for silicate and graphite as $s=3.3$ g cm$^{-3}$ and 2.25 g cm$^{-3}$, respectively, we obtain the mass absorption coefficients at $\lambda =125~\mu$m as $\kappa_{125}=25.9$ and 41.0 cm$^2$ g$^{-1}$ for silicate and graphite, respectively. H08 derived $\kappa_{125}=18.8$ cm$^2$ g$^{-1}$ based on @hildebrand83.

Following H08, we adopt the following expression for $\kappa_\nu$ to estimate the dust mass from the *AKARI* data: $$\begin{aligned}
\kappa_\nu =\kappa_{125}\left(
\frac{\lambda}{125~\mu\mathrm{m}}\right)^{-\beta}\, .\end{aligned}$$ The absorption coefficient adopted in Section \[subsec:properties\] cannot be fitted with a single power law, but the index lies between $\beta =1$ and 2. Thus, if we adopt the wavelength dependence described in Section \[subsec:properties\], the estimated dust mass should be between the dust masses obtained with $\beta =1$ and $\beta =2$. We prefer to adopt this simple power-law expression for $\kappa_\nu$ here, since it can be directly compared with the results in H08 and the simple expression is useful for observational usage.

In Table \[tab:mdust\], we list the dust mass estimated from equation (\[eq:mdust\]). We determine the dust temperature $T_{\rm d}$ by fitting $A\nu^{\beta}B_\nu (T_{\rm d})$ ($A$ is a constant) to the 90 $\mu$m and 140 $\mu$m fluxes. Note that $A$ can be eliminated if we take the flux ratio of those two bands. The 