Galaxies typically have rotation curves which are approximately flat in their outer regions. They usually rise steeply in the innermost regions, often going a bit crazy at first, but then settle down to something that's basically flat and boring. Dwarf galaxies are an exception, often showing curves which are still (slowly) rising, possibly because the stars and gas don't probe the full dark matter halo. But even a few larger galaxies also show curves which are weakly rising or declining.
Recently we looked at massive galaxies which are rotating more quickly than expected, and whether these challenge alternative theories of gravity. It seems to me that they probably do, but critics are right to point out that it matters a great deal as to which value you use to define the rotation of a galaxy, i.e. the peak or the flat part of the curve.
This latest paper looks at galaxies with declining rotation curves. They choose their sample so as to avoid the usual causes of this, like interactions or having a strong bar or bulge in the centre (such that the mass of the innermost baryons becomes significant compared to the extended dark matter). They also select them to have well-resolved rotation curves, so it's not a data artifact or anything daft like that. And unlike the previous paper, they show all of their curves, rather than coyly hiding them away like in the last one.
What I cannot for the life of me understand are their quoted ratios of peak to outermost velocity. Looking at their rotation curves, I'd guestimate the ratios to be no more than a factor of two at the very most, but they give values of 10-40 ! I'm tempted to email them because I can't make sense of that, but the text has been translated from the original Russian so that might make things difficult.
When it comes to the inevitable Tully-Fisher relation (a comparison of rotation speed and luminous mass), they show that their galaxies agree with the standard relation if they use the peak velocity, but are significantly slower than the standard relation predicts if they use the flat velocity. This is exactly the opposite of what Milgrom said when criticising the fast rotators : these authors have done exactly as he suggested, and find the opposite sort of problem ! So the claim of MOND enthusiasts that the Tully-Fisher relation actually has some miniscule scatter if you get the measurements right looks extremely suspicious to me : galaxies actually seem to deviate in all directions, even very massive ones. And furthermore, since the peak velocities here do agree with the standard relation, that makes it rather unlikely that there's been some systematic error in the velocity estimate.
The nice thing about rotation curves, though, is that you're not limited by global relations like Tully-Fisher. You can directly compare a galaxy's observed and predicted rotation throughout its whole disc. For this sample, they find most galaxies agree with MOND's predictions, but not all*. A few require the galaxies to have significantly different stellar mass from the measured value, and/or a different acceleration constant - in the worst case by a factor of six. And it would be a pretty stupid theory indeed if you had to change a fundamental constant for each galaxy.
* And they're interesting curves in their own right : some look flat to me, while others are very clearly and consistently declining, and still others show sudden decreases and then remain flat further out.
There is some scope for a MOND rebuttal here. The galaxies are not all truly isolated (one is even in a cluster). The authors say they have no nearby massive companions capable of creating a significant external field effect, but it could be that they've interacted in the recent past and are still out of equilibrium (I don't know if anyone's modelled how this would affect rotation curves, but I'd be a bit surprised if this caused them to rotate more slowly though). There's enough scope of the complexity in the modelling of disc mass and the structure of the curves and so on that the findings could be challenged. Their most deviant galaxy is interesting in its own right : visually it looks disturbed, but also lonely. MOND or not, something interesting is definitely going on here.
Galaxies with Declining Rotation Curves
A sample of 22 spiral galaxies compiled from published data is studied. The galaxy rotation curves pass through a maximum distance of more than $\sim 1$ kpc from the center with a subsequent decrease in the rotation velocity.
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