This scenario is fully confirmed by more than 30-years’ history of astronomical observations and is now considered as standard. A massive X-ray binary is an inevitable stage preceding the formation of a double compact system after the second supernova explosion of the helium-rich companion in such a stellar system. The formation scenario for binary pulsars proposed immediately after the discovery of PSR 1913+16 [107, 255] has also been tested by subsequent observations of binary pulsars. In fact, the scenario for binary pulsars was proposed even earlier in , but because no binary pulsars were known at that time, it was suggested that all pairs of NS are disrupted at the second NS formation.
It is convenient to separate the evolution of a massive binary into several stages according to the physical state of the binary components, including phases of mass exchange between them. The simplest evolutionary scenario can be schematically described as follows (see Figure 4).
The mass transfer ends when most of the primary’s hydrogen envelope is transferred onto the secondary, so a naked helium core is left. This core can be observed as a Wolf–Rayet (WR) star with intense stellar wind if its mass exceeds [294, 95, 96].
While the mass of the primary star reduces, the mass of the secondary star increases, since the mass transfer at this stage is thought to be quasi-conservative. For not too massive main-sequence stars, , no significant stellar wind mass loss occurs which could, otherwise, remove too much matter from the binary, thereby increasing binary separation. The secondary star acquires large angular momentum due to the infalling material, so that its outer envelope can be spun up to an angular velocity close to the limiting (Kepler orbit) value. Such massive rapidly rotating stars are observed as Be-stars. During the conservative stage of mass transfer, the semimajor axis of the orbit first decreases, reaches a minimum when the masses of the binary components become equal to each other, and then increases. This behavior is dictated by the angular momentum conservation law (31). After the completion of the conservative mass transfer, the initially more massive star becomes less massive than its initially lighter companion.
For the typical parameters the duration of the first RLOF is rather short, of the order of 104 yr, so only several dozens of such binaries are expected to be in the Galaxy.
An important parameter of NS evolution is the surface magnetic field strength. In binary systems, magnetic field, in combination with NS spin period and accretion rate onto the NS surface, determines the observational manifestation of the neutron star (see  for more detail). Accretion of matter onto the NS can reduce the surface magnetic field and spin-up the NS rotation (pulsar recycling) [38, 357, 358, 37].
A note should be made concerning the phase when a common envelope engulfs the first-formed NS and the core of the secondary. Colgate  and Zel’dovich et al.  have shown that hyper-Eddington accretion onto a neutron star is possible if the gravitational energy released in accretion is lost by neutrinos. Chevalier  suggested that this may be the case for the accretion in common envelopes. Since the accretion rates in this case may be as high as , the NS may collapse into a BH inside the common envelope. An essential caveat is that the accretion in the hyper-Eddington regime may be prevented by the angular momentum of the captured matter. The magnetic field of the NS may also be a complication. The possibility of hyper-critical accretion still has to be studied. Nevertheless, implications of this hypothesis for different types of relativistic binaries were explored in great detail by H. Bethe and G. Brown and their coauthors (see, e.g.,  and references therein). Also, the possibility of hyper-Eddington accretion was included in several population synthesis studies with evident result of diminishing the population of NS + NS binaries in favour of neutron stars in pairs with low-mass black holes (see, e.g., [329, 23]).
Detailed studies of possible evolutionary channels which produce merging binary NS can be found in the literature (see, e.g., [419, 420, 229, 329, 13, 449, 23, 171, 82, 453]).
We emphasize that this scenario applies only to initially massive binaries. There exists also a population of NSs accompanied by low-mass companions. A scenario similar to the one presented in Figure 4 may be sketched for them too, with the difference that the secondary component stably transfers mass onto the companion (see, e.g., [167, 185, 186, 410]). This scenario is similar to the one for low- and intermediate-mass binaries considered in Section 7, with the WD replaced by a NS or a BH. Compact low-mass binaries with NSs may be dynamically formed in dense stellar environments, for example in globular clusters. The dynamical evolution of binaries in globular clusters is beyond the scope of this review; see  and  for more detail and further references.
© Max Planck Society and the author(s)