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4.3 Globular cluster processes

When the above evolutionary scenarios are played out in the environment of a globular cluster, additional mechanisms arise that enhance the production of relativistic binaries. New binary systems can be formed by dynamical interaction among three or more single stars or through tidal capture, and the period distribution and binary components of existing binary systems can be altered by interactions with other stars in the cluster. We will discuss here the broad features of these interactions and how they affect the evolution of binary systems toward relativistic binaries.

The formation of binaries during the dynamical evolution of globular clusters can occur either through tidal capture or through N-body interactions. Tidal capture occurs when an encounter between two stars is close enough that significant tides are raised on each. The tides excite non-radial oscillations in the stars. If the energy absorbed in these oscillations is great enough to leave the two stars with negative total energy, then the system will form a binary. This process was originally thought to be the dominant channel through which binaries were formed in globular clusters [24Jump To The Next Citation Point58]. It is now thought to be quite rare, as detailed calculations have shown that the final result is more likely to be coalescence of the two stars [10116198Jump To The Next Citation Point]. Although N-body interactions are less likely to occur than tidally significant two-body interactions, they are now thought to be the dominant channel for the formation of binaries during the evolution of a globular cluster. This process, however, is not likely to produce more than a few binaries during the lifetime of a cluster [24Jump To The Next Citation Point172Jump To The Next Citation Point].

Observations of present binary fractions in globular clusters combined with evolutionary and dynamical simulations indicate initial binary fractions as large as 100% are not unreasonable [120Jump To The Next Citation Point]. The existence of such a population of primordial binaries provides a much more efficient channel for the transformation of the initial distribution in component masses and orbital periods towards higher mass components and shorter orbital periods. This process follows from the interaction of primordial binaries with single stars and other binaries. Three results of the interaction are possible: complete disruption of the binary, an exchange of energy between the binary and the field star, or a replacement of one of the binary components by the field star. When a binary interacts with either a field star or with another binary, the energy of the interaction is shared among all stars in the interaction. The result is that the lowest mass object in the interaction will receive the largest velocity and be more likely to escape the interaction. In general, these interactions are quite complex, and must be studied numerically. A typical exchange interaction between a binary and a field star is shown in Figure 8View Image.

View Image

Figure 8: Example of a binary-field star exchange interaction. The binary comes in from the right (red-white), while the field star (green) enters from the left. After a complicated interaction, the white star is ejected and the newly formed red-green binary is in a more tightly bound orbit. Figure taken from McMillan [154].

If the initial binding energy of the binary is large, the result of these interactions is to shrink the orbit of the new binary as the gravitational energy of the binary is used to bring the field star up to the speeds of the binary components. However, if the binding energy is low, the field star contributes energy to the components of the binary, thereby widening the orbit. This is an example of “Heggie’s Law” [96Jump To The Next Citation Point], which can be summarized as hard binaries get harder and soft binaries get softer. For roughly equal mass stars, a binary is considered “hard” if its binding energy is greater than the average kinetic energy of a field star in the cluster and “soft” if its binding energy is less. For unequal mass encounters, Hills [106] has shown that the ratio of the orbital speeds of the binary components to the speed of the impactor is a better indicator of whether the binding energy will increase or decrease.

The average kinetic energy of a field star in the cluster is sometimes related to an effective temperature of the cluster [96155189Jump To The Next Citation Point] so that 2 ⟨mv ⟩ = 3kT. Numerical studies of the outcome of hard binary interactions indicate that the binding energy of the binary will increase by about 20% with each encounter [117189Jump To The Next Citation Point]. Since the encounter rate is proportional to the semi-major axis (or 1∕E) and the energy increase per encounter is proportional to E, the rate of hardening per relaxation time is independent of the energy and is ⟨ΔE ⟩ ∼ − 0.6kT ∕t bind relax [24Jump To The Next Citation Point]. A common feature of numerical studies of hard binary interactions is the preferential exchange of high-mass stars and stellar remnants with the least massive member of the binary [219Jump To The Next Citation Point]. Thus, the dynamical interactions in a globular cluster drive the initial orbital period distribution toward shorter periods by hardening the short period binaries while disrupting the softer binaries. Through exchange interactions, the mass distribution of the binary components is also driven toward higher mass stars, which further enhances the number of mass-transferring systems that can evolve to become relativistic binaries. A very useful numerical simulation of multiple star interactions is Fewbody [62Jump To The Next Citation Point].

Because stellar remnants can also be exchanged into hard binaries, globular cluster evolution opens up a new channel for the formation of relativistic binaries by introducing evolved components into binary systems that have not yet undergone a mass transfer phase. A particularly promising channel involves the exchange of a neutron star into a binary with a main-sequence star. The binary then undergoes case B or case C mass transfer with a common envelope phase, resulting in a NS–WD binary [198Jump To The Next Citation Point]. Podsiadlowski et al. describe a similar process without requiring the common envelope phase [181]. Similar interactions can occur to produce WD–WD binaries if a massive CO or ONe white dwarf is exchanged into a hard binary. A collaboration of various groups working in stellar dynamics maintains a webpage that provides a number of useful computational tools for comparing how dynamical interactions can affect different binary evolution codes [151Jump To The Next Citation Point].

Black hole binaries can also form as a result of exchange interactions, but the process is different because black hole progenitors will evolve so quickly in relation to the relaxation time of most globular clusters [141218]. One scenario that generates black hole binaries in globular clusters is described by Portegies Zwart and McMillan [189Jump To The Next Citation Point]. Stellar mass black holes of mass M ∼ 10 M ⊙ will be born early in the life of a globular cluster and, through mass segregation, they will quickly sink to the core. Once in the core, these black holes will be so much more massive than the field stars that they will effectively form their own cluster and interact solely with themselves. Single black holes will form binaries with other black holes through three-body encounters; any black holes which are in binaries with other stars will team up with another black hole through exchange encounters. This population of black holes and black hole binaries will then evolve separately from the rest of the cluster as no other stars will be massive enough to affect its dynamics.

Current intermediate mass black hole (IMBH) formation scenarios that involve globular clusters can also affect the dynamics of the globular cluster evolution, and therefore, can affect the evolution of binaries within the cluster. In the two most common scenarios, an IMBH is either formed early in the life of the globular cluster through runaway mergers of massive stars [1857091] or it is formed through the gradual accumulation of black holes throughout the lifetime of the globular cluster [159]. The existence of an IMBH in a globular cluster can also alter its density profile, and this can have an affect on the rest of the dynamics of the cluster [16].

We have seen how the dynamics of globular clusters can enhance the population of progenitors to relativistic binaries, making the standard channels of mass-transfer more likely to occur. In addition, globular cluster dynamics can open up new channels for the formation of relativistic binaries by inserting evolved, stellar remnants such as neutron stars or white dwarfs into binary systems and by shrinking the orbits of binary systems to enhance the likelihood of mass exchange. Finally, binary-single star encounters can simply create relativistic binaries by inserting two evolved objects into a binary and then shrinking the orbit to ultracompact periods. We next discuss the probable rates for the formation of such systems and the dynamical simulations that are used to synthesize globular cluster populations of relativistic binaries.

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