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Radiative transfer in disc galaxies $-$ V. The accuracy of the KB approximation

We investigate the accuracy of an approximate radiative transfer technique that was first proposed by Kylafis & Bahcall (hereafter the KB approximation) and has been popular in modelling dusty late-type galaxies. We compare realistic galaxy models calculated with the KB approximation with those of a three-dimensional Monte Carlo radiative transfer code SKIRT. The SKIRT code fully takes into account of the contribution of multiple scattering whereas the KB approximation calculates only single scattered intensity and multiple scattering components are approximated. We find that the KB approximation gives fairly accurate results if optically thin, face-on galaxies are considered. However, for highly inclined ($i \gtrsim 85^{\circ}$) and/or optically thick (central face-on optical depth $\gtrsim1$) galaxy models, the approximation can give rise to substantial errors, sometimes, up to $\gtrsim 40\%$. Moreover, it is also found that the KB approximation is not always physical, sometimes producing infinite intensities at lines of sight with high optical depth in edge-on galaxy models. There is no "simple recipe" to correct the errors of the KB approximation that is universally applicable to any galaxy models. Therefore, it is recommended that the full radiative transfer calculation be used, even though it's slower than the KB approximation.