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 [24
, 60]. 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, 118, 198
]. 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 [24
, 170
].
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 [122]. 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 8
.
|
The average kinetic energy of a field star in the cluster is sometimes related to an effective temperature
of the cluster [98, 154, 187] 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 [119, 187
]. 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
[24
]. 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 [217
]. 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 [64
].
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 [198]. Podsiadlowski et
al. describe a similar process without requiring the common envelope phase [179]. 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 [151
].
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 [141, 216]. One scenario that generates black hole binaries in globular clusters is described by
Portegies Zwart and McMillan [187]. 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.
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 [183, 72, 93] or it is formed through the gradual accumulation of black holes throughout the lifetime of the globular cluster [158]. 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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