Category: MOND

Missing baryons in LCDM and MOND

Missing baryons in LCDM and MOND

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. In CDM, we expect a relation between dynamical mass and rotation speed of the form Mvir ∝ Vvir3. In MOND the equivalent relation has a different power law, Mb ∝ Vf4.

In CDM we speak of virial quantities – the total mass of everything, including dark matter, and the circular speed way out at the virial radius (typically far outside the luminous extent of a galaxy). In MOND, we use the observed baryonic mass (stars and gas) and the flat rotation speed. These are not the same, so strictly speaking, still incommensurable. But they provide a way to compare the baryonic mass with the total inferred mass.

missingbaryonsinLCDMMOND

This plot shows the detected baryon fraction as a function of mass. The top panel is identical to last time. In ΛCDM we see most of the baryons in the most massive systems, but progressively less in smaller systems. In MOND the situation is reversed. The check-sum is complete in galaxies, but falls short in clusters of galaxies. (Note that the error bars have been divided by an extra power of velocity in the lower panel, which amplifies their appearance.) The reader may judge for himself which of these problems is more serious.

Critics of MOND frequently cite the bullet cluster as having falsified MOND. Period. No room for debate. See the linked press release from NASA: dark_matter_proven.

OK, what kind of dark matter? As discussed previously, we need at least two kinds of dark matter in ΛCDM: non-baryonic cold dark matter (some entirely novel particle) and dark baryons (normal matter not yet detected). Unfortunately, “dark matter” is a rather generic, catch-all term that allows these two distinct problems to be easily confused. We see the need for unseen mass in objects like the bullet cluster, and make the natural leap to conclude that we are seeing the non-baryonic cold dark matter that we expect in cosmology. There it is, case closed.

This is an example of a logical fallacy. There is nothing about the missing mass problem suffered by MOND in clusters that demands the unseen mass be non-baryonic. Indeed, even in ΛCDM we suffer some missing baryon problem on top of the need for non-baryonic cold dark matter. In both theories, there is a missing baryon problem in clusters. In both cases, this missing baryon problem is more severe at small radii, suggestive of a connection with the also-persistent cooling flow problem. Basically, the X-ray emitting gas observed in the inner 200 kpc or so of clusters have time to cool, so it ought to be condensing into – what? Stars? MACHOs? Something normal but as yet unseen.

It is not obvious that cooling flows can solve MOND’s problem in clusters. The problem is both serious and persistent. It was first pointed out in 1988 by The & White, and is discussed in this 2002 Annual Review. A factor or two (or even a bit more) of the expected baryons in clusters are missing (the red portion of the plot above). Note, however, that this problem was known long before the bullet cluster was discovered. From this perspective, it would have been very strange had the bullet cluster not shown the same discrepancy as every other cluster in the sky.

I do not know if the missing mass in clusters is baryonic. I am at a loss to suggest a plausible form that the missing baryons might be lurking in. Certainly others have tried. But lets take a step back and as if it is plausible.

As seen above, we have a missing baryon problem in both theories. It just manifests in different places. Advocates of ΛCDM do not, by and large, seem to consider the baryon discrepancy in galaxies to be a problem. The baryons were blown out, or are there but just not detected yet. No Problem. I’m not as lenient, but if we are to extend that grace to ΛCDM, why not also to MOND?

Recall that Shull et al. found that about 30% of baryons remain undetected in the local universe. In order to solve the problem MOND suffers in clusters, we need a mass in baryons about equal to the ICM wedge in this pie chart:

GlobalMissingBaryons

Note that the missing wedge is much larger than the ICM wedge. There are more than enough baryons out there to solve this problem. Indeed, it hardly makes a dent in the global missing baryon problem. Those baryons “must” be somewhere, so why not some in clusters of galaxies?

The short answer is cognitive dissonance. If one comes to the problem sure of the answer, then one sees in the data what one expects to see. MOND fits rotation curves? That’s just a fluke: it bounces off the wall of cognitive dissonance without serious consideration. MOND needs dark matter in clusters? Well of course – we knew that it had to be wrong in the first place.

I understand this perspective exceedingly well. It is where I started from myself. But the answer I wanted is not the conclusion that a more balanced evaluation of the evidence leads one to. The challenge is not in the evidence – it is to give an unorthodox idea a chance in the first place.

Missing Baryons

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 Ωb ≈ 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. To make matters worse, if we attempt an accounting of where these baryons are, we again fall short. As well as the dynamical missing mass problem, we also have a missing baryon problem.

For a long time, this was also an order of magnitude problem. The stars and gas we could most readily see added up to < 1%, well short of even 5%. More recent work has shown that many, but not all, of the missing baryons are in the intergalactic medium (IGM).  The IGM is incredibly diffuse – a better vacuum than we can make in the laboratory by many orders of magnitude – but it is also very, very, very, well, very big. So all that nothing does add up to a bit of something.

GlobalMissingBaryons

A thorough accounting has been made by Shull et al. (2012). A little over half of detected baryons reside in the IGM, in either the Lyman alpha forest (Ly a in the pie chart above) or in the so-called warm-hot intergalactic medium (WHIM). There are also issues of double-counting, which Shull has taken care to avoid.

Gravitationally bound objects like galaxies and clusters of galaxies contain a minority of the baryons. Stars and cold (HI) gas in galaxies are small wedges of the pie, hence the large problem we initially had. Gas in the vicinity of galaxies (CGM) and in the intracluster medium of clusters of galaxies (ICM) also matter. Indeed, in the most massive clusters, the ICM outweighs all the stars in the galaxies there. This situation reverses as we look at lower mass groups. Rich clusters dominated by the ICM are rare; objects like our own Local Group are more typical. There’s no lack of circum-galactic gas (CGM), but it does not obviously outweigh the stars around L* galaxies.

There are of course uncertainties, so one can bicker and argue about the relative size of each slice of the pie. Even so, it remains hard to make their sum add up to 5% of the closure density. It appears that ~30% of the baryons that we believe to exist from BBN are still unaccounted for in the local universe.

The pie diagram only illustrates the integrated totals. For a long time I have been concerned about the baryon budget in individual objects. In essence, each dark matter halo should start with a cosmically equal share of baryons and dark matter. Yet in most objects, the ratio of baryons to total mass falls well short of the cosmic baryon fraction.

The value of the cosmic baryon fraction is well constrained by a variety of data, especially the cosmic microwave background. The number we persistently get is

fb = Ωb/Ωm = 0.17

or maybe 0.16, depending on which CMB analysis you consult.  But it isn’t 0.14 nor 0.10 nor 0.01. For sticklers, note that this the fraction of the total gravitating mass in baryons, not the ratio of baryons to dark matter: Ωm includes both. For numerologists, note that within the small formal uncertainties, 1/fb = 2π.

This was known long before the CMB experiments provided constraints that mattered. Indeed, one of the key findings that led us to repudiate standard SCDM in favor of ΛCDM was the recognition that clusters of galaxies had too many baryons for their dynamical mass. We could measure the baryon fraction in clusters. If we believe that these are big enough chunks of the universe to be representative of the whole, and we also believe BBN, then we are forced to conclude that Ωm ≈ 0.3.

Why stop with clusters? One can do this accounting in every gravitationally bound object. The null hypothesis is that every object should be composed of the universal composition, roughly 1 part baryons for every 5 parts dark matter. This almost works in rich clusters of galaxies. It fails in small clusters and groups of galaxies, and gets worse as you examine progressively smaller systems. So: not only are we missing baryons in the cosmic sum, there are some missing in each individual object.

missingbaryonsinLCDM

The figure shows the ratio of detected baryons to those expected in individual systems. I show the data I compiled in McGaugh et al. (2010), omitting the tiniest dwarfs for which the baryon content becomes imperceptible on a linear scale. By detected baryons I mean all those seen to exist in the form of stars or gas in each system (Mb = M*+Mg), such that

fd = Mb/(fbMvir)

where Mvir is the total mass of each object. This `virial’ mass is a rather uncertain quantity, but in this plot it can only slide the data up and down a little bit. The take-away is that not a single, gravitationally bound object appears to contain its fair share of cosmic baryons. There is a missing baryon problem not just globally, but in each and every object.

This halo-by-halo missing baryon problem is least severe in the most massive systems, rich clusters. Indeed, the baryon fraction of clusters is a rising function of radius, so a case could be made that the observations simply don’t reach far enough out to encompass a fair total. This point has been debated at great length in the literature, and I have little to add to it, except to observe that rich clusters are perhaps like horseshoes – close enough.

Irrespective of whether we consider the most massive clusters to be close enough to the cosmic baryon fraction or not, no other system comes close to close enough. There is already a clear discrepancy among smaller clusters, and an apparent trend with mass. This trend continues smoothly and continuously over many decades in baryonic mass through groups, then individual L* galaxies, and on to the tiniest dwarfs.

A respectively massive galaxy like the Milky Way has many tens of billions of solar masses in form of stars, and another ten billion or so in the form of cold gas. Yet this huge mass represents only a 1/4 or so of the baryons that should reside in the halo of the Milky Way. As we look at progressively smaller galaxies, the detected baryon fraction decreases further. For a galaxy with a mere few hundred million stars, fd ≈ 6%. It drops below 1% for M* < 107 solar masses.

That’s a lot of missing baryons. In the case of the Milky Way, all those stars and cold gas are within a radius of 20 kpc. The dark matter halo extends out to at least 150 kpc. So there is plenty of space in which the missing baryons might lurk in some tenuous form. But they have to remain pretty well hidden. Joel Bregman has spent a fair amount of his career searching for such baryonic reservoirs. While there is certainly some material out there, it does not appear to add up to be enough.

It is still harder to see this working in smaller galaxies. The discrepancy that is a factor of a few in the Milky Way grows to an order of magnitude and more in dwarfs. A common hypothesis is that these baryons do indeed lurk there, probably in a tenuous, hot gas. If so, direct searches have yet to see them. Another common idea is that the baryons get expelled entirely from the small potential wells of dwarf galaxy dark matter halos, driven by winds powered by supernovae. It that were the case, I’d expect to see a break at a critical mass where the potential well was or wasn’t deep enough to prevent this. If there is any indication of this, it is at still lower mass than shown above, and begs the question as to where those baryons are now.

So we don’t have a single missing mass problem in cosmology. We have at least two. One is the need for non-baryonic dark matter. The other is the need for unseen normal matter: dark baryons. This latter problem has at least two flavors. One is that the global sum of baryons comes up short. The other is that each and every individual gravitationally bound object comes up short in the number of baryons it should have.

An obvious question is whether accounting for the missing baryons in individual objects helps with the global problem. The wedges in the pie chart represent what is seen, not what goes unseen. Or do they? The CGM is the hot gas around galaxies, the favored hiding place for the object-by-object missing baryon problem.

Never mind the potential for double counting. Lets amp up the stars wedge by the unseen baryons indicated in red in the figure above. Just take for granted, for the moment, that these baryons are there in some form, associated in the proper ratio. We can then reevaluate the integrated sum and… still come up well short.

Low mass galaxies appear to have lots of missing baryons. But they are low mass. Even when we boost their mass in this way, they still contribute little to the integral.

This is a serious problem. Is it hopeless? No. Is it easily solved? No. At a minimum, it means we have at least two flavors of dark matter: non-baryonic [cosmic] dark matter, and dark baryons.

Does this confuse things immensely? Oh my yes.

What is theory?

What is theory?

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. We observe a discrepancy between the motions observed in extragalactic systems and what is predicted by application of the known law of gravity to the mass visible in ordinary baryonic matter. Either we need more mass (dark matter) or need to change the force law (modify dynamical laws, i.e., gravity). MOND is just one example of the latter type of hypothesis.

Put this way, dark matter is the more conservative hypothesis. It doesn’t require any change to well established, fundamental theory. There’s just more mass there than we see.

But what is it? Dark matter as so far stated is not a valid scientific hypothesis. It is a concept – there is unseen stuff out there. To turn it into science, we need to hypothesize a specific candidate.

An example of a dark matter candidate that most people would agree has been falsified at this point is brown dwarfs. These are very faint, sub-stellar objects – failed stars if you like, things not quite massive enough to ignite nuclear fusion in their cores to shine as stars. In the early days of dark matter, it was quite reasonable to believe there could be an enormous amount of mass in the sum of these objects. Indeed, the mass spectrum of stars as then known (via the Salpeter IMF) diverged when extrapolated to the low masses of brown dwarfs. It appeared that there had to be lots of them, and their integrated mass could easily add up to lots and lots – potentially enough to be the dark matter.

The hypothesis of brown dwarf-like dark matter, dubbed MACHOs (MAssive Compact Halo Objects), was tested by a series of microlensing experiments. Remarkably, if you stare at the stars in the Large Magellanic Cloud long enough, you should occasionally witness a MACHO pass in front of one of them. You don’t see the MACHO directly, but you can see an enhancement to the brightness of the background star due to the gravitational lensing effect of the MACHO.

Long story short: microlensing events are observed, but not nearly enough are seen for the dark matter halo of the Milky Way to be composed of brown dwarf MACHOs. Nowadays we have a better handle on the stellar mass spectrum. Lots of brown dwarfs are indeed known, but nothing like the numbers necessary to compose the dark matter.

Many of us, including me, never gave MACHOs much of a chance. In order to add up to the total mass density we need in dark matter cosmologically, we need an amount 5 or 6 times as great as the density allowed in baryons by Big Bang Nucleosynthesis. So MACHO dark matter would break some pretty fundamental theory after all.

The most popular hypothesis, then and now, is some form of non-baryonic dark matter. Most prominent among these are WIMPs (Weakly Interacting Massive Particles). This is a valid, specific hypothesis that can be tested in the laboratory. Indeed, it has been. If the WIMP hypothesis were correct, we really should have detected them by now. It only persists because it is very flexible: we can keep adjusting the interaction cross-section to keep them invisible.

It would be a long post to revisit all the ways in which the WIMP hypothesis has repeatedly disappointed. Here I’d like to point out merely that WIMPs are hypothetical particles that exist in a hypothetical supersymmetric sector. There are compelling theoretical arguments in favor of supersymmetry, but so far it too has repeatedly disappointed. Anybody else remember how the decay of the Bs meson was suppose to be the Golden Test of supersymmetry? No? Nobody seems to talk about it anymore because it flunked badly. So supersymmetry itself is in dire shape. No supersymmetry, no WIMPs.

Like WIMPs, supersymmetry can be made more complicated to avoid falsification. This allows it to persist, but it is not the sign of a healthy theory. Still, everybody seems to agree that it is a theory, and most people seem to think it is a good one.

Unlike MACHOs, WIMPs do require a fundamentally new theory. Supersymmetry is not a part of the highly successful Standard Model of particle physics. It is a hypothetical extension thereof. So they aren’t really as conservative as just saying there is some unseen mass. There have to be invisible particles that reside in an entirely novel and itself hypothetical dark sector. That they have never been detected in the laboratory, and so far we have zero laboratory evidence to support the existence of the supersymmetric sector in which they reside, despite enormous (and expensive) effort (e.g., the LHC), might strike some as cause for concern.

So why do WIMPs persist? Time lag and training. If you are an astronomer, you don’t really care what the dark matter particle is, just that it is there. You are unlikely to keep close tabs on the tribulations of dark matter detection experiments. If you are an astroparticle physicist, dark matter particles are your bread and butter. We all know the Standard Model is incomplete; surely the dark matter problem is just a sign of that. Suggesting that the problem might instead be with gravity is to admit that the entire field is an oxymoron. Yes, we need new physics. But that would be the wrong kind of new physics!

winnie-the-pooh-balloon-bees

The MOND hypothesis is an example of the wrong kind of new physics. No new particles; rather, new dynamics. The idea is to tweak the force law below a critical acceleration scale (of order 1 Å/s/s). Intriguingly, this can be interpreted as either a modification of gravity (which gets stronger) or of inertia (which gets less, so particles become easier to push around).

From such a hypothesis, one must construct a proper theory – whatever that is. One thing is for sure – the motivation is the opposite of supersymmetry. Supersymmetry is motivated by theory. It is a Good Idea that therefore ought to be true, even if it appears that Nature declined to implement it. MOND has no compelling theoretical motivation or basis. (Who ordered that?) Rather, it is empirically motivated. It started by seeking a possible explanation for a particular observation: the apparent flatness of spiral galaxy rotation curves. In this regard, it could be considered an effective theory, though it does have strong implications for what the underlying cause is.

The original (1983) MOND formula did not conserve energy or momentum. That’s not a property of a healthy theory. Some people seem to think it is still stuck there.

The first step towards building a proper theory was taken by Bekenstein and Milgrom in 1984 with AQUAL. They introduced an aquadratic Lagrangian that led to a modified Poisson equation, a form of modified gravity. Being derived form a Lagrangian, it automatically satisfies the conservation laws.

Since then, a variety of MOND theories have been posited. By this, I mean distinct theories that lead to the hypothesized behavior at low acceleration. These may be modifications of either gravity or inertia, and can lead to subtly different higher order predictions.

So far most MOND theories are extensions of Newtonian dynamics. MOND always contains Newton in the high acceleration limit, just as General Relativity contains Newton in the appropriate limit. The trick is to write a theory that does both. That’s the theoretical Holy Grail.

The following Venn diagram might help:

GravityTheoryVennDiagram

Both MOND and General Relativity encompass Newtonian dynamics. However, they do not contain each other. Since General Relativity came first, I think when people say MOND is not a theory they usually mean that it doesn’t capture all the previous theory that it needs to. We know General Relativity is correct – so far as we have tested it – so it doesn’t suffice to write down a theory that is merely an extension of Newton. We need a theory that does both – the Holy Grail.

Of course I agree that we want to have it all. I also think it is appropriate to take one step at a time. If Newtonian dynamics is in itself a valid theory – and I think it is – then so too is MOND, as it contains all of Newton in the appropriate limit. MOND is an incomplete theory, but it is certainly a theory.

For many years, an argument against MOND was that Bekenstein had sought the Holy Grail long and hard without success. Bekenstein was really smart, implying that if he couldn’t do it, it couldn’t be done.  In 2004, Bekenstein published TeVeS (for Tensor-Vector-Scalar), the first example of a theory that contained both General Relativity and MOND without obviously having some dreadful failing, like ghosts. The argument then became that TeVeS was inelegant.

It is not clear that TeVeS is the correct generalized version of General Relativity. Indeed, it is not the only such theory possible. Hence the question mark in the Venn diagram. If we falsify TeVeS, it doesn’t falsify the MOND hypothesis – that would be like saying Newton is wrong because Yilmaz gravity isn’t the right version of general relativity. There are many such theories that are possible; TeVeS is just one particular realization thereof.

What theory the question mark in the Venn diagram represents is what we should be trying to figure out. Unfortunately, most scientists interested in the subject are not trained nor equipped to do this sort of work, and for the most part are conditioned to be actively hostile to the project. That’s the wrong kind of new physics!

I find this a strange attitude. We all know that, as yet, there is no widely accepted theory of quantum theory. In this regard, General Relativity is itself incomplete. It is a noble endeavor to seek a quantum theory of gravity. How can we be sure that there is no intermediate step? Perhaps some of the difficulty in getting there stems from playing with an incomplete deck. I sometimes wonder if some string theorist has already come up with the correct theory but discarded it because it predicted this crazy low acceleration behavior he didn’t know might actually be desirable.

Whatever the final theory may be, be it dark matter based or a modification of dynamics, it must explain the empirical phenomena we observe. An enormous amount of galaxy phenomenology can be put down to one simple fact: galaxies behave as if MOND is the effective force law. We can write down a single formula that describes the dynamics of hundreds of measured galaxies and has had tremendous predictive success. If you don’t find that compelling, your physical intuition needs a check up.

What is empirical?

What is empirical?

I find that my scientific colleagues have a variety of attitudes about what counts as a theory. Some of the differences amount to different standards. Others are simply misconceptions about specific theories. This comes up a lot in discussions of MOND. Before we go there, we need to establish some essentials.

What is empirical?

I consider myself to be a very empirically-minded scientist. To me, what is empirical is what the data show.

Hmm. What are data? The results of experiments or observations of the natural world. To give a relevant example, here are some long slit observations of a low surface brightness galaxies (from McGaugh, Rubin, & de Blok 2001).

fig1

What you see are spectra obtained with the Kitt Peak 4m telescope. Spectra run from blue to red from left to right while the vertical axis is position along the slit. Vertical bars are emission lines in the night sky. The horizontal grey stuff is the continuum emission from stars in each galaxy (typically very weak in low surface brightness galaxies). You also see blobby dark bars running more or less up and down, but with an S-shaped bend. These are emission lines of hydrogen (the brightest one), nitrogen (on either side of hydrogen) and sulfur [towards the right edge of (a) and (d)].

I chose this example because you can see the rotation curves of these galaxies by eye directly in the raw data. Night sky lines provide an effective wavelength calibration; you can see one side of each galaxy is redshifted by a greater amount than the other: one side is approaching, the other receding relative to the Hubble flow velocity of the center of each galaxy. With little effort, you can also see the flat part of each rotation curve (Vf) and the entire shape V(R)*sin(i) [these are raw data, not corrected for inclination. You can even see a common hazard to real world data in the cosmic ray that struck near then end of the Hα line in (f)].

Data like these lead to rotation curves like these (from the same paper):

fig3

These rotation curves were measured by Vera Rubin. Vera loved to measure. She liked nothing better than to delve into the data to see what they said. She was very good at it.

Some of these data are good. Some are not. Some galaxies are symmetric (filled and open symbols represent approaching and receding sides), others are not. This is what the real world of galaxy data looks like. With practice, one develops a good intuition for what data are trustworthy and which are not.

To get from the data to these rotation curves, we correct for known effects: the expansion of the universe (which stretches the redshifts by 1+z), the inclination of each galaxy (estimated in this case by the axis ratios of the images), and most importantly, assuming the Doppler effect holds. That is, we make use of the well known relation between wavelength and speed to turn the measured wavelengths of the Hα and other emission lines into velocities. We use the distance to each galaxy (estimated from the Hubble Law) to convert measured position along the slit into physical radius.

This is empirical. Empirical results are as close to the data as possible. Here we make use of two other empirical results, the Doppler effect and the Hubble Law. So there is more to it than just the raw (or even processed) data; we are also making use of previously established facts.

An example of a new empirical fact obtained from data like these is the Baryonic Tully-Fisher relation. This is a plot of the observed baryonic mass in a galaxy (the sum of stars and gas) against the amplitude of flat rotation (Vf).

BTF_LR_TEDxCLE

Here one must utilize some other information to estimate the mass-to-light ratio of the stars. This is an additional step; how we go about it affects the details of the result but not the basic empirical fact that the relation exists.

It is important distinguish between the empirical relation as plotted above, and a function that might be fit to it. The above data are well fit by the formula

Mb = 50 Vf4

with mass measured in solar masses and rotation speed in kilometers per second. The fit is merely a convenient representation of the data. The data themselves are the empirical result.

In this case, the scatter in the data is consistent with what you’d expect for the size of the error bars. The observed relation is consistent with one that has zero intrinsic scatter – a true line. The reason for that might be that it is imposed by some underlying theory (e.g., MOND). Whether MOND is the reason for the Baryonic Tully-Fisher relation is something that can be debated. That the relation exists as an empirical result that must be explained by any theory that attempts to explain the mass discrepancy problem in galaxies cannot.

I would hope it is obvious that theory should explain data. In the context of the mass discrepancy problem, the Baryonic Tully-Fisher relation is one fact that needs to be explained. There are many others. Which interpretation we are driven towards depends a great deal on how we weigh the facts. How important is this particular fact in the context of all others?

I find that many scientists confuse the empirical Baryonic Tully-Fisher relation with the theory MOND. Yes, MOND predicts a Baryonic Tully-Fisher relation, but they are not the same thing. The one we observe is consistent with MOND. It need not be (and is not for some implausible but justifiable assumptions about the stellar mass-to-light ratio). The mistake I see many people make – often reputable, intelligent scientists – is to conflate data with theory. A common line of reasoning seems to be “These data support MOND. But we know MOND is wrong for other reasons. Therefore these data are wrong.” This is a logical fallacy.

More generally, it is OK to incorporate well established results (like the Doppler effect) into new empirical results so long as we are careful to keep track of the entire line of reasoning and are willing to re-examine all the assumptions. In the example of the Baryonic Tully-Fisher relation, the critical assumption is the mass-to-light ratio of the stars. That has minor effects: mostly it just tweaks the slope of the line you fit to the data.

If instead we have reason to doubt the applicability of something deeper, like the applicability of the Doppler formula to galaxies, that would open a giant can of worms: a lot more than the Tully-Fisher relation would be wrong. For this reason, scientists are usually very impatient with challenges to well established results (who hasn’t received email asserting “Einstein was wrong!”?) To many, MOND seems to be in this category.

Consequently, many scientists are quick to dismiss MOND without serious thought. I did, initially. But eventually it had enough predictions come true that I felt compelled to check. (Bekenstein pointed out a long time ago that MOND has had many more predictions come true than General Relativity had had at the time of its widespread acceptance.) When I checked, I found that the incorrect assumption I had made was that MOND could so lightly be dismissed. In my experience since then, most of the people arguing against MOND haven’t bothered to check their facts (surely it can’t be true!), or have chosen to selectively weigh most those that agree with their preconception of what the result should be. If the first thing someone mentions in this context is the Bullet cluster, they are probably guilty of both these things, as this has become the go-to excuse not to have to think too hard about the subject. Cognitive dissonance is rife.

 

Structure Formation Mythology

Do not be too proud of this technological terror you’ve constructed. The ability to simulate the formation of large scale structure is insignificant next to the power of the Force.

– Darth Vader, Lord of the Sith

The now standard cosmology, ΛCDM, has a well developed cosmogony that provides a satisfactory explanation of the formation of large scale structure in the universe. It provides a good fit to both the galaxy power spectrum at low redshift and that of the cosmic microwave background (CMB) at z=1080. This has led to a common misconception among cosmologists that this is only way it can be.

The problem is this: the early universe was essentially homogeneous, while the current universe is not. At the time of recombination, one patch of plasma had the same temperature and density as the next patch to 1 part in 100,000. Look around at the universe now, and you see something very different: galaxies strung along a vast web characterized chiefly by empty space and enormous voids. Trouble is, you can’t get here from there.

Gravity will form structure, making the over-dense patches grow ever denser, in a classic case of the rich getting richer. But gravity is extraordinarily weak. There simply is not enough time in the ~13 Gyr age of the universe for it to make the tiny density variation observed in the CMB into the rich amount of structure observed today.

We need something to goose the process. This is where non-baryonic cold dark matter (CDM) comes in. It outweighs the normal matter, and does not interact with the photons of the CMB. This latter part is critical, as the baryons are strongly coupled to the photons, which don’t let them clump up enough early on. The CDM can. So it starts to form structure early which the baryons subsequently trace. Since structure formed, CDM must exist.

This is a sound line of reasoning. It convinced many of us, including myself, that there had to be some form of non-baryonic mass made of some particle outside the standard model of particle physics. The other key fact was that the gravitating mass density was inferred to outweigh the amount of baryons indicated by Big Bang Nucleosynthesis (Ωm ≫ Ωb).

Does anyone spot the problem with this line of thinking?

It took me a long time to realize what it was. Both the structure formation argument and the apparent fact that Ωm ≫ Ωb implicitly assume that gravity is normal. All we need to know to approach either problem is what Newton and Einstein taught us. Once we make that assumption, we are absolutely locked into the line of reasoning that leads us to CDM.

I worry that CDM is a modern æther. Given our present understanding of physics, it has to exist. In the nineteenth century, so too did æther. Had to. Only problem was, it didn’t.

If, for a moment, we let go of our implicit assumption, then we may realize that what structure formation needs is an extra push (or pull, to make overdensities collapse faster). That extra push may come from CDM, or it may come from an increase in the strength of the effective force law. Rather than being absolute proof of the existence of CDM, the rapid formation of structure might also be another indication that we need to tweak for force law.

I have previously outlined how structure might form in a modified force law like MOND. Early efforts do not provide as good a fit to the power spectrum as ΛCDM. But they provide a much better approximation than did the predecessor of ΛCDM, SCDM.

Indeed, there have been some striking predictive successes. As we probe to ever higher redshift, we see time and again more structure than had been anticipated by ΛCDM. Galaxies form early in MOND, so this is quite natural. So too does the cosmic web, which I predict to be more developed in MOND at redshifts of 3 and even 5. By low redshift, MOND does a much better job of emptying out the voids than does ΛCDM. Ultimately, I expect we may get a test from 21 cm reverberation mapping in the dark ages, where I predict we may find evidence of strong baryonic oscillations. (These predictions were made, and published in refereed journals, in the previous millennium.)

I would not claim that MOND provides a satisfactory description of large scale structure. The subject requires a lot more work.  Structure formation in MOND is highly non-linear. It is a tougher problem than standard perturbation theory. Yet we have lavished tens of thousands of person-years of effort on ΛCDM, and virtually no effort on the harder problem in the case of MOND. Having failed to make an effort does not suffice as evidence.