The next cosmic frontier: 21cm absorption at high redshift

The next cosmic frontier: 21cm absorption at high redshift

There are two basic approaches to cosmology: start at redshift zero and work outwards in space, or start at the beginning of time and work forward. The latter approach is generally favored by theorists, as much of the physics of the early universe follows a “clean” thermal progression, cooling adiabatically as it expands. The former approach is more typical of observers who start with what we know locally and work outwards in the great tradition of Hubble, Sandage, Tully, and the entire community of extragalactic observers that established the paradigm of the expanding universe and measured its scale. This work had established our current concordance cosmology, ΛCDM, by the mid-90s.*

Both approaches have taught us an enormous amount. Working forward in time, we understand the nucleosynthesis of the light elements in the first few minutes, followed after a few hundred thousand years by the epoch of recombination when the universe transitioned from an ionized plasma to a neutral gas, bequeathing us the cosmic microwave background (CMB) at the phenomenally high redshift of z=1090. Working outwards in redshift, large surveys like Sloan have provided a detailed map of the “local” cosmos, and narrower but much deeper surveys provide a good picture out to z = 1 (when the universe was half its current size, and roughly half its current age) and beyond, with the most distant objects now known above redshift 7, and maybe even at z > 11. JWST will provide a good view of the earliest (z ~ 10?) galaxies when it launches.

This is wonderful progress, but there is a gap from 10 < z < 1000. Not only is it hard to observe objects so distant that z > 10, but at some point they shouldn’t exist. It takes time to form stars and galaxies and the supermassive black holes that fuel quasars, especially when starting from the smooth initial condition seen in the CMB. So how do we probe redshifts z > 10?

It turns out that the universe provides a way. As photons from the CMB traverse the neutral intergalactic medium, they are subject to being absorbed by hydrogen atoms – particularly by the 21cm spin-flip transition. Long anticipated, this signal has recently been detected by the EDGES experiment. I find it amazing that the atomic physics of the early universe allows for this window of observation, and that clever scientists have figured out a way to detect this subtle signal.

So what is going on? First, a mental picture. In the image below, an observer at the left looks out to progressively higher redshift towards the right. The history of the universe unfolds from right to left.

cosmicdarkagesillustration
An observer’s view of the history of the universe. Nearby, at low redshift, we see mostly empty space sprinkled with galaxies. At some high redshift (z ~ 20?), the first stars formed, flooding the previously dark universe with UV photons that reionize the gas of the intergalactic medium. The backdrop of the CMB provides the ultimate limit to electromagnetic observations as it marks the boundary (at z = 1090) between a mostly transparent and completely opaque universe.

Pritchard & Loeb give a thorough and lucid account of the expected sequence of events. As the early universe expands, it cools. Initially, the thermal photon bath that we now observe as the CMB has enough energy to keep atoms ionized. The mean free path that a photon can travel before interacting with a charged particle in this early plasma is very short: the early universe is opaque like the interior of a thick cloud. At z = 1090, the temperature drops to the point that photons can no longer break protons and electrons apart. This epoch of recombination marks the transition from an opaque plasma to a transparent universe of neutral hydrogen and helium gas. The path length of photons becomes very long; those that we see as the CMB have traversed the length of the cosmos mostly unperturbed.

Immediately after recombination follows the dark ages. Sources of light have yet to appear. There is just neutral gas expanding into the future. This gas is mostly but not completely transparent. As CMB photons propagate through it, they are subject to absorption by the spin-flip transition of hydrogen, a subtle but, in principle, detectable effect: one should see redshifted absorption across the dark ages.

After some time – perhaps a few hundred million years? – the gas has had enough time to clump up enough to start to form the first structures. This first population of stars ends the dark ages and ushers in cosmic dawn. The photons they release into the vast intergalactic medium (IGM) of neutral gas interacts with it and heats it up, ultimately reionizing the entire universe. After this time the IGM is again a plasma, but one so thin (thanks to the expansion of the universe) that it remains transparent. Galaxies assemble and begin the long evolution characterized by the billions of years lived by the stars the contain.

This progression leads to the expectation of 21cm absorption twice: once during the dark ages, and again at cosmic dawn. There are three temperatures we need to keep track of to see how this happens: the radiation temperature Tγ, the kinetic temperature of the gas, Tk, and the spin temperature, TS. The radiation temperature is that of the CMB, and scales as (1+z). The gas temperature is what you normally think of as a temperature, and scales approximately as (1+z)2. The spin temperature describes the occupation of the quantum levels involved in the 21cm hyperfine transition. If that makes no sense to you, don’t worry: all that matters is that absorption can occur when the spin temperature is less than the radiation temperature. In general, it is bounded by Tk < TS < Tγ.

The radiation temperature and gas temperature both cool as the universe expands. Initially, the gas remains coupled to the radiation, and these temperatures remain identical until decoupling around z ~ 200. After this, the gas cools faster than the radiation. The radiation temperature is extraordinarily well measured by CMB observations, and is simply Tγ = (2.725 K)(1+z). The gas temperature is more complicated, requiring the numerical solution of the Saha equation for a hydrogen-helium gas. Clever people have written codes to do this, like the widely-used RECFAST. In this way, one can build a table of how both temperatures depend on redshift in any cosmology one cares to specify.

This may sound complicated if it is the first time you’ve encountered it, but the physics is wonderfully simple. It’s just the thermal physics of the expanding universe, and the atomic physics of a simple gas composed of hydrogen and helium in known amounts. Different cosmologies specify different expansion histories, but these have only a modest (and calculable) effect on the gas temperature.

Wonderfully, the atomic physics of the 21cm transition is such that it couples to both the radiation and gas temperatures in a way that matters in the early universe. It didn’t have to be that way – most transitions don’t. Perhaps this is fodder for people who worry that the physics of our universe is fine-tuned.

There are two ways in which the spin temperature couples to that of the gas. During the dark ages, the coupling is governed simply by atomic collisions. By cosmic dawn collisions have become rare, but the appearance of the first stars provides UV radiation that drives the WouthuysenField effect. Consequently, we expect to see two absorption troughs: one around z ~ 20 at cosmic dawn, and another at still higher redshift (z ~ 100) during the dark ages.

Observation of this signal has the potential to revolutionize cosmology like detailed observations of the CMB did. The CMB is a snapshot of the universe during the narrow window of recombination at z = 1090. In principle, one can make the same sort of observation with the 21cm line, but at each and every redshift where absorption occurs: z = 16, 17, 18, 19 during cosmic dawn and again at z = 50, 100, 150 during the dark ages, with whatever frequency resolution you can muster. It will be like having the CMB over and over and over again, each redshift providing a snapshot of the universe at a different slice in time.

The information density available from the 21cm signal is in principle quite large. Before we can make use of any of this information, we have to detect it first. Therein lies the rub. This is an incredibly weak signal – we have to be able to detect that the CMB is a little dimmer than it would have been – and we have to do it in the face of much stronger foreground signals from the interstellar medium of our Galaxy and from man-made radio interference here on Earth. Fortunately, though much brighter than the signal we seek, these foregrounds have a different frequency dependence, so it should be possible to sort out, in principle.

Saying a thing can be done and doing it are two different things. This is already a long post, so I will refrain from raving about the technical challenges. Lets just say it’s Real Hard.

Many experimentalists take that as a challenge, and there are a good number of groups working hard to detect the cosmic 21cm signal. EDGES appears to have done it, reporting the detection of the signal at cosmic dawn in February. Here some weasel words are necessary, as the foreground subtraction is a huge challenge, and we always hope to see independent confirmation of a new signal like this. Those words of caution noted, I have to add that I’ve had the chance to read up on their methods, and I’m really impressed. Unlike the BICEP claim to detect primordial gravitational waves that proved to be bogus after being rushed to press release before refereering, the EDGES team have done all manner of conceivable cross-checks on their instrumentation and analysis. Nor did they rush to publish, despite the importance of the result. In short, I get exactly the opposite vibe from BICEP, whose foreground subtraction was obviously wrong as soon as I laid eyes on the science paper. If EDGES proves to be wrong, it isn’t for want of doing things right. In the meantime, I think we’re obliged to take their result seriously, and not just hope it goes away (which seems to be the first reaction to the impossible).

Here is what EDGES saw at cosmic dawn:

nature25792-f2
Fig. 2 from the EDGES detection paper. The dip, detected repeatedly in different instrumental configurations, shows a decrease in brightness temperature at radio frequencies, as expected from the 21cm absorbing some of the radiation from the CMB.

The unbelievable aspect of the EDGES observation is that it is too strong. Feeble as this signal is (a telescope brightness decrement of half a degree Kelvin), after subtracting foregrounds a thousand times stronger, it is twice as much as is possible in ΛCDM.

I made a quick evaluation of this, and saw that the observed signal could be achieved if the baryon fraction of the universe was high – basically, if cold dark matter did not exist. I have now had the time to make a more careful calculation, and publish some further predictions. The basic result from before stands: the absorption should be stronger without dark matter than with it.

The reason for this is simple. A universe full of dark matter decelerates rapidly at early times, before the acceleration of the cosmological constant kicks in. Without dark matter, the expansion more nearly coasts. Consequently, the universe is relatively larger from 10 < z < 1000, and the CMB photons have to traverse a larger path length to get here. They have to go about twice as far through the same density of hydrogen absorbers. It’s like putting on a second pair of sunglasses.

Quantitatively, the predicted absorption, both with dark matter and without, looks like:

predict21cmsignal
The predicted 21cm absorption with dark matter (red broken line) and without (blue line). Also shown (in grey) is the signal observed by EDGES.

 

The predicted absorption is consistent with the EDGES observation, within the errors, if there is no dark matter. More importantly, ΛCDM is not consistent with the data, at greater than 95% confidence. At cosmic dawn, I show the maximum possible signal. It could be weaker, depending on the spectra of the UV radiation emitted by the first stars. But it can’t be stronger. Taken at face value, the EDGES result is impossible in ΛCDM. If the observation is corroborated by independent experiments, ΛCDM as we know it will be falsified.

There have already been many papers trying to avoid this obvious conclusion. If we insist on retaining ΛCDM, the only way to modulate the strength of the signal is to alter the ratio of the radiation temperature to the gas temperature. Either we make the radiation “hotter,” or we make the gas cooler. If we allow ourselves this freedom, we can fit any arbitrary signal strength. This is ad hoc in the way that gives ad hoc a bad name.

We do not have this freedom – not really. The radiation temperature is measured in the CMB with great accuracy. Altering this would mess up the genuine success of ΛCDM in fitting the CMB. One could postulate an additional source, something that appears after recombination but before cosmic dawn to emit enough radio power throughout the cosmos to add to the radio brightness that is being absorbed. There is zero reason to expect such sources (what part of `cosmic dawn’ was ambiguous?) and no good way to make them at the right time. If they are primordial (as people love to imagine but are loathe to provide viable models for) then they’re also present at recombination: anything powerful enough to have the necessary effect will likely screw up the CMB.

Instead of magically increasing the radiation temperature, we might decrease the gas temperature. This seems no more plausible. The evolution of the gas temperature is a straightforward numerical calculation that has been checked by several independent codes. It has to be right at the time of recombination, or again, we mess up the CMB. The suggestions that I have heard seem mostly to invoke interactions between the gas and dark matter that offload some of the thermal energy of the gas into the invisible sink of the dark matter. Given how shy dark matter has been about interacting with normal matter in the laboratory, it seems pretty rich to imagine that it is eager to do so at high redshift. Even advocates of this scenario recognize its many difficulties.

For those who are interested, I cite a number of the scientific papers that attempt these explanations in my new paper. They all seem like earnest attempts to come to terms with what is apparently impossible. Many of these ideas also strike me as a form of magical thinking that stems from ΛCDM groupthink. After all, ΛCDM is so well established, any unexpected signal must be a sign of exciting new physics (on top of the new physics of dark matter and dark energy) rather than an underlying problem with ΛCDM itself.

The more natural interpretation is that the expansion history of the universe deviates from that predicted by ΛCDM. Simply taking away the dark matter gives a result consistent with the data. Though it did not occur to me to make this specific prediction a priori for an experiment that did not yet exist, all the necessary calculations had been done 15 years ago.

Using the same model, I make a genuine a priori prediction for the dark ages. For the specific NoCDM model I built in 2004, the 21cm absorption in the dark ages should again be about twice as strong as expected in ΛCDM. This seems fairly generic, but I know the model is not complete, so I wouldn’t be upset if it were not bang on.

I would be upset if ΛCDM were not bang on. The only thing that drives the signal in the dark ages is atomic scattering. We understand this really well. ΛCDM is now so well constrained by Planck that, if right, the 21cm absorption during the dark ages must follow the red line in the inset in the figure. The amount of uncertainty is not much greater than the thickness of the line. If ΛCDM fails this test, it would be a clear falsification, and a sign that we need to try something completely different.

Unfortunately, detecting the 21cm absorption signal during the dark ages is even harder than it is at cosmic dawn. At these redshifts (z ~ 100), the 21cm line (1420 MHz on your radio dial) is shifted beyond the ionospheric cutoff of the Earth’s atmosphere at 30 MHz. Frequencies this low cannot be observed from the ground. Worse, we have made the Earth itself a bright foreground contaminant of radio frequency interference.

Undeterred, there are multiple proposals to measure this signal by placing an antenna in space – in particular, on the far side of the moon, so that the moon shades the instrument from terrestrial radio interference. This is a great idea. The mere detection of the 21cm signal from the dark ages would be an accomplishment on par with the original detection of the CMB. It appears that it might also provide a decisive new way of testing our cosmological model.

There are further tests involving the shape of the 21cm signal, its power spectrum (analogous to the power spectrum of the CMB), how structure grows in the early ages of the universe, and how massive the neutrino is. But that’s enough for now.

e694e8819c5f9d9d1638e4638a1e7bce

Most likely beer. Or a cosmo. That’d be appropriate. I make a good pomegranate cosmo.


*Note that a variety of astronomical observations had established the concordance cosmology before Type Ia supernovae detected cosmic acceleration and well-resolved observations of the CMB found a flat cosmic geometry.

A brief history of the acceleration discrepancy

A brief history of the acceleration discrepancy

As soon as I wrote it, I realized that the title is much more general than anything that can be fit in a blog post. Bekenstein argued long ago that the missing mass problem should instead be called the acceleration discrepancy, because that’s what it is – a discrepancy that occurs in conventional dynamics at a particular acceleration scale. So in that sense, it is the entire history of dark matter. For that, I recommend the excellent book The Dark Matter Problem: A Historical Perspective by Bob Sanders.

Here I mean more specifically my own attempts to empirically constrain the relation between the mass discrepancy and acceleration. Milgrom introduced MOND in 1983, no doubt after a long period of development and refereeing. He anticipated essentially all of what I’m going to describe. But not everyone is eager to accept MOND as a new fundamental theory, and often suffer from a very human tendency to confuse fact and theory. So I have gone out of my way to demonstrate what is empirically true in the data – facts – irrespective of theoretical interpretation (MOND or otherwise).

What is empirically true, and now observationally established beyond a reasonable doubt, is that the mass discrepancy in rotating galaxies correlates with centripetal acceleration. The lower the acceleration, the more dark matter one appears to need. Or, as Bekenstein might have put it, the amplitude of the acceleration discrepancy grows as the acceleration itself declines.

Bob Sanders made the first empirical demonstration that I am aware of that the mass discrepancy correlates with acceleration. In a wide ranging and still relevant 1990 review, he showed that the amplitude of the mass discrepancy correlated with the acceleration at the last measured point of a rotation curve. It did not correlate with radius.

AccDisc_Sanders1990
The acceleration discrepancy from Sanders (1990).

I was completely unaware of this when I became interested in the problem a few years later. I wound up reinventing the very same term – the mass discrepancy, which I defined as the ratio of dynamically measured mass to that visible in baryons: D = Mtot/Mbar. When there is no dark matter, Mtot = Mbar and D = 1.

My first demonstration of this effect was presented at a conference at Rutgers in 1998. This considered the mass discrepancy at every radius and every acceleration within all the galaxies that were available to me at that time. Though messy, as is often the case in extragalactic astronomy, the correlation was clear. Indeed, this was part of a broader review of galaxy formation; the title, abstract, and much of the substance remains relevant today.

MD1998_constantML
The mass discrepancy – the ratio of dynamically measured mass to that visible in luminous stars and gas – as a function of centripetal acceleration. Each point is a measurement along a rotation curve; two dozen galaxies are plotted together. A constant mass-to-light ratio is assumed for all galaxies.

I spent much of the following five years collecting more data, refining the analysis, and sweating the details of uncertainties and systematic instrumental effects. In 2004, I published an extended and improved version, now with over 5 dozen galaxies.

MDaccpoponly
One panel from Fig. 5 of McGaugh (2004). The mass discrepancy is plotted against the acceleration predicted by the baryons (in units of km2 s2 kpc-1).

Here I’ve used a population synthesis model to estimate the mass-to-light ratio of the stars. This is the only unknown; everything else is measured. Note that the vast majority galaxies land on top of each other. There are a few that do not, as you can perceive in the parallel sets of points offset from the main body. But that happens in only a few cases, as expected – no population model is perfect. Indeed, this one was surprisingly good, as the vast majority of the individual galaxies are indistinguishable in the pile that defines the main relation.

I explored the how the estimation of the stellar mass-to-light ratio affected this mass discrepancy-acceleration relation in great detail in the 2004 paper. The details differ with the choice of estimator, but the bottom line was that the relation persisted for any plausible choice. The relation exists. It is an empirical fact.

At this juncture, further improvement was no longer limited by rotation curve data, which is what we had been working to expand through the early ’00s. Now it was the stellar mass. The measurement of stellar mass was based on optical measurements of the luminosity distribution of stars in galaxies. These are perfectly fine data, but it is hard to map the starlight that we measured to the stellar mass that we need for this relation. The population synthesis models were good, but they weren’t good enough to avoid the occasional outlier, as can be seen in the figure above.

One thing the models all agreed on (before they didn’t, then they did again) was that the near-infrared would provide a more robust way of mapping stellar mass than the optical bands we had been using up till then. This was the clear way forward, and perhaps the only hope for improving the data further. Fortunately, technology was keeping pace. Around this time, I became involved in helping the effort to develop the NEWFIRM near-infrared camera for the national observatories, and NASA had just launched the Spitzer space telescope. These were the right tools in the right place at the right time. Ultimately, the high accuracy of the deep images obtained from the dark of space by Spitzer at 3.6 microns were to prove most valuable.

Jim Schombert and I spent much of the following decade observing in the near-infrared. Many other observers were doing this as well, filling the Spitzer archive with useful data while we concentrated on our own list of low surface brightness galaxies. This paragraph cannot suffice to convey the long term effort and enormity of this program. But by the mid-teens, we had accumulated data for hundreds of galaxies, including all those for which we also had rotation curves and HI observations. The latter had been obtained over the course of decades by an entire independent community of radio observers, and represent an integrated effort that dwarfs our own.

On top of the observational effort, Jim had been busy building updated stellar population models. We have a sophisticated understanding of how stars work, but things can get complicated when you put billions of them together. Nevertheless, Jim’s work – and that of a number of independent workers – indicated that the relation between Spitzer’s 3.6 micron luminosity measurements and stellar mass should be remarkably simple – basically just a constant conversion factor for nearly all star forming galaxies like those in our sample.

Things came together when Federico Lelli joined Case Western as a postdoc in 2014. He had completed his Ph.D. in the rich tradition of radio astronomy, and was the perfect person to move the project forward. After a couple more years of effort, curating the rotation curve data and building mass models from the Spitzer data, we were in the position to build the relation for over a dozen dozen galaxies. With all the hard work done, making the plot was a matter of running a pre-prepared computer script.

Federico ran his script. The plot appeared on his screen. In a stunned voice, he called me into his office. We had expected an improvement with the Spitzer data – hence the decade of work – but we had also expected there to be a few outliers. There weren’t. Any.

All. the. galaxies. fell. right. on. top. of. each. other.

rar
The radial acceleration relation. The centripetal acceleration measured from rotation curves is plotted against that predicted by the observed baryons. 2693 points from 153 distinct galaxies are plotted together (bluescale); individual galaxies do not distinguish themselves in this plot. Indeed, the width of the scatter (inset) is entirely explicable by observational uncertainties and the expected scatter in stellar mass-to-light ratios. From McGaugh et al. (2016).

This plot differs from those above because we had decided to plot the measured acceleration against that predicted by the observed baryons so that the two axes would be independent. The discrepancy, defined as the ratio, depended on both. D is essentially the ratio of the y-axis to the x-axis of this last plot, dividing out the unity slope where D = 1.

This was one of the most satisfactory moments of my long career, in which I have been fortunate to have had many satisfactory moments. It is right up there with the eureka moment I had that finally broke the long-standing loggerhead about the role of selection effects in Freeman’s Law. (Young astronomers – never heard of Freeman’s Law? You’re welcome.) Or the epiphany that, gee, maybe what we’re calling dark matter could be a proxy for something deeper. It was also gratifying that it was quickly recognized as such, with many of the colleagues I first presented it to saying it was the highlight of the conference where it was first unveiled.

Regardless of the ultimate interpretation of the radial acceleration relation, it clearly exists in the data for rotating galaxies. The discrepancy appears at a characteristic acceleration scale, g = 1.2 x 10-10 m/s/s. That number is in the data. Why? is a deeply profound question.

It isn’t just that the acceleration scale is somehow fundamental. The amplitude of the discrepancy depends systematically on the acceleration. Above the critical scale, all is well: no need for dark matter. Below it, the amplitude of the discrepancy – the amount of dark matter we infer – increases systematically. The lower the acceleration, the more dark matter one infers.

The relation for rotating galaxies has no detectable scatter – it is a near-perfect relation. Whether this persists, and holds for other systems, is the interesting outstanding question. It appears, for example, that dwarf spheroidal galaxies may follow a slightly different relation. However, the emphasis here is on slighlty. Very few of these data pass the same quality criteria that the SPARC data plotted above do. It’s like comparing mud pies with diamonds.

Whether the scatter in the radial acceleration relation is zero or merely very tiny is important. That’s the difference between a new fundamental force law (like MOND) and a merely spectacular galaxy scaling relation. For this reason, it seems to be controversial. It shouldn’t be: I was surprised at how tight the relation was myself. But I don’t get to report that there is lots of scatter when there isn’t. To do so would be profoundly unscientific, regardless of the wants of the crowd.

Of course, science is hard. If you don’t do everything right, from the measurements to the mass models to the stellar populations, you’ll find some scatter where perhaps there isn’t any. There are so many creative ways to screw up that I’m sure people will continue to find them. Myself, I prefer to look forward: I see no need to continuously re-establish what has been repeatedly demonstrated in the history briefly outlined above.

RAR fits to individual galaxies

RAR fits to individual galaxies

The radial acceleration relation connects what we see in visible mass with what we get in galaxy dynamics. This is true in a statistical sense, with remarkably little scatter. The SPARC data are consistent with a single, universal force law in galaxies. One that appears to be sourced by the baryons alone.

This was not expected with dark matter. Indeed, it would be hard to imagine a less natural result. We can only salvage the dark matter picture by tweaking it to make it mimic its chief rival. This is not a healthy situation for a theory.

On the other hand, if these results really do indicate the action of a single universal force law, then it should be possible to fit each individual galaxy. This has been done many times before, with surprisingly positive results. Does it work for the entirety of SPARC?

For the impatient, the answer is yes. Graduate student Pengfei Li has addressed this issue in a paper in press at A&A. There are some inevitable goofballs; this is astronomy after all. But by and large, it works much better than I expected – the goof rate is only about 10%, and the worst goofs are for the worst data.

Fig. 1 from the paper gives the example of NGC 2841. This case has been historically problematic for MOND, but a good fit falls out of the Bayesian MCMC procedure employed.  We marginalize over the nuisance parameters (distance and inclination) in addition to the stellar mass-to-light ratio of disk and bulge. These come out a tad high in this case, but everything is within the uncertainties. A long standing historical problem is easily solved by application of Bayesian statistics.

NGC2841_RAR_MCMC
RAR fit (equivalent to a MOND fit) to NGC 2841. The rotation curve and components of the mass model are shown at top left, with the fit parameters at top right. The fit is also shown in terms of acceleration (bottom left) and where the galaxy falls on the RAR (bottom right).

Another example is provided by the low surface brightness (LSB) dwarf galaxy IC 2574. Note that like all LSB galaxies, it lies at the low acceleration end of the RAR. This is what attracted my attention to the problem a long time ago: the mass discrepancy is large everywhere, so conventionally dark matter dominates. And yet, the luminous matter tells you everything you need to know to predict the rotation curve. This makes no physical sense whatsoever: it is as if the baryonic tail wags the dark matter dog.

IC2574_RAR_MCMC
RAR fit for IC 2574, with panels as in the figure above.

In this case, the mass-to-light ratio of the stars comes out a bit low. LSB galaxies like IC 2574 are gas rich; the stellar mass is pretty much an afterthought to the fitting process. That’s good: there is very little freedom; the rotation curve has to follow almost directly from the observed gas distribution. If it doesn’t, there’s nothing to be done to fix it. But it is also bad: since the stars contribute little to the total mass budget, their mass-to-light ratio is not well constrained by the fit – changing it a lot makes little overall difference. This renders the formal uncertainty on the mass-to-light ratio highly dubious. The quoted number is correct for the data as presented, but it does not reflect the inevitable systematic errors that afflict astronomical observations in a variety of subtle ways. In this case, a small change in the innermost velocity measurements (as happens in the THINGS data) could change the mass-to-light ratio by a huge factor (and well outside the stated error) without doing squat to the overall fit.

We can address statistically how [un]reasonable the required fit parameters are. Short answer: they’re pretty darn reasonable. Here is the distribution of 3.6 micron band mass-to-light ratios.

MLdisk_RAR_MCMC
Histogram of best-fit stellar mass-to-light ratios for the disk components of SPARC galaxies. The red dashed line illustrates the typical value expected from stellar population models.

From a stellar population perspective, we expect roughly constant mass-to-light ratios in the near-infrared, with some scatter. The fits to the rotation curves give just that. There is no guarantee that this should work out. It could be a meaningless fit parameter with no connection to stellar astrophysics. Instead, it reproduces the normalization, color dependence, and scatter expected from completely independent stellar population models.

The stellar mass-to-light ratio is practically inaccessible in the context of dark matter fits to rotation curves, as it is horribly degenerate with the parameters of the dark matter halo. That MOND returns reasonable mass-to-light ratios is one of those important details that keeps me wondering. It seems like there must be something to it.

Unsurprisingly, once we fit the mass-to-light ratio and the nuisance parameters, the scatter in the RAR itself practically vanishes. It does not entirely go away, as we fit only one mass-to-light ratio per galaxy (two in the handful of cases with a bulge). The scatter in the individual velocity measurements has been minimized, but some remains. The amount that remains is tiny (0.06 dex) and consistent with what we’d expect from measurement errors and mild asymmetries (non-circular motions).

RAR_MCMC
The radial acceleration relation with optimized parameters.

For those unfamiliar with extragalactic astronomy, it is common for “correlations” to be weak and have enormous intrinsic scatter. Early versions of the Tully-Fisher relation were considered spooky-tight with a mere 0.4 mag. of scatter. In the RAR we have a relation as near to perfect as we’re likely to get. The data are consistent with a single, universal force law – at least in the radial direction in rotating galaxies.

That’s a strong statement. It is hard to understand in the context of dark matter. If you think you do, you are not thinking clearly.

So how strong is this statement? Very. We tried fits allowing additional freedom. None is necessary. One can of course introduce more parameters, but we find that no more are needed. The bare minimum is the mass-to-light ratio (plus the nuisance parameters of distance and inclination); these entirely suffice to describe the data. Allowing more freedom does not meaningfully improve the fits.

For example, I have often seen it asserted that MOND fits require variation in the acceleration constant of the theory. If this were true, I would have zero interest in the theory. So we checked.

Here we learn something important about the role of priors in Bayesian fits. If we allow the critical acceleration g to vary from galaxy to galaxy with a flat prior, it does indeed do so: it flops around all over the place. Aha! So g is not constant! MOND is falsified!

gdagger_MCMC
Best fit values of the critical acceleration in each galaxy for a flat prior (light blue) and a Gaussian prior (dark blue). The best-fit value is so consistent in the latter case that the inset is necessary to see the distribution at all. Note the switch to a linear scale and the very narrow window.

Well, no. Flat priors are often problematic, as they have no physical motivation. By allowing for a wide variation in g, one is inviting covariance with other parameters. As g goes wild, so too does the mass-to-light ratio. This wrecks the stellar mass Tully-Fisher relation by introducing a lot of unnecessary variation in the mass-to-light ratio: luminosity correlates nicely with rotation speed, but stellar mass picks up a lot of extraneous scatter. Worse, all this variation in both g and the mass-to-light ratio does very little to improve the fits. It does a tiny bit – χ2 gets infinitesimally better, so the fitting program takes it. But the improvement is not statistically meaningful.

In contrast, with a Gaussian prior, we get essentially the same fits, but with practically zero variation in g. wee The reduced χ2 actually gets a bit worse thanks to the extra, unnecessary, degree of freedom. This demonstrates that for these data, g is consistent with a single, universal value. For whatever reason it may occur physically, this number is in the data.

We have made the SPARC data public, so anyone who wants to reproduce these results may easily do so. Just mind your priors, and don’t take every individual error bar too seriously. There is a long tail to high χ2 that persists for any type of model. If you get a bad fit with the RAR, you will almost certainly get a bad fit with your favorite dark matter halo model as well. This is astronomy, fergodssake.

The dwarf galaxy NGC1052-DF2

The dwarf galaxy NGC1052-DF2

A recently discovered dwarf galaxy designated NGC1052-DF2 has been in the news lately. Apparently a satellite of the giant elliptical NGC 1052, DF2 (as I’ll call it from here on out) is remarkable for having a surprisingly low velocity dispersion for a galaxy of its type. These results were reported in Nature last week by van Dokkum et al., and have caused a bit of a stir.

It is common for giant galaxies to have some dwarf satellite galaxies. As can be seen from the image published by van Dokkum et al., there are a number of galaxies in the neighborhood of NGC 1052. Whether these are associated physically into a group of galaxies or are chance projections on the sky depends on the distance to each galaxy.

NGC1052-DF2
Image of field containing DF2 from van Dokkum et al.

NGC 1052 is listed by the NASA Extragalactic Database (NED) as having a recession velocity of 1510 km/s and a distance of 20.6 Mpc. The next nearest big beastie is NGC 1042, at 1371 km/s. The difference of 139 km/s is not much different from 115 km/s, which is the velocity that Andromeda is heading towards the Milky Way, so one could imagine that this is a group similar to the Local Group. Except that NED says the distance to NGC 1042 is 7.8 Mpc, so apparently it is a foreground object seen in projection.

Van Dokkum et al. assume DF2 and NGC 1052 are both about 20 Mpc distant. They offer two independent estimates of the distance, one consistent with the distance to NGC 1052 and the other more consistent with the distance to NGC 1042. Rather than wring our hands over this, I will trust their judgement and simply note, as they do, that the nearer distance would change many of their conclusions. The redshift is 1803 km/s, larger than either of the giants. It could still be a satellite of NGC 1052, as ~300 km/s is not unreasonable for an orbital velocity.

So why the big fuss? Unlike most galaxies in the universe, DF2 appears not to require dark matter. This is inferred from the measured velocity dispersion of ten globular clusters, which is 8.4 km/s. That’s fast to you and me, but rather sluggish on the scale of galaxies. Spread over a few kiloparsecs, that adds up to a dynamical mass about equal to what we expect for the stars, leaving little room for the otherwise ubiquitous dark matter.

This is important. If the universe is composed of dark matter, it should on occasion be possible to segregate the dark from the light. Tidal interactions between galaxies can in principle do this, so a galaxy devoid of dark matter would be good evidence that this happened. It would also be evidence against a modified gravity interpretation of the missing mass problem, because the force law is always on: you can’t strip it from the luminous matter the way you can dark matter. So ironically, the occasional galaxy lacking dark matter would constitute evidence that dark matter does indeed exist!

DF2 appears to be such a case. But how weird is it? Morphologically, it resembles the dwarf spheroidal satellite galaxies of the Local Group. I have a handy compilation of those (from Lelli et al.), so we can compute the mass-to-light ratio for all of these beasties in the same fashion, shown in the figure below. It is customary to refer quantities to the radius that contains half of the total light, which is 2.2 kpc for DF2.

dwarfMLdyn
The dynamical mass-to-light ratio for Local Group dwarf Spheroidal galaxies measured within their half-light radii, as a function of luminosity (left) and average surface brightness within the half-light radius (right). DF2 is the blue cross with low M/L. The other blue cross is Crater 2, a satellite of the Milky Way discovered after the compilation of Local Group dwarfs was made. The dotted line shows M/L = 2, which is a good guess for the stellar mass-to-light ratio. That DF2 sits on this line implies that stars are the only mass that’s there.

Perhaps the most obvious respect in which DF2 is a bit unusual relative to the dwarfs of the Local Group is that it is big and bright. Most nearby dwarfs have half light radii well below 1 kpc. After DF2, the next most luminous dwarfs is Fornax, which is a factor of 5 lower in luminosity.

DF2 is called an ultradiffuse galaxy (UDG), which is apparently newspeak for low surface brightness (LSB) galaxy. I’ve been working on LSB galaxies my entire career. While DF2 is indeed low surface brightness – the stars are spread thin – I wouldn’t call it ultra diffuse. It is actually one of the higher surface brightness objects of this type. Crater 2 and And XIX (the leftmost points in the right panel) are ultradiffuse.

Astronomers love vague terminology, and as a result often reinvent terms that already exist. Dwarf, LSB, UDG, have all been used interchangeably and with considerable slop. I was sufficiently put out by this that I tried to define some categories is the mid-90s. This didn’t catch on, but by my definition, DF2 is VLSB – very LSB, but only by a little – it is much closer to regular LSB than to extremely (ELSB). Crater 2 and And XIX, now they’re ELSB, being more diffuse than DF2 by 2 orders of magnitude.

SBdefinitiontable
Surface brightness categories from McGaugh (1996).

Whatever you call it, DF2 is low surface brightness, and LSB galaxies are always dark matter dominated. Always, at least among disk galaxies: here is the analogous figure for galaxies that rotate:

MLdynDisk
Dynamical mass-to-light ratios for rotationally supported disk galaxies, analogous to the plot above for pressure supported disks. The lower the surface brightness, the higher the mass discrepancy. The correlation with luminosity is secondary, as a result of the correlation between luminosity and surface brightness. From McGaugh (2014).

Pressure supported dwarfs generally evince large mass discrepancies as well. So in this regard, DF2 is indeed very unusual. So what gives?

Perhaps DF2 formed that way, without dark matter. This is anathema to everything we know about galaxy formation in ΛCDM cosmology. Dark halos have to form first, with baryons following.

Perhaps DF2 suffered one or more tidal interactions with NGC 1052. Sub-halos in simulations are often seen to be on highly radial orbits; perhaps DF2 has had its dark matter halo stripped away by repeated close passages. Since the stars reside deep in the center of the subhalo, they’re the last thing to be stripped away. So perhaps we’ve caught this one at that special time when the dark matter has been removed but the stars still remain.

This is improbable, but ought to happen once in a while. The bigger problem I see is that one cannot simply remove the dark matter halo like yanking a tablecloth and leaving the plates. The stars must respond to the change in the gravitational potential; they too must diffuse away. That might be a good way to make the galaxy diffuse, ultimately perhaps even ultradiffuse, but the observed motions are then not representative of an equilibrium situation. This is critical to the mass estimate, which must perforce assume an equilibrium in which the gravitational potential well of the galaxy is balanced against the kinetic motion of its contents. Yank away the dark matter halo, and the assumption underlying the mass estimate gets yanked with it. While such a situation may arise, it makes it very difficult to interpret the velocities: all tests are off. This is doubly true in MOND, in which dwarfs are even more susceptible to disruption.

onedoesnotyank

Then there are the data themselves. Blaming the data should be avoided, but it does happen once in a while that some observation is misleading. In this case, I am made queasy by the fact that the velocity dispersion is estimated from only ten tracers. I’ve seen plenty of cases where the velocity dispersion changes in important ways when more data are obtained, even starting from more than 10 tracers. Andromeda II comes to mind as an example. Indeed, several people have pointed out that if we did the same exercise with Fornax, using its globular clusters as the velocity tracers, we’d get a similar answer to what we find in DF2. But we also have measurements of many hundreds of stars in Fornax, so we know that answer is wrong. Perhaps the same thing is happening with DF2? The fact that DF2 is an outlier from everything else we know empirically suggests caution.

Throwing caution and fact-checking to the wind, many people have been predictably eager to cite DF2 as a falsification of MOND. Van Dokkum et al. point out the the velocity dispersion predicted for this object by MOND is 20 km/s, more than a factor of two above their measured value. They make the MOND prediction for the case of an isolated object. DF2 is not isolated, so one must consider the external field effect (EFE).

The criterion by which to judge isolation in MOND is whether the acceleration due to the mutual self-gravity of the stars is less than the acceleration from an external source, in this case the host NGC 1052. Following the method outlined by McGaugh & Milgrom, and based on the stellar mass (adopting M/L=2 as both we and van Dokkum assume), I estimate an internal acceleration of DF2 to be gin = 0.15 a0. Here a0 is the critical acceleration scale in MOND, 1.2 x 10-10 m/s/s. Using this number and treating DF2 as isolated, I get the same 20 km/s van Dokkum et al. estimate.

Estimating the external field is more challenging. It depends on the mass of NGC 1052, and the separation between it and DF2. The projected separation at the assumed distance is 80 kpc. That is well within the range that the EFE is commonly observed to matter in the Local Group. It could be a bit further granted some distance along the line of sight, but if this becomes too large then the distance by association with NGC 1052 has to be questioned, and all bets are off. The mass of NGC 1052 is also rather uncertain, or at least I have heard wildly different values quoted in discussions about this object. Here I adopt 1011 M as estimated by SLUGGS. To get the acceleration, I estimate the asymptotic rotation velocity we’d expect in MOND, V4 = a0GM. This gives 200 km/s, which is conservative relative to the ~300 km/s quoted by van Dokkum et al. At a distance of 80 kpc, the corresponding external acceleration gex = 0.14 a0. This is very uncertain, but taken at face value is indistinguishable from the internal acceleration. Consequently, it cannot be ignored: the calculation published by van Dokkum et al. is not the correct prediction for MOND.

The velocity dispersion estimator in MOND differs when gex < gin and gex > gin (see equations 2 and 3 of McGaugh & Milgrom). Strictly speaking, these apply in the limits where one or the other field dominates. When they are comparable, the math gets more involved (see equation 59 of Famaey & McGaugh). The input data are too uncertain to warrant an elaborate calculation for a blog, so I note simply that the amplitude of the mass discrepancy in MOND depends on how deep in the MOND regime a system is. That is, how far below the critical acceleration scale it is. The lower the acceleration, the larger the discrepancy. This is why LSB galaxies appear to be dark matter dominated; their low surface densities result in low accelerations.

For DF2, the absolute magnitude of the acceleration is approximately doubled by the presence of the external field. It is not as deep in the MOND regime as assumed in the isolated case, so the mass discrepancy is smaller, decreasing the MOND-predicted velocity dispersion by roughly the square root of 2. For a factor of 2 range in the stellar mass-to-light ratio (as in McGaugh & Milgrom), this crude MOND prediction becomes

σ = 14 ± 4 km/s.

Like any erstwhile theorist, I reserve the right to modify this prediction granted more elaborate calculations, or new input data, especially given the uncertainties in the distance and mass of the host. Indeed, we should consider the possibility of tidal disruption, which can happen in MOND more readily than with dark matter. Indeed, at one point I came very close to declaring MOND dead because the velocity dispersions of the ultrafaint dwarf galaxies were off, only realizing late in the day that MOND actually predicts that these things should be getting tidally disrupted (as is also expected, albeit somewhat differently, in ΛCDM), so that the velocity dispersions might not reflect the equilibrium expectation.

In DF2, the external field almost certainly matters. Barring wild errors of the sort discussed or unforeseen, I find it hard to envision the MONDian velocity dispersion falling outside the range 10 – 18 km/s. This is not as high as the 20 km/s predicted by van Dokkum et al. for an isolated object, nor as small as they measure for DF2 (8.4 km/s). They quote a 90% confidence upper limit of 10 km/s, which is marginally consistent with the lower end of the prediction (corresponding to M/L = 1). So we cannot exclude MOND based on these data.

That said, the agreement is marginal. Still, 90% is not very high confidence by scientific standards. Based on experience with such data, this likely overstates how well we know the velocity dispersion of DF2. Put another way, I am 90% confident that when better data are obtained, the measured velocity dispersion will increase above the 10 km/s threshold.

More generally, experience has taught me three things:

  1. In matters of particle physics, do not bet against the Standard Model.
  2. In matters cosmological, do not bet against ΛCDM.
  3. In matters of galaxy dynamics, do not bet against MOND.

The astute reader will realize that these three assertions are mutually exclusive. The dark matter of ΛCDM is a bet that there are new particles beyond the Standard Model. MOND is a bet that what we call dark matter is really the manifestation of physics beyond General Relativity, on which cosmology is based. Which is all to say, there is still some interesting physics to be discovered.

Yes, Virginia, there is a Dark Matter

Yes, Virginia, there is a Dark Matter

Virginia, your little friends are wrong. They have been affected by the skepticism of a skeptical age. They do not believe except they see. They think that nothing can be which is not comprehensible by their little minds. All minds, Virginia, whether they be men’s or children’s, are little. In this great universe of ours man is a mere insect, an ant, in his intellect, as compared with the boundless world about him, as measured by the intelligence capable of grasping the whole of truth and knowledge.

Yes, Virginia, there is a Dark Matter. It exists as certainly as squarks and sleptons and Higgsinos exist, and you know that they abound and give to your life its highest beauty and joy. Alas! how dreary would be the world if there were no Dark Matter. It would be as dreary as if there were no supersymmetry. There would be no childlike faith then, no papers, no grants to make tolerable this existence. We should have no enjoyment, except in observation and experiment. The eternal light with which childhood fills the world would be extinguished.

Not believe in Dark Matter! You might as well not believe in Dark Energy! You might get the DOE to hire men to watch in all the underground laboratories to catch Dark Matter, but even if they did not see Dark Matter coming down, what would that prove? Nobody sees Dark Matter, but that is no sign that there is no Dark Matter. The most real things in the world are those that neither children nor men can see. Did you ever see fairies dancing on the lawn? Of course not, but that’s no proof that they are not there. Nobody can conceive or imagine all the wonders there are unseen and unseeable in the world.

You may tear apart the baby’s rattle and see what makes the noise inside, but there is a veil covering the unseen world which not the best experiment, nor even the united efforts of all the keenest experiments ever conducted, could tear apart. Only faith, fancy, poetry, love, romance, can push aside that curtain and view and picture the supernal beauty and glory beyond. Is it all real? Ah, Virginia, in all this world there is nothing else real and abiding.

No Dark Matter! Thank God! It exists, and it exists forever. A thousand years from now, Virginia, nay, ten times ten thousand years from now, it will continue to make glad the coffers of science.

Paraphrased from the famous letter Yes, Virginia, there is a Santa Claus.

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!)

Whatwesaytotheorists

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.

NFWISOvelocityfield
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:

UGC12687UGC12695vfields
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.

arsenio
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.

Dwarf Galaxies on the Shoulders of Giants

Dwarf Galaxies on the Shoulders of Giants

The week of June 5, 2017, we held a workshop on dwarf galaxies and the dark matter problem. The workshop was attended by many leaders in the field – giants of dwarf galaxy research. It was held on the campus of Case Western Reserve University and supported by the John Templeton Foundation. It resulted in many fascinating discussions which I can’t possibly begin to share in full here, but I’ll say a few words.

Dwarf galaxies are among the most dark matter dominated objects in the universe. Or, stated more properly, they exhibit the largest mass discrepancies. This makes them great places to test theories of dark matter and modified gravity. By the end, we had come up with a few important tests for both ΛCDM and MOND. A few of these we managed to put on a white board. These are hardly a complete list, but provide a basis for discussion.

First, ΛCDM.

LCDM_whiteboard
A few issues for ΛCDM identified during the workshop.

UFDs in field: Over the past few years, a number of extremely tiny dwarf galaxies have been identified as satellites of the Milky Way galaxy. These “ultrafaint dwarfs” are vaguely defined as being fainter than 100,000 solar luminosities, with the smallest examples having only a few hundred stars. This is absurdly small by galactic standards, having the stellar content of individual star clusters within the Milky Way. Indeed, it is not obvious to me that all of the ultrafaint dwarfs deserve to be recognized as dwarf galaxies, as some may merely be fragmentary portions of the Galactic stellar halo composed of stars coincident in phase space. Nevertheless, many may well be stellar systems external to the Milky Way that orbit it as dwarf satellites.

That multitudes of minuscule dark matter halos exist is a fundamental prediction of the ΛCDM cosmogony. These should often contain ultrafaint dwarf galaxies, and not only as satellites of giant galaxies like the Milky Way. Indeed, one expects to see many ultrafaints in the “field” beyond the orbital vicinity of the Milky Way where we have found them so far. These are predicted to exist in great numbers, and contain uniformly old stars. The “old stars” portion of the prediction stems from the reionization of the universe impeding star formation in the smallest dark matter halos. Upcoming surveys like LSST should provide a test of this prediction.

From an empirical perspective, I do expect that we will continue to discover galaxies of ever lower luminosity and surface brightness. In the field, I expect that these will be predominantly gas rich dwarfs like Leo P rather than gas-free, old stellar systems like the satellite ultrafaints. My expectation is an extrapolation of past experience, not a theory-specific prediction.

No Large Cores: Many of the simulators present at the workshop showed that if the energy released by supernovae was well directed, it could reshape the steep (‘cuspy’) interior density profiles of dark matter halos into something more like the shallow (‘cored’) interiors that are favored by data. I highlight the if because I remain skeptical that supernova energy couples as strongly as required and assumed (basically 100%). Even assuming favorable feedback, there seemed to be broad (in not unanimous) consensus among the simulators present that at sufficiently low masses, not enough stars would form to produce the requisite energy. Consequently, low mass halos should not have shallow cores, but instead retain their primordial density cusps. Hence clear measurement of a large core in a low mass dwarf galaxy (stellar mass < 1 million solar masses) would be a serious problem. Unfortunately, I’m not clear that we quantified “large,” but something more than a few hundred parsecs should qualify.

Radial Orbit for Crater 2: Several speakers highlighted the importance of the recently discovered dwarf satellite Crater 2. This object has a velocity dispersion that is unexpectedly low in ΛCDM, but was predicted by MOND. The “fix” in ΛCDM is to imagine that Crater 2 has suffered a large amount of tidal stripping by a close passage of the Milky Way. Hence it is predicted to be on a radial orbit (one that basically just plunges in and out). This can be tested by measuring the proper motion of its stars with Hubble Space Telescope, for which there exists a recently approved program.

DM Substructures: As noted above, there must exist numerous low mass dark matter halos in the cold dark matter cosmogony. These may be detected as substructure in the halos of larger galaxies by means of their gravitational lensing even if they do not contain dwarf galaxies. Basically, a lumpy dark matter halo bends light in subtly but detectably different ways from a smooth halo.

No Wide Binaries in UFDs: As a consequence of dynamical friction against the background dark matter, binary stars cannot remain at large separations over a Hubble time: their orbits should decay. In the absence of dark matter, this should not happen (it cannot if there is nowhere for the orbital energy to go, like into dark matter particles). Thus the detection of a population of widely separated binary stars would be problematic. Indeed, Pavel Kroupa argued that the apparent absence of strong dynamical friction already excludes particle dark matter as it is usually imagined.

Short dynamical times/common mergers: This is related to dynamical friction. In the hierarchical cosmogony of cold dark matter, mergers of halos (and the galaxies they contain) must be frequent and rapid. Dark matter halos are dynamically sticky, soaking up the orbital energy and angular momentum between colliding galaxies to allow them to stick and merge. Such mergers should go to completion on fairly short timescales (a mere few hundred million years).

MOND

A few distinctive predictions for MOND were also identified.

MOND_whiteboard

Tangential Orbit for Crater 2: In contrast to ΛCDM, we expect that the `feeble giant’ Crater 2 could not survive a close encounter with the Milky Way. Even at its rather large distance of 120 kpc from the Milky Way, it is so feeble that it is not immune from the external field of its giant host. Consequently, we expect that Crater 2 must be on a more nearly circular orbit, and not on a radial orbit as suggested in ΛCDM. The orbit does not need to be perfectly circular of course, but is should be more tangential than radial.

This provides a nice test that distinguishes between the two theories. Either the orbit of Crater 2 is more radial or more tangential. Bear in mind that Crater 2 already constitutes a problem for ΛCDM. What we’re discussing here is how to close what is basically a loophole whereby we can excuse an otherwise unanticipated result in ΛCDM.

EFE: The External Field Effect is a unique prediction of MOND that breaks the strong equivalence principle. There is already clear if tentative evidence for the EFE in the dwarf satellite galaxies around Andromeda. There is no equivalent to the EFE in ΛCDM.

I believe the question mark was added on the white board to permit the logical if unlikely possibility that one could write a MOND theory with an undetectably small EFE.

Position of UFDs on RAR: We chose to avoid making the radial acceleration relation (RAR) a focus of the meeting – there was quite enough to talk about as it was – but it certainly came up. The ultrafaint dwarfs sit “too high” on the RAR, an apparent problem for MOND. Indeed, when I first worked on this subject with Joe Wolf, I initially thought this was a fatal problem for MOND.

My initial thought was wrong. This is not a problem for MOND. The RAR applies to systems in dynamical equilibrium. There is a criterion in MOND to check whether this essential condition may be satisfied. Basically all of the ultrafaints flunk this test. There is no reason to think they are in dynamical equilibrium, so no reason to expect that they should be exactly on the RAR.

Some advocates of ΛCDM seemed to think this was a fudge, a lame excuse morally equivalent to the fudges made in ΛCDM that its critics complain about. This is a false equivalency that reminds me of this cartoon:

hqdefault
I dare ya to step over this line!

The ultrafaints are a handful of the least-well measured galaxies on the RAR. Before we obsess about these, it is necessary to provide a satisfactory explanation for the more numerous, much better measured galaxies that establish the RAR in the first place. MOND does this. ΛCDM does not. Holding one theory to account for the least reliable of measurements before holding another to account for everything up to that point is like, well, like the cartoon… I could put an NGC number to each of the lines Bugs draws in the sand.

Long dynamical times/less common mergers: Unlike ΛCDM, dynamical friction should be relatively ineffective in MOND. It lacks the large halos of dark matter that act as invisible catchers’ mitts to make galaxies stick and merge. Personally, I do not think this is a great test, because we are a long way from understanding dynamical friction in MOND.

Non-evolution with redshift: If the Baryonic Tully-Fisher relation and the RAR are indeed the consequence of MOND, then their form is fixed by the theory. Consequently, their slope shouldn’t evolve with time. Conceivably their normalization might (e.g., the value of a0 could in principle evolve). Some recent data for high redshift galaxies place constraints on such evolution, but reports on these data are greatly exaggerated.

These are just a few of the topics discussed at the workshop, and all of those are only a few of the issues that matter to the bigger picture. While the workshop was great in every respect, perhaps the best thing was that it got people from different fields/camps/perspectives talking. That is progress.

I am grateful for progress, but I must confess that to me it feels excruciatingly slow. Models of galaxy formation in the context of ΛCDM have made credible steps forward in addressing some of the phenomenological issues that concern me. Yet they still seem to me to be very far from where they need to be. In particular, there seems to be no engagement with the fundamental question I have posed here before, and that I posed at the beginning of the workshop: Why does MOND get any predictions right?