As a professional physicist, my maths probably falls in your 'terrible assumptions' category so I am almost certainly not the right guy to ask to help ;-) however, my interest is piqued, twice actually, once to know which assumptions you consider are especially terrible,  and again to know how a spiral galaxy is similar to intestines.

The big problem with astrophysics is really that we are mainly stuck with observations we can make from here, or at least from either side of the sun 6 months apart, and the rest is really just theoretical.

I'm sure you know this, but for the benefit of others who may may not and then once they do, perhaps may be encouraged to join in, if we were to assume that the bright part of a galaxy shows where most of the mass is, (and assign a very estimated star and planet mass based on a combination of brightness and spectrum) then most of the mass is near the center, and at the dim edge of a galaxy things get more spread out, so there should not be much mass. Therefore, objects orbiting far from the center of the galaxy should move slower than objects closer to the center, just like the planets in our solar system actually do- which do that because most of the mass is at the sun - so mercury has a shorter year than we do, while the far out planets have much longer ones.

However, the observations of our local galaxy, AKA 'the milky way', and probably by now others as well, (my degree dates from the 80s and there will have been some considerable process since then) does not do this, and when folk plotted velocities of the stars vs. their distances from the center of the galaxy the stars were not behaving in the way anticipated. Stars farther away from the center were moving much faster than predicted - either gravity is not really square law or there is more mass enclosed in the orbits of the outer parts of galaxies than we can observe. The fact that we are unable to see this mass, because it is not emitting light, means it is known colloquially as "dark" matter.

Anyway, interested to see where it goes, if not much help to the original question,

Mike.

RE: my interest is piqued, twice actually, once to know which assumptions you consider are especially terrible,  and again to know how a spiral galaxy is similar to intestines.

Second part first.

My PhD was modelling the electrical activity in the human intestine.The intestine was modeled as a series of linked nonlinear oscillators.

The activity is an oscillating voltage that varies in frequency from the duodenum all the way down the intestine. One of the interesting findings was that a group of the oscillations would synchronise and progress down the intestine providing a potential mechanism that explained peristalsis. Google my name and mathematical model intestine.

A spiral galaxy can also be modelled as a set of linked oscillators

Re the first part. Astrophysicist assume that in the outer regions the stars do not interact with each other and are subject only to the force of the "enclosed mass"  which is calculated using Newton's Shell theorem.

As you probably know, Newton's Shell theorem is only valid in the context of a spherically symmetrical body of uniform and continuous mass and the predicted rotation curve you refer to applies only approximately to planets in a star system. IMHO, it is unreasonable to apply Newton's Shell theorem and Kepler's laws of planetary motion to a spiral galaxy.

Recent observations show that stars in galaxies that are relatively isolated behave differently from those closely grouped. It seems that stars in the outer region of a galaxy are influenced by other galaxies, so it is highly likely that these stars influence each other.

The assumptions used to predict rotation curves and mass profiles in a spiral galaxy result in models that are highly linearised. A spiral galaxy is a  rotating, complex, nonlinear system and my PhD taught me that that if you neglect the nonlinearities you'll get the wrong behaviours.

There's a lot more wrong with the accepted approach to interpreting observations of a spiral galaxy, but IMO, the real biggie is the use of Newton's Shell theorem. And if you read the literature on Dark Matter, there is no mention of that little assumption.

Thanks for responding

Bernard