Monte-Carlo radiative models of the diffuse Galactic light (DGL) in our Galaxy are calcu- lated using the dust radiative transfer code MoCafe, which is three-dimensional and takes full account of multiple scattering. The code is recently updated to use a fast voxel traversal algorithm, which has dramatically increased the computing speed. The radiative transfer models are calculated with the gen- erally accepted dust scale-height of 0.1 kpc. The stellar scale-heights are assumed to be 0.1 or 0.35 kpc, appropriate for far-ultraviolet (FUV) and optical wavelengths, respectively. The face-on optical depth, measured perpendicular to the Galactic plane, is also varied from 0.2 to 0.6, suitable to the optical to FUV wavelengths, respectively. We find that the DGL at high Galactic latitudes is mostly due to backward or large-angle scattering of starlight originating from the local stars within a radial distance of r < 0.5 kpc from the Earth. On the other hand, the DGL measured in the Galactic plane is mostly due to stars at a distance range that corresponds to an optical depth of ≈ 1 measured from the Earth. Therefore, the low-latitude DGL at the FUV wavelength band would be mostly caused by the stars located at a distance of r . 0.5 kpc and the optical DGL near the Galactic plane mainly originates from stars within a distance range of 1 . r . 2 kpc. We also calculate the radiative transfer models in a clumpy two-phase medium. The clumpy two-phase models provide lower intensities at high Galactic latitudes compared to the uniform density models, because of the lower effective optical depth in clumpy media. However, no significant difference in the intensity at the Galactic plane is found.

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.

Scattering of incident light by the interstellar dust is usually approximated by Henyey-Greenstein scattering phase function. Recently, Draine (2003) proposed a new analytic phase function with two parameters. We describe an algorithm to generate random numbers distributed according to the Draine’s function, and compare two phase functions. It is also derived exact solutions of two parameters for given values ⟨cosθ⟩ and ⟨cos2θ⟩ . It is found that Henyey-Greenstein function with g = ⟨cosθ⟩ provides a good approximation for ${\lambda}\;>\;2000{\AA}$. At shorter wavelengths, more realistic phase function may be needed for radiative transfer models.

When a new counting experiment is proposed, it is crucial to predict whether the desired source signal will be detected, or how much observation time is required in order to detect the signal at a certain significance level. The concept of the a priori prediction of the detection limit in a newly proposed experiment should be distinguished from the a posteriori claim or decision whether a source signal was detected in an experiment already performed, and the calculation of statistical significance of a measured source signal. We formulate precise definitions of these concepts based on the statistical theory of hypothesis testing, and derive an approximate formula to estimate quickly the a priori detection limit of expected Poissonian source signals. A more accurate algorithm for calculating the detection limits in a counting experiment is also proposed. The formula and the proposed algorithm may be used for the estimation of required integration or observation time in proposals of new experiments. Applications include the calculation of integration time required for the detection of faint emission lines in a newly proposed spectroscopic observation, and the detection of faint sources in a new imaging observation. We apply the results to the calculation of observation time required to claim the detection of the surface thermal emission from neutron stars with two virtual instruments.

We are often faced with the task of having to estimate the hydrogen and helium ionizing luminosities of massive stars in the study of H II regions and the warm ionized medium (WIM). Using the results of the most complete compilation of stellar parameters (the effective temperature, stellar radius and surface gravity) and the latest Kurucz stellar atmosphere models, we calculate the ionizing photon luminosities in the H0andHe0 continua from O3 to B5 stars. We compared the theoretical Lyman-continuum luminosity with the observationally inferred luminosity of the H II region around α Vir, and found that the theoretical value is higher than the observed value in contrast to the eariler result.

The warm ionized medium (WIM) outside classical H II regions is a fundamental gas-phase constituent of the Milky Way and other late-type spiral galaxies, and is traced by faint emission lines at optical wavelengths. We calculate the photoionization models of the WIM in the Galaxy by a stellar UV radiation with the effective temperature 35,000 K assuming not only spherical geometry but also plane parallel geometry, and compare the results with the observed emission line ratios. We also show the dependence of the emission line ratios on various gas-phase abundances. The emergent emission-line ratios are in agreement with the average-values of observed ratios of [S II] λ6716/Hα, [N II] λ6583/Hα, [O I] λ6300/Hα, [O III] λ5007/Hα, He I λ5876/Hα. However, their extreme values could not be explained with the photoionization models. It is also shown that the addition of all stellar radiation from the OB stars in the Hipparcos stellar catalog resembles that of an O7-O8 type star.

When we measure a source signal in the presence of a background rate that has been independently measured, the usual approach is to obtain an estimate of the background rate by observing an empty part of the sky, and an estimate of the source signal plus background rate by observing the region where a source signal is expected. The source signal rate is then estimated by subtracting the background rate from the source signal plus background rate. However, when the rates or their observation times are small, this procedure can lead to negative estimates of the source signal rate, even when it should produce a positive value. By applying the Bayesian approach, we solve the problem and prove that the most probable value of source signal rate is zero when the observed total count is smaller than the expected background counts. It is also shown that the results from the conventional method is consistent with the most probable value obtained from the Bayesian approach when the source signal is large or the observation time is long enough.