1 Introduction

It is well known that when the two components of a binary system are sufficiently close to each other, their mutual irradiation is very important. The study of close binary stars is of great importance in stellar astrophysics. The atmospheres of the components of a close binary system are distorted mainly by two physical effects: (1) rotation of the component and (2) the tidal effect due to the presence of its companion. These effects make the atmospheres of these stars non-spherical. de Jager (1992) summarized the problem of non-spherical atmospheres and flows in outer layers of young stars and other objects during the workshop at Baltimore. Non-sphericity changes the density distribution of the matter through which the radiation passes and as a consequence, the lines formed in such medium are modified. In addition to this, the presence of the secondary component's light falling on such a distorted components' atmosphere will affect the line profiles formed in these atmospheres. One also encounters the systematic mass motions in the atmospheres of these stars.

In the observational aspects of the problem Yu. Skulskij (1993) studied the variability of equivalent widths with phases and other characteristics of absorption and emission components of SiII $\lambda\lambda$6347, 6371 in the study of $\beta$ Lyre with CCD spectra. The variation of the absorption line equivalent widths depends on the orbital modulation and on the structure of the circumstellar gas in the close binary system. Fergusson & James (1994) studied the eclipsing binary BE UMa for its reflection effect and as cataclysmic variable progenitor characteristics. The reflection effect is due to the relatively close proximity (about $8\ R_\odot$) of a late type secondary of a very hot $T \sim$ 10⁵ $\rm S_dO$ star.

Parthasarathy et al. (1990) analyzed the ultraviolet spectrum (1175 Å to 3200 Å) of the hydrogen-poor binary star HD 30353. The high resolution spectra show stellar wind profiles of NV, CIV, SiIV, CII, SiII, AlII, AlIII, MgII and FeII resonance lines. These profiles appear to shift towards the shorter side of the spectrum. They concluded that extended and multiple shells exist in the atmosphere with a source at temperature of 30000 K, which could be a O-type or an early B-type star as suggested by the far UV flux distribution.

Theoretical studies about the reflection effect using actual model atmospheres are more recent. All the three possible combinations (i.e., when primary and secondary components are hot and hot, cool and cool, and hot and cool) are studied by Buerger (1969, 1972); Nordlund & Vaz (1990); and Claret & Gemenz (1992) respectively. Vaz (1985) and Wilson (1990) reviewed several aspects of reflection effect. They found that irradiation from the secondary component will effect the lines and as well as equivalent widths. They also found that the theoretical bolometric albedos have been found to be in good agreement with the observations. Peraiah & Srinivasa Rao (1983) studied the effects of reflection on the formation of spectral lines in a purely scattering atmosphere and studied how the equivalent width changes due to irradiation from the secondary. However these calculations were done in static atmospheres.

The purpose of this study is to compute the spectral lines formed in the expanding atmospheres with light of the secondary falling on it. These atmospheres are distorted due to the combined effect of self rotation and tidal effect by the presence of the secondary component.

The transfer of radiation incident on the atmosphere of the component from the companion cannot be studied by using any symmetric solution of the equation of transfer. This needs a special treatment. We adopt angle-free one dimensional model (see Wing 1962; Sobolev 1963; Grant 1968). This procedure gives a fairly accurate solution provided we take large number of rays. The disadvantage in this technique is that either the angle dependence or frequency dependence cannot be incorporated.

Since it is difficult to handle asymmetric atmospheres in the radiative transfer calculations, we restrict our calculations to spherical geometry in this problem. As the gases in the atmospheres of close binaries move with large velocities, the problem can be treated in the comoving frame only. The solution of the radiative transfer equation in the comoving frame is given in Peraiah (1980). The radiation in the atmosphere consists of (1) self radiation of the component and (2) the incident radiation from the atmosphere of the companion. We need to treat the combination of these two radiation fields for calculations of the line profiles. The case of distorted atmosphere due to self rotation and tidal effect will be taken up in a subsequent paper.