USAAAO — 2026 First Round

A quickly-moving black hole passes through the center of a large star cluster. While the black hole does not experience any direct collisions with any stars in the cluster or significantly disrupt any stellar atmospheres, the black hole imparts a fraction of its momentum to several stars in the cluster close to the black hole’s trajectory. (This is known as dynamic gravitational friction and can be explained purely with Newtonian mechanics.) Some time passes, and due to complex multi-body interactions, the additional energy and momentum get distributed over the entire star cluster. After a sufficiently long time, which of the following statements are likely TRUE regarding the system (compared to before the black hole event), assuming no further perturbations occur? (I) The average peak blackbody emission wavelength among stars in the cluster decreases significantly. (II) Stars are on average further apart from each other than they were before. (III) Stars have lower relative velocities with respect to each other than they had before.