## Dark matter doesn’t stack up!

The case for dark matter arose to explain a curious discrepancy between the rotational speed of stars in spiral galaxies and the speed they are predicted to rotate around the galactic centre. For the full story, check out wikipedia here.

Basically, using Newtonian physics, the rotational speed of the outer stars should drop away dramatically as the distance from the galactic centre increases. See the graph below.

Rotational speed of stars around galactic centre

As you can see, the actual observed speed (B) is much higher than the calculated speed (A). In order to explain this, a large number of people have backed the idea of hidden mass or ‘dark matter’ that might cause an acceleration of the stars in the outer reaches of the galaxy. Others, taking a more drastic approach have taken an axe to the maths that Newton devised, coming up with MOND (Modified Newtonian Dynamics) or variants of it.

I am on the side of those who aren’t convinced of dark matter. For a start, where would you place this dark matter assuming it behaved gravitationally, broadly the way the same way normal mass does, so that it would have a larger effect on the outer edges of the galaxy than nearer in? I’ve not seen any theories on what this distribution would look like. Maybe the dark matter would be distributed in a kind of doughnut shape around the outer edge. If so, an explanation would need to be found for this weird clumping. Or perhaps dark matter is distributed like the matter, concentrated around the galactic hub, but acts contrary to gravity to slow the centre down. But dark matter reducing the gravitational pull doesn’t make any sense for two reasons; 1) observations of gravitational lensing seem to prove that gravity is stronger than our predictions for the mass of galaxies not weaker and 2) any weakening of gravity at the centre would still lead to a graph with a similar shape to (A) in the diagram above, just flatter.

So I wondered whether there was a less drastic approaches than tearing up the Newtonian rule book. I don’t have the maths to create of model for what I have in mind but I can explain it and hope that someone brighter than me can crunch the numbers. What I have in mind is that we already have a better toolset for predicting the behaviour of bodies orbiting gravity wells and that is space-time. Einstein’s brilliant theory of General Relativity includes two side-effects; one, ‘rotational frame dragging’ and the other, much less well researched ‘linear frame dragging’.

Until recently, rotational frame dragging was an unproven theory. But then a NASA funded experiment Gravity Probe B proved its existence. Rotational frame dragging is the effect on free-floating body of a nearby spinning mass. The rotating mass imparts a rotational force on the nearby body. Although this effect would be felt by stars around a massive galactic core, it’s not the side-effect I’m interested in. My theory is that linear frame dragging, assuming it also exists, is at least partially responsible for dragging the outer stars around the galactic centre.

Linear Frame Dragging in a Galaxy

If you’ve ever stood near the edge of a platform as a train went by at high speed, you may have felt the wind of the passing train pull at you as it whistles past. In the vacuum of space, the curvature of space-time is substituted for air and the possibility arises that the enormous mass of millions of stars on one side of a galaxy moving in an approximation of a straight line for a fraction of a second would tend to impart some of their energy to their neighbours. The two-way nature of the effect and of the energy exchange is important. So stars on the inside would tend to lose their energy to the outer stars, thus making the outer stars rotate faster and slowing the inner stars down.

Clearly, without the formulae, this theory isn’t going anywhere. Furthermore, with my slender grasp of mathemetics and insanely busy day job, it’s unlikely that I’ll be able to enhance this blog with the proof any time soon. Hopefully though, someone learned will spot this post and spend some time on it for me.

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### 2 Responses to Dark matter doesn’t stack up!

1. Harple says:

Sadly, that someone learned is not me…… you lost me on about line 4. You’re far too bright my love. It continues to amaze and inspire me. Mx

• dimorphism says:

I don’t suppose Brian Cox is a pal of yours is he? Maybe you’ve done work for him? If so, please point him at this page. ğŸ˜‰

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