Category: Cosmology

Pulp Science

Pulp Science

g1_pulp_fiction

Vincent: Want to talk about MOND?

Jules: No man, I don’t consider MOND.

Vincent: Are you biased?

Jules: Nah, I ain’t biased, I just don’t dig MOND, that’s all.

Vincent: Why not?

Jules: MOND is an ugly theory. I don’t consider ugly theories.

Vincent: MOND makes predictions that come true. Fits galaxy data gooood.

Jules: Hey, MOND may fit every galaxy in the universe, but I’d never know ’cause I wouldn’t consider the ugly theory. MOND has no generally covariant extension. That’s an ugly theory. I ain’t considering nothin’ that ain’t got a proper cosmology.

Vincent: How about ΛCDM? ΛCDM has lots of small scale problems.

Jules: I don’t care about small scale problems.

Vincent: Yeah, but do you consider ΛCDM to be an ugly theory?

Jules: I wouldn’t go so far as to call ΛCDM ugly, but it’s definitely fine-tuned. But, ΛCDM’s got the CMB. The CMB goes a long way.

Vincent: Ah, so by that rationale, if a theory of modified dynamics fit the CMB, it would cease to be an ugly theory. Is that true?

Jules: Well, we’d have to be talkin’ about one charming eff’n theory of modified dynamics. I mean, it’d have to be ten times more charmin’ than MOND, you know what I’m sayin’?

xkcd’d

xkcd’d

So the always humorous, unabashedly nerdy xkcd recently published this comic:

astrophysics

This hits close to home for me, in many ways.

First, this is an every day experience for me. Hardly a day goes by that I don’t get an email, or worse, a phone call, from some wanna-be who has the next theory of everything. I try to be polite. I even read some of what I get sent. Mostly this is a waste of my time. News flash: at most, only one of you can be right. If the next Einstein is buried somewhere amongst these unsolicited, unrefereed, would-be theories, I wouldn’t know, because I do not have the time to sort through them all.

Second, it is true – it is a logical possibility that what we call dark matter is really just a proxy for a change in the law of gravity on galactic scales. It is also true that attempts to change the law of gravity on large scales do not work to explain the dark matter problem. (Attempts to do this to address the dark energy problem are a separate matter.)

Third, it is a logical fallacy. The implication of the structure of the statement is that the answer has to be dark matter. One could just as accurately turn the statement on its head and say “Yes, everybody has already had the idea, maybe it isn’t modified gravity – there’s just a lot of invisible mass on large scales!’ It sounds good but it doesn’t really fit the data.”

The trick is what data we’re talking about.

I have reviewed this problem many times (e.g., McGaugh & de Blok 1998, Sanders & McGaugh 2002, McGaugh 2006, Famaey & McGaugh 2012, McGaugh 2015). Some of the data favor dark matter, some favor modified gravity. Which is preferable depends on how we weigh the different lines of evidence. If you think the situation is clear cut, you are not well informed of all the facts.* Most of the data that we cite to require dark matter are rather ambiguous and can usually be just as well interpreted in terms of modified gravity. The data that isn’t ambiguous points in opposite directions – see the review papers.

Note that I was careful above to say “galactic scales.” The scale that turns out to matter is not a size scale but an acceleration scale. Galaxies aren’t just big. The centripetal accelerations that hold stars in their orbits are incredibly low: about one part in 1011 of what we feel on the surface of the Earth. The only data that test gravity on this acceleration scale are the data that evince the missing mass problem. We only infer the need for dark matter at these very low accelerations. So while it is not possible to construct an empirically successful theory that modifies gravity on some large length scale, it remains a possibility that a modification can be made on an acceleration scale.

That the mass discrepancy problem occurs on an acceleration scale and not at some length scale has been known for many years. Failing to make the distinction between a length scale and an acceleration scale is fine for a comic strip. It is not OK for scientists working in the field. And yet I routinely encounter reasonable, intelligent scientists who are experts in some aspect of the dark matter problem but are unaware of this essential fact.

To end with another comic, the entire field is easily mocked:

bloomcountydarkmatter

The astute scientific reader will recognize that Mr. Breathed is conflating dark matter with dark energy. Before getting too dismissive, consider how you would go about explaining to him that our cosmic paradigm requires not just invisible mass to provide extra gravity, but also dark energy to act like antigravity. Do you really think that doubling down on ad hoc hypotheses makes for a strong case?

*Or worse, you may fall prey to cognitive dissonance and confirmation bias.

What is the Baryon Density, Anyway?

To continue… we had been discussing the baryon content of the universe, and the missing baryon problem. The problem exists because of a mismatch between the census of baryons locally and the density of baryons estimated from Big Bang Nucleosynthesis (BBN). How well do we know the latter? Either extremely well, or perhaps not so well, depending on which data we query.

At the outset let me say I do not doubt the basic BBN picture. BBN is clearly one of the great successes of early universe cosmology: it is pretty clear this is how the universe works. However, the absolute value we obtain for Ωb depends on the mutual agreement of independent measurements of the abundances of different isotopes. These agree well enough to establish the BBN paradigm, but not so well as to discount all debate about the exact value of Ωb – contrary to the impression one might get from certain segments of the literature.

BBN is thoroughly discussed elsewhere so I won’t belabor it here. In a nutshell, the primordial abundance of the isotopes of the light elements – especially deuterium, helium, and lithium relative to hydrogen – depends on the baryon density. Each isotope provides an independent constraint. This is perhaps the most (only?) over-constrained problem in cosmology.

It is instructive to look at the estimates of the baryon density over time. These are usually quoted as the baryon density multiplied by the square of the Hubble parameter normalized to 100 km/s/Mpc (Ωbh2). This is a hangover from the bad old days when we didn’t know H0 to a factor of 2.

bbnblog

The graph shows the baryon densities estimated by various methods by different people over the years. It starts with the compilation of Walker et al. (1991). By this time, BBN was already a mature subject, with an authoritative answer based on evidence from all the isotopes. Ωbh2 = 0.0125 ± 0.0025. It was Known, Khaleesi.

In the mid-90s there was a debate about the primordial deuterium abundance, largely between Hogan and Tytler. Deuterium (red tirangles) is a great isotope to measure for BBN because it is very sensitive to the baryon density, as it tends to get gobbled up into heavier isotopes like helium when there are lots of baryons around to react with. Moreover, one could measure it in the absorption along the line of sight to high redshift QSOs, presumably catching it before any nasty interstellar processing has polluted the primordial abundance. Unfortunately, Hogan found a high D/H (and hence a low baryon density) while Tytler found low D/H (hence high Ωbh2). This is a rare case when one side (Hogan) actually admitted error, and the standard density shot up to 0.019. At the time (1998) that seemed outrageously high, 2.6σ above the previous standard value. But we had bigger problems to wrap our head around (Λ) at the time, so this was accepted without much fuss.

The other elements (helium and lithium) preferred something in between at that time. Their uncertainties were large enough this didn’t seem a big deal. Helium in particular is notoriously hard to pin down. Not only is the measurement hard to make, but helium (unlike deuterium) is not particularly sensitive to the baryon density. You get about a quarter helium by mass out of BBN for any reasonable baryon density, so it is a great indicator that the basic picture is correct. But you really have to nail down the third decimal point to help distinguish between slightly lower or higher Ωb. So the new normal became Ωbh2 = 0.019 ± 0.001.

That was the summation of decades of work, but it wasn’t to last long. In 2000, cosmic microwave background (CMB) experiments like BOOMERanG and MAXIMA began to resolve the acoustic power spectrum. A funny thing emerged: the second peak was lower than expected. (At least by other people. I totally nailed this prediction.) In order to explain the low second peak conventionally (in the context of ΛCDM), one had to crank up the baryon density. This first point from the CMB (blue in plot above) was well above previously suspected levels.

Note the dotted lines in the figure. These denote the maximum baryon density (horizontal line) before the first relevant CMB data (vertical line). No isotope of any light element had ever suggested Ωbh2 > 0.02 prior to CMB constraints. Once those became available, this changed.

The change happened first to deuterium, which has not suggested Ωbh2 < 0.02 since the CMB said so. Helium was slower to respond, but it has also drifted slowly upward. Lithium has remained put. This is a serious problem that has not been satisfactorily resolved. The general presumption seems to be that this is a detail to be blamed on stellar rotation or some similarly obscure mechanism.

Different communities work on each of these elements. Deuterium is the subject of high redshift astronomy, a field closely coupled to cosmology. Helium is the subject of nearby galaxies, a field aware of cosmology but less strongly tied to it. Lithium is measured in stars, a field that is not coupled to cosmology. Given the long history of confirmation bias in cosmology, it is hard not to be suspicious of the temporal variation in BBN baryon density estimates. The isotope most closely associated with cosmology, deuterium, quickly fell in line with the “right” result from the CMB. Helium has more gradually followed suit, while lithium continues to prefer lower baryon densities.

I do not doubt the sincerity of any particular measurement. But people talk. They have arguments about what is right and why. The communities that are closest are most likely to influence each other. Those further apart are less likely to be swayed. If we were suffering from confirmation bias, this is what it would look like.

The ΛCDM picture requires us to believe the CMB value, currently  Ωbh2 = 0.02230 ± 0.00023 (Planck 2015). You simply cannot fit the acoustic power spectrum with a number much different. Modern deuterium measurements are consistent with that, within the errors, so that has to be right, no? Lets just ignore lithium.

If instead we ignore the CMB and its associated baggage, this is not at all obvious. Perhaps the pre-CMB deuterium measurement is the one to trust. That is a bit higher than lithium, but consistent within the errors. Helium can go either way. So from a pure BBN (no CMB) perspective, maybe it is lithium and the other isotopes that are right and it is CMB fits that are misleading.

Where does this leave us with the missing baryons? The figure below shows the time evolution of the baryon density. The area is proportional to Ωbh2. This has grown over time, by an amount greater than the stated uncertainties (the circles show the change in area allowed). The baryon density has nearly doubled, being now ~4σ above the Known value of Walker.

baryoncontentblog

As the baryon density has grown, the missing baryon problem has grown worse. If we still had the classical Walker baryon density, there would be no missing baryon problem at al.  Indeed, Shull’s inventory is a bit too large, though it is consistent within the errors. If we go up to the pre-CMB deuterium value, then there is a missing baryon problem. It is big enough to solve the cluster problem in MOND, but without a lot left over. If we insist on the CMB-fitted baryon density, then the missing baryon problem is severe, at a level where it is hard to figure where else they could be.

IF ΛCDM is the right picture, then I think a high baryon density is unavoidable. Accepting this, there must then be something wrong with lithium. There is no lack of papers motivated by this line of reasoning, though the most common approach seems to be to ignore lithium entirely. I’ve heard a lot of talks bragging about the excellent agreement between BBN and the CMB, but this  really only applies to post-CMB deuterium.

IF BBN, as originally posed, is correct so that lithium and the other pre-CMB measurements are not misleading, then it becomes impossible to fit the CMB with pure General Relativity. This is the case even if we spot it non-baryonic cold dark matter and dark energy. This situation might be considered a motivation to seek extensions of the theory.

Regardless of where the right answer ultimately lies, there is real tension between primordial lithium measurements and the ΛCDM interpretation of the CMB. Something is fishy in the state of the early universe.

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.

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.

And then there were six

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

– John von Neumann

The simple and elegant cosmology encapsulated by the search for two numbers has been replaced by ΛCDM. This is neither simple nor elegant. In addition to the Hubble constant and density parameter, we now also require distinct density parameters for baryonic mass, non-baryonic cold dark matter, and dark energy. There is an implicit (seventh) parameter for the density of neutrinos.

Now we also include the power spectrum as cosmological parameters (σ8, n). These did not use to be considered on the same level as the Big Two. They aren’t: they concern structure formation within the world model, not the nature of the world model. But I guess they seem more important once the Big Numbers are settled.

Here is a quick list of what we believed, then and now:

 

Paramater SCDM ΛCDM
H0 50 70
Ωm 1.0 0.3
Ωbh2 0.0125 0.02225
ΩΛ 0.7
σ8 0.5 0.8
n 1.0 0.96

 

There are a number of “lesser” parameters, like the optical depth to reionization. Plus, the index n can run, one can invoke scale dependent non-linear biasing (a rolling fudge factor for σ8), and people talk seriously about the time evolution of antigravity the dark energy equation of state.

From the late ’80s to the early ’00s, all of these parameters (excepting only n) changed by much more than their formal uncertainty or theoretical expectation. Even big bang nucleosynthesis – by far the most robustly constrained – suffered a doubling in the mass density of baryons. This should be embarrassing, but most cosmologists assert it as a great success while quietly sweeping the lithium problem under the carpet.

The only thing that hasn’t really changed is our belief in Cold Dark Matter. That’s not because it is more robust. It is because it is much harder to detect, let alone measure.

Two Numbers

Cosmology used to be called the hunt for two numbers. It was simple and elegant. Nowadays we need at least six. It is neither simple nor elegant. So how did we get here?

The two Big Numbers are, or at least up till the early-90s were, the Hubble constant H0 and the density parameter Ω. These told us Everything. Or so we thought.

The Hubble constant is the expansion rate of the universe. Not only does it tell us how fast the universe is expanding, it sets the size scale through the Hubble distance-velocity relation. Moreover, its inverse is the Hubble time – essentially the age of the universe. A Useful and Important Number. To seek to measure it was a noble endeavor into which much toil and treasure was invested. Getting this right was what the Hubble Space Telescope was built for.

The density parameter measures the amount of stuff in the universe. Until relatively recently, it was used exclusively to refer to the mass density – the amount of gravitating stuff normalized to the critical density. The critical density is the over/under point where there is enough gravity to counteract the expansion of the universe. If Ω < 1, there isn’t enough, and the universe will expand forever. If Ω > 1, there’s more than enough, and the universe will eventually stop expanding and collapse. It controls the fate of the universe.

Just two numbers controlled the size, age, and ultimate fate of the universe. The hunt was on.

Of course, the hunt had been on for a long time, ever since Hubble discovered that the universe was expanding. For the first fifty years it largely shrank, then settled into a double valued rut between two entrenched camps. Sandage and collaborators found H0 = 50 km/s/Mpc while de Vaucoulers found a value closer to 100 km/s/Mpc.

The exact age of the universe depends a little on Ω as well as the Hubble constant. If the universe is empty, there is no gravity to retard its expansion. The age of such a `coasting’ universe is just the inverse of the Hubble constant – about 10 Gyr (10 billion years) for H0 = 100 and 20 Gyr for H0 = 50. If instead the universe has the critical density Ω = 1, the age is just 2/3 of the coasting value.

The difference in age between empty and critical ages is not huge by cosmic standards, but it nevertheless played an important role in guiding our thinking. Stellar evolution places a constraint on the ages of the oldest stars. These are all around a Hubble time old. That’s good – it looks like the first stars formed near the beginning of the universe. But we can’t have stars that are older than the universe they live in.

In the 80s, a commonly quoted age for the oldest stars was about 18 Gyr. That’s too old for de Vaucoulers’s H0 = 100 – even if the universe is completely empty. Worse, Ω = 1 is the only natural scale in cosmology; it seemed to many like the most likely case – a case bolstered by the advent of Inflation. In that case, the universe could be at most 13 Gyr old, even adopting Sandage’s H0 = 50. It was easy to imagine that the ages of the oldest stars were off by that much (indeed, the modern number is closer to 12 Gyr) but not by a lot more: Ages < 10 Gyr with H0 = 100 were right out.

Hence we fell into a double trap. First, there was confirmation bias: the ages of stars led to a clear preference for who must be right about the Hubble constant. Then Inflation made a compelling (but entirely theoretical) case the Ω had to be exactly 1 – entirely in mass. (There was no cosmological constant in those days.  You were stupid to even consider that.) This put further pressure on the age problem. A paradigm emerged with Ω = 1 and H0 = 50.

There was a very strong current of opinion in the 80s that this had to be the case. Inflation demanded Ω = 1, in which case H0 = 50 was the only sensible possibility. You were stupid to think otherwise.

That was the attitude into which I was indoctrinated. I wouldn’t blame any particular person for this indoctrination; it was more of a communal group-think. But that is absolutely the attitude that reigned supreme in the physics departments of MIT and Princeton in the mid-80s.

I switched grad schools, having decided I wanted data. Actual observational data; hands on telescopes. When I arrived at the University of Michigan in 1987, I found a very different culture among the astronomers there. It was more open minded. Based on measurements that were current at the time, H0 was maybe 80 or so.

At first I rejected this heresy as obviously insane. But the approach was much more empirical. It would be wrong to say that it was uninformed by theoretical considerations. But it was also informed by a long tradition of things that must be so turning out to be just plain wrong.

Between 1987 and 1995, the value of the Big Numbers changed by amounts that were inconceivable. None of the things that must be so turned out to be correct. And yet now, two decades later, we are back to the new old status quo, where all the parameters are Known and Cannot Conceivably Change.

Feels like I’ve been here before.

Rethinking the Dark Matter Paradigm

I travel to Cambridge, MA tomorrow to participate in the workshop Rethinking the Dark Matter Paradigm (I had nothing to do with the choice of title). I went to college at MIT in the ’80s, so is a bit back to the future for me in space as well as time. There is a lot to rethink, or nothing at all, depending on who you ask. I’m curious to see if any of us are willing to think beyond I was right all along!

One of the compelling notions that emerged in the ’80s was non-baryonic dark matter. Baryons are the massive particles (protons & neutrons) of which normal stuff is made. It was well established by that time that the light elements were produced in the early universe by Big Bang Nucleosynthesis (BBN). It became clear in the ’80s that the mass density of normal stuff produced by BBN did not add up to the mass we needed to explain a whole host of astronomical observations, in both cosmology and galaxy dynamics. In short, Einstein’s General Relativity plus the baryons we could see did not suffice to explain the universe.

There were two obvious paths forward. Modify Einstein’s theory, or invoke unseen non-baryonic matter. The latter course seems by far the more plausible. No one had a compelling reason to challenge Einstein’s highly successful theory. On the other hand, there were plenty of reasons in particle physics to imagine new particles outside the standard model, particularly in the hypothesized supersymmetric sector.

It was quickly realized that large scale structure would only grow if this new stuff were composed of slow moving, non-relativistic particles – a condition summarized as dynamically “cold.” Hence Cold Dark Matter (CDM) was born. Weakly Interacting Massive Particles (WIMPs) from supersymmetry were a good candidate to be the CDM.

Thus began the marriage of astronomy and particle physics, two fields divided by a common interest in dark matter and cosmology. The heated embrace of the honeymoon has long since worn off, to the point that some of us are ready to rethink the whole paradigm.

This is no small step. Though I’ve come to doubt the existence of CDM, I still feel very comfortable with it.  First love, and all. More importantly, it has been the one essential item in cosmology that has remained unchanged through the turbulent ’90s and on to today. But that is a longer story that will take many posts to tell.

For now, we’ll go see how much rethinking we’re willing to do.