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Introduction

In the early 1980s, our understanding of binary star evolution  based on the pioneer work by Paczynski (1971)[150], Tutukov and Yungelson (1973)[195], van den Heuvel and Heise (1972)[201], allowed us to construct a general evolutionary scenario  which successfully explained the genesis of well-studied normal stars and offered potential explanation for new X-ray sources discovered in space experiments. It was recognized then that the evolution of binary systems looks like a branching genealogical tree whose nodes include important physical processes, such as the mass exchange between binary components, the common envelope  stage (CE), loss of orbital angular momentum at the expense of gravitational wave  emission and the magnetic stellar wind,  etc.

On the other hand, it was clear that dramatic new processes should occur after a compact star (white dwarf (WD),  neutron star (NS) or black hole  (BH)) has been formed in a binary system. Taking account of these processes was especially important in the cases of WD and NS as they can have strong magnetic  fields and rotate rapidly. Here, we come across a new phenomenon in stellar evolution - the evolution of gravitating magnetic compact stars  (gravimagnetic rotators).  The original idea goes back to pioneer work by V.F. Schwartzman (Schwartzman 1970a, 1971)[173, 176], Illarionov and Sunyaev (1975)[76], Bisnovatyi-Kogan and Komberg (1975)[16], Shakura (1975)[178], Wickramasinghe and Whelan (1975)[212], Lipunov and Shakura (1976)[109], Savonije and van den Heuvel (1977)[171], and Lipunov (1982a)[98], and means that astrophysical manifestations of the magnetized compact star are mainly determined by its interaction with the surrounding plasma by means of two types of physical fields: electromagnetic and gravitational, and the evolution itself represents a gradual change of the character of this interaction. The universality of such an approach is not only its ability to explain apparently such different objects as radiopulsars,  X-ray pulsars,  X-ray bursters, cataclysmic variables,   polars,  transient  X-ray sources, etc., but also its ability to predict completely new and still undiscoverd objects.

Therefore, the realistic treatment of binary star evolution must include both types of evolution: the nuclear evolution for the normal stars, and the rotational evolution for the compact magnetized stars. The last fact complicates the evolutionary tree to such a point that the need for a special numerical tool for studying binary evolution (the Scenario Machine), analysis of the observed picture and approval of the evolutionary scenarios becomes quite obvious (Kornilov and Lipunov, 1983a,b)[85, 86]. Now it consists of a large numerical code that incorporates the crucial physical processes in binary systems and takes into account:

(a)

mass exchange between binary components;

(b)

loss of the orbital momentum due to gravitational waves; 

(c)

loss of the orbital momentum due to magnetic wind; 

(d)

evaporation of normal stars by radiopulsars;

(e)

spin evolution  of magnetic compact stars. 

The history of the Scenario Machine can be briefly summarized as follows.

• (a + e) Massive binaries  ( ) (Kornilov and Lipunov, 1983a,b, 1984)[85, 86, 87].
• (a + b + c + e) Low-mass binaries ( ) (Lipunov and Postnov, 1987a,b, 1988a).[114, 112, 116]
• (a) Massive binaries  (Dewey and Cordes, 1987).[45]
• (a + b + c + d + e) All mass (Lipunov et al., 1994a,b[123, 124]; see Lipunov, 1991).[106]
• (a + b + c) All mass (Tutukov and Yungelson, 1993b).[197]
• (a + b + c) Low-mass binaries (Kolb and Ritter, 1992[83]; de Kool, 1992;[42] Kolb and de Kool, 1994)[84].

Apart from giving an explanation for the known evolutionary stages of binary systems, this code proved to be a powerful tool for studying evolutionary links between different binary star populations (Lipunov, 1994)[108]. The results obtained with the Scenario Machine include the following.

• Prediction of nearly 100 new stages of binary systems with magnetized compact companions,
• Prediction of millisecond X-ray accreting pulsars  (see Kornilov and Lipunov, 1983b[86]), later confirmed by discovery of A0538-66 (P=0.067 s),
• Explanation of some of the ultrasoft superluminous sources  as superaccreting compact stars in binaries (Lipunov et al., 1993[122]), which was confirmed by the discovery of a transient  X-ray pulsar RX J0059.2-7138 in the Small Magellanic Cloud  (SMC) (Hughes, 1994[68]),
• Prediction and estimation of the number of binary radiopulsars  with OB-stars ( 1 per 700 visible galactic pulsars) (Kornilov and Lipunov, 1984;[87] Lipunov and Prokhorov, 1987[115]), which was confirmed by discovery of PSR B1259-63 (Johnston et al., 1992[78]),
• Estimation of the number of binary radiopulsars with black holes  (Lipunov et al., 1994b[124]); binary PSR B0042-73  in the SMC (Kaspi et al., 1994[81]; Lipunov et al., 1995e[127]) might be an example (see, however, Bell et al., 1995[11]),
• Calculation of the gravitational wave background formed by galactic and extragalactic binaries  (Lipunov and Postnov, 1987a, 1988[113, 116]; Lipunov et al., 1987a, 1995a[120, 125]).

Many important physical effects were shown to follow from the modern evolutionary scenario, among which are those listed below

• Anisotropy  of supernova explosions  giving ``kick''-velocities  of young pulsars  of 70-100 km/s (assuming a -function-like kick velocity distribution; Kornilov and Lipunov (1984)[87]; similar estimates are given by Dewey and Cordes (1987)[45]), a more detailed discussion will be given below,
• A significant evolution of supernova rates and binary NS merging  rates at cosmological distances (Lipunov and Postnov, 1988[116]; Lipunov et al., 1995c[129]);
• A strong link between the relative number of binary radiopulsars  with different compact components and star burst  formation history (Lipunov et al., 1995e[127]).