Dark Matter vs MOND: A Tug of War


Today’s astrobite was written by guest author Ali Lezeik. Ali is doing his master studies in theoretical physics at the University of Cologne. He is interested in the physics of the early universe, from inflationary theory to quantum gravity. Gravity is so elusive, and has been puzzling physicists for centuries, Ali claims he is one of the lucky victims who had gravity raising his curiosity.


TitleAbsence of a fundamental acceleration scale in galaxies

Authors: Davi C. Rodrigues, Valerio Marra, Antonino del Popolo, and Zahra Davari

First Author’s institution: Federal University of Espírito Santo

Status: Published in Nature; closed access


A very brief history of Gravity

When Vera Rubin made her discovery on galaxy rotations back in the 70’s, she knew she was onto something that would be the center of scientific discussion for the decades to come, and still is to our modern times.

If we look across the universe, we will notice how everything rotates, the Earth and planets rotates around the Sun, our Sun along with the whole Solar system sit near the Orion arm of our Milky Way galaxy, a spiral galaxy, which itself is rotating. All of these motions obeyNewton’s law of gravitation, that is the orbital speed of objects decrease as their distance from the center of mass they orbit increases. This is known as the inverse square law of gravitation. Newton’s Law are tremendously successful, as they described the motion of objects under gravity very well, from falling apples to the motion of the Earth around the Sun, however not precisely accurate, in other words, the laws had their limitation. Newton’s law failed to explain some phenomena, which required a search for a bigger, more accurate picture of gravity, and that’s exactly the reason why Rubin’s discovery had a hugeimpact.


What is Dark matter anyway and why do we need it?

Rubin noticed that there is a discrepancy between observed galaxy rotation curves– A plot of the orbital speeds of visible stars or gas in a galaxy versus their radial distance from that galaxy’s center, and theoretical predictions, i.e. Newton’s law. In other words, stars revolve around their galaxy’s center at a constant speed or increases as you move away from that center, that is as the distance between the star and the center of the galaxy increases. In contrast, the orbital speeds of planets in planetary systems and moons orbiting planets decline with distance. And with such high speeds, stars on the edges of these spiral galaxies should fly away, getting unbounded from their orbits. Imagine yourself holding onto a very fast rotating wheel; if you are not applying a good grip onto that wheel, you will end up losing it and flying away. In physics terms, the centrifugal force generated from the rotation will push you away. However, we do not see stars flying away from the edges of these galaxies, hinting that there is some hidden force holding them to it. Remember how gravity works – the more mass you have, the stronger the pulling force is. But the only mass seen in the galaxies is the mass of their content, from gas and dust to planets and stars. Or is it? This exact question has led to the birth of the Dark Matter hypothesis, which suggests that there exists mysterious invisible matter that is holding galaxies from falling apart.

Fig.1 Rotation curve of spiral galaxy Messier 33 (yellow and blue points with error bars), and a predicted one from distribution of the visible matter (gray line). The discrepancy between the two curves can be accounted for by adding a dark matter halo surrounding the galaxy. Source: Wikipedia

But let’s not jump into conclusions here. Although dark matter is the leading candidate to explain these galaxy rotation curves, others are trying to see the problem from a different perspective. After all, we have reached our conclusions assuming our current knowledge is already true, Dark Matter would never have been hypothesized if it weren’t for the inaccuracy and failure for Newton’s laws.


MOND, an alternative?

Another candidate theory doubts that Newton’s law, as we understand it, fully explains these rotation curves, claiming it needs some modification. This other candidate is known as MOND, MOdified Newtonian Dynamics.

MOND is an alternative explanation to the Dark Matter hypothesis that seeks to solve the galaxy rotation curve problem. MOND calls for a revision of Newton’s law, and as extraordinary as this suggestion sounds, it does offer potential solutions to some otherwise troubling problems in galactic dynamics. It proposes that there is a fundamental acceleration scale a0 that should be added to the classically known

Newton’s law. And with this new scale, at very large radii and small accelerations, gravity decays with distance more slowly than Newton’s inverse square law. This removes the need for dark matter, providing a clear explanation for the tight non- Newtonian correlation between visible matter and radial acceleration. Job done it seems, after all, why bother trying to find matter that is seemingly undetectable when you can fix your old theories. Well, not quite.

Fig.2 Probability distributions of a0 for the 193 galaxies studied (black dots). The global best-fit value of a0 is shown by a dashed line. It is evident that many galaxies are not quite compatible with the global best fit. The 1σ, 3σ, and 5σ, red orange and yellow regions respectively present the chances of a correlation between the theory and the given data. 5σ means there’s a big correlation, supporting the theory, 1σ tells you that the theory does not correspond well to experimental results we can see, most of the correlations we have are of 1σ, making MOND fail in front of the observational results.

In a new study published by Davi Rodrigues et. al of Federal University of Espírito Santo in Brazil, Rodrigues and his team have examined the rotation curves of 193 disk galaxies, to see if there truly does exist such a universal fundamental acceleration scale a0. This is done by first assuming that there exists a universal fundamental acceleration scale a0, and then examining a rotation curve of a galaxy. Having done this, the observed rotation curve is compared to the theoretical rotation curve that would be plotted by following classical Newtonian dynamics, then the difference between the two plots would yield, roughly speaking, a0. Doing this for the 193 galaxies, the standard deviation of a0 – the amount of variation or dispersion of a0 from its average value is too large. In other words, what was realized is that for each galaxy Rodrigues and his team studied, a unique scale factor was being found, a0 seems to be coming from the internal dynamics of each galaxy, meaning that this scale factor is emergent from within each galaxy and hence NOT a universal scale factor. It can be viewed as if a0 is just compensating for DM in the Dark Matter hypothesis. This study rules out MOND, leading to the victory of the Dark Matter hypothesis


Fate of MOND

Other groups doubt Rodrigues’ argument, calling it inaccurate, for it does not take into account the plane of inclination of disk galaxies relative to the angle of observation – which is an additional source of error in the authors’calculations.

Whether Rodrigues’ analysis missed something or not, the tug of war between the Dark Matter hypothesis and MOND is looking to be won by Dark Matter. But nevertheless, and as controversial MOND sounds, more galaxies have to bestudied with more precision to make sure that there is truly no correlation between the different a0 values, until then MOND cannot be ruled out entirely. Afterall, scientists should never be held back by their traditional scientific prejudice, and should seek the truth with full skepticism.

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  1. However, there is much more phenomena where dark matter is involved, not only galaxy rotation curves. The galaxies in galaxy cluster are too fast to be gravitationally bound by visible matter (discovered by Fritz Zwicky ca 50 years before Vera Rubini’s research). The matter distribution after galaxy clusters collisions does not agree with visible matter distribution. And many other observations. MOND is not capable to explain any of these observations. So I think MOND is dead regardless of inaccuratness of the Rodrigues’ analysis.

  2. Dark matter is a supersolid that fills ’empty’ space, strongly interacts with ordinary matter and is displaced by ordinary matter. What is referred to geometrically as curved spacetime physically exists in nature as the state of displacement of the supersolid dark matter. The state of displacement of the supersolid dark matter is gravity.

    The supersolid dark matter displaced by a galaxy pushes back, causing the stars in the outer arms of the galaxy to orbit the galactic center at the rate in which they do.

    Displaced supersolid dark matter is curved spacetime.

    The reason for the mistaken notion the galaxy is missing dark matter is that the galaxy is so diffuse that it doesn’t displace the supersolid dark matter outward and away from it to the degree that the dark matter is able to push back and cause the stars far away from the galactic center to speed up.

    It’s not that there is no dark matter connected to and neighboring the visible matter. It’s that the galaxy has not coalesced enough to displace the supersolid dark matter to such an extent that it forms a halo around the galaxy.

    A galaxy’s halo is not a clump of dark matter traveling with the galaxy. A galaxy’s halo is displaced supersolid dark matter.

  3. There was an interesting paper on arXiv last year suggesting that this problem could be solved if it wasn’t a0 that was a universal constant, but rather that the value of G * a0 was a constant and the force of G varied inversely with a0 on a per-galaxy scale.

    I don’t know how you would test the value of G in different galaxies, but it would be an interesting test to perform.


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