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I'm reading on Wikipedia about Halo Stars that orbit the center of the galaxy at a high inclination away from the plane of the Milky Way. It seems that at some point, these stars must dive back into the core of our galaxy at very high relative velocities. This causes me to wonder...wouldn't this, combined with the greater density of stars in the core, cause a large number of stellar collisions in the galactic core?

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Not really, stellar collisions are a rare event. I'll try to make an answer in a while. – Py-ser Jul 1 '14 at 6:30

The answer is yes. Stellar collisions are events that occur mainly in Globular clusters due to their high stellar density. The likelihood of these events is highly dependent on the stellar density. As we know the galactic centers concentrate large amounts of matter and, of course, thousads of stars which are mainly in the old red main sequence. However, recent observations hane shown as the existence of young stellar clusters located in the Galactic center of Milky in contrast with our models and predictions about the galactic structures. It is currently believed that in these clusters occur a lot of stellar collisions. For more information there is a related paper here.

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Very good, thank you. It seems I was wrong. But, from a quick look at the paper, it seems there are no observational evidences for this, even if many arguments point to the expectation of such events. – Py-ser Jul 9 '14 at 1:32
Stellar collisions occur about once every 10000 years in the globular clusters surrounding the Milky way:… – Wayfaring Stranger Jul 12 '14 at 23:18
And such events "almost never" happen to stars like the sun, in the main part of the galaxy's disc. The distances between stars are just too vast. – James Kilfiger Sep 20 '15 at 8:30

A high density of stars definitely increases the chances of collisions, however, the high velocity of a halo star orbiting wouldn't increase its chances. Since the halo star is traveling very quickly, the halo star would only spend a small amount of time near the galactic core. Additionally, it would have less time to get deflected, gravitationally, by other stars in the core.

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