Last time, I addressed some of the problems posed by the radial acceleration relation for galaxy formation theory in the LCDM cosmogony. Predictably, some have been quick to assert there is no problem at all. The first such claim is by Keller &

So the radial acceleration relation is a new law of nature. What does it mean? One reason we have posed it as a law of nature is that it is interpretation-free. It is a description of how nature works – in this case, a rule for how galaxies rotate. Why nature behaves thus is another matter.

Flat rotation curves were the first clear evidence that the dynamics of galaxies do not follow the same rules as planetary systems. But they do follow rules. These include asymptotic flatness, Tully-Fisher, the luminosity-size-rotation curve shape relation (aka the `universal‘ rotation curve), Renzo’s rule, and the central density relation.

Previously I noted how we teach about Natural Law, but we no longer speak in those terms. All the Great Laws are already know, right? Surely there can’t be such things left to discover! That rotation curves tend towards asymptotic flatness is, for all practical purposes, a law of nature. It is tempting to leap straight to the interpretation (dark matter!), but it is worth appreciating the discovery for itself.

People often ask for a straight up comparison between ΛCDM and MOND. This is rarely possible because the two theories are largely incommensurable. When one is eloquent the other is mute, and vice-versa. It is possible to attempt a comparison about how bad the missing baryon problem is in each.

A long standing problem in cosmology is that we do not have a full accounting of all the baryons that we believe to exist. Big Bang Nucleosynthesis (BBN) teaches us that the mass density in normal matter is Ω _b ≈ 5%. One can put a more precise number on it, but that’s close enough for our purposes here. Ordinary matter fails to account for the closure density by over an order of magnitude.

or why Vera Rubin and Albert Bosma deserve a Nobel Prize Natural Law: a concise statement describing some aspect of Nature. In the sciences, we teach about Natural Law all the time. We take them for granted. But we rarely stop and think what we mean by the term. Usually Natural Laws are items of textbook knowledge.

I promised more results from SPARC. Here is one. The dynamical mass surface density of a disk galaxy scales with its central surface brightness. This may sound trivial: surface density correlates with surface brightness. The denser the stars, the denser the mass. Makes sense, yes? Turns out, this situation is neither simple nor obvious when dark matter is involved.

We have a new paper that introduces SPARC: Spitzer Photometry & Accurate Rotation Curves. SPARC is a database of 175 galaxies with measured HI rotation curves and homogeneous near-infrared [3.6 micron] surface photometry obtained with the Spitzer Space Telescope. It provides the largest cohesive dataset currently available of disk galaxy mass models. SPARC represents all known types of rotating galaxies.

OK, I’m not even going to try to answer that one. But I am going to do some comparison exploration. A complaint often leveled against MOND is that it is not a theory. Or not a complete theory. Or somehow not a proper one. Sometimes people confuse MOND with the empirical observations that display MONDian phenomenology. I would say that MOND is a hypothesis, as is dark matter.