than smaller equilibrum grains, exposed to the same ISRF. Therefore, adding larger grains would increase the submillimetre emissivity of the model, and allow us to fit the SPIRE fluxes, without having to go to low starlight intensities. However, having large grains or having colder dust would give the same discrepancies in terms of gas-to-dust mass ratios. Moreover, a significant excess of large grains would flatten the UV rise of the extinction curve, contradicting the observations of several lines of sight within the LMC (Gordon et al. 2003).

Another feature of our model is that we have been forced to lower the abundance of non-PAH small grains (a < 10 nm; both carbon and silicate grains) by a factor of 2. Without this modification, we were not able to get good fits of the MIPS_{24  μm} of the diffuse regions. This modification has a very minor effect on the dust mass (≲ 10%), and it is systematic, thus it has no impact on our conclusions. However, this is puzzling since the fit of the extinction curves of the LMC indicates a larger fraction of small grains (e.g. Weingartner & Draine 2001). The fact is that the Zubko et al. (2004, BARE-GR-S) model has a higher small grain contribution in MIPS_24 μm than the Draine & Li (2007). On the other hand, replacing graphite by amorphous carbon, as shown in this paper, allows us to get rid of the 30 μm graphite feature, and decrease the contribution of small grains in the MIPS_24 μm band, making the 24 μm fit better without having to alter the size distribution. This is another indirect consistency check of the conclusion of this paper.

A.3. Overview of the derived PAH properties

Although the scope of our paper was not to discuss the PAH properties, their abundance is a natural output of our model. In this section, we summarize these results.

Table A.2 shows the PAH mass fractions for the two models. This parameter is relatively well constrained and does not vary significantly with spatial resolution. Indeed, it depends essentially on the IRAC_8 μm-to-total-IR luminosity ratio. The mass fraction for the “AC model” is systematically higher, since the bulk of the dust is more emissive.

	Fig. A.2 PAH mass fraction, fPAH. The map is shown for the “AC model”, at spatial resolution R1 (54 pc).
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	Fig. B.1 Classes of observed SEDs for the “standard model”. The SEDs are normalised by their integrated IR luminosity, LIR. The classes are ordered according to their specific power . The classes derived with the “AC model” are very similar. Only the specific power is systematically scaled up by a factor of  ≃ (Fig. 5).
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Figure A.2 shows the spatial distribution of the mass fraction of PAHs, f_PAH (Eq. (3)). We confirm the Paradis et al. (2009) results showing an excess of PAH emission toward the stellar bar. However, f_PAH is biased by the fact that, in absence of detailed mid-IR spectrum, we have arbitrarily fixed the charge fraction to 1/2. The charge fraction controls the emissivity of the C-C modes (Galliano et al. 2008b). Therefore, it is difficult to uniquely interpret this excess emissivity by a local increase of the PAH abundance.

Fig. B.2 Bias in the dust mass estimate as a function of the starlight intensity, for both models. In each panel, we plot the ratio of the median of the dust masses measured by fitting the randomly perturbed SEDs of Fig. B.1 () to the actual dust mass of the unperturbed SED (). This quantity is plotted as a function of the actual average starlight intensity  ⟨ U ⟩ . The color code of the classes is identical to Fig. B.1. We clearly see that for high starlight intensities, the dust mass is systematically underestimated by a factor up to 2.

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© ESO, 2011