Properties of Dust Grains Probed with Extinction Curves

Modern data of the extinction curve from the ultraviolet to the near infrared are revisited to study the property of dust grains in the Milky Way (MW) and the Small Magellanic Cloud (SMC). We confirm that the graphite-silicate mixture of grains yields the observed extinction curve with the simple power-law distribution of the grain size but with a cutoff at some maximal size: the parameters are tightly constrained to be $q = 3.5 \pm 0.2$ for the size distribution $a^{-q}$ and the maximum radius $a_{max} = 0.24 \pm 0.05$ um, for both MW and SMC. The abundance of grains, and hence the elemental abundance, is constrained from the reddening versus hydrogen column density, E(B-V)/N_H. If we take the solar elemental abundance as the standard for the MW, >56 % of carbon should be in graphite dust, while it is <40 % in the SMC using its available abundance estimate. This disparity and the relative abundance of C to Si explain the difference of the two curves. We find that 50-60 % of carbon may not necessarily be in graphite but in the amorphous or the glassy phase. Iron may also be in the metallic phase or up to ~80 % in magnetite rather than in silicates, so that the Mg/Fe ratio in astronomical olivine is arbitrary. With these substitutions the parameters of the grain size remain unchanged. The mass density of dust grains relative to hydrogen is $\rho_{dust}/\rho_H = 1/(120 {+10 \atop -16})$ for the MW and $1/(760 {+70 \atop -90}) for the SMC under some abundance constraints. We underline the importance of the wavelength-dependence slope of the extinction curve in the near infrared in constructing the dust model: if$A_{\lambda} \propto \lambda^{-gamma}$ with gamma ~ 1.6, the power-law grain-size model fails, whereas it works if gamma ~ 1.8-2.0.