Supposed New Law of Nature Now Looks Like Statistical Error (Patreon)

[This is a transcript with links to references.]

This is a rare case in which I talk about some of my own work. It’s about the biggest current controversy in astrophysics, does dark matter exist or do we instead need to change the law of gravity.

If you’ve followed me for some while, then you’ll know that my opinion on this has switched back and forth a few times. In this most recent iteration, it’s flipped back to it’s probably dark matter. Then again… it’s complicated. Let’s have a look.

 It’s one of those problems that’s easy to understand but very difficult to solve. Let us look as an example at a galaxy like the Milky Way that is a spiral galaxy.  We can use Einstein’s theory of General Relativity to calculate how fast the stars in these spiral arms should move. The velocity of these stars is a function of the distance from the centre of the galaxy. The closer they are to the centre, they faster they need to move to stay on a stable orbit.

If you plot the dependence of the velocity of the stars as a function of the distance from the centre,  as you calculate it with Einstein’s theory, then that function drops. It’s called a “rotation curve”.  The problem is  that for most galaxies we observe, these rotation curves do not drop. For stars far away from the galactic centre they remain roughly constant. This is what is called a flat rotation curve. It’s also the case for the Milky Way.

 So we have an observation that doesn’t agree with the prediction which is bad. The dark matter solution is now to say, well there’s just more stuff in the milky way, and that increases the mass that is pulling on the star.  Galaxies all have a big halo of dark matter, it’s just that we can’t see this stuff and it goes right through us. And if there is more mass pulling on the star, then it will move faster.

The alternative idea has become known as modified Newtonian Dynamics, MOND for short. It’s to say the mass remains what it is, instead, if you get to the far-out stars, then the gravitational force is just stronger.  This is the basic idea put forward by Mordehai Milgrom already in 1985.

Now of course you can’t just change the gravitational force as you please because we’ve tested this gazillions of times on our own planet and in the solar system. Every time Elon Musk launches a satellite, he’s testing the law of gravity and you don’t mess with Elon.

So Milgrom said,  the law of gravity changes only when accelerations are very small. And remember that the acceleration depends on the force.  Near this planet or our in the solar system in general the gravitational force is fairly strong, but the gravitational force coming from the overall mass of the galaxy becomes quite weak the farther away you are from the centre. And then this new law kicks in. The typical acceleration scale at which it takes over is usually called a nought.

 Amazingly enough it turned out that this simple   idea indeed works for a lot of galaxies and with the almost same acceleration scale as a cross-over. It looks and feels like a new fundamental law. .Better still, MOND gives rise to some correlations between observables like that between the mass of the galaxy and the asymptotic velocity. And that fits with observations. For some types of galaxies this was a prediction that was later found to be correct.

 Yes, MOND has problems with some other observations, like big galaxy clusters. But then again dark matter also has problems with some kinds of observations like galactic cores. So it’s not that easy to decide which one is better.

There have been some papers claiming that this universal acceleration scale actually doesn’t work because there are some galaxies for which hit doesn’t fit. But as other researchers have pointed out that’s not a good argument because an exception doesn’t make the rule go away. It’s like saying John got measles even though he was vaccinated, therefore vaccines don’t work! But then how do you explain the drop of measles cases following vaccination campaigns.

It's similar with MOND. We know that it works for a lot of galaxies  and no matter how much you torture the data that isn’t going away. The question is how do you explain this?  The issue that most of these studies is that they don’t actually compare MOND and dark matter.  They say MOND is bad  or dark matter is bad.  But okay, so they’re both bad, that doesn’t help us. We want to know which is the least bad.

And this brings me to our new paper, and I should say that actually I did pretty much nothing.  The work was all done by Mariia and Anton, I just said that this would be an interesting question to look at. This paper is on the pre-print server; it has not yet been peer-reviewed. We looked at a sample of about 150 galaxies and asked, what works better to explain the observed rotation curves, dark matter or MOND. The relevant thing to know is that MOND has fewer numbers to adjust for each galaxy than dark matter. For dark matter you have to say how much of the stuff there is and how it’s distributed, whereas for MOND you have just this one acceleration scale.

So the question is whether the additional parameters in the dark matter model are justified by the improvements in data fitting.

The brief answer is yes as you see in this figure. More galaxies are fit well by dark matter  than by MOND  even accounting for the difference in parameters.  The reason is that there are some galaxies which just won’t fit with the idea that the universal parameter is actually universal.

 Even more worrying, the galaxies for which MOND works better are those for which there are few data points or the data points have large uncertainties. In this figure the vertical axis is a measure for the uncertainty of the data and you see that the higher the uncertainty the more magenta points,  that are the galaxy better fit with MOND.

This makes it seem like MOND is preferred for cases in which there is little data to fit just because MOND has fewer parameters. It looks like MOND is just an artifact of statistical analysis.

Now I have to be honest when I first saw this result, I thought it must be wrong. Because we know from other studies that MOND actually works well to explain even small details in rotation curves because there are features in the visible matter distribution that fit with features of the rotation curve. This is known as Renzo’s ruleand you see an example in this figure, see how the visible matter traces the rotation curve. So these two things don’t fit together in my head. Then again, this result is what it is and we can’t just sweep it under the rug.

It is also compatible with the other study that I talked about recently on wide binary systems that found MOND works better if one includes low quality data.

So this is why at the moment I’ve kinda flipped back from MOND to dark matter, but who knows maybe I’ll change my mind with the next paper, stay tuned.