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Astron. Astrophys. 327, 620-635 (1997)

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1. Introduction

The dominant feature in the evolution of stars in tight binaries, and the one which distinguishes it from the evolution of single stars is the presence of various forms of mass transfer between the two stars. Mass transfer occurs in many different types of systems, to widely varying effects (cf.: Shore 1994 ): contamination of the envelope of a less evolved star with chemically processed elements, as in Barium stars; winds from one star, which may be visible as a screen in front of the other, as in EM Car, AO Cas, and most notably the binary PSR 1259-63 (Johnston et al. 1992 ; Kochanek 1993 ; Melatos et al. 1995 ; Johnston et al. 1995 ); catastrophic mass transfer, by common envelope phase, as in W UMa systems; or a slow, steady mass transfer by Roche lobe overflow (RLOF).

Mass transfer is particularly interesting if one considers the evolution of a system with at least one degenerate star. In these cases, mass transfer produces spectacular effects, resulting in part from the intense magnetic and gravitational fields of the compact objects - pulsed X-ray emission, nuclear burning, novae outbursts, and so on. Also, since the mass transfer rates can be high, and orbital period measurements accurate, one may see the dynamical effects of mass transfer on the binary orbit, as in Cygnus X-3 (van Kerkwijk et al. 1992 ; van den Heuvel 1994 ).

In the case of cataclysmic variables (CVs) and low mass X-ray binaries (LMXBs), one has a highly evolved, compact star (CVs and LMXBs contain white dwarfs and neutron stars, respectively) and a less evolved main sequence or red giant star. Mass transfer usually proceeds by accretion onto the compact object, and is secularly stable. The transfer may be accompanied by a stellar wind from the mass-losing star, or ejection of matter from the accretor, as in novae and galactic jet sources.

There are various unanswered questions in the evolution of LMXBs into low mass binary pulsars (LMBPs, in which a millisecond radio pulsar is in a binary with a low mass white dwarf companion) and of CVs. Among these are the problem of the disparate birthrates of the LMXBs and the LMBPs (Kulkarni & Narayan 1988 ), estimation of the strength of X-ray heating induced winds from the donor star (London et al., 1981 ; London & Flannery 1982 ; Tavani & London 1993 ; Banit & Shaham 1992 ), effects of X-ray heating on the red giant structure (Podsiadlowski 1991 ; Harpaz & Rappaport 1991 ; Frank et al. 1992 ; Hameury et al. 1993 ), et c.

The problem of mass transfer in binaries by Roche lobe overflow has received a good deal of attention in the literature over the past few decades, typically in investigations of one aspect or another of orbital evolution or stability. Ruderman et al. (1989 ) examined mass transfer by isotropic winds and accretion, in investigating the evolution of short period binary X-ray sources with extreme mass ratios, such as PSR 1957+20 and 4U1820-30. King & Kolb (1995 ) developed models with accretion and (typically) isotropic re-emission of transferred matter, in the context of the period gap in cataclysmic variables.

The aim of this paper is to present a unified treatmant of binary orbital evolution and stability, with relevant equations in a general form. The limits of pure modes of mass transfer and extreme mass ratios are presented and examined, to gain a qualitative understanding of slow, non-disruptive mass transfer in its various forms.

The paper is organised as follows. Kinematic equations for orbital evolution, assuming mass transfer through some well-specified mode(s), are derived in Sect. (2). Conditions for and regions of stability are derived in Sect. (3). The theory is applied to LMXBs in Sect. (4), and conclusions drawn in the final section. Two appendices contain further details on the unified models and on comparisons among the various limits of the models.

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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998