Ok so they are usually found in globular clusters and can consider orbits in a static spherically symmetric gravitational field. The orbits are randomly scattered. Would these be considered to be collisional or collisionless orbits?
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They are pretty collisionless. As a rough estimate, the time to a close encounter within radius $r$ is $\tau \approx 1/(\pi r^2 v \rho)$ where $v$ is the average velocity ($\approx$ 20 km/s) and $\rho$ the average number density ($\approx$ 0.4 per parsec on average, 100-1000 times more in the core). So for <1 AU encounters that gives $\tau\approx 10^{15}$ years, while the timescale is a 1000 times less in the core - $10^{12}$ years, still really long. Still, 100 AU encounters thappen much more often and a lot of weak interactions sum up, so the cluster relaxes in a few hundred million years anyway.
To complicate things slightly, three-body encounters can generate binaries, and "hard" binaries (binding energy bigger than average kinetic energy in the cluster) tend to become harder when interacting randomly with other stars ("Heggie’s law").
But actual stellar mergers likely mostly happen right now due to hard binaries evolving into giant stars and dissipating their orbital velocity rather than actual random close encounters.
Anders Sandberg
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