Ain’t no cusps here

Ain’t no cusps here

It has been twenty years since we coined the phrase NFW halo to describe the cuspy halos that emerge from dark matter simulations of structure formation. Since that time, observations have persistently contradicted this fundamental prediction of the cold dark matter cosmogony. There have, of course, been some theorists who cling to the false hope that somehow it is the data to blame and not a shortcoming of the model.

That this false hope has persisted in some corners for so long is a tribute to the power of ideas over facts and the influence that strident personalities wield over the sort objective evaluation we allegedly value in science. This history is a bit like this skit by Arsenio Hall. Hall is pestered by someone calling, demanding Thelma. Just substitute “cusps” for “Thelma” and that pretty much sums it up.

All during this time, I have never questioned the results of the simulations. While it is a logical possibility that they screwed something up, I don’t think that is likely. Moreover, it is inappropriate to pour derision on one’s scientific colleagues just because you disagree. Such disagreements are part and parcel of the scientific method. We don’t need to be jerks about it.

But some people are jerks about it. There are some – and merely some, certainly not all – theorists who make a habit of pouring scorn on the data for not showing what they want it to show. And that’s what it really boils down to. They’re so sure that their models are right that any disagreement with data must be the fault of the data.

This has been going on so long that in 1996, George Efstathiou was already making light of it in his colleagues, in the form of the Frenk Principle:

“If the Cold Dark Matter Model does not agree with observations, there must be physical processes, no matter how bizarre or unlikely, that can explain the discrepancy.”

There are even different flavors of the Strong Frenk Principle:

1: “The physical processes must be the most bizarre and unlikely.”
2: “If we are incapable of finding any physical processes to explain the discrepancy between CDM models and observations, then observations are wrong.”

In the late ’90s, blame was frequently placed on beam smearing. The resolution of 21 cm data cubes at that time was typically 13 to 30 arcseconds, which made it challenging to resolve the shape of some rotation curves. Some but not all. Nevertheless, beam smearing became the default excuse to pretend the observations were wrong.

This persisted for a number of years, until we obtained better data – long slit optical spectra with 1 or 2 arcsecond resolution. These data did show up a few cases where beam smearing had been a legitimate concern. It also confirmed the rotation curves of many other galaxies where it had not been.

So they made up a different systematic error. Beam smearing was no longer an issue, but longslit data only gave a slice along the major axis, not the whole velocity field. So it was imagined that we observers had placed the slits in the wrong place, thereby missing the signature of the cusps.

This was obviously wrong from the start. It boiled down to an assertion that Vera Rubin didn’t know how to measure rotation curves. If that were true, we wouldn’t have dark matter in the first place. The real lesson of this episode was to never underestimate the power of cognitive dissonance. People believed one thing about the data quality when it agreed with their preconceptions (rotation curves prove dark matter!) and another when it didn’t (rotation curves don’t constrain cusps!)


So, back to the telescope. Now we obtained 2D velocity fields at optical resolution (a few arcseconds). When you do this, there is no where for a cusp to hide. Such a dense concentration makes a pronounced mark on the velocity field.

Velocity fields of the inner parts of zero stellar mass disks embedded in an NFW halo (left panel) and a pseudo-isothermal (ISO) halo (right panel). The velocity field is seen under an inclination angle of 60°, and a PA of 90°. The boxes measure 5 × 5 kpc2. The vertical minor-axis contour is 0 km s−1, increasing in steps of 10 km s−1 outwards. The NFW halo parameters are c= 8.6 and V200= 100 km s−1, the ISO parameters are RC= 1 kpc and V= 100 km s−1. From de Blok et al. 2003, MNRAS, 340, 657 (Fig. 3).

To give a real world example (O’Neil et. al 2000; yes, we could already do this in the previous millennium), here is a galaxy with a cusp and one without:

The velocity field of UGC 12687, which shows the signature of a cusp (left), and UGC 12695, which does not (right). Both galaxies are observed in the same 21 cm cube with the same sensitivity, same resolution, etc.

It is easy to see the signature of a cusp in a 2D velocity field. You can’t miss it. It stands out like a sore thumb.

The absence of cusps is typical of dwarf and low surface brightness galaxies. In the vast majority of these, we see approximately solid body rotation, as in UGC 12695. This is incredibly reproducible. See, for example, the case of UGC 4325 (Fig. 3 of Bosma 2004), where six independent observations employing three distinct observational techniques all obtain the same result.

There are cases where we do see a cusp. These are inevitably associated with a dense concentration of stars, like a bulge component. There is no need to invoke dark matter cusps when the luminous matter makes the same prediction. Worse, it becomes ambiguous: you can certainly fit a cuspy halo by reducing the fractional contribution of the stars. But this only succeeds by having the dark matter mimic the light distribution. Maybe such galaxies do have cuspy halos, but the data do not require it.

All this was settled a decade ago. Most of the field has moved on, with many theorists trying to simulate the effects of baryonic feedback. An emerging consensus is that such feedback can transform cusps into cores on scales that matter to real galaxies. The problem then moves to finding observational tests of feedback: does it work in the real universe as it must do in the simulations in order to get the “right” result?

Not everyone has kept up with the times. A recent preprint tries to spin the story that non-circular motions make it hard to obtain the true circular velocity curve, and therefore we can still get away with cusps. Like all good misinformation, there is a grain of truth to this. It can indeed be challenging to get the precisely correct 1D rotation curve V(R) in a way that properly accounts for non-circular motions. Challenging but not impossible. Some of the most intense arguments I’ve had have been over how to do this right. But these were arguments among perfectionists about details. We agreed on the basic result.

There ain’t no cusp here!

High quality data paint a clear and compelling picture. The data show an incredible amount of order in the form of Renzo’s rule, the Baryonic Tully-Fisher relation, and the Radial Acceleration Relation. Such order cannot emerge from a series of systematic errors. Models that fail to reproduce these observed relations can be immediately dismissed as incorrect.

The high degree of order in the data has been known for decades, and yet many modeling papers simply ignore these inconvenient facts. Perhaps the authors of such papers are simply unaware of them. Worse, some seem to be fooling themselves through the liberal application of the Frenk’s Principle. This places a notional belief system (dark matter halos must have cusps) above observational reality. This attitude has more in common with religious faith than with the scientific method.

Declining Rotation Curves at High Redshift?

Declining Rotation Curves at High Redshift?

A recent paper in Nature by Genzel et al. reports declining rotation curves for high redshift galaxies. I have been getting a lot of questions about this result, which would be very important if true. So I thought I’d share a few thoughts here.

Nature is a highly reputable journal – in most fields of science. In Astronomy, it has a well earned reputation as the place to publish sexy but incorrect results. They have been remarkably consistent about this, going back to my earliest grad school memories, like a quasar pair being interpreted as a wide gravitational lens indicating the existence of cosmic strings. This was sexy at that time, because cosmic strings were thought to be a likely by-product of cosmic Inflation, threading the universe with remnants of the Inflationary phase. Cool, huh? Many Big Names signed on to this Exciting Discovery, which was Widely Discussed at the time. The only problem was that it was complete nonsense.

Genzel et al. look likely to build on this reputation. In Astronomy, we are always chasing the undiscovered, which often means the most distant. This is a wonderful thing: the universe is practically infinite; there is always something new to discover. An occasional downside is the temptation to over-interpret and oversell data on the edge.

Lets start with some historical perspective. Here is the position-velocity diagram of NGC 7331 as measured by Rubin et al. (1965):


The rotation curve goes up, then it goes down. One would not claim the discovery of flat rotation curves from these data.

Here is the modern rotation curve of the same galaxy:


As the data improved, the flattening became clear. In order to see this, you need to observe to large radius. The original data didn’t do that. It isn’t necessarily wrong; it just doesn’t go far enough out.

Now lets look at the position-velocity diagrams published by Genzel et al.:


They go up, they go down. This is the normal morphology of the rotation curves of bright, high surface brightness galaxies. First they rise steeply, then they roll over, then they decline slowly and gradually flatten out.

It looks to me like the Genzel el al. data do the first two things. They go up. They roll over. Maybe they start to come down a tiny bit. Maybe. They simply do not extend far enough to see the flattening, if it is there. Their claim that the rotation curves are falling is not persuasive: this is asking more of the data than is warranted. Historically, there are many examples of claims of “declining” rotation curves. DDO 154 is one famous example. These claims were not very persuasive at the time, and did not survive closer examination.

I have developed the habit of looking at the data before I read the text of a paper. I did that in this case, and saw what I expected to see from years of experience working on low redshift galaxies. I wasn’t surprised until I read the text as saw the claim that these galaxies somehow differed from those at low redshift.

It takes some practice to look at the data without being influenced by lines drawn to misguide the eye. That’s what the model lines drawn in red do. I don’t have access to the data, so I can’t re-plot them without those lines. So instead I have added, by eye, a crude estimate of what I would expect for galaxies like this. In most cases, the data do not distinguish between falling and flat rotation curves. In the case labeled 33h, the data look slightly more consistent with a flat rotation curve. In 10h, they look slightly more consistent with a falling rotation curve. That appearance is mostly driven by the outermost point with large error bars on the approaching side. Taken literally, this velocity is unphysical: it declines faster than Keplerian. They interpret this in terms of thick disks, but it could be a clue that Something is Wrong.

The basic problem is that the high redshift data do not extend to large radii. They simply do not go far enough out to distinguish between flat and declining rotation curves. Most do not extend beyond 10 kpc. If we plot the data for NGC 7331 with R < 10 kpc, we get this:


Here I’ve plotted both sides in order to replicate the appearance of Genzel’s plots. I’ve also included an exponential disk model in red. Never mind that this is a lousy representation of the true mass model. It gives a good fit, no?

The rotation curve is clearly declining. Unless you observe further out:


The data of Genzel et al. do not allow us to distinguish between “normal” flat rotation curves and genuinely declining ones.

This is just taking the data as presented. I have refrained from making methodological criticisms, and will continue to do so. I will only note that it is possible to make a considerably more sophisticated, 3D analysis. Di Teodoro et al. (2016) have done this for very similar data. They find much lower velocity dispersions (not the thick disks claimed by Genzel et al.) and flat rotation curves:


There is no guarantee that the same results will follow for the Genzel et al. data, but it would be nice to see the same 3D analysis techniques applied.

Since I am unpersuaded that the Genzel et al. data extend far enough out to test for flat rotation, I looked for a comparison that I could make so far as the data do go. Fig. 3 of Genzel et al. shows the dark matter fraction as a function of circular velocity. This contains the same information as Fig. 12 of McGaugh (2016), which I re-plot here in terms of the dark matter fraction:

The dark matter fraction for the local galaxies (gray circles) discussed in McGaugh (2016) as a function of circular velocity (left) and surface density (right). The star is the Milky Way. Blue points with red circles are the data of Genzel et al. The left panel is equivalent to their Fig. 3.

The data of Genzel et al. follow the trends established by local galaxies. They are confined to the bright, high surface brightness end of these relations, but that is to be expected: the brightest galaxies are always the most readily observed, especially at high redshift.

Genzel et al. only plot the left panel. As I have shown many times before, the strongest correlation of dynamical-to-baryonic mass is with surface brightness, not mass or its proxies luminosity and circular velocity. This is an essential aspect of the mass discrepancy problem; it is unfortunate that many scientists working on the topic appear to remain unaware of this basic fact.

From these diagrams, I infer that there is no discernible evolution in the properties of bright galaxies out to high redshift (z = 2.4 for their most distant case). The data presented by Genzel et al. sit exactly where one would expect from the relations established by local galaxies. That in itself might seem surprising, and perhaps warrants a Letter to Nature. But most of the words in Genzel et al. are about a surprising sort of evolution in which galaxy rotation curves decline at high redshift, so they have less dark matter then than now. I do not see that their data sustain such an interpretation.

So far everything I have said is empirical. If I put on a theory hat, the claims of Genzel et al. persist in making no sense.

First, ΛCDM. Fundamental to the ΛCDM cosmogony is the notion that dark matter halos form first, with baryons falling in subsequently. It has to happen in that order to satisfy the constraints on the growth of structure from the cosmic microwave background. The temperature fluctuations in the CMB are small because the baryons haven’t yet been able to clump up. In order for them to form galaxies as quickly as observed, the dark matter must already be forming the seeds of dark matter halos for the baryons to subsequently fall into. Without this order of battle, our explanation of structure formation is out the window.

Next, MOND. If rotation curves are indeed falling as claimed, this would falsify MOND, or at least make it a phenomenon that only applies in the local universe. But, as discussed, the high-z galaxies look like local ones. That doesn’t falsify MOND; it rather encourages the basic picture of structure formation we have in that context: galaxies form early and settle down into the form the modified force law stipulates. Indeed, the apparent lack of evolution implies that Milgrom’s acceleration constant a0 is indeed constant, and does not vary (as sometimes speculated) in concert with the expansion rate as hinted at by the numerical coincidence a0 ~ cH0. I cannot place a meaningful limit on the evolution of a0 from the data as presented, but it appears to be small. Rather than falsifying MOND, the high-z data look to be consistent with it – so far as they go.

So, in summary: the data at high redshift appear completely consistent with those at low redshift. The claim of falling rotation curves would be problematic to both ΛCDM and MOND. However, this claim is not persuasive – the data simply do not extend far enough out.

Early 21st century technology has enabled us to do at high redshift what could barely be done at low redshift in the mid-20th century. That’s impressive. But these high-z data look a lot like low-z data circa 1970. A lot has changed since then. Right now, for the exploration of the high redshift universe, I will borrow one of Vera Rubin’s favorite phrases: These are Early Days.