A colleague from an online forum has kindly looked into the new galaxy rotation hypothesis and posted the following. Unfortunately I haven't had time to go through it in detail, but it looks like a reaonable first attempt imo:
Based on the following assumptions:
Galaxies exist for billions of years, so the stars in the outer halo must be in relatively stable orbits,
Almost all of the visible mass in the galaxy is at the galactic core,
There is no ``hidden mass'' (i.e. dark matter), and
Newtonian mechanics (F = ma) are valid for analyzing halo star trajectories,
We have the following assertions:
The motion of the halo stars must be centripetal, and
Any gravitational field exerted by the galaxy must be almost completely divergenceless in the halo.
The first assertion implies that there is a center-pulling force (F) on the halo stars (of mass m) creating a velocity (v) of:
F = mv2 / r
Where r is the distance the halo star is from the galactic core. For standard Newtonian gravity the force is:
F = GMm / r2
Where G is the Gravitational constant, and M is the mass of the galactic core. The velocity of a halo star is then:
v = (GM / r)0.5
To match to experimental data, we want the velocity of the halo start to be a constant - i.e. not depend on r. The easiest way of achieving this is to set the gravity to:
F = GMm / r
And then we have:
v = (GM)0.5
This theory has two major problems with it:
This force would ``break'' all existing planetary orbits, and
This force has a non-zero divergence.
The second easiest approach is to add a term to Newtonian gravity. There is no ``spiral force'' that will work, such a force would constantly speed up the rotation of halo stars (or constantly slow down, depending on the direction), and the halo would either be flung off into space or collapse into the core. Since we do not observe this happening, we can rule it out.
We can't simply add rn terms to Newtonian gravity either, because they are not divergenceless, and would never cancel out the 1/r2 from Newtonian gravity unless they canceled out the force entirely (i.e. no centripetal motion).
The simplest solution that I can think of is to add some sort of gravitational equivalent to the Lorentz force as follows:
F = m (GM / r2 + bvrn)
Where b and n are to be determined.
This gives us a velocity of:
v = b / 2 rn+1 + r / 2 ( b2r2n - 4 GM / r2)0.5
If we set n = -1, we then have a velocity of:
v = b / 2 + ( b2 - 4 GM )0.5
Which is independent of r, as desired.
Unfortunately... the only Lorentz-type field that is divergence-free has 1/r3 dependence, no 1/r.
If we don't use divergenceless fields, then we are basically postulating dark matter all over again.
