We developed an efficient Monte-Carlo algorithm to solve dust-scattering radiative transfer problems for continuum radiation. The method calculates the scattered intensities for various anisotropic factors ( gi) all at once, while actual photon packets are tracked following a scattering phase function given by a single anisotropic factor ( g0). The algorithm was tested by applying the method to a dust cloud embedding a star at the cloud center and found to provide accurate results within the statistical fluctuation that is intrinsic in Monte-Carlo simulations. It was found that adopting g0 = 0.4 - 0.5 in the algorithm is most efficient. The method would be efficient in estimating the anisotropic factor of the interstellar dust by comparing the observed data with radiative transfer models.

The Henyey-Greenstein (H-G) phase function, which is characterized by a single parameter, has been generally used to approximate the realistic dust-scattering phase function in investigating scattering properties of the interstellar dust. Draine (2003) proposed a new analytic phase function with two parameters and showed that the realistic phase function is better represented by his phase function. If the H-G and Draine's phase functions are significantly different, using the H-G phase function in radiative transfer models may lead to wrong conclusions about the dust-scattering properties. Here, we investigate whether the H-G and Draine's phase functions would indeed produce significant differences in radiative transfer calculations for two simple configurations. For the uniformly distributed dust with an illuminating star at the center, no significant difference is found. However, up to ~ 20% of difference is found when the central star is surrounded by a spherical-shell dust medium and the radiation of λ < 2000 Å is considered. It would mean that the investigation of dust-scattering properties using the H-G phase function may produce errors of up to ~ 20% depending on the geometry of dust medium and the radiation wavelength. This amount of uncertainty would be, however, unavoidable since the configurations of dust density and radiation sources are only approximately available.

We present a Monte-Carlo simulation code, which solves the problem of dust-scattering in interstellar dust clouds with arbitrary light source distribution and dust density structure, and calculate the surface brightness distribution. The method is very flexible and can be applied to radiative transfer problems occurring not only in a single dust cloud, but also in extragalactic dust environment. We compare, for performance test, the result of Monte-Carlo simulation with the well-known analytic approximation for a spherically symmetric homogeneous cloud. We find that the Code approximation gives a very accurate result.

A plane-parallel model of the diffuse Galactic light (DGL) is calculated assuming exponential disks of interstellar dust and OB stars, by solving exactly the radiative transfer equation using an iterative method. We perform a radiative transfer calculation for a model with generally accepted scale heights of stellar and dust distribution and compare the results with those of van de Hulst & de Jong for a constant slab model. We also find that the intensity extrapolated to zero dust optical depth has a negative value, against to the usual expectation.

We present analytical approximations for calculating the scattering and escape of non-ionizing photons from a plane-parallel medium with uniformly illuminated by external sources. We compare the results with the case of a spherical dust cloud. It is found that more scattering and absorption occur in the plane-parallel geometry than in the spherical geometry when the optical depth perpendicular to the plane and the radial optical depth of the sphere are the same. The results can provide an approximate way to estimate radiative transfer in a variety interstellar conditions and can be applied to the dust-scattered diffuse Galactic light.