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Astron. Astrophys. 360, 969-990 (2000)

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1. Introduction

It is only a few years since the realization that irradiation of the donor star of a semi-detached binary by accretion luminosity generated in the vicinity of a compact accretor can have far-reaching consequences for the long-term evolution of such binary systems. Podsiadlowski (1991), treating irradiation in spherical symmetry, first addressed this problem in the context of the evolution of low-mass X-ray binaries (LMXBs). Later, Gontikakis & Hameury (1993), Hameury et al. (1993), and Ritter (1994) pointed out that spherically symmetric irradiation is probably not an adequate approximation for the case in point. Preliminary calculations by Ritter (1994) showed that the reaction of low-mass stars to anisotropic irradiation is qualitatively (and quantitatively) different from that to isotropic irradiation. Subsequently, King et al. (1995, 1996b, 1997), hereafter KFKR95, KFKR96 and KFKR97, Ritter et al. (1995, 1996a,b), Hameury & Ritter (1997), hereafter HR97, and McCormick & Frank (1998), hereafter MF98, have dealt with the case of anisotropic irradiation in various ways and detail. In most of the above-quoted papers reference was made to a paper by the present authors in which a detailed and systematic treatment of the basic properties of anisotropic irradiation of low-mass stars was to be found. The preparation of this material has been much delayed. The main purpose of the present paper is to close this gap in the recent literature, and to provide the base for further research.

For this purpose we shall discuss in Sect. 2 in some detail the basic concepts of computing the mass transfer rate in a semi-detached binary with and without irradiation, and present observational evidence and theoretical arguments in support of the notion of anisotropic irradiation. In Sect. 3 we shall present a simple analytic calculation which shows that the reaction of a low-mass star to anisotropic irradiation is qualitatively and quantitatively different from what one obtains in the isotropic case. We show also that the simple analytic results are fully supported by corresponding calculations of full 1D stellar models (hereafter simply referred to as full stellar models). In Sect. 4 we study the stability of mass transfer in binaries in which the donor star is exposed to irradiation generated by the accreting companion. In Sect. 5 we shall present a more detailed semi-analytic model than the one in Sect. 3 for the reaction of a low-mass star to anisotropic irradiation in the limit of small fluxes. The implications of the instability against irradiation-induced runaway mass transfer for the long-term evolution of CVs and LMXBs is discussed in Sect. 6. In Sect. 7 we shall present and discuss results of numerical computations of the secular evolution of CVs subject to the irradiation instability. A summary of our main results and our main conclusions are given in the final Sect. 8.

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© European Southern Observatory (ESO) 2000

Online publication: August 23, 2000