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"How can we explain these (flat curve) rotation speeds whilst at the same time still obeying Newton's rule of gravitation and without inventing any new entities".
I want to state that I believe in Newton's laws being applicable anywhere and everywhere, since they are fundamental laws (or at least, rules) and so are not negotiable.
The thing that surprises me is that you say the halo is effectively solid! Well not solid exactly but with constant density from the galactic center outwards?
To avoid unnecessarily complicating the theory of gravity, we should consider all the alternative explanations and ultimately choose the most elegant one, even if it turns out to be a combination unseen mass and missing parts of the formula. Occam's razor should be seen as a suggestion, not a law.