I’ve been wanting to expand on the previous post ever since I wrote it, which is over a month ago now. It has been a busy end to the semester. Plus, there’s a lot to say – nothing that hasn’t been said before, somewhere, somehow, yet still a lot to cobble together into a coherent story – if that’s even possible. This will be a long post, and there will be more after to narrate the story of our big paper in the ApJ.

I was raised to believe that it was rude to tell people I told you so . Yet that’s pretty much the essence of the scientific method: we test hypotheses by making predictions, then checking to see which told us the correct result in advance of the experiment. So: I told you so. Our paper on massive galaxies at high redshift is out in the Astrophysical Journal today.

Some people have asked me to comment on the Scientific American article What if We Never Find Dark Matter? by Slatyer & Tait. For the most part, I find it unobjectionable – from a certain point of view.

When I wrote about Nobel prizes a little while back, I did not expect to return to the subject.

Who we give prizes to is more a matter of sociology than science. Good science is a prerequisite, but after that it is a matter of which results we value in the here and now. Results that are guaranteed to get a Nobel prize, like the detection of dark matter, attract many suitors who pursue them vigorously. Results that come as a surprise can be more important than the expected results, but it takes a lot longer to recognize and appreciate them.

The time is approaching when Nobel prizes are awarded. This inevitably leads to a lot of speculation and chattering rumor. Last year one publication, I think it was Physics Today , went so far as to publish a list of things various people thought should be recognized. This aspirational list was led, of course, by dark matter.

I have said I wasn’t going to attempt to teach an entire graduate course on galaxy dynamics in this forum, and I’m not. But I can give some pointers for those who want to try it for themselves. It also provides some useful context for fans of Deur’s approach. The go-to textbook for this topic is Galactic Dynamics by Binney & Tremaine.

Given recent developments in the long-running hunt for dark matter and the difficulty interpreting what this means, it seems like a good juncture to re-up* this: The history of science is a decision tree. Vertices appear where we must take one or another branching. Sometimes, we take the wrong road for the right reasons. A good example is the geocentric vs. heliocentric cosmology.

I want to take another step back in perspective from the last post to say a few words about what the radial acceleration relation (RAR) means and what it doesn’t mean. Here it is again: This information was not available when the dark matter paradigm was developed. We observed excess motion, like flat rotation curves, and inferred the existence of extra mass. That was perfectly reasonable given the information available at the time.

In the previous post, we discussed how lensing data extend the Radial Acceleration Relation (RAR) seen in galaxy kinematics to very low accelerations. Let’s zoom out now, and look at things at higher accelerations and from a historical perspective.

Flat rotation curves and the Baryonic Tully-Fisher relation (BTFR) both follow from the Radial Acceleration Relation (RAR). In Mistele et al. (2024b) we emphasize the exciting aspects of the former; these follow from the RAR in the Mistele et al. (2024a). It is worth understanding the connection. First, the basic result: The RAR of weak lensing extends the RAR from kinematics to much lower accelerations.