The formation of binaries during the dynamical
evolution of globular clusters can occur either through tidal
capture or through -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 [19
, 43]. 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 [11, 83, 134
]. Although
-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 [19
, 117
].
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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” [70], 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 [75] 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 [70, 105, 127] so that
. 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 [85, 127
]. Since the
encounter rate is proportional to the semi-major axis (or
) and the energy increase per encounter is
proportional to
, the rate of hardening per relaxation
time is independent of the energy and is
[19
]. 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 [151
]. 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.
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 [134]. Podsiadlowski
et al. describe a similar process without
requiring the common envelope phase [123].
Similar interactions can occur to produce WD-WD binaries if a
massive CO or ONe white dwarf is exchanged into a hard binary.
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 [96, 150]. One
scenario that generates black hole binaries in globular clusters is
described by Portegies Zwart and McMillan [127]. Stellar mass black
holes of mass
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.
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.