James
I want to focus in on a point which I feel is significant. I have mentioned it previously, however I think I can clarify. Its important, because it is what hints at a very simple mathematical law that will describe this relationship we seek.
We have spent time in consideration of spiral galaxies whereby the apparent mass density, observed star number density, falls of by square of the radius. However, the amount of mass present that can be inferred by flat rotation velocities, indicates there is a very systematic and tidy formula for adding to the Baryons mass value, to the fourth power.
So with that scenario in mind, I ask you to consider a contrasting circumstance. Imagine a spiral galaxy whereby the apparent mass density, observed star number density does not fall of by square of the galaxy radius, but remains constant density throughout. Conceivably this will further accentuate this variable mass function we hypothesize, leading to increasing rotational velocities at increasing radius, rather than merely constant rotational velocities. So sweeping galaxy arms, will be straight spokes instead.
The reason this is very significant in my mind, is because it is a natural extension of our hypothesis, evidenced by basic consideration of geometric symmetries. But also because 2/3 of spiral galaxies display this characteristic motion in their interiors, in the form of bar spirals. Conceivably where the observed star number density might transition towards a constant, in the inner galactic bulge. Just like a bike wheel spoke expresses increased velocity at increased radius.
So an extension of our original hypothesis, which can be summed up as, an increase in mass to the forth power at increased galaxy radius, to "flatten" galaxy rotation curves. It would instead be summed up as, an increase in mass to the fourth power at increased galaxy radius, to "accelerate" galaxy rotation curves.
Because convention has no prescription for increasing velocity at increased galaxy radius, they speculate the spiral bars are temporary phenomena. But I am not aware of any photographic interpretations of bars transitioning in or out of formation? Which suggests they maybe stable and persistent.
That this is a natural extension of our rather dramatic hypothesis, and that galaxies do appear to exhibit accelerated rotation curves. Well, it is rather uncanny, I do think. If this does turn out to be the case, then the proportional symmetries that I point too, will be expressible as a relation of volume of space, and the apparently observed star number density within that volume of space.
Steve
