  Optical properties of dust aggregates are important at various astrophysical
environments. To find a reliable approximation method for optical properties of
dust aggregates, we calculate the opacity and the asymmetry parameter of dust
aggregates by using a rigorous numerical method, the T-Matrix Method (TMM), and
then the results are compared to those obtained by approximate methods; the
Rayleigh-Gans-Debye (RGD) theory, the effective medium theory (EMT), and the
distribution of hollow spheres method (DHS). First of all, we confirm that the
RGD theory breaks down when multiple scattering is important. In addition, we
find that both EMT and DHS fail to reproduce the optical properties of dust
aggregates with fractal dimension of 2 when the incident wavelength is shorter
than the aggregate radius. In order to solve these problems, we test the mean
field theory (MFT), where multiple scattering can be taken into account. We
show that the extinction opacity of dust aggregates can be well reproduced by
MFT. However, it is also shown that MFT is not able to reproduce the scattering
and absorption opacities when multiple scattering is important. We successfully
resolve this weak point of MFT, by newly developing a modified mean field
theory (MMF). Hence, we conclude that MMF can be a useful tool to investigate
radiative transfer properties of various astrophysical environments. We also
point out an enhancement of the absorption opacity of dust aggregates in the
Rayleigh domain, which would be important to explain the large millimeter-wave
opacity inferred from observations of protoplanetary disks.
