I started this blog as a place to discuss science, and have refrained from discussing overtly political matters. This is no longer possible. Today is June 10, 2020 – the date set to strike for black lives. I want to contribute in a tiny way by writing here. If that seems inappropriate to you or otherwise makes you uncomfortable, then that probably means that you need to read it and reflect on the reasons for your discomfort.
To start, I quote the statement made by my colleagues and myself:
The CWRU Department of Astronomy stands in solidarity with our Black colleagues and fellow citizens across the United States in expressing what should be a clear moral absolute: that people of color should enjoy the same freedoms as other Americans to life, liberty, and the pursuit of happiness. We condemn the de facto system of racial oppression that leads to pervasive police brutality up to and including the extrajudicial murders of Black Americans like George Floyd and far too many others.
We strive to build an academic community that welcomes, encourages, and supports students and scientists of color. To achieve this goal, we recognize that we must continually reflect on the injustices faced by under-represented and marginalized people, and repair the institutional structures that place them at a disadvantage. We encourage our colleagues in astronomy, throughout academia, and more broadly across society to do the same.
We will participate in the Strike for Black Lives this Wednesday, June 10, and encourage others to join us.
As the current chairperson of the CWRU Department of Astronomy, I was initially reluctant to post something about the Black Lives Matter movement on the department website. It is a different thing to make a statement on behalf of an organization of many people than it is to do so for oneself. Moreover, we are a science entity, not a political one. But we are also people, and cannot separate our humanity from our vocation. There comes a point when way too much is ever so much more than more than enough. We have reached such a point. So when I contacted my colleagues about doing this, there was unanimous agreement and eager consent to do so among all the faculty and scientific staff.
I value the freedom of speech enshrined in the first amendment of the constitution of the United States of America. I think it is worth reproducing here:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
Freedom of speech is often construed to mean the right to espouse whatever opinion one might hold, and I think that is indeed an essential personal freedom that Americans take for granted in a way that is rather special in the history of humankind. Note also that the first amendment explicitly includes “the right of the people peaceably to assemble” – a right that Americans sometimes exercise but also frequently attempt to deny to each other.
Why does this come up now? Well, if you haven’t been keeping up with current events, George Floyd died in custody after being arrested in Minneapolis, sparking protests – peaceable assemblages – across the country and around the world.
In the last sentence, I intentionally use a misleading structure common in both the press and in police reports: “George Floyd died…”, as if it were something that just happened, like a butterfly happening to pass by. Indeed, the initial police report on the incident stated that Floyd “seemed to be in medical distress” while omitting mention of any causal factor for that distress. Similarly, the medical examiner’s report exonerated the police, attributing Floyd’s death to “underlying medical conditions.”
That is some major league bullshit.
The cause of Floyd’s death is not mysterious. Officer Derek Chauvin crushed Floyd’s windpipe by kneeling on his neck for eight minutes and forty six seconds. That is considerably longer than the longest TV commercial break you have ever been modestly annoyed by. Who among us has never raged WILL THESE COMMERCIALS NEVER END? Now imagine feeling the life being crushed out of you for a considerably longer period while lying flat on your belly with your hands already cuffed behind your back. That’s right – George Floyd was already handcuffed and on the ground while being pinned by the neck. In no way can this be construed as resisting arrest. He was already under police control and in no position to resist anything, up to and including being murdered.
A more accurate statement using the active voice would be “Police arrested George Floyd, then brutally murdered him as he lay helplessly handcuffed on the ground.” There was an obvious cause for his “medical distress:” Derek Chauvin’s knee and body weight. “Underlying conditions” played no role. Before being pinned and crushed, Floyd was alive. After, he was dead. It didn’t matter if he had been suffering from terminal cancer: that’s not what killed him. Officer Chauvin did. There is no alleged about it: we can all personally witness this heinous act through now-ubiquitous video recordings.
The more puritanical grammarians might object that I am not merely using the active voice that the police and coroner’s report (and some press accounts) take care to avoid. I am also using pejorative adverbs: brutally and helplessly. Yes. Yes I am. Because those words apply. If you want an illustration to go along with the dictionary definition of these words, then go watch all 8:46 of the execution of George Floyd.
As egregious as this case is, it is not an isolated incident. That both the police and coroner’s reports whitewash the incident with intentionally vague and passive language is a dead give away that this is standard operating procedure. They’ve done it before. Many times. So many times that there is a well-rehearsed language of obfuscation to subvert the plain facts of the matter.
This event has sparked protests around the country because it illustrates an all too familiar pattern of police behavior in black communities. I’ve heard various people say things like “It can’t be that bad.” Yet this systematic police brutality is what protesters are saying is their life experience of being black in America. Are you in a position to know better than they?
I’ve heard people say worse things. Like blaming the victim. Floyd was a career criminal, so he deserved what he got. This is such a common sentiment, apparently, that it affected a Google search I did the other day. I was trying to look up a geology term, and got as far as typing “geo” when Google auto-suggested
Really? This is such a common conceit that the mere three letters g e o leads Google to think I’m searching on George Floyd’s criminal past? I can think of a lot of more likely things to follow from g e o. Given the timing, I can see how his name would come up quickly. Just his name. Why add on “criminal past”? How many people must be doing that search for this to be Google’s top hit?
News flash: people are supposed to be innocent until proven guilty. It is the purpose of police to apprehend suspects and that of the courts and a jury of citizens to decide guilt or innocence. Whatever the alleged crime, the punishment is not summary execution by the police on the spot. As much as some few of them seem to want to be, the police are not and should not be Judge Dredd.
The same victim-blaming is going on with the protests. People have assembled in communities all over the country to protest – a right guaranteed by the first amendment. As near as I can tell, most of these assemblies have been peaceable. Given the righteous, raw anger over the arbitrary state-abetted murder of American citizens, it is hardly surprising that some of these assemblies devolve into riots. The odds of this happening are seen time and again to be greatly enhanced when the police show up to “keep order.” All too often we have seen the police act as the aggressors and instigators of violence. If you haven’t seen that, then you are not paying attention – or not following a credible news source. Fox, OANN, Breitbart, the Sinclair broadcasting network – these are not credible new sources. They are propaganda machines that are keen on focusing attention on the bad behavior of a minority of protesters in the hopes that you’ll be distracted from the police brutality that sparked the demonstrations in the first place.
Victim-blaming is an excuse closet racists use to dodge engagement with the real issue of police misconduct. “He was a career criminal! He deserved it!” and “Riots are bad! Police must keep order and protect property!” These are distractions from the real issue. Property is not as important as life, liberty, and the pursuit of happiness. Black Americans are not assured of any of those. When they peacefully assemble to petition the government for a redress of grievances, they are met with masses of police in riot gear hurling flash-bangs and teargas. Even if a few of these assemblages lead to riots and some looting, so what? That is nothing in comparison with existential threat to life and liberty suffered by all too many Americans because of the color of their skin.
An old friend tried to make the case to me that, basically, “mobs are bad.” I reacted poorly to his clueless but apparently sincere buy-in to the misdirection of victim-blaming, and felt bad about it afterwards. But he was wrong, in an absolute moral sense, and I have no patience left for blaming the victim. Yes. Mobs are bad. Duh. But going straight to that willfully misses the point. This didn’t start with mob violence out nowhere. It started with the systematic oppression of an entire group of American citizens defined in literally the most superficial way possible – the pigmentation of their skin. The police have many roles in our society, some for the good, some not. One of the bad roles has been as enforcers of a de facto system of white supremacy – a system so deeply ingrained that most white people aren’t even aware that it exists.
I would like to believe, as many white folk apparently do, that white supremacy is a thing of the past. An ugly chapter in our past now relegated to the dustbin of history. Yet I look around and see that it is alive and well all around us.
We – all of us who are American citizens – have an obligation to make things better for our fellow citizens. At a very minimum, that means listening to their concerns, not denying their experience. Just because it is horrible doesn’t make it untrue. So don’t try to tell me about the evils of riots and mobs until you first engage with the underlying causes therefore. These are mere symptoms of the societal cancer that is white supremacy. They are natural, inevitable reactions to decades upon decades of degradation and disenfranchisement heaped on top of centuries of dehumanization through slavery and lynchings. Until you acknowledge and engage meaningfully with these brutal aspects of history and modern-day reality, you have zero credibility to complain about any of their toxic offspring. Doing so is a clear sign that you are part of the problem.
This is a wise truth that has often been poorly interpreted. I despise some of the results that this sports quote has had in American culture. It has fostered a culture of bad sportsmanship in some places: an acceptance, even a dictum, that the ends justify the means – up to and including cheating, provided you can get away with it.
Winning every time is an impossible standard. In any competitive event, someone will win a particular game, and someone else will lose. Every participant will be on the losing side some of the time. Learning to lose gracefully despite a great effort is an essential aspect of sportsmanship that must be taught and learned, because it sure as hell isn’t part of human nature.
But there is wisdom here. The quote originates with a football coach. Football is a sport where there is a lot of everything – to even have a chance of winning, you have to do everything right. Not just performance on the field, but strategic choices made before and during the game, and mundane but essential elements like getting the right personnel on the field for each play. What? We’re punting? I thought it was third down!
You can do everything right and still lose. And that’s what I interpret the quote to really mean. You have to do everything to compete. But people will only judge you to be successful if you win.
To give a recent example, the Kansas City Chiefs won this year’s Superbowl. It was only a few months ago, though it seems much longer in pandemic time. The Chiefs dominated the Superbowl, but they nearly didn’t make it past the AFC Championship game.
The Tennessee Titans dominated the early part of the AFC Championship game. They had done everything right. They had peaked at the right time as a team in the overly long and brutal NFL season. They had an excellent game plan, just as they had had in handily defeating the highly favored New England Patriots on the way to the Championship game. Their defense admirably contained the high octane Chiefs offense. It looked like they were going to the Superbowl.
Then one key injury occurred. The Titans lost the only defender who could match up one on one with tight end Travis Kelce. This had an immediate impact on the game, as they Chiefs quickly realized they could successfully throw to Kelce over and over after not having been able to do so at all. The Titans were obliged to double-cover, which opened up other opportunities. The Chief’s offense went from impotent to unstoppable.
I remember this small detail because Kelce is a local boy. He attended the same high school as my daughters, playing on the same field they would (only shortly later) march on with the marching band during half times. If it weren’t for this happenstance of local interest, I probably wouldn’t have noticed this detail of the game, much less remember it.
The bigger point is that the Titans did everything right as a team. They lost anyway. All most people will remember is that the Chiefs won the Superbowl, not that the Titans almost made it there. Hence the quote:
“Winning isn’t everything. It’s the only thing.”
The hallmark of science is predictive power. This is what distinguishes it from other forms of knowledge. The gold standard is a prediction that is made and published in advance of the experiment that tests it. This eliminates the ability to hedge: either we get it right in advance, or we don’t.
The importance of such a prediction depends on how surprising it is. Predicting that the sun will rise tomorrow is not exactly a bold prediction, is it? If instead we have a new idea that changes how we think about how the world works, and makes a prediction that is distinct from current wisdom, then that’s very important. Judging how important a particular prediction may be is inevitably subjective.
It is rare that we actually meet the gold standard of a priori prediction, but it does happen. A prominent example is the prediction of gravitational lensing by General Relativity. Einstein pointed out that his theory predicted twice the light-bending that Newtonian theory did. Eddington organized an expedition to measure this effect during a solar eclipse, and claimed to confirm Einstein’s prediction within a few years of it having been made. This is reputed to have had a strong impact that led to widespread acceptance of the new theory. Some of that was undoubtedly due to Eddington’s cheerleading: it does not suffice merely to make a successful prediction, that it has happened needs to become widely known.
It is impossible to anticipate every conceivable experimental result and publish a prediction for it in advance. So there is another situation: does a theory predict what is observed? This has several standards. The highest standard deserves a silver medal. This happens when you work out the prediction of a theory, and you find that it gives exactly what is observed, with very little leeway. If you had had the opportunity to make the prediction in advance, it would have risen to the gold standard.
Einstein provides another example of a silver-standard prediction. A long standing problem in planetary dynamics was the excess precession of the perihelion of Mercury. The orientation of the elliptical orbit of Mercury changes slowly, with the major axis of the ellipse pivoting by 574 arcseconds per century. That’s a tiny rate of angular change, but we’ve been keeping very accurate records of where the planets are for a very long time, so it was well measured. Indeed, it was recognized early that precession would be cause by torques from other planets: it isn’t just Mercury going around the sun; the rest of the solar system matters too. Planetary torques are responsible for most of the effect, but not all. By 1859, Urbain Le Verrier had worked out that the torques from known planets should only amount to 532 arcseconds per century. [I am grossly oversimplifying some fascinating history. Go read up on it!] The point is that there was an excess, unexplained precession of 43 arcseconds per century. This discrepancy was known, known to be serious, and had no satisfactory explanation for many decades before Einstein came on the scene. No way he could go back in time and make a prediction before he was born! But when he worked out the implications of his new theory for this problem, the right answer fell straight out. It explained an ancient and terrible problem without any sort of fiddling: it had to be so.
The data for the precession of the perihelion of Mercury were far superior to the first gravitational lensing measurements made by Eddington and his colleagues. The precession was long known and accurately measured, the post facto prediction clean and irresolute. So in this case, the silver standard was perhaps better than the gold standard. Hence the question once posed to me by a philosopher of science: why we should care if the prediction came in advance of the observation? If X is a consequence of a theory, and X is observed, what difference does it make which came first?
In principle, none. In practice, it depends. I made the hedge above of “very little leeway.” If there is zero leeway, then silver is just as good as gold. There is no leeway to fudge it, so the order doesn’t matter.
It is rare that there is no leeway to fudge it. Theorists love to explore arcane facets of their ideas. They are exceedingly clever at finding ways to “explain” observations that their theory did not predict, even those that seem impossible for their theory to explain. So the standard by which such a post-facto “prediction” must be judged depends on the flexibility of the theory, and the extent to which one indulges said flexibility. If it is simply a matter of fitting for some small number of unknown parameters that are perhaps unknowable in advance, then I would award that a bronze medal. If instead one must strain to twist the theory to make it work out, then that merits at best an asterisk: “we fit* it!” can quickly become “*we’re fudging it!” That’s why truly a priori prediction is the gold standard. There is no way to go back in time and fudge it.
An important corollary is that if a theory gets its predictions right in advance, then we are obliged to acknowledge the efficacy of that theory. The success of a priori predictions is the strongest possible sign that the successful theory is a step in the right direction. This is how we try to maintain objectivity in science: it is how we know when to suck it up and say “OK, my favorite theory got this wrong, but this other theory I don’t like got its prediction exactly right. I need to re-think this.” This ethos has been part of science for as long as I can remember, and a good deal longer than that. I have heard some argue that this is somehow outdated and that we should give up this ethos. This is stupid. If we give up the principle of objectivity, science would quickly degenerate into a numerological form of religion: my theory is always right! and I can bend the numbers to make it seem so.
Hence the hallmark of science is predictive power. Can a theory be applied to predict real phenomena? It doesn’t matter whether the prediction is made in advance or not – with the giant caveat that “predictions” not be massaged to fit the facts. There is always a temptation to massage one’s favorite theory – and obfuscate the extent to which one is doing so. Consequently, truly a priori prediction must necessarily remain the gold standard in science. The power to make such predictions is fundamental.
Predictive power in science isn’t everything. It’s the only thing.
As I was writing this, I received email to the effect that these issues are also being discussed elsewhere, by Jim Baggot and Sabine Hossenfelder. I have not yet read what they have to say.
I haven’t written much here of late. This is mostly because I have been busy, but also because I have been actively refraining from venting about some of the sillier things being said in the scientific literature. I went into science to get away from the human proclivity for what is nowadays called “fake news,” but we scientists are human too, and are not immune from the same self-deception one sees so frequently exercised in other venues.
So let’s talk about something positive. Current grad student Pengfei Li recently published a paper on the halo mass function. What is that and why should we care?
One of the fundamental predictions of the current cosmological paradigm, ΛCDM, is that dark matter clumps into halos. Cosmological parameters are known with sufficient precision that we have a very good idea of how many of these halos there ought to be. Their number per unit volume as a function of mass (so many big halos, so many more small halos) is called the halo mass function.
An important test of the paradigm is thus to measure the halo mass function. Does the predicted number match the observed number? This is hard to do, since dark matter halos are invisible! So how do we go about it?
Galaxies are thought to form within dark matter halos. Indeed, that’s kinda the whole point of the ΛCDM galaxy formation paradigm. So by counting galaxies, we should be able to count dark matter halos. Counting galaxies was an obvious task long before we thought there was dark matter, so this should be straightforward: all one needs is the measured galaxy luminosity function – the number density of galaxies as a function of how bright they are, or equivalently, how many stars they are made of (their stellar mass). Unfortunately, this goes tragically wrong.
This figure shows a comparison of the observed stellar mass function of galaxies and the predicted halo mass function. It is from a recent review, but it illustrates a problem that goes back as long as I can remember. We extragalactic astronomers spent all of the ’90s obsessing over this problem. [I briefly thought that I had solved this problem, but I was wrong.] The observed luminosity function is nearly flat while the predicted halo mass function is steep. Consequently, there should be lots and lots of faint galaxies for every bright one, but instead there are relatively few. This discrepancy becomes progressively more severe to lower masses, with the predicted number of halos being off by a factor of many thousands for the faintest galaxies. The problem is most severe in the Local Group, where the faintest dwarf galaxies are known. Locally it is called the missing satellite problem, but this is just a special case of a more general problem that pervades the entire universe.
Indeed, the small number of low mass objects is just one part of the problem. There are also too few galaxies at large masses. Even where the observed and predicted numbers come closest, around the scale of the Milky Way, they still miss by a large factor (this being a log-log plot, even small offsets are substantial). If we had assigned “explain the observed galaxy luminosity function” as a homework problem and the students had returned as an answer a line that had the wrong shape at both ends and at no point intersected the data, we would flunk them. This is, in effect, what theorists have been doing for the past thirty years. Rather than entertain the obvious interpretation that the theory is wrong, they offer more elaborate interpretations.
Theorists persist because this is what CDM predicts, with or without Λ, and we need cold dark matter for independent reasons. If we are unwilling to contemplate that ΛCDM might be wrong, then we are obliged to pound the square peg into the round hole, and bend the halo mass function into the observed luminosity function. This transformation is believed to take place as a result of a variety of complex feedback effects, all of which are real and few of which are likely to have the physical effects that are required to solve this problem. That’s way beyond the scope of this post; all we need to know here is that this is the “physics” behind the transformation that leads to what is currently called Abundance Matching.
Abundance matching boils down to drawing horizontal lines in the above figure, thus matching galaxies with dark matter halos with equal number density (abundance). So, just reading off the graph, a galaxy of stellar mass M* = 108 M☉ resides in a dark matter halo of 1011 M☉, one like the Milky Way with M* = 5 x 1010 M☉ resides in a 1012 M☉ halo, and a giant galaxy with M* = 1012 M☉ is the “central” galaxy of a cluster of galaxies with a halo mass of several 1014 M☉. And so on. In effect, we abandon the obvious and long-held assumption that the mass in stars should be simply proportional to that in dark matter, and replace it with a rolling fudge factor that maps what we see to what we predict. The rolling fudge factor that follows from abundance matching is called the stellar mass–halo mass relation. Many of the discussions of feedback effects in the literature amount to a post hoc justification for this multiplication of forms of feedback.
This is a lengthy but insufficient introduction to a complicated subject. We wanted to get away from this, and test the halo mass function more directly. We do so by use of the velocity function rather than the stellar mass function.
The velocity function is the number density of galaxies as a function of how fast they rotate. It is less widely used than the luminosity function, because there is less data: one needs to measure the rotation speed, which is harder to obtain than the luminosity. Nevertheless, it has been done, as with this measurement from the HIPASS survey:
The idea here is that the flat rotation speed is the hallmark of a dark matter halo, providing a dynamical constraint on its mass. This should make for a cleaner measurement of the halo mass function. This turns out to be true, but it isn’t as clean as we’d like.
Those of you who are paying attention will note that the velocity function Martin Zwaan measured has the same basic morphology as the stellar mass function: approximately flat at low masses, with a steep cut off at high masses. This looks no more like the halo mass function than the galaxy luminosity function did. So how does this help?
To measure the velocity function, one has to use some readily obtained measure of the rotation speed like the line-width of the 21cm line. This, in itself, is not a very good measurement of the halo mass. So what Pengfei did was to fit dark matter halo models to galaxies of the SPARC sample for which we have good rotation curves. Thanks to the work of Federico Lelli, we also have an empirical relation between line-width and the flat rotation velocity. Together, these provide a connection between the line-width and halo mass:
Once we have the mass-line width relation, we can assign a halo mass to every galaxy in the HIPASS survey and recompute the distribution function. But now we have not the velocity function, but the halo mass function. We’ve skipped the conversion of light to stellar mass to total mass and used the dynamics to skip straight to the halo mass function:
The observed mass function agrees with the predicted one! Test successful! Well, mostly. Let’s think through the various aspects here.
First, the normalization is about right. It does not have the offset seen in the first figure. As it should not – we’ve gone straight to the halo mass in this exercise, and not used the luminosity as an intermediary proxy. So that is a genuine success. It didn’t have to work out this well, and would not do so in a very different cosmology (like SCDM).
Second, it breaks down at high mass. The data shows the usual Schechter cut-off at high mass, while the predicted number of dark matter halos continues as an unabated power law. This might be OK if high mass dark matter halos contain little neutral hydrogen. If this is the case, they will be invisible to HIPASS, the 21cm survey on which this is based. One expects this, to a certain extent: the most massive galaxies tend to be gas-poor ellipticals. That helps, but only by shifting the turn-down to slightly higher mass. It is still there, so the discrepancy is not entirely cured. At some point, we’re talking about large dark matter halos that are groups or even rich clusters of galaxies, not individual galaxies. Still, those have HI in them, so it is not like they’re invisible. Worse, examining detailed simulations that include feedback effects, there do seem to be more predicted high-mass halos that should have been detected than actually are. This is a potential missing gas-rich galaxy problem at the high mass end where galaxies are easy to detect. However, the simulations currently available to us do not provide the information we need to clearly make this determination. They don’t look right, so far as we can tell, but it isn’t clear enough to make a definitive statement.
Finally, the faint-end slope is about right. That’s amazing. The problem we’ve struggled with for decades is that the observed slope is too flat. Here a steep slope just falls out. It agrees with the ΛCDM down to the lowest mass bin. If there is a missing satellite-type problem here, it is at lower masses than we probe.
That sounds great, and it is. But before we get too excited, I hope you noticed that the velocity function from the same survey is flat like the luminosity function. So why is the halo mass function steep?
When we fit rotation curves, we impose various priors. That’s statistics talk for a way of keeping parameters within reasonable bounds. For example, we have a pretty good idea of what the mass-to-light ratio of a stellar population should be. We can therefore impose as a prior that the fit return something within the bounds of reason.
One of the priors we imposed on the rotation curve fits was that they be consistent with the stellar mass-halo mass relation. Abundance matching is now part and parcel of ΛCDM, so it made sense to apply it as a prior. The total mass of a dark matter halo is an entirely notional quantity; rotation curves (and other tracers) pretty much never extend far enough to measure this. So abundance matching is great for imposing sense on a parameter that is otherwise ill-constrained. In this case, it means that what is driving the slope of the halo mass function is a prior that builds-in the right slope. That’s not wrong, but neither is it an independent test. So while the observationally constrained halo mass function is consistent with the predictions of ΛCDM; we have not corroborated the prediction with independent data. What we really need at low mass is some way to constrain the total mass of small galaxies out to much larger radii that currently available. That will keep us busy for some time to come.
I was contacted today by a colleague at NASA’s Goddard Space Flight Center who was seeking to return some photographic plates of Halley’s comet that had been obtained with the Burrell Schmidt telescope. I at first misread the email – I get so many requests for data, I initially assumed that he was looking for said plates. That sent me into a frenzy of where the heck are they? about data obtained by others well before my time as the director of the Warner & Swasey Observatory. Comet Halley last came by in 1986.
Fortunately, reading comprehension kicked in, and I realized that all I really needed to figure out was where they should go. The lower pressure version of where the heck are they? That would be the Pisgah Astronomical Research Institute, which has had the good sense to archive the vast treasury of astronomical plates that many observatories obtained in the pre-digital era but don’t always have the ability to preserve. But this post isn’t about that; it is just a spark to the memory.
In 1986, I was a first-year graduate student in the Princeton physics department. As such, I had at that time little more competence in observing the sky than any other physicist (practically none). Nevertheless, I traipsed out into an open field at the dark edge of town on a clear night with a pair of binoculars and a vague knowledge of what part of the sky Comet Halley should be in. How hard could it be to spot the most famous comet in history?
Impossibly hard. There was nothing to see, so far as I could find. The apparition of 1986 was a bust. This informed in me a bad attitude towards comets. There had never been a good apparition in my lifetime (all of 22 years at that point), and Halley certainly wasn’t one. I accepted that decent comets must be a rare occurrence.
Flash forward a decade to 1996, by which time I was an accomplished observer with a good working knowledge of the celestial sphere. A new comet was discovered – Hyakutake – and with it came much hype. Yeah, yeah, I’d heard it all before. Boring. Comets were always a flop.
Comet Hyakutake made a close approach to Earth in March of 1996. Its wikipedia page is pretty good, with a nice illustration of its orbit and its path on the sky as perceived from the Earth. I was working at DTM at the time, where there were lots of planetary scientists as well as a few astronomers. Someone posted an ephemeris, so despite my distrust of comets I found myself peeking at what its trajectory would be. Nevertheless, we had a long period of cloudy weather, so there was nothing to see even if there was something to see, which I expected there wasn’t.
At this time, my elder daughter Caitlyn was two years old. I made a habit of taking her out and pointing things out in the sky. We watched the sunset, the moon set after it near new moon, and the moon rise near full moon. She seemed content to listen to her old man babble about the lights in the sky. Apparently more of that sank in than I realized.
My wife Anne was teaching at Loyola, and her department chair had invited us over for a party around the vernal equinox. We enjoyed the adult company and Caitlyn put up well with it – up to a point. It got dark and we bid our farewells and headed out. We had parked across the street, and on the way out Betsy (our hostess) said “Stacy – you’re an astronomer. Where’s the comet?”
I got this pained expression. Stupid comets. But it had cleared up for the first time in nearly a week, and looking up from the front door, I could quickly orient myself on the sky. Doing so, I realize that the comet was behind the house. So I pointed up and over, towards the back yard and through the roof: “Over there.” I continued across the street to the car with the toddler cradled in my left arm, fiddling with the keys with my right hand.
We did not have a nice car: one had to insert the key manually into the door to unlock it. As I went around the car to get to the driver’s side, I was focused on this mundane task. It did not occur to me to look up in the direction I had just pointed. I felt Caitlyn stretch her arm to point at the sky, exclaiming “Fuzzy thing!”
I looked up. There is was: a big, bright, fuzzy ball. A brilliant cometary apparition, the coma easily visible even in Baltimore. My two-year old daughter spotted it and accurately classified it before I even looked up.
Comet Hyakutake was an amazing event. Not only spectacular to look at, but it drove home celestial mechanics in a visceral way. It was at this time very close to Earth (by the scale of such things). That meant it made noticeable progress in its orbit from night to night. You couldn’t see it moving just staring at it, but one night is was here, the next night it was there, the following night over there. It was skipping through the constellations at a dizzying speed for an object that takes c. 70,000 years to complete one orbit. But we were close enough that one could easily see the progress it made across the sky from night to night, if not minute to minute. If you wanted to take a picture with a telescope, you had to track the telescope to account for this – hence the star trails in the image above: the stars appear as streaks because the telescope is moving with the comet, not with the sky.
This figure (credit: Tom Ruen) shows the orbital path of Comet Huyakutake projected on the sky (constellations outlined in blue). Most of the time, the comet is far away near the aphelion of its orbit. As it fell in towards the sun, its path made annual ellipses due to the reflex motion of the Earth’s own orbit – the parallax. These grew in size until the comet came sweeping by in the month of March, 1996. Think about it: it spent tens of thousands of years spiraling down towards us, only to shoot by, transitioning well across the sky in only a couple of weeks. Celestial mechanics made visible.
Not long after Hyakutake started to fade, Comet Hale-Bopp became visible. Hale-Bopp did not pass as close to the Earth as Hyakutake, so it didn’t leap across the sky like Tom Bombadil. But Hale-Bopp was a physically larger comet. As such, it got bright and stayed bright for a long time, remaining visible to the naked eye for a record year and half. In the months after Hyakutake’s apparition, we could see Hale-Bopp chasing the sunset from the balcony of our apartment. Caitlyn and I would sit there and watch it as the twilight faded into dark. Her experience of comets had been the opposite of mine: where in my thirty years (before that point) they had been rare and disappointing, in her (by then) three years they had been common and spectacular.
The sky is full of marvels. You never know when you might get to see one.
I happened to visit this blog as a visitor from a computer not mine. Seeing it that way made me realize how obnoxious the ads had become. So WordPress’s extortion worked; I’ve agreed to send them a few $ every month to get rid of the ads. With it comes a new domain name: tritonstation.com. Bookmarks to the previous website (tritonstation.wordpress.com) should redirect here. Let me know if a problem arises, or the barrage of ads fails to let up. I may restructure the web page so there is more here than just this blog, but that will have to await my attention in my copious spare time.
Physics and Astronomy are two fields divided by a common interest in how the universe works. There is a considerable amount of overlap between some sub-fields of these subjects, and practically none at all in others. The aims and goals are often in common, but the methods, assumptions, history, and culture are quite distinct. This leads to considerable confusion, as with the English language – scientists with different backgrounds sometimes use the same words to mean rather different things.
A few terms that are commonly used to describe scientists who work on the subjects that I do include astronomer, astrophysicist, and cosmologist. I could be described as any of the these. But I also know lots of scientists to whom these words could be applied, but would mean something rather different.
A common question I get is “What’s the difference between an astronomer and an astrophysicist?” This is easy to answer from my experience as a long-distance commuter. If I get on a plane, and the person next to me is chatty and asks what I do, if I feel like chatting, I am an astronomer. If I don’t, I’m an astrophysicist. The first answer starts a conversation, the second shuts it down.
Flippant as that anecdote is, it is excruciatingly accurate – both for how people react (commuting between Cleveland and Baltimore for a dozen years provided lots of examples), and for what the difference is: practically none. If I try to offer a more accurate definition, then I am sure to fail to provide a complete answer, as I don’t think there is one. But to make the attempt:
Astronomy is the science of observing the sky, encompassing all elements required to do so. That includes practical matters like the technology of telescopes and their instruments across all wavelengths of the electromagnetic spectrum, and theoretical matters that allow us to interpret what we see up there: what’s a star? a nebula? a galaxy? How does the light emitted by these objects get to us? How do we count photons accurately and interpret what they mean?
Astrophysics is the science of how things in the sky work. What makes a star shine? [Nuclear reactions]. What produces a nebular spectrum? [The atomic physics of incredibly low density interstellar plasma.] What makes a spiral galaxy rotate? [Gravity! Gravity plus, well, you know, something. Or, if you read this blog, you know that we don’t really know.] So astrophysics is the physics of the objects astronomy discovers in the sky. This is a rather broad remit, and covers lots of physics.
With this definition, astrophysics is a subset of astronomy – such a large and essential subset that the terms can and often are used interchangeably. These definitions are so intimately intertwined that the distinction is not obvious even for those of us who publish in the learned journals of the American Astronomical Society: the Astronomical Journal (AJ) and the Astrophysical Journal (ApJ). I am often hard-pressed to distinguish between them, but to attempt it in brief, the AJ is where you publish a paper that says “we observed these objects” and the ApJ is where you write “here is a model to explain these objects.” The opportunity for overlap is obvious: a paper that says “observations of these objects test/refute/corroborate this theory” could appear in either. Nevertheless, there was a clearly a sufficient need to establish a separate journal focused on the physics of how things in the sky worked to launch the Astrophysical Journal in 1895 to complement the older Astronomical Journal (dating from 1849).
Cosmology is the study of the entire universe. As a science, it is the subset of astrophysics that encompasses observations that measure the universe as a physical entity: its size, age, expansion rate, and temporal evolution. Examples are sufficiently diverse that practicing scientists who call themselves cosmologists may have rather different ideas about what it encompasses, or whether it even counts as astrophysics in the way defined above.
Indeed, more generally, cosmology is where science, philosophy, and religion collide. People have always asked the big questions – we want to understand the world in which we find ourselves, our place in it, our relation to it, and to its Maker in the religious sense – and we have always made up stories to fill in the gaping void of our ignorance. Stories that become the stuff of myth and legend until they are unquestionable aspects of a misplaced faith that we understand all of this. The science of cosmology is far from immune to myth making, and often times philosophical imperatives have overwhelmed observational facts. The lengthy persistence of SCDM in the absence of any credible evidence that Ωm = 1 is a recent example. Another that comes and goes is the desire for a Phoenix universe – one that expands, recollapses, and is then reborn for another cycle of expansion and contraction that repeats ad infinitum. This is appealing for philosophical reasons – the universe isn’t just some bizarre one-off – but there’s precious little that we know (or perhaps can know) to suggest it is a reality.
Nevertheless, genuine and enormous empirical progress has been made. It is stunning what we know now that we didn’t a century ago. It has only been 90 years since Hubble established that there are galaxies external to the Milky Way. Prior to that, the prevailing cosmology consisted of a single island universe – the Milky Way – that tapered off into an indefinite, empty void. Until Hubble established otherwise, it was widely (though not universally) thought that the spiral nebulae were some kind of gas clouds within the Milky Way. Instead, the universe is filled with millions and billions of galaxies comparable in stature to the Milky Way.
We have sometimes let our progress blind us to the gaping holes that remain in our knowledge. Some of our more imaginative and less grounded colleagues take some of our more fanciful stories to be established fact, which sometimes just means the problem is old and familiar so boring if still unsolved. They race ahead to create new stories about entities like multiverses. To me, multiverses are manifestly metaphysical: great fun for late night bull sessions, but not a legitimate branch of physics.
So cosmology encompasses a lot. It can mean very different things to different people, and not all of it is scientific. I am not about to touch on the world-views of popular religions, all of which have some flavor of cosmology. There is controversy enough about these definitions among practicing scientists.
I started as a physicist. I earned an SB in physics from MIT in 1985, and went on to the physics (not the astrophysics) department of Princeton for grad school. I had elected to study physics because I had a burning curiosity about how the world works. It was not specific to astronomy as defined above. Indeed, astronomy seemed to me at the time to be but one of many curiosities, and not necessarily the main one.
There was no clear department of astronomy at MIT. Some people who practiced astrophysics were in the physics department; others in Earth, Atmospheric, and Planetary Science, still others in Mathematics. At the recommendation of my academic advisor Michael Feld, I wound up doing a senior thesis with George W. Clark, a high energy astrophysicist who mostly worked on cosmic rays and X-ray satellites. There was a large high energy astrophysics group at MIT who studied X-ray sources and the physics that produced them – things like neutron stars, black holes, supernova remnants, and the intracluster medium of clusters of galaxies – celestial objects with sufficiently extreme energies to make X-rays. The X-ray group needed to do optical follow-up (OK, there’s an X-ray source at this location on the sky. What’s there?) so they had joined the MDM Observatory. I had expressed a vague interest in orbital dynamics, and Clark had become interested in the structure of elliptical galaxies, motivated by the elegant orbital structures described by Martin Schwarzschild. The astrophysics group did a lot of work on instrumentation, so we had access to a new-fangled CCD. These made (and continue to make) much more sensitive detectors than photographic plates.
Empowered by this then-new technology, we embarked on a campaign to image elliptical galaxies with the MDM 1.3 m telescope. The initial goal was to search for axial twists as the predicted consequence of triaxial structure – Schwarzschild had shown that elliptical galaxies need not be oblate or prolate, but could have three distinct characteristic lengths along their principal axes. What we noticed instead with the sensitive CCD was a wonder of new features in the low surface brightness outskirts of these galaxies. Most elliptical galaxies just fade smoothly into obscurity, but every fourth or fifth case displayed distinct shells and ripples – features that were otherwise hard to spot that had only recently been highlighted by Malin & Carter.
At the time I was doing this work, I was of course reading up on galaxies in general, and came across Mike Disney’s arguments as to how low surface brightness galaxies could be ubiquitous and yet missed by many surveys. This resonated with my new observing experience. Look hard enough, and you would find something new that had never before been seen. This proved to be true, and remains true to this day.
I went on only two observing runs my senior year. The weather was bad for the first one, clearing only the last night during which I collected all the useful data. The second run came too late to contribute to my thesis. But I was enchanted by the observatory as a remote laboratory, perched in the solitude of the rugged mountains, themselves alone in an empty desert of subtly magnificent beauty. And it got dark at night. You could actually see the stars. More stars than can be imagined by those confined to the light pollution of a city.
It hadn’t occurred to me to apply to an astronomy graduate program. I continued on to Princeton, where I was assigned to work in the atomic physics lab of Will Happer. There I mostly measured the efficiency of various buffer gases in moderating spin exchange between sodium and xenon. This resulted in my first published paper.
In retrospect, this is kinda cool. As an alkali, the atomic structure of sodium is basically that of a noble gas with a spare electron it’s eager to give away in a chemical reaction. Xenon is a noble gas, chemically inert as it already has nicely complete atomic shells; it wants neither to give nor receive electrons from other elements. Put the two together in a vapor, and they can form weak van der Waals molecules in which they share the unwanted valence electron like a hot potato. The nifty thing is that one can spin-polarize the electron by optical pumping with a laser. As it happens, the wave function of the electron has a lot of overlap with the nucleus of the xenon (one of the allowed states has no angular momentum). Thanks to this overlap, the spin polarization imparted to the electron can be transferred to the xenon nucleus. In this way, it is possible to create large amounts of spin-polarized xenon nuclei. This greatly enhances the signal of MRI, and has found an application in medical imaging: a patient can breathe in a chemically inert [SAFE], spin polarized noble gas, making visible all the little passageways of the lungs that are otherwise invisible to an MRI. I contributed very little to making this possible, but it is probably the closest I’ll ever come to doing anything practical.
The same technology could, in principle, be applied to make dark matter detection experiments phenomenally more sensitive to spin-dependent interactions. Giant tanks of xenon have already become one of the leading ways to search for WIMP dark matter, gobbling up a significant fraction of the world supply of this rare noble gas. Spin polarizing the xenon on the scales of tons rather than grams is a considerable engineering challenge.
Now, in that last sentence, I lapsed into a bit of physics arrogance. We understand the process. Making it work is “just” a matter of engineering. In general, there is a lot of hard work involved in that “just,” and a lot of times it is a practical impossibility. That’s probably the case here, as the polarization decays away quickly – much more quickly than one could purify and pump tons of the stuff into a vat maintained at a temperature near absolute zero.
At the time, I did not appreciate the meaning of what I was doing. I did not like working in Happer’s lab. The windowless confines kept dark but for the sickly orange glow of a sodium D laser was not a positive environment to be in day after day after day. More importantly, the science did not call to my heart. I began to dream of a remote lab on a scenic mountain top.
I also found the culture in the physics department at Princeton to be toxic. Nothing mattered but to be smarter than the next guy (and it was practically all guys). There was no agreed measure for this, and for the most part people weren’t so brazen as to compare test scores. So the thing to do was Be Arrogant. Everybody walked around like they were too frickin’ smart to be bothered to talk to anyone else, or even see them under their upturned noses. It was weird – everybody there was smart, but no human could possible be as smart as these people thought they were. Well, not everybody, of course – Jim Peebles is impossibly intelligent, sane, and even nice (perhaps he is an alien, or at least a Canadian) – but for most of Princeton arrogance was a defining characteristic that seeped unpleasantly into every interaction.
It was, in considerable part, arrogance that drove me away from physics. I was appalled by it. One of the best displays was put on by David Gross in a colloquium that marked the take-over of theoretical physics by string theory. The dude was talking confidently in bold positivist terms about predictions that were twenty orders of magnitude in energy beyond any conceivable experimental test. That, to me, wasn’t physics.
More than thirty years on, I can take cold comfort that my youthful intuition was correct. String theory has conspicuously failed to provide the vaunted “theory of everything” that was promised. Instead, we have vague “landscapes” of 10500 possible theories. Just want one. 10500 is not progress. It’s getting hopelessly lost. That’s what happens when brilliant ideologues are encouraged to wander about in their hyperactive imaginations without experimental guidance. You don’t get physics, you get metaphysics. If you think that sounds harsh, note that Gross himself takes exactly this issue with multiverses, saying the notion “smells of angels” and worrying that a generation of physicists will be misled down a garden path – exactly the way he misled a generation with string theory.
So I left Princeton, and switched to a field where progress could be made. I chose to go to the University of Michigan, because I knew it had access to the MDM telescopes (one of the M’s stood for Michigan, the other MIT, with the D for Dartmouth) and because I was getting married. My wife is an historian, and we needed a university that was good in both our fields.
When I got to Michigan, I was ready to do research. I wanted to do more on shell galaxies, and low surface brightness galaxies in general. I had had enough coursework, I reckoned; I was ready to DO science. So I was somewhat taken aback that they wanted me to do two more years of graduate coursework in astronomy.
Some of the physics arrogance had inevitably been incorporated into my outlook. To a physicist, all other fields are trivial. They are just particular realizations of some subset of physics. Chemistry is just applied atomic physics. Biology barely even counts as science, and those parts that do could be derived from physics, in principle. As mere subsets of physics, any other field can and will be picked up trivially.
After two years of graduate coursework in astronomy, I had the epiphany that the field was not trivial. There were excellent reasons, both practical and historical, why it was a separate field. I had been wrong to presume otherwise.
Modern physicists are not afflicted by this epiphany. That bad attitude I was guilty of persists and is remarkably widespread. I am frequently confronted by young physicists eager to mansplain my own field to me, who casually assume that I am ignorant of subjects that I wrote papers on before they started reading the literature, and who equate a disagreement with their interpretation on any subject with ignorance on my part. This is one place the fields diverge enormously. In physics, if it appears in a textbook, it must be true. In astronomy, we recognize that we’ve been wrong about the universe so many times, we’ve learned to be tolerant of interpretations that initially sound absurd. Today’s absurdity may be tomorrow’s obvious fact. Physicists don’t share this history, and often fail to distinguish interpretation from fact, much less cope with the possibility that a single set of facts may admit multiple interpretations.
Cosmology has often been a leader in being wrong, and consequently enjoyed a shady reputation in both physics and astronomy for much of the 20th century. When I started on the faculty at the University of Maryland in 1998, there was no graduate course in the subject. This seemed to me to be an obvious gap to fill, so I developed one. Some of the senior astronomy faculty expressed concern as to whether this could be a rigorous 3 credit graduate course, and sent a neutral representative to discuss the issue with me. He was satisfied. As would be any cosmologist – I was teaching LCDM before most other cosmologists had admitted it was a thing.
At that time, 1998, my wife was also a new faculty member at John Carroll University. They held a welcome picnic, which I attended as the spouse. So I strike up a conversation with another random spouse who is also standing around looking similarly out of place. Ask him what he does. “I’m a physicist.” Ah! common ground – what do you work on? “Cosmology and dark matter.” I was flabbergasted. How did I not know this person? It was Glenn Starkman, and this was my first indication that sometime in the preceding decade, cosmology had become an acceptable field in physics and not a suspect curiosity best left to woolly-minded astronomers.
This was my first clue that there were two entirely separate groups of professional scientists who self-identified as cosmologists. One from the astronomy tradition, one from physics. These groups use the same words to mean the same things – sometimes. There is a common language. But like British English and American English, sometimes different things are meant by the same words.
“Dark matter” is a good example. When I say dark matter, I mean the vast diversity of observational evidence for a discrepancy between measurable probes of gravity (orbital speeds, gravitational lensing, equilibrium hydrostatic temperatures, etc.) and what is predicted by the gravity of the observed baryonic material – the stars and gas we can see. When a physicist says “dark matter,” he seems usually to mean the vast array of theoretical hypotheses for what new particle the dark matter might be.
To give a recent example, a colleague who is a world-reknowned expert on dark matter, and an observational astronomer in a physics department dominated by particle cosmologists, noted that their chairperson had advocated a particular hiring plan because “we have no one who works on dark matter.” This came across as incredibly disrespectful, which it is. But it is also simply clueless. It took some talking to work through, but what we think he meant was that they had no one who worked on laboratory experiments to detect dark matter. That’s a valid thing to do, which astronomers don’t deny. But it is a severely limited way to think about it.
To date, the evidence for dark matter to date is 100% astronomical in nature. That’s all of it. Despite enormous effort and progress, laboratory experiments provide 0%. Zero point zero zero zero. And before some fool points to the cosmic microwave background, that is not a laboratory experiment. It is astronomy as defined above: information gleaned from observation of the sky. That it is done with photons from the mm and microwave part of the spectrum instead of the optical part of the spectrum doesn’t make it fundamentally different: it is still an observation of the sky.
And yet, apparently the observational work that my colleague did was unappreciated by his own department head, who I know to fancy himself an expert on the subject. Yet existence of a complementary expert in his own department didn’t ever register him. Even though, as chair, he would be responsible for reviewing the contributions of the faculty in his department on an annual basis.
To many physicists we astronomers are simply invisible. What could we possibly teach them about cosmology or dark matter? That we’ve been doing it for a lot longer is irrelevant. Only what they [re]invent themselves is valid, because astronomy is a subservient subfield populated by people who weren’t smart enough to become particle physicists. Because particle physicists are the smartest people in the world. Just ask one. He’ll tell you.
To give just one personal example of many: a few years ago, after I had published a paper in the premiere physics journal, I had a particle physics colleague ask, in apparent sincerity, “Are you an astrophysicist?” I managed to refrain from shouting YES YOU CLUELESS DUNCE! Only been doing astrophysics formy entire career!
As near as I can work out, his erroneous definition of astrophysicist involved having a Ph.D. in physics. That’s a good basis to start learning astrophysics, but it doesn’t actually qualify. Kris Davidson noted a similar sociology among his particle physics colleagues: “They simply declare themselves to be astrophysicsts.” Well, I can tell you – having made that same mistake personally – it ain’t that simple. I’m pleased that so many physicists are finally figuring out what I did in the 1980s, and welcome their interest in astrophysics and cosmology. But they need to actually learn the subject, just not assume they’ll pick it up in a snap without actually doing so.
I haven’t written here since late January, which not coincidentally was early in the Spring semester. Let’s just say it was… eventful. Mostly in an administrative way, which is neither a good way, nor an interesting way.
Not that plenty interesting hasn’t happened. I had a great visit to Aachen for the conference Dark Matter & Modified Gravity. Lots of emphasis on the philosophy of science, as well as history and sociology. Almost enough to make me think there is hope for the future. Almost. From there I visited CP3 in Odense where I gave both a science talk and a public talk at the Anarkist beer & food lab. It was awesome – spoke to a packed house in a place that was clearly used as a venue for rock concerts most of the time. People actually came out on a crappy night in February and paid a cover to hear about science!
I’d love to simply write my Aachen talk here, or the public Odense talk, and I should, but – writing takes a lot longer than talking. I’m continually amazed at how inefficient human communication is. Writing is painfully slow, and while I go to great lengths to write clearly and compellingly, I don’t always succeed. Even when I do, reading comprehension does not seem to be on an upward trajectory in the internet age. I routinely get accused of ignoring this or that topic by scientists too lazy to do a literature search wherein they would find I had written a paper on that. This has gotten so bad that it is currently a fad to describe as natural a phenomenon I explicitly showed over 20 years ago was the opposite of natural in LCDM. Faith in dark matter overpowers reason.
So many stories to tell, so little time to tell them. Some are positive. But far too many are the sordid sort of human behavior overriding the ideals of science. Self awareness is in short supply, and objectivity seems utterly forgotten as a concept, let alone a virtue. Many scientists no longer seem to appreciate the distinction between an a priori prediction and a post-hoc explanation pulled out of one’s arse when confronted with confounding evidence.
Consequently, I have quite intentionally refrained from ranting about bad scientific behavior too much, mostly in a mistaken but habitual “if you can’t say anything nice” sort of way. Which is another reason I have been quiet of late: I really don’t like to speak ill of my colleagues, even when they deserve it. There is so much sewage masquerading as science that I’m holding my nose while hoping it flows away under the bridge.
So, to divert myself, I have been dabbling in art. I am not a great artist by any means, but I’ve had enough people tell me “I’d buy that!” that I finally decided to take them at their word (silly, I know) and open a Zazzle store. Which immediately wants me to add links to it, which I find myself unprepared to do. I have had an academic website for a long time (since 1996, which is forever in internet years) but it seems really inappropriate to put them there. So I’m putting them here because this is the only place I’ve got readily available.
So the title “shameless commercialism” is quite literal. I hadn’t meant to advertise it here at all. Just find I need a web page, stat! It ain’t like I’ve even had time to stock the store – it is a lot more fun to do science than write it up; similarly, it is a lot more fun to create art than it is to market it. So there is only the one inaugural item so far, an Allosaurus on a T-shirt. Seems to fit the mood of the past semester.
There is a tendency when teaching science to oversimplify its history for the sake of getting on with the science. How it came to be isn’t necessary to learn it. But to do science requires a proper understanding of the process by which it came to be.
The story taught to cosmology students seems to have become: we didn’t believe in the cosmological constant (Λ), then in 1998 the Type Ia supernovae (SN) monitoring campaigns detected accelerated expansion, then all of a sudden we did believe in Λ. The actual history was, of course, rather more involved – to the point where this oversimplification verges on disingenuous. There were many observational indications of Λ that were essential in paving the way.
Modern cosmology starts in the early 20th century with the recognition that the universe should be expanding or contracting – a theoretical inevitability of General Relativity that Einstein initially tried to dodge by inventing the cosmological constant – and is expanding in fact, as observationally established by Hubble and Slipher and many others since. The Big Bang was largely considered settled truth after the discovery of the existence of the cosmic microwave background (CMB) in 1964.
The CMB held a puzzle, as it quickly was shown to be too smooth. The early universe was both isotropic and homogeneous. Too homogeneous. We couldn’t detect the density variations that could grow into galaxies and other immense structures. Though such density variations are now well measured as temperature fluctuations that are statistically well described by the acoustic power spectrum, the starting point was that these fluctuations were a disappointing no-show. We should have been able to see them much sooner, unless something really weird was going on…
That something weird was non-baryonic cold dark matter (CDM). For structure to grow, it needed the helping hand of the gravity of some unseen substance. Normal matter matter did not suffice. The most elegant cosmology, the Einstein-de Sitter universe, had a mass density Ωm= 1. But the measured abundances of the light elements were only consistent with the calculations of big bang nucleosynthesis if normal matter amounted to only 5% of Ωm = 1. This, plus the need to grow structure, led to the weird but seemingly unavoidable inference that the universe must be full of invisible dark matter. This dark matter needed to be some slow moving, massive particle that does not interact with light nor reside within the menagerie of particles present in the Standard Model of Particle Physics.
CDM and early universe Inflation were established in the 1980s. Inflation gave a mechanism that drove the mass density to exactly one (elegant!), and CDM gave us hope for enough mass to get to that value. Together, they gave us the Standard CDM (SCDM) paradigm with Ωm = 1.000 and H0 = 50 km/s/Mpc.
It is hard to overstate the ferver with which the SCDM paradigm was believed. Inflation required that the mass density be exactly one; Ωm < 1 was inconceivable. For an Einstein-de Sitter universe to be old enough to contain the oldest stars, the Hubble constant had to be the lower of the two (50 or 100) commonly discussed at that time. That meant that H0 > 50 was Right Out. We didn’t even discuss Λ. Λ was Unmentionable. Unclean.
SCDM was Known, Khaleesi.
Λ had attained unmentionable status in part because of its origin as Einstein’s greatest blunder, and in part through its association with the debunked Steady State model. But serious mention of it creeps back into the literature by 1990. The first time I personally heard Λ mentioned as a serious scientific possibility was by Yoshii at a conference in 1993. Yoshii based his argument on a classic cosmological test, N(m) – the number of galaxies as a function of how faint they appeared. The deeper you look, the more you see, in a way that depends on the intrinsic luminosity of galaxies, and how they fill space. Look deep enough, and you begin to trace the geometry of the cosmos.
At this time, one of the serious problems confronting the field was the faint blue galaxies problem. There were so many faint galaxies on the sky, it was incredibly difficult to explain them all. Yoshii made a simple argument. To get so many galaxies, we needed a big volume. The only way to do that in the context of the Robertson-Walker metric that describes the geometry of the universe is if we have a large cosmological constant, Λ. He was arguing for ΛCDM five years before the SN results.
Yoshii was shouted down. NO! Galaxies evolve! We don’t need no stinking Λ! In retrospect, Yoshii & Peterson (1995) looks like a good detection of Λ. Perhaps Yoshii & Peterson also deserve a Nobel prize?
A very influential 1995 paper by Ostriker & Steinhardt did a lot to launch ΛCDM. I was impressed by the breadth of data Ostriker & Steinhardt discussed, all of which demanded low Ωm. I thought the case for Λ was less compelling, as it hinged on the age problem in a way that might also have been solved, at that time, by simply having an open universe (low Ωm with no Λ). This would ruin Inflation, but I wasn’t bothered by that. I expect they were. Regardless, they definitely made that case for ΛCDM three years before the supernovae results. Their arguments were accepted by almost everyone who was paying attention, including myself. I heard Ostriker give a talk around this time during which he was asked “what cosmology are you assuming?” to which he replied “the right one.” Called the “concordance” cosmology by Ostriker & Steinhardt, ΛCDM had already achieved the status of most-favored cosmology by the mid-90s.
Ostriker & Steinhardt neglected to mention an important prediction of Λ: not only should the universe expand, but that expansion rate should accelerate! In 1995, that sounded completely absurd. People had looked for such an effect, and claimed not to see it. So I wrote a brief note pointing out the predicted acceleration of the expansion rate. I meant it in a bad way: how crazy would it be if the expansion of the universe was accelerating?! This was an obvious and inevitable consequence of ΛCDM that was largely being swept under the rug at that time.
I mean[t], surely we could live with Ωm < 1 but no Λ. Can’t we all just get along? Not really, as it turned out. I remember Mike Turner pushing the SN people very hard in Aspen in 1997 to Admit Λ. He had an obvious bias: as an Inflationary cosmologist, he had spent the previous decade castigating observers for repeatedly finding Ωm < 1. That’s too little mass, you fools! Inflation demands Ωm = 1.000! Look harder!
By 1997, Turner had, like many cosmologists, finally wrapped his head around the fact that we weren’t going to find enough mass for Ωm = 1. This was a huge problem for Inflation. The only possible solution, albeit an ugly one, was if Λ made up the difference. So there he was at Aspen, pressuring the people who observed supernova to Admit Λ. One, in particular, was Richard Ellis, a great and accomplished astronomer who had led the charge in shouting down Yoshii. They didn’t yet have enough data to Admit Λ. Not.Yet.
By 1998, there were many more high redshift SNIa. Enough to see Λ. This time, after the long series of results only partially described above, we were intellectually prepared to accept it – unlike in 1993. Had the SN experiments been conducted five years earlier, and obtained exactly the same result, they would not have been awarded the Nobel prize. They would instead have been dismissed as a trick of astrophysics: the universe evolves, metallicity was lower at earlier times, that made SN then different from now, they evolve and so cannot be used as standard candles. This sounds silly now, as we’ve figured out how to calibrate for intrinsic variations in the luminosities of Type Ia SN, but that is absolutely how we would have reacted in 1993, and no amount of improvements in the method would have convinced us. This is exactly what we did with faint galaxy counts: galaxies evolve; you can’t hope to understand that well enough to constrain cosmology. Do you ever hear them cited as evidence for Λ?
Great as the supernovae experiments to measure the metric genuinely were, they were not a discovery so much as a confirmation of what cosmologists had already decided to believe. There was no singular discovery that changed the way we all thought. There was a steady drip, drip, drip of results pointing towards Λ all through the ’90s – the age problem in which the oldest stars appeared to be older than the universe in which they reside, the early appearance of massive clusters and galaxies, the power spectrum of galaxies from redshift surveys that preceded Sloan, the statistics of gravitational lenses, and the repeated measurement of 1/4 < Ωm < 1/3 in a large variety of independent ways – just to name a few. By the mid-90’s, SCDM was dead. We just refused to bury it until we could accept ΛCDM as a replacement. That was what the Type Ia SN results really provided: a fresh and dramatic reason to accept the accelerated expansion that we’d already come to terms with privately but had kept hidden in the closet.
Note that the acoustic power spectrum of temperature fluctuations in the cosmic microwave background (as opposed to the mere existence of the highly uniform CMB) plays no role in this history. That’s because temperature fluctuations hadn’t yet been measured beyond their rudimentary detection by COBE. COBE demonstrated that temperature fluctuations did indeed exist (finally!) as they must, but precious little beyond that. Eventually, after the settling of much dust, COBE was recognized as one of many reasons why Ωm ≠ 1, but it was neither the most clear nor most convincing reason at that time. Now, in the 21st century, the acoustic power spectrum provides a great way to constrain what all the parameters of ΛCDM have to be, but it was a bit player in its development. The water there was carried by traditional observational cosmology using general purpose optical telescopes in a great variety of different ways, combined with a deep astrophysical understanding of how stars, galaxies, quasars and the whole menagerie of objects found in the sky work. All the vast knowledge incorporated in textbooks like those by Harrison, by Peebles, and by Peacock – knowledge that often seems to be lacking in scientists trained in the post-WMAP era.
Despite being a late arrival, the CMB power spectrum measured in 2000 by Boomerang and 2003 by WMAP did one important new thing to corroborate the ΛCDM picture. The supernovae data didn’t detect accelerated expansion so much as exclude the deceleration we had nominally expected. The data were also roughly consistent with a coasting universe (neither accelerating nor decelerating); the case for acceleration only became clear when we assumed that the geometry of the universe was flat (Ωm+ΩΛ = 1). That didn’t have to work out, so it was a great success of the paradigm when the location of the first peak of the power spectrum appeared in exactly the right place for a flat FLRW geometry.
The consistency of these data have given ΛCDM an air of invincibility among cosmologists. But a modern reconstruction of the Ostriker & Steinhardt diagram leaves zero room remaining – hence the tension between H0 = 73 measured directly and H0 = 67 from multiparameter CMB fits.
In cosmology, we are accustomed to having to find our way through apparently conflicting data. The difference between an expansion rate of 67 and 73 seems trivial given that the field was long riven – in living memory – by the dispute between 50 and 100. This gives rise to the expectation that the current difference is just a matter of some subtle systematic error somewhere. That may well be correct. But it is also conceivable that FLRW is inadequate to describe the universe, and we have been driven to the objectively bizarre parameters of ΛCDM because it happens to be the best approximation that can be obtained to what is really going on when we insist on approximating it with FLRW.
Though a logical possibility, that last sentence will likely drive many cosmologists to reach for their torches and pitchforks. Before killing the messenger, we should remember that we once endowed SCDM with the same absolute certainty we now attribute to ΛCDM. I was there, 3,000 internet years ago, when SCDM failed. There is nothing so sacred in ΛCDM that it can’t suffer the same fate, as has every single cosmology ever devised by humanity.
Today, we still lack definitive knowledge of either dark matter or dark energy. These add up to 95% of the mass-energy of the universe according to ΛCDM. These dark materials must exist.
This Thanksgiving, I’d highlight something positive. Recently, Bob Sanders wrote a paper pointing out that gas rich galaxies are strong tests of MOND. The usual fit parameter, the stellar mass-to-light ratio, is effectively negligible when gas dominates. The MOND prediction follows straight from the gas distribution, for which there is no equivalent freedom. We understand the 21 cm spin-flip transition well enough to relate observed flux directly to gas mass.
In any human endeavor, there are inevitably unsung heroes who carry enormous amounts of water but seem to get no credit for it. Sanders is one of those heroes when it comes to the missing mass problem. He was there at the beginning, and has a valuable perspective on how we got to where we are. I highly recommend his books, The Dark Matter Problem: A Historical Perspective and Deconstructing Cosmology.
In bright spiral galaxies, stars are usually 80% or so of the mass, gas only 20% or less. But in many dwarf galaxies, the mass ratio is reversed. These are often low surface brightness and challenging to observe. But it is a worthwhile endeavor, as their rotation curve is predicted by MOND with extraordinarily little freedom.
Though gas rich galaxies do indeed provide an excellent test of MOND, nothing in astronomy is perfectly clean. The stellar mass-to-light ratio is an irreducible need-to-know parameter. We also need to know the distance to each galaxy, as we do not measure the gas mass directly, but rather the flux of the 21 cm line. The gas mass scales with flux and the square of the distance (see equation 7E7), so to get the gas mass right, we must first get the distance right. We also need to know the inclination of a galaxy as projected on the sky in order to get the rotation to which we’re fitting right, as the observed line of sight Doppler velocity is only sin(i) of the full, in-plane rotation speed. The 1/sin(i) correction becomes increasingly sensitive to errors as i approaches zero (face-on galaxies).
The mass-to-light ratio is a physical fit parameter that tells us something meaningful about the amount of stellar mass that produces the observed light. In contrast, for our purposes here, distance and inclination are “nuisance” parameters. These nuisance parameters can be, and generally are, measured independently from mass modeling. However, these measurements have their own uncertainties, so one has to be careful about taking these measured values as-is. One of the powerful aspects of Bayesian analysis is the ability to account for these uncertainties to allow for the distance to be a bit off the measured value, so long as it is not too far off, as quantified by the measurement uncertainties. This is what current graduate student Pengfei Li did in Li et al. (2018). The constraints on MOND are so strong in gas rich galaxies that often the nuisance parameters cannot be ignored, even when they’re well measured.
To illustrate what I’m talking about, let’s look at one famous example, DDO 154. This galaxy is over 90% gas. The stars (pictured above) just don’t matter much. If the distance and inclination are known, the MOND prediction for the rotation curve follows directly. Here is an example of a MOND fit from a recent paper:
This is terrible! The MOND fit – essentially a parameter-free prediction – misses all of the data. MOND is falsified. If one is inclined to hate MOND, as many seem to be, then one stops here. No need to think further.
If one is familiar with the ups and downs in the history of astronomy, one might not be so quick to dismiss it. Indeed, one might notice that the shape of the MOND prediction closely tracks the shape of the data. There’s just a little difference in scale. That’s kind of amazing for a theory that is wrong, especially when it is amplifying the green line to predict the red one: it needn’t have come anywhere close.
Here is the fit to the same galaxy using the same data [already] published in Li et al.:
Now we have a good fit, using the same data! How can this be so?
I have not checked what Ren et al. did to obtain their MOND fits, but having done this exercise myself many times, I recognize the slight offset they find as a typical consequence of holding the nuisance parameters fixed. What if the measured distance is a little off?
Distance estimates to DDO 154 in the literature range from 3.02 Mpc to 6.17 Mpc. The formally most accurate distance measurement is 4.04 ± 0.08 Mpc. In the fit shown here, we obtained 3.87 ± 0.16 Mpc. The error bars on these distances overlap, so they are the same number, to measurement accuracy. These data do not falsify MOND. They demonstrate that it is sensitive enough to tell the difference between 3.8 and 4.1 Mpc.
One will never notice this from a dark matter fit. Ren et al. also make fits with self-interacting dark matter (SIDM). The nifty thing about SIDM is that it makes quasi-constant density cores in dark matter halos. Halos of this form are not predicted by “ordinary” cold dark matter (CDM), but often give better fits than either MOND of the NFW halos of dark matter-only CDM simulations. For this galaxy, Ren et al. obtain the following SIDM fit.
This is a great fit. Goes right through the data. That makes it better, right?
Not necessarily. In addition to the mass-to-light ratio (and the nuisance parameters of distance and inclination), dark matter halo fits have [at least] two additional free parameters to describe the dark matter halo, such as its mass and core radius. These parameters are highly degenerate – one can obtain equally good fits for a range of mass-to-light ratios and core radii: one makes up for what the other misses. Parameter degeneracy of this sort is usually a sign that there is too much freedom in the model. In this case, the data are adequately described by one parameter (the MOND fit M*/L, not counting the nuisances in common), so using three (M*/L, Mhalo, Rcore) is just an exercise in fitting a French curve. There is ample freedom to fit the data. As a consequence, you’ll never notice that one of the nuisance parameters might be a tiny bit off.
In other words, you can fool a dark matter fit, but not MOND. Erwin de Blok and I demonstrated this 20 years ago. A common myth at that time was that “MOND is guaranteed to fit rotation curves.” This seemed patently absurd to me, given how it works: once you stipulate the distribution of baryons, the rotation curve follows from a simple formula. If the two don’t match, they don’t match. There is no guarantee that it’ll work. Instead, it can’t be forced.
As an illustration, Erwin and I tried to trick it. We took two galaxies that are identical in the Tully-Fisher plane (NGC 2403 and UGC 128) and swapped their mass distribution and rotation curve. These galaxies have the same total mass and the same flat velocity in the outer part of the rotation curve, but the detailed distribution of their baryons differs. If MOND can be fooled, this closely matched pair ought to do the trick. It does not.
Our failure to trick MOND should not surprise anyone who bothers to look at the math involved. There is a one-to-one relation between the distribution of the baryons and the resulting rotation curve. If there is a mismatch between them, a fit cannot be obtained.
We also attempted to play this same trick on dark matter. The standard dark matter halo fitting function at the time was the pseudo-isothermal halo, which has a constant density core. It is very similar to the halos of SIDM and to the cored dark matter halos produced by baryonic feedback in some simulations. Indeed, that is the point of those efforts: they are trying to capture the success of cored dark matter halos in fitting rotation curve data.
Dark matter halos with a quasi-constant density core do indeed provide good fits to rotation curves. Too good. They are easily fooled, because they have too many degrees of freedom. They will fit pretty much any plausible data that you throw at them. This is why the SIDM fit to DDO 154 failed to flag distance as a potential nuisance. It can’t. You could double (or halve) the distance and still find a good fit.
This is why parameter degeneracy is bad. You get lost in parameter space. Once lost there, it becomes impossible to distinguish between successful, physically meaningful fits and fitting epicycles.
Astronomical data are always subject to improvement. For example, the THINGS project obtained excellent data for a sample of nearby galaxies. I made MOND fits to all the THINGS (and other) data for the MOND review Famaey & McGaugh (2012). Here’s the residual diagram, which has been on my web page for many years:
These are, by and large, good fits. The residuals have a well defined peak centered on zero. DDO 154 was one of the THINGS galaxies; lets see what happens if we use those data.
The first thing one is likely to notice is that the THINGS data are much better resolved than the previous generation used above. The first thing I noticed was that THINGS had assumed a distance of 4.3 Mpc. This was prior to the measurement of 4.04, so lets just start over from there. That gives the MOND prediction shown above.
And it is a prediction. I haven’t adjusted any parameters yet. The mass-to-light ratio is set to the mean I expect for a star forming stellar population, 0.5 in solar units in the Sptizer 3.6 micron band. D=4.04 Mpc and i=66 as tabulated by THINGS. The result is pretty good considering that no parameters have been harmed in the making of this plot. Nevertheless, MOND overshoots a bit at large radii.
Constraining the inclinations for gas rich dwarf galaxies like DDO 154 is a bit of a nightmare. Literature values range from 20 to 70 degrees. Seriously. THINGS itself allows the inclination to vary with radius; 66 is just a typical value. Looking at the fit Pengfei obtained, i=61. Let’s try that.
The fit is now satisfactory. One tweak to the inclination, and we’re done. This tweak isn’t even a fit to these data; it was adopted from Pengfei’s fit to the above data. This tweak to the inclination is comfortably within any plausible assessment of the uncertainty in this quantity. The change in sin(i) corresponds to a mere 4% in velocity. I could probably do a tiny bit better with further adjustment – I have left both the distance and the mass-to-light ratio fixed – but that would be a meaningless exercise in statistical masturbation. The result just falls out: no muss, no fuss.
Hence the point Bob Sanders makes. Given the distribution of gas, the rotation curve follows. And it works, over and over and over, within the bounds of the uncertainties on the nuisance parameters.
One cannot do the same exercise with dark matter. It has ample ability to fit rotation curve data, once those are provided, but zero power to predict it. If all had been well with ΛCDM, the rotation curves of these galaxies would look like NFW halos. Or any number of other permutations that have been discussed over the years. In contrast, MOND makes one unique prediction (that was not at all anticipated in dark matter), and that’s what the data do. Out of the huge parameter space of plausible outcomes from the messy hierarchical formation of galaxies in ΛCDM, Nature picks the one that looks exactly like MOND.
It is a bad sign for a theory when it can only survive by mimicking its alternative. This is the case here: ΛCDM must imitate MOND. There are now many papers asserting that it can do just this, but none of those were written before the data were provided. Indeed, I consider it to be problematic that clever people can come with ways to imitate MOND with dark matter. What couldn’t it imitate? If the data had all looked like technicolor space donkeys, we could probably find a way to make that so as well.
Cosmologists will rush to say “microwave background!” I have some sympathy for that, because I do not know how to explain the microwave background in a MOND-like theory. At least I don’t pretend to, even if I had more predictive success there than their entire community. But that would be a much longer post.
For now, note that the situation is even worse for dark matter than I have so far made it sound. In many dwarf galaxies, the rotation velocity exceeds that attributable to the baryons (with Newton alone) at practically all radii. By a lot. DDO 154 is a very dark matter dominated galaxy. The baryons should have squat to say about the dynamics. And yet, all you need to know to predict the dynamics is the baryon distribution. The baryonic tail wags the dark matter dog.
But wait, it gets better! If you look closely at the data, you will note a kink at about 1 kpc, another at 2, and yet another around 5 kpc. These kinks are apparent in both the rotation curve and the gas distribution. This is an example of Sancisi’s Law: “For any feature in the luminosity profile there is a corresponding feature in the rotation curve and vice versa.” This is a general rule, as Sancisi observed, but it makes no sense when the dark matter dominates. The features in the baryon distribution should not be reflected in the rotation curve.
The observed baryons orbit in a disk with nearly circular orbits confined to the same plane. The dark matter moves on eccentric orbits oriented every which way to provide pressure support to a quasi-spherical halo. The baryonic and dark matter occupy very different regions of phase space, the six dimensional volume of position and momentum. The two are not strongly coupled, communicating only by the weak force of gravity in the standard CDM paradigm.
One of the first lessons of galaxy dynamics is that galaxy disks are subject to a variety of instabilities that grow bars and spiral arms. These are driven by disk self-gravity. The same features do not appear in elliptical galaxies because they are pressure supported, 3D blobs. They don’t have disks so they don’t have disk self-gravity, much less the features that lead to the bumps and wiggles observed in rotation curves.
Elliptical galaxies are a good visual analog for what dark matter halos are believed to be like. The orbits of dark matter particles are unable to sustain features like those seen in baryonic disks. They are featureless for the same reasons as elliptical galaxies. They don’t have disks. A rotation curve dominated by a spherical dark matter halo should bear no trace of the features that are seen in the disk. And yet they’re there, often enough for Sancisi to have remarked on it as a general rule.
It gets worse still. One of the original motivations for invoking dark matter was to stabilize galactic disks: a purely Newtonian disk of stars is not a stable configuration, yet the universe is chock full of long-lived spiral galaxies. The cure was to place them in dark matter halos.
The problem for dwarfs is that they have too much dark matter. The halo stabilizes disks by suppressing the formation of structures that stem from disk self-gravity. But you need some disk self-gravity to have the observed features. That can be tuned to work in bright spirals, but it fails in dwarfs because the halo is too massive. As a practical matter, there is no disk self-gravity in dwarfs – it is all halo, all the time. And yet, we do see such features. Not as strong as in big, bright spirals, but definitely present. Whenever someone tries to analyze this aspect of the problem, they inevitably come up with a requirement for more disk self-gravity in the form of unphysically high stellar mass-to-light ratios (something I predicted would happen). In contrast, this is entirely natural in MOND (see, e.g., Brada & Milgrom 1999 and Tiret & Combes 2008), where it is all disk self-gravity since there is no dark matter halo.
The net upshot of all this is that it doesn’t suffice to mimic the radial acceleration relation as many simulations now claim to do. That was not a natural part of CDM to begin with, but perhaps it can be done with smooth model galaxies. In most cases, such models lack the resolution to see the features seen in DDO 154 (and in NGC 1560 and in IC 2574, etc.) If they attain such resolution, they better not show such features, as that would violate some basic considerations. But then they wouldn’t be able to describe this aspect of the data.
Simulators by and large seem to remain sanguine that this will all work out. Perhaps I have become too cynical, but I recall hearing that 20 years ago. And 15. And ten… basically, they’ve always assured me that it will work out even though it never has. Maybe tomorrow will be different. Or would that be the definition of insanity?
In the last post, I noted some of the sociological overtones underpinning attitudes about dark matter and modified gravity theories. I didn’t get as far as the more scientifically interesting part, which illustrates a common form of reasoning in physics.
“the only way these theories can be reconciled with observations is by effectively, and very precisely, mimicking the behavior of cold dark matter on cosmological scales.”
Leaving aside just which observations need to be mimicked so precisely (I expect they mean power spectrum; perhaps they consider this to be so obvious that it need not be stated), this kind of reasoning is both common and powerful – and frequently correct. Indeed, this is exactly the attitude I expressed in my review a few years ago for the Canadian Journal of Physics, quoted in the image above. I get it. There are lots of positive things to be said for the standard cosmology.
This upshot of this reasoning is, in effect, that “cosmology works so well that non-baryonic dark matter must exist.” I have sympathy for this attitude, but I also remember many examples in the history of cosmology where it has gone badly wrong. There was a time, not so long ago, that the matter density had to be the critical value, and the Hubble constant had to be 50 km/s/Mpc. By and large, it is the same community that insisted on those falsehoods with great intensity that continues to insist on conventionally conceived cold dark matter with similarly fundamentalist insistence.
I think it is an overstatement to say that the successes of cosmology (as we presently perceive them) prove the existence of dark matter. A more conservative statement is that the ΛCDM cosmology is correct if, and only if, dark matter exists. But does it? That’s a separate question, which is why laboratory searches are so important – including null results. It was, after all, the null result of Michelson & Morley that ultimately put an end to the previous version of an invisible aetherial medium, and sparked a revolution in physics.
Here I point out that the same reasoning asserted by Bertone & Tait as a slam dunk in favor of dark matter can just as accurately be asserted in favor of MOND. To directly paraphrase the above statement:
“the only way ΛCDM can be reconciled with observations is by effectively, and very precisely, mimicking the behavior of MOND on galactic scales.”
This is a terrible problem for dark matter. Even if it were true, as is often asserted, that MOND only fits rotation curves, this would still be tantamount to a falsification of dark matter by the same reasoning applied by Bertone & Tait.
Lets look at just one example, NGC 1560:
MOND fits the details of this rotation curve in excruciating detail. It provides just the right amount of boost over the Newtonian expectation, which varies from galaxy to galaxy. Features in the baryon distribution are reflected in the rotation curve. That is required in MOND, but makes no sense in dark matter, where the excess velocity over the Newtonian expectation is attributed to a dynamically hot, dominant, quasi-spherical dark matter halo. Such entities cannot support the features commonly seen in thin, dynamically cold disks. Even if they could, there is no reason that features in the dominant dark matter halo should align with those in the disk: a sphere isn’t a disk. In short, it is impossible to explain this with dark matter – to the extent that anything is ever impossible for the invisible.
NGC 1560 is a famous case because it has such an obvious feature. It is common to dismiss this as some non-equilibrium fluke that should simply be ignored. That is always a dodgy path to tread, but might be OK if it were only this galaxy. But similar effects are seen over and over again, to the point that they earned an empirical moniker: Renzo’s Rule. Renzo’s rule is known to every serious student of rotation curves, but has not informed the development of most dark matter theory. Ignoring this information is like leaving money on the table.
MOND fits not just NGC 1560, but very nearly* every galaxy we measure. It does so with excruciatingly little freedom. The only physical fit parameter is the stellar mass-to-light ratio. The gas fraction of NGC 1560 is 75%, so M*/L plays little role. We understand enough about stellar populations to have an idea what to expect; MOND fits return mass-to-light ratios that compare well with the normalization, color dependence, and band-pass dependent scatter expected from stellar population synthesis models.
One can also fit rotation curve data with dark matter halos. These require a minimum of three parameters to the one of MOND. In addition to M*/L, one also needs at least two parameters to describe the dark matter halo of each galaxy – typically some characteristic mass and radius. In practice, one finds that such fits are horribly degenerate: one can not cleanly constrain all three parameters, much less recover a sensible distribution of M*/L. One cannot construct the plot above simply by asking the data what it wants as one can with MOND.
The “disk-halo degeneracy” in dark matter halo fits to rotation curves has been much discussed in the literature. Obsessed over, dismissed, revived, and ultimately ignored without satisfactory understanding. Well, duh. This approach uses three parameters per galaxy when it takes only one to describe the data. Degeneracy between the excess fit parameters is inevitable.
From a probabilistic perspective, there is a huge volume of viable parameter space that could (and should) be occupied by galaxies composed of dark matter halos plus luminous galaxies. Two identical dark matter halos might host very different luminous galaxies, so would have rotation curves that differed with the baryonic component. Two similar looking galaxies might reside in rather different dark matter halos, again having rotation curves that differ.
The probabilistic volume in MOND is much smaller. Absolutely tiny by comparison. There is exactly one and only one thing each rotation curve can do: what the particular distribution of baryons in each galaxy says it should do. This is what we observe in Nature.
The only way ΛCDM can be reconciled with observations is by effectively, and very precisely, mimicking the behavior of MOND on galactic scales. There is a vast volume of parameter space that the rotation curves of galaxies could, in principle, inhabit. The naive expectation was exponential disks in NFW halos. Real galaxies don’t look like that. They look like MOND. Magically, out of the vast parameter space available to galaxies in the dark matter picture, they only ever pick the tiny sub-volume that very precisely mimics MOND.
The ratio of probabilities is huge. So many dark matter models are possible (and have been mooted over the years) that it is indefinably huge. The odds of observing MOND-like phenomenology in a ΛCDM universe is practically zero. This amounts to a practical falsification of dark matter.
I’ve never said dark matter is falsified, because I don’t think it is a falsifiable concept. It is like epicycles – you can always fudge it in some way. But at a practical level, it was falsified a long time ago.
That is not to say MOND has to be right. That would be falling into the same logical trap that says ΛCDM has to be right. Obviously, both have virtues that must be incorporated into whatever the final answer may be. There are some efforts in this direction, but by and large this is not how science is being conducted at present. The standard script is to privilege those data that conform most closely to our confirmation bias, and pour scorn on any contradictory narrative.
In my assessment, the probability of ultimate success through ignoring inconvenient data is practically zero. Unfortunately, that is the course upon which much of the field is currently set.
*There are of course exceptions: no data are perfect, so even the right theory will get it wrong once in a while. The goof rate for MOND fits is about what I expect: rare, but more frequent for lower quality data. Misfits are sufficiently rare that to obsess over them is to refuse to see the forest for a few outlying trees.
Here’s a residual plot of MOND fits. See the peak at right? That’s the forest. See the tiny tail to one side? That’s an outlying tree.