MOND, Dark Matter, and more technical discussion than you'd probably like

I’ve written a number of posts about the observational evidence behind dark matter. In yesterday’s io9, Alasdair Wilkins wrote a provocative story about an interesting paper by University of Maryland Astronomer Stacy McGaugh. The paper is a study of 47 gas rich galaxies, in which the rotation curves and gas masses are estimated. Stacy shows the relationship between rotational velocity and baryonic (ordinary) mass is exactly what a simple MOND calculation (without dark matter) would predict:
$M_bpropto V_f^4$
and, he argues, standard general relativity using dark matter, fits quite badly.

Alasdair cited my previous article, and I was delighted to get an email from Stacy arguing the merits of MOND. As the discussion has gotten rather lengthy and very technical, I decided to post it all here. Blockquoted text represents an email either to me or from me, while comments outside the quotes are simply my own commentary. Stacy McGaugh is aware of this page, and has given his permission to quote our discussion. I’ve done minimal editing, except for formatting and addition of a few potentially helpful links.

2/25/2011
9:00am
From: Stacy McGaugh
To: Dave Goldberg

Hello,

Someone pointed out to me your postings on io9 where you lay out some of the evidence for dark matter. Of course, I was hung up on that for a long time myself – when the first prediction of MOND came true in my data, I was very angry. How could this stupid theory get any prediction right when there was so much evidence for dark matter? It took me a long time to realize that this was an epistomological problem. Most of this evidence does not distinguish between dark matter or a failing of the equations from which we infer its existence.

I agree that it is a tall order to build a generally covariant theory with MOND in the appropriate limit. However, there is nothing in MOND that contradicts anything we actually test about GR, so saying that GR works provides no constraint whatsoever on the viability of MODN. At the same time, many of us assume that there must be some grander theory of everything that unites gravity with the other fundamental forces. So which is it: is GR inviolate and we can’t imagine expanding on it [so by extension, we should see no mond, hear no mond, speak no mond] or must there necessarily be something beyond GR that makes gravity a quantum theory?

2/25/2011
5:15 pm
From: Dave Goldberg
To: Stacy McGaugh

Dear Stacy,

I wanted to take a look at your paper before responding. It really is a very nice piece of work. But there are still a number of things that trouble me.

First, you point out in your email (rightly) that gravity and the other forces need to be unified, and so in that sense GR _must_ be incorrect. This is true, but it’s a problem that plagues all low-energy theories. For example, atomic physics does an outstanding job of understanding atoms while all the while pretending (incorrectly) that protons and neutrons are fundamental particles. Under normal energy conditions, the quark nature of matter simply doesn’t apply. Chemistry is another level of remove entirely, and the nuclei of atoms can be considered fundamental. The known problems facing GR are at the very high energy scale. It is, of course, possible that GR has more than flaw, one at the Planck scale, and one at the 1.2e-10 m/s2 scale (which is extremely low energy).

But MOND, as you well know (and cite), is not, itself, a covariant, geometric theory of gravity. It is _a_ low-energy limit of TeVeS. When I say “_a_ limit”, what I mean is that there are a number of tunable parameters in TeVeS, and one of those degrees of freedom finds expression in the MOND a_0 parameter, which could be measured experimentally. MOND, by this standard, can really only be probed on a relatively small range. GR, on the other hand (which has essentially only two free parameters: Newton’s constant and a Cosmological constant), can be directly investigated from earth and solar system scales (on which it has passed with flying colors) to galaxy and cluster scales (lensing and rotation curves) to cosmological scales in the measurement of Type Ia supernovae the CMB. Observations generate some rather unfortunate side-effects: dark matter and dark energy, which is, of course, what prompt the search for alternate theories of gravity in the first place. However, what attracts me to GR is that dark matter and energy, whatever their other flaws, are measured consistently on all scales.

I hasten to point out that while we get consistent pictures of DM on all scales, this not to say that all systems have an equal mix of DM and baryonic matter. While I am very impressed with fit that you get for MOND in figure 2, I would not concede that the Lambda CDM model has been fairly tested. It is not obvious to me (or to simulations) that our understanding of galaxy formation is sufficient to simply plug in a constant value of f_b, nor that that value should be the universal baryon ratio. Galaxies differ dramatically based on their history, and this would certainly affect the slope, as well as the normalization of such a curve.

If your question to me is “what would it take to convince you that MOND was correct,” I would respond:

Continued failure of supersymmetry detection at the LHC and elsewhere, and failure to detect dark matter directly in particle detectors.
Predictions from TeVeS which have “natural” values of free parameters, and are shown to produce at least as good of fits as DM/GR models not only to rotation curves, but also to lens mass measurements, time delays, power spectrum evolution, baryonic wiggles, and CMB measurements.

In the absence of that, I feel that the weight of the evidence still falls on the side of GR+DM+DE.

Sincerely,

Dave

2/26/2011
10:30am
From: Stacy McGaugh
To: Dave Goldberg

Thanks [again] for your detailed and thoughtful reply. Hopefully I am clear-headed enough this morning to make a worthy attempt at a reply. If you wish to post this thread to your blog, you have my blessing. Much of the best of the history of science is encapsulated in correspondence between scientists. Not that I mean to imply that our discussion rises to that level, but people don’t write letters any more so this form of the historical record may other wise be lost. If we can make it accessible to the public through the internet, so much the better.

Let me respond to each of the point you raise as you raise them below.

Dear Stacy,

I wanted to take a look at your paper before responding. It really is a very nice piece of work. But there are still a number of things that trouble me.

Just a few? My mind has been in turmoil over these issues for over 15 years now!

First, you point out in your email (rightly) that gravity and the other forces need to be unified, and so in that sense GR _must_ be incorrect. This is true, but it’s a problem that plagues all low-energy theories. For example, atomic physics does an outstanding job of understanding atoms while all the while pretending (incorrectly) that protons and neutrons are fundamental particles. Under normal energy conditions, the quark nature of matter simply doesn’t apply. Chemistry is another level of remove entirely, and the nuclei of atoms can be considered fundamental. The known problems facing GR are at the very high energy scale. It is, of course, possible that GR has more than flaw, one at the Planck scale, and one at the 1.2e-10 m/s² scale (which is extremely low energy).

Sure. I usually hear this phrased in terms of size scales: qunatum effects are on tiny scales where as MOND/dark energy are on huge scales: hence nothing to do with the quantum theory of gravity. Maybe this is so, but 1/(small scale) is a big scale, so it is not obvious to me that these are inevitably separate effects (very low and very high energy). I agree that this is the natural assumption, but we don’t really know the consequences of a quantum theory of gravity until we have it. So my only really point is that surprises can happen, and we should not be so bold as to presume that the obvious assumption will in the end hold.

Indeed, if MOND expresses some important aspect of a deeper truth, then those theorists trying to unite the fundamental forces are playing without a full deck. For all I know, MONDian behavior falls naturally out of some subset of string theory (or branes, or whatever the theoretical flavor du jour is) but the people who work on such things immediately dismiss those solutions as obviously wrong simply because they’re unaware that such behavior might be a good thing.

I doubt it. But just because it seems unlikely to me doesn’t guarantee it cannot be so.

But MOND, as you well know (and cite), is not, itself, a covariant, geometric theory of gravity. It is _a_ low-energy limit of TeVeS. When I say “_a_ limit”, what I mean is that there are a number of tunable parameters in TeVeS, and one of those degrees of freedom finds expression in the MOND a_0 parameter, which could be measured experimentally. MOND, by this standard, can really only be probed on a relatively small range. GR, on the other hand (which has essentially only two free parameters: Newton’s constant and a Cosmological constant), can be directly investigated from earth and solar system scales (on which it has passed with flying colors) to galaxy and cluster scales (lensing and rotation curves) to cosmological scales in the measurement of Type Ia supernovae the CMB. Observations generate some rather unfortunate side-effects: dark matter and dark energy, which is, of course, what prompt the search for alternate theories of gravity in the first place. However, what attracts me to GR is that dark matter and energy, whatever their other flaws, are measured consistently on all scales.

OK. There are many issues to address here. Certainly MOND is not a generally covariant theory. For it to be integrated into our wider understanding, it needs to represent the appropriate limit of some more general theory, TeVeS being a possible example. And of course whatever that is should hopefully be unifiable with the quantum realm, just as we hope, so far in vain, that GR ought to be.

I don’t think it is fair to characterize MOND as a low energy limit of TeVeS. That may be true, but it is not the only possibility nor is it the historical order of events. Rather, I would say that TeVeS is an early attempt to incorporate MOND into a generally covariant framework.

It is written in considerable generality, which has the unfortunate side effect of giving it a number of free parameters that are not native to the simple one-scale (a0) modification of MOND. Maybe the right version of TeVeS can be considerably simplified (Einstein-Aether theories are an example of a family of theories that live within the larger set of possibilities that TeVes can encompass). Or maybe there is still some other theory to be developed (Milgrom has recently posited a bimetric form of covariant MOND). I take a long view of this – we do not call the Poisson Equation the Newton Equation, nor the Robertson-Walker metric the Einstein metric. It takes time and brains – a lot of both – to sort these things out. Indeed, for the longest time, people told me “Bekenstein is really smart, and he hasn’t been able to make MOND into a relativistic theory, therefore it is impossible.” That was the refrain for 20 years, until Bekenstein introduced TeVeS. Now the refrain is “TeVeS is ugly.” Maybe so. Maybe turning MOND into a “proper” theory is an impossible task. Or maybe the “right” theory looks rather different from TeVeS. At least Bekenstein is trying.

I am not impressed by the argument that MOND can only be tested over a small range, whereas GR thrives over a large one. I think we are agreed that whatever theory is correct has to reproduce the known successes of GR. MOND doesn’t contradict those, though as we’ve already discussed at length, it is not obvious what the correct generally covariant theory is. Certainly TeVeS does what GR does where it is well tested – one throws out theories that don’t do that.

It is true, as you say that MONDian behavior only occurs over a modest dynamic range – accelerations < a0. Reliable data probe down to 0.1 a0; a bit lower in some cases. But that is also the range over which dark matter exists. So it suffers the same lack of dynamic range. At least in MOND there is a clear boundary where you do and don't deviate from Newtonian behavior. Dense systems (with a > a0) should so no evidence of mass discrepancies in MOND, and they don’t. It is not obvious that this should be the case with dark matter. Why don’t globular clusters have dark matter? Baryonic physics, you say. But the Jeans scale after recombination would make globular clusters the obvious first thing to form in the first minihalos. And they have the right ages. Yet that have no dark matter. Why not? Why not some dark matter in the solar system? Why, in essence, is dark matter only inferred to exist in systems with a < a0? OK, in rich clusters of galaxies the mass discrepancy kicks in around 2*a0. I'm old enough to remember when cosmologists would be ecstatic to come within a factor of two of something. Heck, I'm still happy if I can fit an NFW halo to and LSB galaxy rotation curve and have it come within a factor of two of what LCDM predicts for a concentration. But to return to your point about dynamic range: the lack of evidence for dark matter in systems with a -> a0 is a strange lacking in dynamic range. Why no dark matter much above this scale? Why does the amount of dark matter scale as a0/a for a < a0? That's an empirical fact that has no natural explanation in our conventional picture.

He also promises more later. In particular, I am eager to see his response to my comments regarding using a constant dark matter/baryon density in galaxies.

I will comment, briefly, on one of the objections he raises. He asks why there isn’t any dark matter in globulars or in the solar system. I will speak to the solar system, in particular, because we can do the calculation in some detail. Using a circular velocity of about 250 km/s (and I’ve seen recent estimates that put it a bit higher), and a distance from the center of the galaxy at about 8kpc, the density interior to the solar radius is about:
$rhosimeq 3.6times 10^{-21}kg/m^3$
This is roughly a million times the density of space generally, but it’s still very, very empty. Alternately, we can express the density of DM as:
$rhosimeq 0.05 M_odot/pc^3$
And thus the contribution of dark matter to a $10^5M_odot$ , several parsec globular cluster will be less than a hundredth of a per cent.

In the solar system, the effect is even smaller. Even within the radius of Neptune is somewhere along the lines of
$M_{DM,< Neptune}simeq 7times 10^{-13}M_odot [/latex] Dark matter can't collapse. It is dissipationless, so within galaxies it has an approximately isothermal radial profile and not much structure otherwise. In other words, it's not that dark matter doesn't exist in the solar system or in globulars, it's just that space is generally so empty that the additional mass really doesn't count for much on those scales. 2/26/2011 4:40pmm From: Stacy McGaugh To: Dave Goldberg <blockquote> Right. Where were we? <blockquote> But MOND, as you well know (and cite), is not, itself, a covariant, geometric theory of gravity. It is _a_ low-energy limit of TeVeS. When I say ``_a_ limit'', what I mean is that there are a number of tunable parameters in TeVeS, and one of those degrees of freedom finds expression in the MOND a_0 parameter, which could be measured experimentally. MOND, by this standard, can really only be probed on a relatively small range. GR, on the other hand (which has essentially only two free parameters: Newton's constant and a Cosmological constant), can be directly investigated from earth and solar system scales (on which it has passed with flying colors) to galaxy and cluster scales (lensing and rotation curves) to cosmological scales in the measurement of Type Ia supernovae the CMB. Observations generate some rather unfortunate side-effects: dark matter and dark energy, which is, of course, what prompt the search for alternate theories of gravity in the first place. However, what attracts me to GR is that dark matter and energy, whatever their other flaws, are measured consistently on all scales. </blockquote> OK. I would agree that GR passes solar system tests with flying colors. And the binary pulsar. Galaxy and cluster scales (lensing and rotation curves) to cosmological scales I do not agree with. We can fit those things only by invoking dark matter and dark energy. Taken at face value, Newton/GR obviously fail the test of rotation curves and gravitational lensing. That's why we invented dark matter. It is entirely circular to claim this as a success. One might put it another way: GR requires dark matter to remain viable. Not just some ordinary matter that would help fill out the census of big bang nucleosynthesis. No, we need an entirely new form of mass in non-baryonic dark matter composed of some as yet unidentified new form of subatomic particle. Our best guess is that these are WIMPS, but we really don't know what it is. We just know it has to outweigh baryons by a factor of ~5, and can't interact with them too strongly or we would have detected them by now. We act like we're sure this stuff exists, but we merely infer its existence from the failure of GR to fit rotation curves etc. without it. I guess I want a higher standard of proof: I want to see bonafide laboratory detections. Until we have those, I don't see how we can claim to know dark matter exists. To back up a bit, I accepted the reasoning for non-baryonic cold dark matter as much as any one, and for long believed it as much as any one. The arguments that I found most persuasive were the mismatch of dynamical mass and baryonic mass from BBN (Om >> Ob) and the growth of structure - you can't get to the lumpy universe of the present day from the smooth initial condition seen in the CMB without somehow amplifying the growth rate of density perturbations. Either one of these, on their own, is a powerful argument. Together they seemed to absolutely require CDM, so I believed it. So, as I said before, I was really angry when MOND's predictions cam true in my data for LSB galaxies. How could this happen? But after a while, I decided that if a theory had its predictions come true, I was obliged to pay it due respect. So I started looking at other data, seeking (ever more desperately) for a reason NOT to believe MOND. I found lots of claims to have falsified MOND, but few of them withstood scrutiny. The authors of many of these studies seemed to be willing themselves to find fault with MOND in spite of their own data. Something just weren't right. (I wrote this up in a series of papers in the ApJ in 1998.) But what about cosmology? To be sure, MOND by itself gives no satisfactory cosmology. [Given the history of the subject, I'm not sure that's a bad thing - are we really the first generation to finally get it right? Or just the most recent to be sure we had?] However, MOND contradicts nothing that we know empirically about cosmology (Hubble expansion, BBN, CMB). And, to my shock and lasting chagrin, I realized it was a possible loophole in the seemingly iron clad reasoning that led us to believe in CDM. Om > Ob we infer by measuring Om through gravitational effects. If one attempts this with MOND, one finds Om ~ Ob (I did this in '98). For structure formation, we need to speed up the growth of density fluctuations. Conventionally, we invoke dark matter that doesn't interact with photons so it can clump up early without leaving too much of an imprint on the CMB. In a theory like MOND, you've made the long range force law stronger, so fluctuations mat start small by they grow faster than the d ~ a we'd predict conventionally. Without CDM, fluctutation growth would initially be suppressed in MOND, but MOND is inherently non-linear, so once things get into the MOND regime, structure formation should really take off. There is no guarantee that this will work out in detail, but that has yet to be tested. I would predict that MOND forms structre fast after a slow start, so that L* galaxies would already by forming by z ~ 10, big clusters might be in place at z ~ 3, and the cosmic web of large scale structure should already be emerging, voids, filaments, and all, at z ~4 or 5. That's not the same as LCDM, at least as it stands now. For now, the real point is that the same arguments that lead us to CDM might just as well point to MOND. I do agree that dark matter and dark energy are measured consistently by many different methods. These all point to the same region in OL-Om-H0 space. [I have my students extract from the literature lots constraints of on these every time I teach cosmology.] This didn't have to work out. One might hope that by now, if LCDM were wrong, we would have excluded all possible parameter combinations. We certainly have excluded a lot (remember standard CDM before it transmorgrified into standard LambdaCDM?) So I do take this consitency seriously. Indeed, I would say that on the scales of systems > 1,000 km/s (clusters, LSS, all the probes of the metric) the universe does indeed look like LCDM. But on scales < 300 km/s, it looks a lot more like MOND. If we're going to contemplate a fundamental revision of theory as prompted by MOND (and I think that is what people are truly uncomfortable with), then what does cosmology look like? I don't know. But I do know that it has to look like GR in the appropriate limit, which as we discussed above, is very broad. So perhaps the "right" metric in our hypothetical greater theroy is very close to the standard Robertson-Walker metric. Presumably there would be some difference, but how would this manifest itself? Perhaps by driving us into a crazy corner of parameter space where we have to reinvent the cosmological constant? Once we've done that, I'd expect to keep getting the same answer every time we pose the question: "what value of Lambda do the data want?" It becomes a matter of pounding the square peg into the round hole. Sure it'll work if you pound hard enough, but does a universe with OL = 0.7 really look right to you? Certainly a universe with MOND doesn't look right! but is Lambda really preferable or simply more familiar? <blockquote>I hasten to point out that while we get consistent pictures of DM on all scales, this not to say that all systems have an equal mix of DM and baryonic matter. While I am very impressed with fit that you get for MOND in figure 2, I would not concede that the Lambda CDM model has been fairly tested. It is not obvious to me (or to simulations) that our understanding of galaxy formation is sufficient to simply plug in a constant value of f_b, nor that that value should be the universal baryon ratio. Galaxies differ dramatically based on their history, and this would certainly affect the slope, as well as the normalization of such a curve. </blockquote> Ah, the particulars of LCDM. In the submitted version of this Letter, I studiously avoided all mention of LCDM. It was simply: here is a hypothesis (MOND) that makes a prediction we can now test cleanly, and gee, it works. However, I'm sure you've experienced the peer review process, and the referees (there were two, in parallel) asked, quite reasonably, what LCDM predicts. Well, nothing specific is the short answer. There are lots and lots of models in the literature, none of which are entirely consistent with the data (though some recent ones come close), and none with each other (hardly encouraging for repeatability). I certainly agree that the baryon fraction of cosmic structures doesn't have to be a constant - I wrote a whole ‘nother paper on exactly this point a year ago [I always publish the conventional analysis first]. However, it is a pretty darn obvious place to start (see, e.g., Mo, Mao, & White 1998). From this I made what I consider a simple, generic point: sure, you could build a model to match the data - any competent theorist can do that much - but it must inevitably be fine-tuned because there aint no scatter in the observed relation. How can we expect for each halo to ``know'' exactly what fraction of baryons it is supposed to render visible so as to fall on the baryonic TF relation with zero intrinsic scatter? Does that not strike you as a fine-tuning problem? How seriously you consider this depends entirely on how seriously you take fine tuning problems. A lot of cosmologists I've talked with seem unfazed by them. But what could be worse? Once we've convinced ourselves that the universe is full of some invisible, untoucahble mass, how do we disabuse ourselves of this notion should it happen to be incorrect? Does the notion of dark matter constitute a falsifiable scientific hypothesis? If so, how would we go about it? We could confirm the existence of dark matter (or at least WIMPs) through direct detection experiments. But if these continue to come up empty? Do we say ``oh, it aint there!'' or do we just move the goal post by twiddling the dark matter model to reduce the interaction cross section to safely unobservable levels? The fine-tuning is much worse than people seem to appreciate. It is well established that MOND fits rotation curves well, and I often hear the dismissive statements to the effect of ``that's all it does.'' That's not actually true, and I suspect the people who say this haven't bothered learning much about it. But lets just take this one apparent fact: MOND provides a simply formula that maps between what Newton predicts for just the observed stars and gas and the observed rotation curve. It is the effective force law in galaxies. I say effective, because I am open to other explanations for why this happens - but there does nees to be a good one! But where have I heard this before… Oh yeah, this guy Newton said everything happens as if F ~ Mm/d2: a simple formula to map between what you see and what you get. He said HAPPENS AS IF not MUST BE - remember, at that time, people were perturbed by how you could have action at a distance at all. Yet this simple formula suffices to explain (and predict) just about everything in the solar system (the precession of the perihelion of Mercury being the subtle but crucial exception). So suppose I was trying to tell you that really the solar system runs on an inverse cube force law. It just looks like it is inverse square because there is dark matter arranged just so as to always make it look that way. Where do you tell me to get off? <blockquote> If your question to me is ``what would it take to convince you that MOND was correct,'' I would respond: 1. Continued failure of supersymmetry detection at the LHC and elsewhere, and failure to detect dark matter directly in particle detectors. </blockquote> For how long? When do we say enough is enough? I would prefer to believe in the conventional cosmology - after all these years, it is still more familiar to me, and I have a very well developed intuition for dark matter that becomes useless if MOND is right. But what is convenient for us has no bearing on how the universe works. So I guess I expect a higher standard - to convince me that dark matter is correct, I want to see multiple independent experimental detections of WIMPs. A plauisble explanation for MONDian phenomenology would also be nice - most of the literature on this point can be summarized as ``We're sure LCDM is right, so surely it must work out!'' <blockquote> 2. Predictions from TeVeS which have ``natural'' values of free parameters, and are shown to produce at least as good of fits as DM/GR models not only to rotation curves, but also to lens mass measurements, time delays, power spectrum evolution, baryonic wiggles, and CMB measurements. </blockquote> Fair enough - if we are going to hypothesize a new force law, it has to work everywhere all the time. Personally, I myself remain more comfortable with the conventional dark cosmology. That's what I grew up with. But I don't think the Universe is overly concerned with where our comfort zones are. Even so, I think you may under-appreciate how much has already been done on exactly the things you cite. TeVeS was devised to do lensing - it automatically gives the same lensing signal as GR+dark matter for the DM distribution that matches what you need to get a MONDian fit. (Indeed, this was hard - getting lensing to even go in the right direction caused lots of potential theories to be thrown out before TeVeS.) I discussed power spectrum evolution a bit above. Here one must invoke the same lame excuse that LCDM invokes for galaxies: it is non-linear. I hear a lot that this means we could expect galaxies to do any damn thing in LCDM, which I think is a cop out. So I'm trying to do better with the power spectrum evolution. But it is a problem that is as hard and MOND as galaxy formation is in LCDM. (Still, some attempts have been made. For just one, see the 2002 ARA&A review I coautored with Sanders.) And as for the CMB - I am very well aware of that! Are you aware who correctly predicted the amplitude ratio of the first-to-second peak? Not fit it post facto - predicted it, a priori. </blockquote> There is a lot in here, to be sure, but the major argument points to the fact that GR and observations are not compatible without dark matter. And I absolutely agree with Stacy that we need to be looking for dark matter particles in a lab. However, the only experiment which seemed to have a real shot at probing that sector is the LHC, which has thus far only taken less than 0.1% of its total data. In this case, I'd say that we have not been looking long enough. A priori we would have expected it to be extremely tough to detect a <a href="http://en.wikipedia.org/wiki/Weakly_interacting_massive_particle">WIMP</a>, whether or not supersymmetry turns out to be correct. As a result, I would say it's staggeringly more likely that we simply have not detected the dark matter particle than that GR is wrong on scales much larger than the Planck scale. It is often portrayed as though we just throw dark matter into the equation wherever it is needed. However, that's simply not the case. The complete list of dark matter assumptions are these: <ol> <li>There is a relatively massive, neutral, stable particle which comprises something like 5 times the total mass of the baryonic material in the universe. <li>The initial distribution of these particles were adiabatic (which means that slightly overdense regions of photons and baryons also corresponded to slightly overdense regions of dark matter particles), and the power spectrum of perturbations is the tilted power law predicted by inflation. </ol> And that's it. Everything else: the flatness of the universe now, the ``baryonic wiggles'' in the power spectrum (which if we're pointing out what each of us predicted, I'd like to point out that I was among the first <a href="http://adsabs.harvard.edu/abs/1998ApJ...495...29G">to predict</a> would be <a href="http://adsabs.harvard.edu/abs/2010MNRAS.401.2148P">measured in the SDSS dataset</a>), the CMB spectrum, the age and evolution of the universe, and yes, the rotation curves of galaxies. It is a much simpler model than TeVeS, let alone MOND. MOND, itself, is insufficient for the task. Though it only introduces 1 additional parameter, it does not have the fundamental symmetries that make GR so pleasingly simple. TeVeS has many more free parameters. Stacy is right that TeVeS can be made to fit lensing. Of course it can. The tensor (Te) part of TeVeS essentially is GR. It would be surprising if it couldn't be made to fit observations. The question is whether there is any reason to suppose that the introduction of many free parameters is really fundamentally more elegant than introducing a particle that we simply haven't observed yet. I'd take it a step further. How does one account for systems like the <a href="http://en.wikipedia.org/wiki/Bullet_cluster">Bullet Cluster</a> (and there are now something like half a dozen similar systems) which show from lensing that the mass of the cluster is nowhere near the gas? As for questions about detailed predictions of rotation curves… Stacy is absolutely correct that numerical modeling doesn't provide a particularly good fit. The problem is that it is incredibly difficult to model the formation and evolution of a galaxy, and trying to do it in a cosmological context, doubly so. Though the a_0 parameter of MOND seems to fit the data well, it is worth remembering that MOND was initially introduced to deal with this exact problem. It is little surprise that it is able to fit rotation curves well. Stacy's objection seems to be that since we have not yet detected dark matter, MOND seems equally likely. I disagree, but applaud his own work. The difference is that we do not need to wait for experimental evidence to give greater support to MOND/TeVeS. The task is to provide the minimal invariant model that fits the data — all of the data, self-consistently — as well as dark matter+dark energy+DM does. At that point, tell us how many additional parameters needed to be included. We can then debate which way Occam's razor slices. 2/27/2011 6:33am From: Dave Goldberg To: Stacy McGaugh <blockquote> Hi Stacy, You've certainly given me, and my readers, a lot to think about. I've posted your emails, and a few quick follow-ups, on my blog. I may send a bit more, but I wanted to address one issue directly, and that is the question of predicting the CMB. You note your paper from 1999 in which you described the then best measurements of the 2nd peak of the CMB. With WMAP, observations have come along tremendously since then, and the standard LCDM model fits the data spectacularly, and the relative height of the 2nd peak is significantly higher than the initial estimates have suggested. Have you revisited the question of the CMB power spectrum? Dave </blockquote> 2/27/2011 11:43am From: Stacy McGaugh To: Dave Goldberg <blockquote> I last published on the CMB power spectrum in 2004 (ApJL). The second peak has not budged from my 1999 prediction. I have sometimes heard people say that ``the data changed on you'' but that isn't true. When I showed that the prediction fit the Boomerang data (2000 ApJL), the second peak was not yet even apparent in the data, so I further predicted that it would resolve out in better data at a specific level. It did - that is what both Boomerang and WMAP subsequently saw. I didn't even feel like I could write another paper on it at that time (2001/2002) - there was nothing new to say. Now the third peak of course is higher than I predicted in 1999. It is also lower than LCDM predicted a priori - try plotting the fit to the year 1 WMAP data against subsequant data releases. But there is a difference - LCDM can be fit to the updated data, my ansatz for MOND cannot. All that means is that my ansatz breaks down, not that it is inconceivable to have a covariant theory for MOND that could fit this. Nevertheless, I do agree that LCDM fits the WMAP data very well. That doesn't mean as much to me as it seems to a lot of people. Every time the data are updates, we tweak the parameters. The first tweak was to raise the baryon density to get that second peak. I discuss this in detail in my 2004 paper (see, in particular, the figure recounting the history of BBN). Once you've done that, then the rest pretty much follows. So then the question is whether that is the correct baryon density. It is consistent with Deuterium, yes, but not Lithium - at least, not at the time. People seem to have a habit of getting the ``right'' answer since then. As Peebles has repeatedly stressed, we are not yet to the point where LCDM is overconstrained. It fits the CMB brilliantly, yes. But it makes use of many parameters to do so. We know the values of all those parameters quite well, and it didn't have to work out that it was possible. So that much I do indeed take very seriously. But does that prove dozens of WIMPs are passing through our heads at any given moment? I think not - it just tells us how many WIMPs we need to fit the data. IF we can detect those in lab experiments, in the right numbers, I will breathe a very deep sigh of relief. </blockquote> I have to take a bit of an issue with some of the moving targets presented here. I commend Stacy for his work, but the fact that he was able to predict a spectrum from MOND which is now known not to fit actual measurements of the Cosmic Microwave Background is not an argument in favor of MOND. And I disagree that the standard model of cosmology, or the most important elements of it, are not dramatically over-constrained by observational evidence. There are, of course, tweaks, including epoch of reionization, the running index of the power spectrum, and the like, but the main numbers: <ol> <li> [latex]Omega_{DM}$ (the dark matter contribution to the density of the universe)

$Omega_{b}$ (the baryonic, or ordinary contribution to the density of the universe)

$Omega_{DE}$ (the dark energy contribution to the density of the universe)

$w$ (the pressure of dark energy)

$sigma_8$ (the amplitude of primordial fluctuations)

$n_S$ (the slope of the primordial power spectrum)

$H_0$ (the Hubble constant, which is the current expansion rate of the universe)

produce a ridiculously good fit to observation. Even within the CMB, we have now measured something like 11 independent numbers: the overall amplitude, and the peaks and relative amplitude of the first five acoustic peaks. We have Hubble constant measurements from strong lensing time delays. We have supernova acceleration measurements. We have lensing maps of clusters. We have an outstandingly good prediction (and fit) of the power spectrum of galaxies, which includes a very definite contribution of the baryon/dark matter ratio, in the form of baryonic “wiggles.” In fact, each of these 7 parameters are so over-constrained that even before the first WMAP release, each of the parameters (with the possible exception of the $n_s$ ) was already known with fairly high accuracy. WMAP simply confirmed and refined other measurements.

We also have big bang nucleosynthesis estimates. As Stacy correctly points out, the lithium measurement is, indeed, different from prediction, but the helium-4 (the easy one), and the helium-3 and deuterium estimates are precisely in tune with the dark matter+GR predictions, and most emphatically not in accord with baryon only (MONDian) predictions. If you were to ask how I think the discrepancy will be resolved, I would simply respond that taking primordial measurements is staggeringly difficult. It’s only in the last 15 years or so that we were even able to measure deuterium in the oldest stars, which is something 100,000 more abundant than lithium.

These are just the simplest measurements, the ones that don’t actually require knowing any detailed astrophysics about the growth of galaxies and the like. Understanding the formation and evolution of galaxies and clusters is a tough problem. However, what handle we do seem to have seems to suggest that either our understanding of gravity is wrong (the MOND argument) or there is significant dark matter.

MOND, itself, is really only able to address this last argument. The rest can to some degree be addressed by a more general TeVeS theory, but again:

Besides universe-specific parameters (like what the universe actually contains), the TeVeS theory has at least half a dozen free parameters and a free function to boot. Even if the fits were identical (which they currently are not) a simple argument based on simplicity would compel me toward the GR+DM answer.
MOND, along with every other alternate gravity theory is currently completely unable to explain systems like the Bullet Cluster (image at top). This is a system that has undergone recent collision and the lensing and X-ray data clearly show that the bulk of the matter and the gas in the system are cleanly separated from one another. There are something like half a dozen other systems that behave similarly.

2/28/2011
3:43pm
From: Stacy McGaugh
To: Dave Goldberg

I agree with most of what you say. I would, in fact, make a stronger statement about clusters. It isn’t just the bullet cluster or colliding systems that show extra mass in MOND, it is all rich clusters. This missing mass problem for MOND was first pointed out by The & White in 1992, but the data have improved and become much more convincing since then. Sanders (1999, 2003) has shown that this is a persistent result in many rich clusters.

I think that is a grave problem for MOND. Is it fatal? Perhaps. But it is the only place in the universe where MOND consistently fails, and only by a factor of two or so. Now, we both seem to believe in big bang nucleosynthesis, so you will presumably agree when I note that there should be a lot more baryons in the universe than we have accounted for as of yet. Rich clusters are rare, so if you do the integrals, you will see that there are plenty of baryons available to fill in this gap. Do I think that plausible? No, not really. But as long as there are so many dark baryons out there, the bullet cluster certainly does not compel us to believe that there has to be some new, non-baryonic form of cold dark
matter.

There is another side to the cluster story, which isn’t as much discussed. The collision velocity of the bullet cluster is uncomfortably high in LCDM. That is attributed to hydrodynamic effects, but the last calculation I saw published (Lee & Komatsu 2010, ApJ, 718, 60) put the probability of having such a cluster in LCDM at only a few parts in a
billion. On the flip side, the observed collision speed is natural in MOND (2008, MNRAS, 383, 417).
More generally, as we go down in mass from clusters to groups, we deviate from the universal baryon fraction of LCDM. We also need to invoke extra entropy to explain the X-ray temperature mass relation. Both
of these things occur because groups and clusters parallel the mass-rotation velocity relation of MOND. There is an offset – the dark matter mentioned above – but the exponents of the relations are more consistent with MOND than with LCDM. So it is possible to argue clusters either way.

As for big bang nucleosynthesis, I think you meant to say the measurements “most emphatically ARE in accord with baryon only (MONDian) predictions.” The baryon density I estimate without dark matter from the
CMB agrees with all the light element isotopes: see http://www.astro.umd.edu/~ssm/mond/BBNLCDMMOND.jpg
You can judge for yourself which (if any) is better. I do note a disturbing trend in recent data to “get the right number” as estimated from the WMAP LCDM fit. Before CMB data were available, no measurement
suggested Omega_bh^2 > 0.02. The highest was deuterium at 0.019 +/- 0.001 (which is consistent with my MONDian estimate). You make it sound as if we knew Obega_baryon before BOOMERanG and WMAP. I certainly thought we did – that’s what I based my 1999 predictions on. The small second peak forced Ob upwards. For a whole year (post BOOMERanG) the interpretation was “well, the light elements were close, but not quite
right.” Since CMB observations renormalized the “right” baryon density upwards, the independent data have migrated that direction. This reminds me of how measurements of the Hubble constant always seemed to get the
“right” answer back when the right answer was H0 = 50. Or 100. But not something in between.

Finally, I agree that parsimony is important. Occam’s razor is what drove me to consider MOND in the first place. TeVeS isn’t MOND. It is just one possible parent theory. Don’t conflate the complexity of one with the simplicity encapsulated in the data. Try (as I have) to build a dark matter model that reproduces the observed MONDian phenomenology.

Then lets talk about what’s simpler.

But if TeVeS isn’t MOND, or rather, if MOND isn’t any covariant theory, then we get to throw it out, out of hand. It has to be a low energy theory of something, or there’s nothing, really, to argue against. If not TeVeS, then what?

Stacy generally takes the position that DM+GR is untenable, or perhaps suspicious, because it doesn’t fit particular data as well as another theory (MOND) does. In particular, he refers to rotation curves and the like, but then when discussing something like BBNS, we are forced put everything in a GR paradigm. It is true that during the epoch of BBNS, all we really care about is the baryon density (plus other details like the number of neutrino species that neither theory says much about), and in that sense a baryon-only MONDian theory fits with BBNS observations as well as a DM+Baryon theory with the same total number of baryons. But the point is that you need a background theory to govern the expanding universe, and MOND doesn’t by itself do that.

The other point with which I take serious issue is this idea that somehow theory is creeping up to meet observation. Models are fit to observation, of course. That’s how science is done. One can always retroactively look for patterns of data moving in one direction or another. I don’t think it terribly interesting to talk about historical errors in the size of errors. The fact that people misjudged errors in one direction or another doesn’t invalidate current measurements. If Stacy (or anyone else, for that matter) wishes to take issue with how the WMAP best paramater spectrum is fit or any other measurement, by all means, do so. There is an insidious implication that people are fudging the data to fit a theory which I do not like. And to make the point clear, we’re not talking about factors of five here (the sort of errors that would be required for dark matter to really be baryonic matter). The case he cites is that most estimates prior to WMAP put the baryonic density at:
$Omega_b h^2le 0.02$
The current WMAP-7 estimate is:
$Omega_b h^2simeq 0.022$
One might even call the previous estimates “basically right.”

Finally, it is worth noting that all of the models in which MOND seems to do better than dark matter is in what we might call “nonlinear astrophysics.” In other words, things like the matter or CMB power spectra (on most scales) are straightforward exercises in linear fluid dynamics in an expanding universe. GR+DM gets them exactly right. MOND does not, or has little to say about them. The same is true for lensing, especially in systems where we’re simply identifying the existence of large clumps of matter. But in some systems which are most certainly not linear, systems in which we need to do detailed numerical modeling of evolution and dynamics, MOND seems to do a better job. Of course. MOND was designed and motivated based on these systems. But the point is that these nonlinear systems are not perfectly understood and we know it. I find it far more plausible to suggest that we simply don’t understand very much about galaxy formation and evolution or cluster collision (the problem he refers to in the bullet cluster) than that MOND is correct.

2 Responses to MOND, Dark Matter, and more technical discussion than you'd probably like

anand srivastava says:

March 18, 2011 at 9:09 am

My problem with DM+GR is not that it does not fit the data.
My problem is that MOND fits the data without needing DM.
Since this equation works well at the galactic scale everywhere. There can only be two solutions.
1) DM does not exist at Galactic scale.
2) DM position in space is defined by BMs position in space. This is simply untenable if we believe DM to be separate particles. Also BM is not supposed to interact with DM except by gravitational force. This is totally non-sensible

So the real solution is that DM does not exist at the galactic scale.
I would have had no problem with DM, if MOND did not work so well at galactic scale.

The fact that MOND does not work as well at cluster or higher scales makes no difference. It is probably an indication that some form of DM exists on those scales. I don’t even think that MOND can be enhanced to form a theory. TeVeS is just a toy theory that shows how to build one, but I am pretty sure the encompassing physical theory will be discovered from a totally unexpected direction. The recent Verlinde’s theory of Entropic gravity looks interesting.

I liken MOND to an Empirical law. Any quantum theory of gravity needs to bring out MOND or it is not physical. Since GR in its present form does not predict MOND, it is not physical.

It is as simple as that. Empirical laws must be explained by all physical theories. If Newtons gravitational theory did not explain Kepler’s laws, it would be as useless (at the solar system scale) as GR is presently (at the galactic scale).

Richard Moody Jr. says:

March 17, 2012 at 1:52 pm

One simple assumption unites dark matter, MOND, dark energy and gravity (?). If we assume that dark matter repels matter i.e. it is push rather than a pull we can account for all of the above.

First of all isn’t a major problem with MOND sans dark matter that you don’t have enough time to build the massive walls and clear out the voids? Estimates I’ve read require upwards of 100 billion years at known rates of motion of the galaxies when there is no dark matter.

1) Dark matter gives you walls and voids (there is a great computer simulation of dark matter showing this “Matter in the Universe at Present: The Last Word on Nothing”) and can form walls and voids within the 13.7 billion year time frame,

2) If dark matter is expelled by matter once the galaxies form MOND takes over,

3) There would be severe attentuation or no hits in experiments on earth,

4) It obviates the need for dark energy and permits an increase in the rate of expansion of the universe.

5) What is even too much for me to speculate it would establism gravity itself as a push rather than a pull.

MOND, Dark Matter, and more technical discussion than you'd probably like

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