The influence of scattering on the extinction of stars

Aims: In photometric measurements of stars, one usually assumes that all photons have reached the observer on a direct path and neglects the fraction that has been scattered. However, in observations of distant stars, for instance when they are in another galaxy, this fraction is not negligible. We investigate how scattered light enhances the flux and affects the extinction curve.
Methods: We compute the radiative transfer in a dusty medium using various techniques at wavelengths where dust emission is absent. Among the configurations considered are: a) homogeneous spheres with a central star; b) an infinite layer of stars behind or mixed with an infinite layer of dust which may be homogeneous or clumpy; c) one star in or behind a homogeneous or clumpy block of dust. In all cases, we define in analogy to the extinction optical depth τ an effective optical thickness τ^eff such that the flux attenuation is given by the factor exp(-τ^eff).
Results: a) We compute τ^eff and analyze how it depends, in different geometries, on the extinction optical depth, the dust albedo, the scattering phase function and the spatial resolution of the measurement; b) we calculate effective extinction curves towards single stars in clumpy and homogeneous media adopting standard optical dust properties. They show marked differences to the standard reddening curve; c) when determining τ^eff for a collection of spatially unresolved stars, we find discrepancies with some of the results in the literature.
Conclusions: When one converts the apparent magnitude of a star or a star cluster into an absolute magnitude, scattered light should be taken into account whenever the spatial resolution with which the measurement was performed corresponds to a linear scale over which the scattering optical depth around the source is greater than the relative observational error. One may try to determine τ^eff by solving the radiative transfer for an assumed distribution of stars and dust, or search for representative calculations in the literature, for example in the figures of this paper.