Predicting Proxima Centauri's Orbit

The best way to persuade others to accept a new paradigm is to find an anomaly that embarrasses the old one. The galaxy rotation problem should be such a thing, but the old theory has been propped-up by dark matter which is flexible enough to fudge a solution.

The goal then is to find an anomaly which dark matter cannot fudge. Its Achilles' heel is scale, since, to work for full-sized galaxies, dark matter must have a tendency to spread out smoothly to explain why it stays out in the galactic halo, so dark matter shouldn't effect dynamics on smaller scales. One possible test then is to use globular clusters, smaller bound collections of stars within galaxies. They do indeed show a very similar rotational anomaly (Scarpa et al., 2006) but they are not simple enough to provide a clean test. Smaller and simpler are wide binary stars and again, a similar, orbital, anomaly has been seen (Hernandez et al., 2011) but the data is still too noisy. Recently, I've become interested in a wide 'trinary' for which the data is a bit better: our closest neighbour: the Alpha Centauri system.

I've talked about this before: this triple star system is interesting because the first two stars orbit close together so their masses are well determined from their orbits, but the third star orbits far from them in a low acceleration regime where MiHsC should apply. Sure enough, there is an anomaly. The third star, Proxima, has an orbit that is so fast that it should spin off into deep space with the centrifugal force, since the known mass of the the other two stars is too small to gravitationally bind it. Yet, other data, for example the similar chemistry of the three stars and the fact that they all seem to move together in the sky suggest that Proxima is bound to the system, but according to Newton, it can't be with that fast orbit.

This makes a nice experiment because the mass of the central two stars can't be increased to bind Proxima (their masses are too well known) and dark matter can't be used either (too small a scale). MoND (Modified Newtonian Dynamics) can be applied here, and can be thought of either as an increase in the gravitational constant, or a decrease in the inertial mass, but MoND has no physical model (no reason) behind it and it needs an adjustable parameter called a0 to be set by hand, again with no apparent reason.

MiHsC can also be used to predict the orbit, and it has a clear reason, and no adjustable parameters are needed. It predicts that the low acceleration of Proxima reduces its inertial mass so it can more easily be bent into a bound orbit by the small observed mass of the central two stars. The observed orbital velocity of Proxima and the various predictions of it are as follows:

Observed = 0.53 +/- 0.14 km/s   (to be improved by new ESA GAIA data)

Newton    = 0.34 +/- 0.02 km/s   (no wriggle room)
MoND      = 0.42 +/- 0.2 km/s    (if a0 is set to 1.2*10^-10 m/s^2)
MiHsC     = 0.65 +/- 0.02 km/s   (no wriggle room)

Newton and Einstein disagree with the data (unless the assumed orbit is extreme, which it could be) and dark matter can't be applied to this case. Both MoND and MiHsC agree with the data, and so they reconcile the chemical, co-moving and orbital data, but MiHsC does it with a reason and without the need for an adjustable parameter. I have just submitted a paper on this, so a reviewer somewhere is having fun.

References

Hernandez, X., M.A. Jimenez and C. Allen, 2011. Wide binaries as a critical test of classical gravity. Euro. Phys. J. C., 72, 1884. Preprint.

Scarpa, R., G. Marconi, R. Gilmozzi, 2006. Globular clusters as a test for gravity in the weak acceleration regime. Proceedings of the 1st crisis in cosmology conference. Am. Inst. Phys Proceedings series, Vol. 822. Preprint.