  Context. Dust grains coagulate to form dust aggregates in protoplanetary
disks. Their porosity can be extremely high in the disks. Although disk
emission may come from fluffy dust aggregates, the emission has been modeled
with compact grains. Aims. We aim to reveal the mass opacity of fluffy
aggregates from infrared to millimeter wavelengths with the filling factor
ranging from 1 down to $10^{-4}$. Methods. We use Mie calculations with an
effective medium theory. The monomers are assumed to be 0.1 ${\rm \mu m}$ sized
grains, which is much shorter than the wavelengths that we focus on. Results.
We find that the absorption mass opacity of fluffy aggregates are characterized
by the product $a\times f$, where $a$ is the dust radius and $f$ is the filling
factor, except for the interference structure. The scattering mass opacity is
also characterized by $af$ at short wavelengths while it is higher in more
fluffy aggregates at long wavelengths. We also derive the analytic formula of
the mass opacity and find that it reproduces the Mie calculations. We also
calculate the expected difference of the emission between compact and fluffy
aggregates in protoplanetary disks with a simple dust growth and drift model.
We find that compact grains and fluffy aggregates can be distinguished by the
radial distribution of the opacity index $\beta$. The previous observation of
the radial distribution of $\beta$ is consistent with the fluffy case, but more
observations are required to distinguish between fluffy or compact. In
addition, we find that the scattered light would be another way to distinguish
between compact grains and fluffy aggregates.
