[Keysh]

The problem isn't so much the flatness of the rotation curve, but its continued high value: as you go farther and farther out in distance, it should drop rapidly because most of the visible matter is concentrated toward the center of the galaxy, but it doesn't. This implies that there is more matter, less centrally concentrated than the visible matter.

Note that most "rotation curves" are actually measured from gas, not stars, and also that strong gravitational interactions between individual stars are extremely rare except in very dense star clusters and galactic nuclei, due to the increasingly large distances between stars as you go out from galactic centers. The time required for individual stellar interactions in the main or outer parts of galaxies to significantly affect their motions is much larger than the age of the universe (see, e.g., https://en.wikipedia.org/wiki/Stellar_dynamics).

Finally, this wouldn't address other evidence for dark matter, like the halos of hot (millions or tens of millions of K) intergalactic gas in galaxy clusters. The pressure of the gas should have driven the gas to expand way billions of years ago, if you assume that only the gravity of the individual galaxies and the gas itself is restraining it.

[Retric]

Edited.

> strong gravitational interactions between individual stars are extremely rare except in very dense star clusters

We’re talking 225 million years for the sun to orbit the galaxy, rare events become commonplace on those timescales. Anyway, I’m sure someone has actually done this kind of simulation I’m just curious about what the result is and how they did it.

[Keysh]

You don't need a simulation; you just need an understanding of Newtonian gravity, basic algebra and a bit of calculus, and some knowledge of stellar masses, velocities, and space densities. This is a standard part of the grad school curriculum (even the advanced undergrad level) in astronomy; here's an example with the math in some lecture notes from an undergrad course at Caltech (by George Djorgovski): https://sites.astro.caltech.edu/~george/ay20/Ay20-Lec15x.pdf

The mean time for the orbit of a star to be significantly randomized by weak, intermediate-distance interactions (e.g., the kind the Sun is experiencing now from neighboring stars) is the relaxation time, and for a star like the Sun it's of order several trillion years.

The mean time between strong gravitational interactions, where the gravity of a single nearby star significantly changes the orbit of a star (perhaps more like what you were imagining), is of order one quadrillion (10^15) years.

(Note that the numbers are for the density of the stars at the Sun's orbit; further out, where you start to get to the point where dark-matter effects really show up, the density is lower, and so these times would be even longer.)

Those are examples of "extremely rare" even on timescales of the age of the universe.