Dark matter replacement: MOND

MOND and dark matter both aim to explain a key pattern identified by Vera Rubin in the 1970s – the ‘flat’ rotation curves in the outer reaches of galaxies

What if, some argued, the laws of Newtonian gravity were not as rock-solid as generally thought? In 1983, Israeli physicists suggested that the problem would disappear with a relatively simple tweak to the puzzlingly way that gravity tails off over the largest of cosmic distances.

Newton’s equations suggest that the strength of gravity declines according to an ‘inverse square law’ – doubling the distance between two masses reduces the gravity between them to a quarter of its former strength. Milgrom’s ‘modified Newtonian dynamics’ (MOND) theory suggested that at great distances, when the acceleration due to gravity becomes 100-billion-times weaker than we experience on the surface of the Earth, its decline becomes a simple inverse relationship (where doubling the distance halves the strength). If one relationship changed gradually to the other on scales of tens of thousands of light years, then gravity above these scales would be much stronger than Newtonian predictions, explaining why stars in the outer reaches of galaxies move so fast.

However, MOND itself is simply a ‘paradigm’ – a framework for thinking about the problem. Over the following years, Milgrom and his colleague Jacob Bekenstein worked to develop it into a complete theory where the equations match up precisely to the evidence observed from galaxy rotation curves.

Developing a form that can work even in the extreme situations of general relativity took considerably longer, but in 2004, Bekenstein produced ‘tensor-vector-scalar gravity’ (TeVeS) theory, a model of gravity that can, at least in theory, replace both Newtonian gravity and general relativity.

But, despite these advances, MOND remained on the fringes while most astronomers chased after dark matter. Supporters picked away at areas where the dark matter paradigm seemingly failed to match observations of the real universe, but MOND was also vulnerable to such criticisms. And even when TeVeS emerged as a possible description of how gravity might work, it didn’t really explain why it would work that way.

In the past decade, however, that has changed with the emergence of a new theory called ‘emergent gravity’, pioneered by theoretical physicist Erik Verlinde at the University of Amsterdam. While previous theories were driven by the need to explain galaxy rotation curves, Verlinde’s work started out as a way of looking at the biggest problem in modern science.

“In physics we have two great theories, explains Margot Brouwer, “Einstein’s general relativity explains everything on large scales, and quantum mechanics works to explain the very small scales of atomic nuclei and elementary particles. But, when we try to combine the two scales, the equations don’t work out, and so far nobody’s been able to make a theory that combines general relativity with quantum mechanics.”

Verlinde’s theory is too complex to explore here in detail, but at its heart is a description of how complex quantum phenomena link separated areas of space-time to create the ‘emergent force’ that we experience as gravitation. On relatively small scales, gravity in Verlinde’s theory behaves just like that of Newtonian physics and general relativity – the only significant difference is that, as the strength of

“The search for dark matter particles has continued for decades, but so far no suitable candidate has been detected”

gravity trails off over huge distances, the pattern of its decline changes from an inverse-square law to a simple inverse relationship – the same pattern used by MOND theories.

A key test for any truly scientific theory is that it should make predictions that can be tested, and for Brouwer, Verlinde’s prediction was too tempting to ignore. Fortunately, her research interests provide her with an ideal situation in which to test it. “My main research topic is studying the distribution of gravity around galaxies, and the way that we do this uses a phenomenon called weak gravitational lensing. Einstein’s general relativity shows that gravity is essentially the same as curvature of space-time, so when light from a distant galaxy passes through space-time that is curved by the mass of another galaxy, the light from the more distant galaxy will get distorted.”

Brouwer’s work involves measuring the distortion of light from many different background galaxies, as it passes a single foreground system. This allows her to map the distribution of mass and gravity, but means taking dark matter into account: “In the dark matter paradigm you would have the galaxy surrounded by a cloud of dark matter – you can approximately know the mass of the visible galaxy, but it’s not easy to predict the mass of the dark matter cloud – often that’s what we’re trying to figure using the gravitational lensing method.”

Verlinde’s ideas, however, provide an opportunity to turn Brouwer’s usual methods on their head.

“The theory gives a prediction for how the gravitational distortion around a galaxy will be distributed based on the mass of visible stars and gas in that galaxy. Dark matter does not exist, so all the gravity originates from the normal matter, and we can work out the distribution of gravity around the galaxy and the space-time distortions arising from that. That’s what I calculated, and when I compared that to measurements of the gravitational lensing effect, to my surprise they were in fact an exact match.”

When the findings were published last year, some observed that traditional dark matter models could also produce a good match for the observed lensing effects – but Brouwer explains that’s missing the point. “In the dark matter model you can change the percentage of dark to visible matter for each individual galaxy, which makes it easier to adjust the gravity and match perfectly with the lensing effects you detect. Verlinde’s model makes a more direct prediction with none of these ‘free parameters’, and the fact that it matches so well immediately grabbed my attention.”

But while the Verlinde theory may have cleared this first hurdle in style, there are still many problems in thinking that some form of MOND could easily replace dark matter. As mentioned

“So far nobody’s been able to make a theory that combines general relativity with quantum mechanics” Margot Brouwer

above, the dark matter paradigm is supported not just by galaxy rotation, but in complex situations such as galaxy cluster collisions (where dark matter appears to separate from the luminous matter) and the early days of the universe (where dark matter began to clump together and form the beginnings of today’s web-like cosmic structure while luminous matter was still in chaos).

Unfortunately, it’s just too early to know whether emergent gravity might have its own solutions to these sorts of observations, as Margot Brouwer explains. “One of the main criticisms of Verlinde’s theory from an observational point of view is that it can only make fairly rudimentary predictions for spherically symmetric, static and isolated mass distributions. Because I was studying lensing around individual galaxies that aren’t doing too much crazy stuff, I was able to test Verlinde’s theory for this particular case. But, so far, the theory can’t make predictions for more ‘messy’ situations.”

Erik Verlinde is now working on extensions of the theory that could explain how gravity works in more complex conditions, but it could be many years before that work comes to fruition. In the meantime, as Brouwer points out, the case is far from proven. “Just because I worked on Verlinde’s theory, that certainly doesn’t mean I don’t believe in dark matter. There are a lot of challenges still, and of course there’s still a hope that one day they’ll track down dark matter particles (though they’ve been looking for a very long time!). "There are all kinds of strange things going on in the universe where we absolutely seem to still need it, so I certainly wouldn’t say that dark matter is dead.”

For now we can only wait for theorising and testing to be done.

By measuring the lensing of light from multiple galaxies, astronomers can map the gravity and suggested distribution of dark matter

Motion of galaxies in the Coma Cluster led Zwicky to suggest the existence of dark matter weighing at least 400-times more than estimated calculations

125 Mpc/h 31.25 Mpc/h The formation of structure in the early universe, when the pressure of radiation was forcing normal matter particles apart, is more important evidence for dark matter that rival theories cannot yet explain

Gravity declines following ‘inverse square’ law Gravity declines inversely with distance 4. Modified gravity solution MOND and related theories suggest that all the gravity stars experience is due to luminous matter, but that the decline in gravity...

1. Dark matter solution The ‘dark matter paradigm’ suggests that galaxies are surrounded by a much heavier halo of dark matter, whose gravity influences the orbits of stars further from the core. ‘Halo’ of dark matter with rotating galaxy embedded near...

2. Expected motion If a galaxy’s mass matched its distribution of luminous matter, then Newtonian gravity suggests that stars should orbit more slowly at greater distances from the core.

3. Real orbits Measurements by astronomers show that, beyond a certain distance from the core, stars all tend to orbit at a certain speed, suggesting they are experiencing unexpectedly strong gravity.

Some astronomers claim that the orbits of small satellite galaxies around the Milky Way are better explained by MOND than by dark matter