Testing MiHsC in Dwarf Galaxies

The best test of MiHsC is to find circumstances where it is likely to appear - that is, in systems in the deep of space with very low accelerations. I've recently been looking into some ideal candidates: Milky Way dwarf spheroidal galaxies. The Milky Way has lots of these tiny systems orbiting around it and some of them are so wispy that they should show up MiHsC, and they do. The plot below shows the five wispiest cases I could find that also have observations of their stars' orbital velocity. In the figure the x-axis shows the visible mass of the system (in Solar masses) and the y-axis (black squares) shows the velocity (km/s), for the dwarfs Segue-1, Triangulum-II, Bootes, Coma Berenices and Ursa Major 2. The error bars (uncertainties) are also shown.

The first thing that can be done is to calculate the maximum orbital speed that Newton would allow without the systems becoming gravitational unbound given their visible mass (general relativity predicts similarly). These maximum Newtonian velocities are shown with crosses and are much smaller than the stars' observed speed which implies that the dwarfs should explode centrifugally (inertially) because of the inability of their visible mass to bind them gravitationally. However, they look bound. Dark matter enthusiasts will no doubt say "Just add dark matter", but in the case of Segue and Triangulum-II you have to add 2600 and 3600 times as much dark matter as the visible matter, which makes the dark matter hypothesis look ridiculous.

Another possibility is to use MoND, Milgrom's empirical formula that modifies gravity or inertia, and the results of that are shown in the Figure by the triangles. MoND uses an adjustable parameter a0 of 1.8x10^-10 m/s^2 and also predicts too low a maximum velocity: outside the uncertainties in the observed velocities in all but one case: Coma Berenices, but it is much better than Newton, or 'naked' GR.

Finally, the predicted maximum velocity of MiHsC is shown by the diamonds (using the same method I used for full scale galaxies in the reference below). MiHsC is the closest to the observations and agrees, given the error bars, with all but one of the observations (Triangulum 2). It certainly performs the best, which is impressive given that, unlike dark matter and MoND it has no adjustability. My goal now is to emulate Gandalf and collect a few more dwarfs, the lighter the better.

References

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. A&SS, 342, 2, 575-578.  Preprint