4.1 Compact binaries with NSs

Compact binaries with NS and BH components are descendants of initially massive binaries with M1 ≳ (8 –10)M ⊙. The evolutionary scenario of massive binaries was elaborated shortly after the discovery of binary X-ray sources [415Jump To The Next Citation Point408427] and is depicted in Figure 4View Image.
View Image

Figure 4: Evolutionary scenario for the formation of neutron stars or black holes in close binaries.

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 [107255] has also been tested by subsequent observations of binary pulsars. In fact, the scenario for binary pulsars was proposed even earlier in [415], 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 4View Image).

  1. Initially, two high-mass OB main-sequence stars are separated and are inside their Roche lobes. Tidal interaction is very effective so that a possible initial eccentricity vanishes before the primary star M1 fills its Roche lobe. The duration of this stage is determined by the hydrogen burning time of the primary and typically is several million years (for massive main-sequence stars, the time of core hydrogen burning is − 2 tnucl ∝ M). The star burns out hydrogen in its central parts, so that a dense central helium core with a mass 1.4 MHe ≃ 0.1 (M ∕M ⊙) forms by the time when the star leaves the main sequence. The expected number of such binaries in the Galaxy is around 104.
  2. After core hydrogen exhaustion, the primary leaves the main sequence and starts to expand rapidly. When its radius approaches the Roche lobe (see Equation (51View Equation)), mass transfer onto the secondary, less massive star which still resides on the main sequence begins. The mass-transfer rate can be crudely estimated as M ˙∼ M1 ∕τKH, where τKH = GM 21∕R1L1 is the primary’s thermal time scale.

    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 (7– 8)M ⊙ [2949596].

    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, M ≲ 40 M ⊙, 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 (31View Equation). 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.

  3. The duration of the WR stage is about several 105 yr, so the Galactic number of such binaries should be several hundreds.
  4. At the end of the thermonuclear evolution, the WR star explodes as Ib (or Ic) supernova to become a NS or BH. The inferred Galactic type Ib SN rate is around 10–2 per year, at least half of them should be in binaries. At this stage the disruption of the binary is possible (e.g., if the mass lost during the symmetric SN explosion exceeds 50% of the total mass of the pre-SN binary, or even smaller in the presence of the kick velocity; see Section 3.3 above). Some runaway Galactic OB-stars must have been formed in this way.
  5. If the system survives the first SN explosion, a rapidly rotating Be star in pair with a young NS appears. Orbital evolution following the SN explosion is described above by Equations (40View Equation45View Equation). The orbital eccentricity after the SN explosion is high, so enhanced accretion onto the NS occurs at the periastron passages. Most of about 100 Galactic Be/X-ray binaries [336] are formed in this way. The duration of this stage depends on the binary parameters, but in all cases it is limited by the time left for the (now more massive) secondary to burn hydrogen in its core.

    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 [221] for more detail). Accretion of matter onto the NS can reduce the surface magnetic field and spin-up the NS rotation (pulsar recycling) [3835735837Jump To The Next Citation Point].

  6. The secondary expands to engulf the NS. The common envelope stage begins and after ∼ 103 yr ends up with the formation of a WR star with a compact companion surrounded by an expanding envelope (Cyg X-3 may serve as an example), or the NS merges with the helium core during the common envelope to form a still hypothetic Thorne–Żytkow (TZ) object. The fate of TZ stars remains unclear (see [17] for the recent study). Single (possibly, massive) NS or BH should descend from them.

    A note should be made concerning the phase when a common envelope engulfs the first-formed NS and the core of the secondary. Colgate [61] and Zel’dovich et al. [475] have shown that hyper-Eddington accretion onto a neutron star is possible if the gravitational energy released in accretion is lost by neutrinos. Chevalier [56] 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 ∼ 0.1M yr−1 ⊙, 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., [45] 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., [329Jump To The Next Citation Point23Jump To The Next Citation Point]).

  7. The secondary WR ultimately explodes as a type Ib supernova leaving behind a double NS binary, or the system is disrupted to form two single high-velocity NSs or BHs. Even for a symmetric SN explosion the disruption of binaries after the second SN explosion could result in the observed high average velocities of radiopulsars (see Section 3.4 above). In the surviving close binary NS system, the older NS is expected to have faster rotation velocity (and possibly higher mass) than the younger one because of the recycling at the preceding accretion stage. The subsequent orbital evolution of such double NS systems is entirely due to GW emission (see Section 3.1.4) and ultimately leads to the coalescence of the components.

Detailed studies of possible evolutionary channels which produce merging binary NS can be found in the literature (see, e.g., [419Jump To The Next Citation Point420Jump To The Next Citation Point229Jump To The Next Citation Point329Jump To The Next Citation Point134492317182453]).

We emphasize that this scenario applies only to initially massive binaries. There exists also a population of NSs accompanied by low-mass [∼ (1 –2)M ⊙] companions. A scenario similar to the one presented in Figure 4View Image may be sketched for them too, with the difference that the secondary component stably transfers mass onto the companion (see, e.g., [167185186410]). 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 [27Jump To The Next Citation Point] and [37] for more detail and further references.

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