What'd happen if two stars collided? Could it happen? Would the speed/mass change the result?
I suppose it would depend on the mass of the stars and if they slammed head on it glanced off of each other. I suppose it's possible for two brown dwarfs to hit each other and continue on their way (like two big planets colliding, something happened to Uranus to cause it to be on it's side yet it's still in one piece.) I would think a medium sized star could probably absorb a small star with only a massive explosion, but be able to hold itself together. Big stars would shred each other and catastrophically blow up. Neutron stars would merge into a black hole and release a gamma ray burst.
If a large star absorbs a small star or two small stars merge, they're final velocity would probably obey normal rules of elastic collisions, mass would be the combined mass of both minus whatever got blown off in the collision.
As newjerseyrunner stated, it really depends on the mass of the two stars. However, that is precisely what is being suggested with the star HV2112 discovered in 2014 in the Small Magellanic Cloud - a collision between a Red Supergiant and a neutron star. Such collisions are also known as a Thorne–Żytkow Object.
The collision between a neutron star and a white dwarf has also been suggested as the cause behind short (< 2 second) gamma-ray bursts. Additionally, the "Blue Stragglers" found in clusters are suggested to be the result of either stellar collisions, or a mass transfer from another star(s).
Keep in mind that stellar collisions are extremely rare events.
Astronomers discover first Thorne-Żytkow object, a bizarre type of hybrid star - Colorado University News Center
Discovery of a Thorne-Zytkow object candidate in the Small Magellanic Cloud - arXiv 1406.0001 (free reprint)
Two Stars Collide; a New Star Is Born - New York Times
V1309 Scorpii: merger of a contact binary - Astronomy & Astrophysics (paid subscription)
V1309 Scorpii: merger of a contact binary - arXiv 1012.0163 (free reprint)
Implications for the Formation of Blue Straggler Stars from HST Ultraviolet Observations of NGC 188 - arXiv 1510.04290 (free reprint)
Whatever can happen, usually does happen. The puzzle is fathoming what actually did happen. Galaxies collide, and sometimes stars do. Both are fairly rare events. So are gamma and xray bursts. Eliminate the impossible and the truth is always what remains.
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