Infrared dust arcs around stars - I. Effect of the radiation pressure

In this paper we consider the istribulion of interstellar dust in the vicinity of a star under the influence of stellar gravitation and radiation pressure. This study is applicable to stars with relatively weak stellar wind and strong radiation, when the stellar radiation has swept out the interstellar dust much further from the star than the position of the bow shock created by an interaction of the stellar and interstellar plasma flows. In this case the number density of dust for a particular dust-grain radius can be calculated analytically based on the classical 'cold model'. The dust density distribution for a mixture of dust grains with different radii is calculated. We also calculate intensity maps of thermal infrared emission at 24 wia from dust due to heating by stellar radiation. It is shown that the obtained maps of infrared emission strongly depend on the model parameters: the material of dust grains, the dust-size distribution assumed in the interstellar medium and the approach used to calculate the dust temperature. A bright distinct arc in the intensity maps is seen for graphite dust grains and almost disappears for silicates. Absolute values of intensity in the case of graphite are several orders of magnitude larger than for silicates due to more intensive heating of graphite. A possible application of the presented theory is proposed as an algorithm for analysis of the observational images of the infrared arc around the star.