Has the dark matter mystery been solved?

by John G. Hartnett

Unseen dark matter has been invoked several times to solve problems in astrophysics and cosmology. Historically the most significant problem has been the rotation curves of galaxies, particularly spiral galaxies. Using the Doppler Effect the speeds of the stars and gases in the disk regions of spiral galaxies can be measured. See Figure 1.

By now hundreds of thousands of galaxies have been measured this way. What is observed is that the speeds of the stars, and the gases beyond where the stars are observed, are much greater than it would appear Newtonian physics allows for. 

As a result it has been suggested that there is an invisible halo of cold non-interacting matter. This putative invisible halo has the needed gravitational effect on the stars and gases but it cannot be seen, hence it is called dark matter. Dark matter is alleged not to be normal atomic matter, made from protons and neutrons (which are known as baryons), but some sort of slowly moving (cold) exotic non-baryonic matter. Weakly Interacting Massive Particles (WIMPs) were suggested.

And until recently it was believed that WIMPs might be the lowest mass stable supersymmetric particle, called a neutralino, but 10 years of experiments at the Large Hadron Collider (LHC) has disproven the theory upon which such a speculation was based.¹ Other laboratory investigations with supersensitive detectors, deep underground, have failed to detect any type of particle that could be considered a candidate for dark matter.²

On the cosmological scale

Considerations for a sizable content of dark matter have been also discussed in a cosmological context. The need for these have come about because of various problems with the standard model.^3,4,5

When we put this all together we can generally say that dark matter (and other dark sector entities) are really only needed in astrophysics and cosmology.^6,7 But the lack of detection of any type of dark matter in laboratory experiments has driven some to speculate and develop new physical theories to explain what we observe astronomically.^8,9

And there are two cosmological reasons why cosmologists need non-baryonic (non-normal atomic) cold dark matter (CDM). One is that the measured density of the gravitating mass in the universe as determined by astronomical measurements¹⁰ appears to considerably exceed that of normal matter as constrained by big bang nucleosynthesis (BBN). BBN does present other problems but we won’t go into them here.³

The amount of matter needed in the universe is six times the observed amount of baryonic (normal atomic) matter. Therefore it is believed that the density of particles that don’t comprise normal atomic matter, i.e. the non-baryonic matter, is about five times the amount of the baryonic matter.

Dark matter in the form of black holes, supermassive or otherwise, has implications for BBN. If dark matter was real and, as now suggested, comprised of stellar size black holes (i.e. non-baryonic matter) in the early universe, then the black holes would have had to have formed in the first minute after the beginning of the universe. Otherwise the black holes would have had an observable effect on BBN. The details of this are now also being debated and recalculations being made.¹²

A second cosmological reason is that gravity itself is too weak to grow, on the available cosmic timescales, the presently observed structures (e.g., galaxies, clusters, superclusters and long galactic filaments) from the alleged smooth initial condition observed in the cosmic microwave background (CMB), unless something was available to accelerate the growth process.

Additional matter with a density much higher than the observed matter density could have done it. But if it was normal atomic matter, i.e. baryons, it would be observable and would have shown up in the observations of the CMB radiation. Therefore this new non-baryonic matter must not interact with the photons of the CMB like ordinary atomic matter allegedly does.

Another look at rotation curves

When we measure the speed of planets in the solar system, the measurement of a planet’s constant speed (v) in orbit around the sun and its distance from the sun (r) allows us to determine the mass of the sun (M_s). Considering only the sun and an orbiting planet this is a two-body problem and all that is needed is Newton’s equation for this two-body problem to solve for the mass of the sun. The only unknown is M_s, the mass of the sun. With near circular orbits (a planet’s acceleration around the sun is very close to zero, i.e. r′′≈0). It follows that¹¹

where G is Newton’s gravitational constant.

Similarly, we can write down an almost identical equation for the enclosed mass, M(r), within the orbit of any star at a distance r from the centre of a galaxy.

In this case M(r) gives you the mass enclosed inside the orbit of the star you are measuring. It is not constant but depends on the distance r the star (or circulating gas) is from the centre of the galaxy under investigation. But this is where the assumption of dark matter comes from.

If we plot the speed of the stars, v (and the same for gases outside the radius of visible stars), as a function of distance, r, from the centre of a galaxy we typically get the result shown in Figure 2. But as can be seen, stars (and gases) move “too fast” when they are outside the central nucleus of the galaxy (indicated by the hump in the Newtonian curve).

The observed speeds are much faster than what is expected from standard Newtonian physics. But Newtonian physics works very well in the solar system. The more distant a planet is from the sun the slower it moves. Why then doesn’t the same physics work for galaxies?

From this result shown in Figure 2 and known Newtonian physics it is usually concluded that one of the following must be true:¹¹

1. The galaxy is dissipating, or
2. Newtonian physics is incorrect, or
3. Massive amounts of unobserved halo dark matter exist.

On bullet point 1, the implication is that the galaxy under observation is not in equilibrium, which possibly could be argued because we have not observed galaxies over millions of years to see any structural evolution. But let us assume here (as is generally assumed) that all observations are consistent with stable equilibrium conditions. In fact Eq. (2), which is the basis of the problem, implicitly assumes an equilibrium condition.

On bullet point 2, since under weak gravity, which is the case in most regions of a galaxy, apart from maybe inside or near a supermassive black hole at the core of the galaxy under consideration, Einstein’s general relativity theory produces the same equations of motion as Newton’s law of gravitation. Therefore, for circular motion of bodies in orbit we only need consider Newtonian physics.

Science

On bullet point 3, it is obligatory on those who profess to believe the existence of some unseen exotic type of matter that does not respond to or is not detectable by electromagnetic radiation to produce evidence of the existence of even one such particle in a laboratory experiment, especially considering that they require the matter of this galaxy to be about 85% dark matter. This is the typical percentage of additional unseen matter if one were to accept the answer is dark matter in the form of a spherical halo around not only our galaxy but also most spiral galaxies of which we are aware.

However, due to the lack of any laboratory evidence in favour of the existence of any new particles that might comprise halo dark matter in hundreds of thousands of galaxies, it has now been suggested that dark matter could be comprised of millions, even billions, of stellar-size black holes.¹² See Figure 3. This suggestion has come about after the detection of stellar-size black holes by the LIGO gravitational wave detectors.¹³

The notion that stellar mass (10 to 100 times the mass of the sun) black holes could be dark matter in halos of galaxies is currently being debated. In the 1990s microlensing all but ruled out the possibility of swarms of such black holes but now it is said that the surveys were too short and longer surveys are needed. It is also argued that black holes in excess of 10 solar masses would have long ago settled in the centres of galaxies and any in the regions surrounding galaxies would leave the galaxies ruffled up, but observations indicate the opposite—compact and unruffled.¹²

Stars have drag

It could be said that there is one aspect that needs to be added to bullet point 2. It may not be new physics that is needed but the correct application of the known physics. If an incorrect boundary condition was assumed or an incomplete application was made of the known physics where one aspect was not properly modelled, then this might just solve the problem of the rotation curves without the need to “invent” exotic dark matter.

This is what has now been proposed.¹¹ The application of Eq. (2) as described above neglects the billion-body problem and therefore neglects drag between the individual members of the system. Donald Saari, a mathematician¹⁴ who has worked on this problem, writes in the online Scientific American SciAm News,¹¹ that the

… general properties of billion-body Newtonian systems are unknown, so astronomers developed creative approximations to study galactic systems. Intuition for a standard approach comes from star-soup type pictures of galaxies, with bodies pulling others along (as in Figure 1). This star-soup appearance suggests approximating actual N-body systems with a continuum …

And that continuum approximation results in Eq. (2), which then leads to the dark matter conundrum.

The illustration often used in reference to Einstein’s general relativity theory (and remember Newtonian physics can be derived from GR) is that “masses tell space how to curve and the curved space tells the masses how to move”. This in effect assumes the masses in a galaxy are a continuum and thus curve the space in the galaxy in a smooth fashion.

The individual stars are neglected in favour of a smooth continuum of matter density. And in the modelling the matter density is modelled in this fashion. But by approximating the billion-body system of a galaxy as a continuum of smoothed-out matter it appears that something is neglected in the application of the standard Newtonian physics.

Saari did the billion-body system calculations and found that¹¹

… a star’s Newtonian rotational velocity is the M(r) gravitational effect plus dragging terms; these larger v values exaggerate M(r) values of [Eq.] (2). As dragging is more pronounced at larger distances, expect this error to incorrectly predict halos. …. No solution has halos, yet [Eq.] (2) incorrectly predicts massive ones! These egregious errors manifest differences between systems of discrete bodies and approximations; actual systems involve dragging effects, while continuum approximations ignore this crucial dynamic. (emphases added)

Conclusion

Saari ends the online SciAm News article with his own conclusion.¹¹

“This casts doubt about a standard argument claiming massive amounts of dark matter.”

There you have it! I have not personally checked his maths but his work is published in good journals including The Astronomical Journal.¹⁵ I have also published in that journal and I know it takes some effort to get published there.

The relevance for biblical creationists is just as important as it is for cosmic evolutionists. The problem of galaxy rotation curves has been an issue for a very long time and no matter to which cosmogony you subscribe, you still have to explain how galaxies hold together over billions of years if the standard application of Newtonian physics is correct.¹⁶

Of course, a biblical creationist might argue that the galaxies are not in equilibrium, because the universe is not billions of years old. That is a possibility but one I believe not very likely. It is more likely that God created all galaxies in a stable configuration, just as he did the sun and the solar system, and all other systems in the galaxy. Those stable systems exhibit operational physics, which, in principle, we can investigate. Now it seems we can add one more thing, the operational physics of galaxies is standard Newtonian when all factors are correctly included.

For the big bang cosmologist this is a big problem. Up to this point the 80% of all galaxy matter being dark matter is consistent with what they need in big bang cosmology. Without this five times the amount of non-baryonic matter to baryonic matter in the universe the standard big bang cosmology does not agree with the cosmological observations, such as from high-redshift-supernova measurements and even the fluctuations in CMB radiation. In my opinion, it was brave for Scientific American to publish Saari’s news item. Let’s see if his work gains any traction.

If this pans out, for me it is a relief. We can continue to use standard physics in the cosmos and no longer need to look for alternative theories⁹ to explain what we could not up until now.

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