Dark Matter: Now You See It, Now You Don’t

Two interesting claims about dark matter this week, and on the face of it, completely contradictory, but in fact, not obviously so. Before saying one word more, let me repeat my mantra — something that all physicists know but relatively few non-scientists appreciate — most claims of a radical new result turn out to be largely or completely wrong. This is not because physicists are stupid but because doing science at the forefront of knowledge involves using novel techniques that might have unknown pitfalls, and also because a single small mistake can create a fake effect (as we saw most recently with the OPERA neutrino speed measurement.)  And because nasty statistical accidents can play tricks on you.

Both claims that I’m about to describe use novel techniques, and their analyses have not been repeated by anyone else. At this point you should understand that both are tentative, and (based on the history of radical claims) the odds are against them. Both might be wrong. That said, both analyses look to me as though they’ve been reasonably well done, and if a mistake has been made, it will require someone far more expert in dark matter studies than I am to point it out.

So let me describe them in turn, to the best of my ability.

Now You See It

First, the claim (which I mentioned in yesterday’s post) of a possible signal of photons being produced with an energy of somewhere around 130 GeV in locations near (but not necessarily extremely near) the center of the Milky Way galaxy. I recently wrote an article on how you can get photons of a definite energy from dark matter annihilation, which I encourage you to read first if you haven’t already, since I’m going to assume you know what’s in it.

Christoph Weniger has put out a preprint (not yet peer-reviewed) in which he uses data collected by the Fermi Large Area Telescope (a satellite experiment that measures gamma-rays, i.e. high energy photons). He looks at their data in particular regions of the galaxy, of various sizes, that include its center. These are regions where he calculates (based on certain assumptions) that a photon signal from dark matter would most easily be detected. What he’s looking for are places where the signal from dark matter would be expected to be large and background from astrophysical processes would be relatively small.

Fig. 1: Taken from Weniger's paper. Left, the region in which photons are selected; the galactic center is at the middle of the picture and the white areas reach well into the galactic bulge (see Figure 3 below.) Right, two classes of data in black and purple dots show the number (not exactly, but let me skip this detail) of photons versus the energy of the photon. A notable excess above a smooth background appears somewhere around 129 GeV (marked with a blue vertical dashed line). You can ignore the black dashed line.

He looks in five such regions, and in three of them he finds that when he plots the number of photons versus the energy per photon, there is an excess for photons with energy roughly centered around 129 GeV. (The three regions aren’t independent of one another, so this isn’t three independent excesses but rather one excess viewed three ways.) I won’t show you all of the data (you can look at Figure 1 of his preprint for the whole thing) but in my own Figure 1 is an example plot, showing at left one region that he is looking in (including the galactic center and two bulbous regions above and below the center) and at right the data. You can see a bump around 130 GeV (the blue vertical dashed line is at 129; the black dots and the purple dots represent two data sets; the gray dashes represent a smooth fit to the data sets.) Weniger then looks at the region near 130 more carefully, as shown in Figure 2 (again there is a lot more information in the preprint.) The green dashes are a fit that is a smooth structureless curve, while the red dashes are a fit to a smooth curve plus the blue curve at the bottom, which is shaped the way a signal from dark matter would be expected to look. (See my article on how why this is what you expect.)  The blue curve is rather wide because no experiment is perfect, and the Fermi Telescope is no exception; the actual energies of the photons would be expected to form a very narrow peak were it not for these imperfections. Weniger’s claim is that the red curve fits the data (black points, with vertical uncertainty bars showing one standard deviation) much better than the green curve, indicating the presence of a signal.

Fig. 2: From Weniger's paper, a more precise analysis of the data, showing the number (really the number this time, unlike Figure 1 above) of photons observed with a given energy E. Top: the data is in black dots, green is the best fit to a smooth distribution, red is the best fit to a smooth distribution plus the blue peak centered around 129. Bottom: the difference between the data and the red fit, showing that the fit works pretty well statistically.

Now, one has to step back here. If you take any data that approximates a smooth curve, you will always find bumps and wiggles on it. That’s just basic statistics; the number of events will sometimes be a little higher and sometimes a little lower than you expect. The question is not if there’s a bump somewhere; it’s whether there is a statistically significant bump, one which is so large that it is unlikely to have occurred by accident. What Weniger claims (and I cannot easily verify) is that the bump he sees has a statistical significance of 3.3 standard deviations after taking into account, conservatively, the look-elsewhere effect. (Without the look-elsewhere effect the significance is 4.6 standard deviations.) Naively that’s a one in a thousand effect, big enough to take seriously — but such effects sometimes go away with more data, so it’s not completely convincing yet.

And meanwhile, the question remains whether he did his statistical calculation correctly. I’ve watched previous theorists claim 3 standard deviation effects and then be contradicted by expert experimentalists, who tend to understand the subtleties of statistical arguments better. So before we take this result too seriously, we need to hear what other experts, including those from the Fermi Telescope itself, have to say.

As Weniger himself emphasizes in his title, this is at best a tentative detection, and as he points out in his abstract, it will be several years before we have enough data to be sure whether this is a fluke or a real signal. So I am afraid that even if Weniger has identified a real effect, we may have no choice but to be patient for two to four years and hope nothing goes wrong with the Fermi satellite… unless someone can put up a competing experiment in the meantime, or find corroborating evidence in some other way.

Now You Don’t

The second paper in question (peer-reviewed; here’s a pdf) is by Moni Bidin, Carraro, Menendez and Smith. They claim that there is no sign of any dark matter within a region around the sun of about ten thousand or so light years in radius. [A light year is the distance light travels in a year; for comparison, it takes light less than three seconds to travel to the moon and back.] The Milky Way’s center, where dark matter is expected to be most abundant and where Weniger is looking for photons from dark matter annihilation, is about twenty-five thousand light years away from the Sun, so the region that this group is studying lies far from the center; see Figure 3.

Fig. 3: The Milky Way galaxy consists of stars and other ordinary matter (white) and is believed to lie within a large, complicated, and poorly understood `halo' of dark matter with many sub-haloes. The possible detection of photons from dark matter is coming from the central region of the galaxy marked in green. The claim that gravitational effects of dark matter are not being observed, suggesting dark matter is in less than expected quantities, is being made within the red region centered around the sun. Note that this is a sketch, and all locations and densities indicated are very approximate.

Their approach is to study the gravitational effects of nearby matter, as reflected by the motions of a small sample of the stars that lie within a few thousand light years of the sun.  [Sorry -- I still don't understand their method well enough to explain it to non-experts, but will fill in more details if and when I do.] . And they claim that the motions of those stars suggest that the only matter nearby is the ordinary matter we can see around us, with no dark matter in addition. They claim their results rule out almost all existing guesses/models for how the dark matter in the galaxy is distributed. This is shown in Figure 4. The result of the paper is the solid black line I have marked “Data”, with uncertainties marked with 1 and 3 standard deviation bands labeled “1 s.d.” and “3 s.d.”  The line marked VIS is their estimate for what the effect of all the VISible matter in the sun’s vicinity would be. The line marked MIN is their estimate for the effect of visible matter plus what they view as the MINimal expected amount of dark matter. The other lines represent the expected effects of dark matter distributed in halos of various different shapes proposed by various experts.

Fig. 4: Taken from Moni Biden et al., with my additional annotation. A quantity called surface density obtained from star data (black line marked "Data", with 1 and 3 standard deviation uncertainties in dotted and dashed lines) compared against an estimate (VIS) of what it would look like if only visible matter were present in the region relatively nearby to the sun (see Figure 3) and various models of how dark matter might be distributed in the galaxy (MIN being what the authors claim is the minimal option, SHM being a common assumption.) No uncertainty estimates on the grey lines are provided.

There are two questions you have to ask of such claims.

  • First, did they do a correct analysis? Is the result that they present, and the uncertainty on that result, accurately obtained?
  • Second, did they interpret their analysis correctly? Do they really rule out there being any significant amount of dark matter in the vicinity of the sun?

I can’t evaluate their particular method; it’s somewhat complicated and lies outside my expertise and intuition. (Nor do I know much about the star data that is used as an input to their method.) But it appears quite interesting and somewhat innovative. They authors present a long list of assumptions on which their technique rests, and argue that relaxing the assumptions doesn’t change the answer that much. We’ll have to wait for experts to tell us if they feel that the assumptions are too strong, or if there are hidden assumptions that are even more important and worrying than the ones that were mentioned. But with so many assumptions, it wouldn’t surprise me if the uncertainties are underestimated.

You might ask: does this paper suggest that there is no such thing as dark matter, and that we need to modify gravity to explain effects often attributed to dark matter? Well, you can’t jump to this conclusion, because the method used by these authors assumes that gravity isn’t modified. So if you modify gravity, you’d also potentially modify this result too. You’d need to redo their analysis carefully with your favorite modification of gravity before you could learn anything.

One thing I do know is that the distribution of dark matter in our galaxy is very poorly known. The models of dark matter that they claim to rule out have significant uncertainties, and these grey lines in Figure 4 really aren’t narrow lines — they are thick bands. For instance, dark matter may be very clumpy, not smooth, whereas all of the halos they consider are assumed to be reasonably smooth. They claim that the lines shown are the most conservative possible versions of any given model, but I suspect that experts in these models would disagree; we’ll have to ask. And there’s no way that we know the amount of visible matter in the sun’s general vicinity to such precision as the line marked VIS would suggest; that too should be a thick band. So I think we need to be very careful interpreting this graph. It doesn’t say “there’s no dark matter in the vicinity.” It says “there can’t be as much dark matter as the models were expecting.” And maybe that’s just a statement that I’ve heard before — was it at the start of this paragraph? — that the distribution of dark matter in our galaxy is very poorly known.  If the dark matter halo is sufficiently clumpy and complex, the current result may reflect things going on near the sun but might not reflect anything overly significant about the overall properties of the halo.

One type of experiment for which the amount of dark matter in the local neighborhood is very important is the search to directly detect the rare collisions of dark matter particles with atomic nuclei. [I've briefly described some of this effort here, but I need to write a longer article about it.] Obviously, the less dark matter there is near the Earth, the harder it is to find these particles. The authors of the paper go so far as to say that such efforts might be impossible because their results suggest the amount of dark matter around the Earth is “negligible”. Well.  Hmm.  Given what they’ve actually shown (Figure 4), the only thing they can actually say is that the amount of dark matter is somewhat smaller than people assume, but certainly not that it’s negligible. Even if the amount of dark matter were 20 percent of what people expected, that just would mean it would take longer to find any particular type of dark matter — but there are many possible types to look for. The real implication would be that what people currently think is known about dark matter particles would have to be somewhat weakened.  But people already know that the local density of dark matter is very uncertain, so the current result’s impact on what people think they know would be limited.

So while the method is interesting and their result very intriguing, I would worry at this point that they are going way too far with their interpretation of it. We’ll need to see the method verified, the assumptions tested, and the approach applied to larger groups of stars with resulting smaller uncertainties before we can be sure the result is as dramatic as the authors claim.

A sociological comment: Frankly, I would trust this result more if it hadn’t been for the strongly worded and almost inflammatory press release that accompanied this paper.  In my experience, when papers are made public at the same time as a press release, the more confident the press release sounds, the less likely the paper is correct. Why? Because when people are so confident in their result that they immediately put out a powerful statement for the press and public to read, well before their expert colleagues have had some time to consider, test and criticize the result, it says a lot about their personalities and scientific approach. Nothing humble about these folks! They are absolutely certain there’s no dark matter around here whatsoever, and that they couldn’t possibly have overlooked anything. Well, in my experience, that attitude often leads to subtle unconscious biases. It appears, from the way this paper and the press release are worded, that these authors really wanted to show there was no dark matter nearby… that they had a strong prior agenda. It’s always better not to have a strong bias, when you start a scientific analysis, as to what the result is going to be.

But even if this paper turns out not to be correct in its results or its interpretation, it is very interesting in that it shows that it is feasible to measure the local dark matter density using a method of this type. Surely the method can be improved and applied to larger data samples in the future. So it seems to me that the authors already deserve credit for some pioneering work that may herald an era of better and better measurements of this type, which might lead us eventually to a more convincing understanding of how dark matter is distributed across our galaxy — or perhaps even show that the current conventional view of dark matter’s role in the galaxy is mistaken.

And of course, if the result is correct, then it will be important to interpret it very carefully, and understand what it does and doesn’t imply.  I feel that the only thing this paper can be said to show is that there is relatively little dark matter in the region near the sun, but the galaxy is a very big place, the dark matter is expected to be distributed in a complex fashion, and most of the dark matter is expected to be near the center. See Figure 3.   Consequently I think we really don’t know that much yet.   But this is a research area worth keeping a close eye on.

And meanwhile, we’d also better seek a second opinion before we get overly excited.

Detected? Rejected?

So, has dark matter been detected at the center of the galaxy? Has dark matter been rejected in the sun’s galactic neighborhood? Claims by scientists like these have to be treated with respect — both of these groups are breaking new ground. They’ve done work that is challenging and interesting and innovative — and risky as a result. Either or both papers may be wrong; history shows that the odds are against them.  Much as we’d like to know today what their results mean, we have no choice but to be patient, for it will likely take a few years of additional measurements and scientific debate for nature’s true story to be revealed.

76 responses to “Dark Matter: Now You See It, Now You Don’t

  1. Dark Matter is like the Chesshire’s cat!

  2. Allow me one more word ; it is not only the existence of D.M. but also the configuration / distribution / morphology of it…..we are here in front of a much much more kind of a mystery…..as we must explain the mechanism concerned.

    • Carroll described the result out of Chile as relating to the “lumpiness” of dark matter and how that fits current models. The authors are not arguing against the existence of DM itself with this data.

  3. Sean Carroll has a short write-up about this as well. He and his colleagues at Cal Tech seem skeptical at the moment – “nothing to lose sleep over yet” as he puts it.

    Also there is news from the Dark Matter particle detector front. I guess the field is pretty hot at the moment.

  4. It is not the lumpiness / distribution per se , it is the mechanism implementing that morphology which is assumed to direct the structure of the cosmos as a whole.

    • I’m not an expert – would you mind a little bit of elaboration? You are saying the paper seems to contradict the models for how matter and DM became lumpy in the first place — inflation models?

  5. Any chance something special happens when the dark matter falls on a black hole?
    A quick search on google says we should not expect anything special or any radiation from that. But there is a hope that dark matter traveling at close-to-light speed is not so ‘dark’ and around the black holes there is a place where this can happen.

    • It is possible that there is something interesting that happens, yes, but I’m not sure I’ve seen it worked out. I’d have to do some calculations. Probably the interesting opportunities only arise for black holes at the centers of galaxies, where there is the most dark matter falling in.

  6. Hi Matt, I have a few questions:

    I read now an then in the newspapers that it is likely that at the center of our galaxy there is a black whole. Should I understand from your articles that there is a high concentration of dark mater rather than a black hole?

    If I understand it well, the only think we know about dark mater is it’s gravitational effects. But that means dark mater is sensible to the gravitational force (and I assume in the same way as the ordinary matter). Why is it then so difficult to know/model where the dark mater is located?

    Can that “halo” of dark mater be just a field with no particles (ripples)?

    • There is both a large concentration of dark matter in the region around the center, and a very massive black hole dead center. But the black hole is much smaller than the region where the dark matter becomes potentially dense enough for annihilation.

      The problem with knowing where the dark matter is stems from not being able to measure gravitational effects on distant objects very easily. It is hard to tell, looking at an individual star, what is pulling on it. All we can tell is how fast it’s moving, but that is not enough to tell us how it is accelerating (which would directly tell us how it is being pulled.) So the methods have to be more clever than this.

      Dark matter might not be particles, and fields may be involved in a more complex way, but this is an advanced topic. The most likely situation is that it is particles, but it’s not certain.

  7. Thank you, Professor. What if we were inside a clump of dark matter? How would we know, if these techniques work as they are proposed to?

    • Roughly, stars on the outskirts of a large clump of matter will move faster on average than those on the outskirts of smaller clumps; but beyond this basic observation, I don’t want to say anything about the precise method used, because I haven’t had time to study it properly yet.

  8. This is perhaps too long as a response in the comment section, it probably deserves an article all its own, but what are some of the most popular theoretical ideas behind dark matter. We seem to have made a lot of progress on the observational side in search of dark matter, its gravitational effects at least in the past twenty years, but has there been much progress on the theoretical side of things? Also, which theories have the best chance of being supported or highly disfavored in the near future with results from the LHC and other experiments?

    • Indeed, this requires a long answer. All I will say for now is this: making models of dark matter is easy — way too easy. We have dozens of possibilities for dark matter in the literature, maybe hundreds. All you need is a theory that predicts (or allows) a stable particle that is affected by neither the electromagnetic nor the strong nuclear force. With rather little fiddling, you can often get roughly the right amount of it to be left over after the Big Bang.

      Some of these theories would be noticed at the LHC. Some wouldn’t. It would be hard to give you a useful list with so many possibilities lying around.

      Dark energy is a much harder nut to crack.

  9. Pingback: The Absence of Darkness: Where is the “missing” dark matter? « Diary of an Alien Incarnate

  10. To add a little background… it’s been known for a long time that there is no dynamical evidence (from the motions of planets in the Solar System, or nearby stars) for dark matter in the disk of the galaxy near the Sun. This is not surprising, because the estimated dark matter density in the Solar neighborhood is small compared to the density of ordinary matter (because the latter is concentrated into quite a thin slab, whereas the dark matter is closer to being spherical). It’s also hard to make a precise accounting, because much of the ordinary mass is in very low mass stars that are faint and whose numbers are hence quite uncertain. It’s for these reasons that the new paper studies rather larger scales, considerably beyond the immediate Solar neighborhood, within which there should be more dark matter. However, on those larger scales we don’t know very well the structure of even the luminous components of the galaxy (such as the “thick disk” which is the focus here and whose properties are particularly controversial), and hence whether they have the properties or obey the simplifying assumptions in the analysis.

  11. Hmm. Apparently my earlier post didn’t make it. Here it is without reference urls to arxiv preprints 1001.2308v2 and 0910.1152v1, both of which made it into reputable peer reviewed journals, I should add:

    Primordial intermediate mass black holes of about 100,000 stellar masses aren’t ruled out by anything, including microlensing studies or the orbits of wide binaries, and if the inflationary epoch was not a linear expansion, but sped up before it slowed down, then there would be plenty of density for the observed baryon and nucleosynthesis ratios. The WIMP theorists don’t have a shred of empirical evidence compared to the dozens of intermediate mass black holes confirmed in the past couple years, and WIMPs can’t explain cuspy halos or the dwarf galaxy distribution. The only thing WIMPs explain is how WIMP theorists can get hundreds of millions of dollars in grant money to try to detect those figments of their imagination, and they’ve been making such money hand over fist.

    When will Occam’s Razor return to cosmology?

    …Furthermore, nobody has a theory of supermassive black hole formation which doesn’t involve agglomeration of intermediate mass primordial black holes implying that orders of magnitude more of the latter, again, of about 100,000 stellar masses, don’t still exist today.

    • Theorists getting hundreds of millions of dollars?!! WOW!! How can I apply?

      Let’s go through the numbers.

      There are of order 1000 particle theory faculty in the world. Maybe a hundred of them do WIMP theory in the US or some other country with a lot of money to spend on science.

      A good senior theorist in the US gets $90 – 130k a year from grants. A third of it goes to support the university. That leaves $60-90k to spend on a postdoc, or on a student, which typically costs $50-70k (salary, tuition, and health insurance). The faculty are also supposed to pay two months of their salary out of that dough. It also covers any travel to conferences for faculty, postdocs and students.

      Theorists who are pre-tenure get less, except for a select few.

      In some countries people get more, but in most they get less.

      Furthermore, most WIMP theorists work on many things, not just WIMPS.

      So stop throwing irresponsible claims around, please. We are not talking about hundreds of millions for theoretical WIMP physicists, and we are also not talking about people living high on the hog. Almost all of the money that is spent goes to pay for younger people and to support higher educational institutions; and faculty have been struggling to pay for postdocs and for students.

      That said, primordial black holes, are, as you say, viable candidates for dark matter at this point. On the other hand, the Fermi satellite — which was designed to do many different things, not just look for WIMPs! — may be seeing photons at 130 GeV consistent with dark matter particle annihilation. So. We’ll see.

      • I count at least a half dozen WIMP or particle dark matter detection experiments awarded grants in the past few years, from $12 million to $136 million each. In each case I can see no evidence that the PIs do not have essentially total control of the budget. I certainly hope that all of those projects are on the up-and-up, free from kickbacks from contractors to PIs, and I have no reason to believe that they are not. But the idea that these theories with no empirical observations behind them are being funded in such quantities when dozens of intermediate mass black holes are being confirmed every year simply does not pass the smell test.

        • Oh, now this is ridiculous. In your last message you talked about funding for theoreticians working on WIMPs. Now you change the rules and start counting experimentalists. That’s really low on the ethics scale; a classic Rush Limbaugh move — when beaten, change the rules.

          Yes, the money is different there, because you need more people and more material to do actual experiments. Typically experimental groups are funded at 5-10 times what theorists are funded; more students are needed, more postdocs are needed, technicians are needed, and you actually have to build real stuff.

          Next you start implying that PIs have full control of their budgets. That is not true. The granting agencies from the government maintain oversight; there are yearly reports, and I have served on committees that look at how money is spent. Furthermore, there are multiple senior faculty on all of those experiments, not a single royal physicist who can do whatever he or she wants, so there are checks and balances; a group that does not do its share for an experiment will get into serious trouble. In fact I believe the expenditures are a matter of public record that you can look up or request. So your snide “I certainly hope” shows you have no idea how money is actually used and monitored in this field. You should learn something before casting aspersions on other people.

          Finally: are you suggesting that the evidence in favor of intermediate mass black holes as the dark matter is so solid that no effort should be made to consider alternatives? If so, you are alone. I certainly know experts who believe that the dark matter may be from black holes, but I don’t know any serious scientist who would suggest that the case is closed and that other possibilities should be discarded. I would support continued effort to clarify how many black holes there are, and the expenditure of money to do so. I would also support continued effort to search for a particle physics explanation, and the expenditure of money to do so. The amounts of money may be different because of the relative difficulty of either research direction, but until one or the other is found to be the dark matter, both should be pursued.

          Meanwhile, your extreme and nasty attitude completely undermines your argument. It suggests you have a strong agenda and that your opinions are not even-handed; for this reason I discount your scientific opinion.

      • I would think that the experimentalists building the detectors have quite a bit of overlap with the theoreticians defining the parameters of what to look for.

        “are you suggesting that the evidence in favor of intermediate mass black holes as the dark matter is so solid that no effort should be made to consider alternatives?”

        Yes, I am. The cuspy halo problem alone should rule out all of the WIMP theories, but we have the dwarf galaxy distribution, the complete lack of empirical evidence. We have no data at all about any changes in the rate of expansion which might have occurred during the inflationary epoch, so arguments about the baryon ratios are worse than meaningless: They imply that we have information about what is necessarily unknown.

        “If so, you are alone.”

        No, I am not. Professor Paul Frampton and his several coauthors have been publishing in reputable peer reviewed journals on the subject since the initial results from microlensing studies, well before there were more than two confirmed intermediate mass black holes. There was some discussion about the orbits of wide binary stars from 2003-2007, but those were resolved in favor of allowing black holes as all dark matter.

        “your extreme and nasty attitude completely undermines your argument. It suggests you have a strong agenda and that your opinions are not even-handed; for this reason I discount your scientific opinion.”

        Tell me which statements are so objectionable and I will retract them in favor of alternate phrasing to which I hope you will not object. Surely there is some way to suggest that scientists are not above the corrupting influence of money which does not seem nasty and extreme.

        • Actually, the overlap is very minimal. I work very closely with the experimentalists at the LHC. Do you think I’ve seen a dime of their money? No. There is a sharp funding line. Theorists get theory money; experimentalists get experimental money. The line is crossed only with very special grants, such as Physics Frontier Centers, and they are very few and very far between. Furthermore, I cannot use even my own grant money for personal gain except for the two months of summer salary that researchers are expected to pay for from their grants. Every dime I spend on travel is scrutinized by my university. And if I ever skirted the law and misused my grant money, not only would I lose my grants permanently, I would quite possibly be fired by my university. That’s not counting the possibility of going to jail. It’s not a crony system; there are tight controls — as there should be. I advise you to learn something first before you talk about the corruption that you imagine. Particle physics is not like some other fields.

          About the science:

          a) the cuspy halo problem does NOT rule out all of the WIMP theories. Period. I have watched this problem ebb and flow for fifteen years; dynamics of the centers of galaxies are still too poorly understood for such a draconian conclusion. Do you think particle physicists never talk to galaxy simulation experts?

          b) the dwarf galaxy distribution is still far too poorly known for a definite conclusion. Same point.

          c) Lack of empirical evidence is not evidence against. We had a lack of empirical evidence for neutrino mixing for decades; many people argued that the solar neutrino problem was just about not precisely understanding the temperature of the sun. Neutrino experiments cost a lot, too. But they were worth it, and the naysayers were wrong. Which is not to say the naysayers were stupid or foolish (and I am not calling you stupid or foolish either) but that the expenditure of money to find out was worth it.

          d) I have not spoken to Frampton, but I would be quite surprised indeed to hear that his recommendation would be to shut down all dark matter experiments as a waste of time and money. Perhaps you could obtain a quote from him that says this?

  12. I think the second paper id related rather to the homogenity of the dark matter then the amount of it. If the Space were filled up by homogenous dark matter, we would not notice it at all in local mesurements regadless its amount.

  13. “… the less dark matter there is near the Earth, the harder it is to find these particles.” According to Milgrom, there are no dark matter particles and the so-called dark matter consists of the failure of Newton’s laws of motion with respect to gravity.
    http://en.wikipedia.org/wiki/Mordehai_Milgrom
    My judgment of the situation is that Milgrom, McGaugh, and Kroupa are correct about Milgrom’s law (and before them Fritz Zwicky and Vera Rubin had the right idea). Should Milgrom have won the Nobel prize 20 years ago?

    • Thank you for your personal judgment. The nice thing about science is that we make collective judgments as a community, and the opinions of individuals don’t matter.

      As I stated in the article, the study that I described ASSUMES that Einstein/Newton gravity holds in deriving its results. For you to use its results as support of your case is intellectually void.

      MOND (not Milgrom’s) continues to be studied elsewhere, but this particular paper does not provide support for it.

  14. I have no reasons to think that Milgrom is not right. But the problem has more i.e. four dimensions. Mass, time, space and energy are variable because they are not independent. This means that gravitational effects are only predictable/calculable to a certain extent i.e. with limited precision and may lead to wrong conclusion0s. Like the existence of elusive dark something.

    • The current paper is doing something relatively simple: only Newtonian gravity is needed, because stars are all moving slowly, and the distribution of matter is not rapidly changing. So we don’t need to appeal to anything so subtle.

  15. 1) Science 336(6078), 147 (2012) “Sparks Fly over Shoestring Test of ‘Holographic Principle’”
    2) Phys. Rev. Lett. 108, 165502 (2012) “Chiral Surfaces Self-Assembling in One-Component Systems with Isotropic Interactions”
    3) MOND and 1.2×10^(-10) m-sec^(-2) Milgrom acceleration.
    4) Conservation of angular momentum arises from vacuum isotropy plus Noether’s theorems.
    5) A geometric parity Eotvos experiment is sensitive to 5×10^(-14) difference/average, opposite shoes falling on a vacuum trace left foot. Observable vacuum trace anisotropy sources observable trace non-conservation of angular momentum. Dark matter is falsified with 2400:1 signal to noise in 90 days, by the book, on a bench top, in http://www.mazepath.com/uncleal/erotor1.jpg existing (.jpg) apparatus. (The loaded torsion pendulum rotor is fist-sized.) The worst it can do is succeed. Somebody should look.

    • Uncle Al — please try not to combine 5 ideas (or more) into one place. Just do one at a time. Here, your 5 ideas are (1) controversial but irrelevant for dark matter (2) completely irrelevant (3) it’s a nice idea, but at least right now it doesn’t work very well explaining all the data that supports the dark matter hypothesis (4) true, but irrelevant (5) wrong. If you give me one idea at a time I’d be willing to respond to it. Dumping long lists into comments isn’t helpful; I can neither respond nor leave them sitting there for others to read and be confused by.

  16. On dark Matter (or likewise the Higgs boson or the WIMP)

    They seek it here, they seek it there,
    those physicists seek it everywhere.
    Is it in heaven?, is it in hell?,
    that demmed, elusive particle.

  17. Angelina Crofton

    Hiya. This may be really silly, but is it possible that dark matter is at least partially composed of cosmic string or even domain walls? I heard on the radio (probably Science Friday, quite a while ago) that many extensions of the Standard Model would cause these to be formed via the Kibble Mechanism during symmetry breaking phase transitions. Obviously long strings would have a very characteristic observational signature, but if they’d broken up into little loops, they’d probably just look like lumps from far away, wouldn’t they? Would the expected distribution of cosmic string remnants match the claimed discrepancy between these dark matter experiments, or are there significant constraints on present day cosmic string density? If they’re a fairly generic feature of intermediate GUTs, they must be out there somewhere, mustn’t they? I feel like I’m missing something very obvious. Thanks so much!

    • Such loops of string can decay away rapidly, shrinking down to nothing by radiating gravitational or electromagnetic waves. They would be long gone. See for instance http://www.damtp.cam.ac.uk/research/gr/public/cs_interact.html

      If the world is such that these strings can sometimes radiate down to a minimal lump that is stable, that lump would act just like a particle — there’s no observable difference between a lump that’s a leftover from a cosmic string and any other particle. And you wouldn’t get enough of them to make dark matter.

      Long cosmic strings have been studied actively and sought observationally, but would not behave at all like dark matter — they cannot reproduce the observed effects of dark matter, such as the rotation curves of galaxies, the lensing effects, etc.

      Same statements apply to domain walls: big domain walls are a cosmological disaster, little closed surfaces of domain walls would be long gone (or collapsed down to particle-like lumps.)

      Primordial black holes are a better candidate.

  18. Angelina Crofton

    Thanks so much. But the reference you gave
    http://www.damtp.cam.ac.uk/research/gr/public/cs_interact.html
    seems like mostly PR and doesn’t go into much detail. In particular, I don’t see how they’re accounting for the angular momentum of these string loops. As a large cosmic string loop forms it will randomly acquire angular momentum from the gravitational background, right?. As the loop shrinks, its ang mom will become increasingly important – it surely won’t radiate away fast enough to ignore. So could typical small loops actually have enough ang mom to stabilize them against further decay? (Like an elastic band spinning so fast that centrifugal force keeps it stretched out. Or a figure skater who can’t pull her arms that final inch into her body). I don’t see how they’re taking this into account – they seem to be performing their calcs in a flat or uniformly curved background spacetime, so their string is an over-simplified model that will never acquire the ang mom I’m talking about. What am I missing? It must be something very obvious.

  19. Concerning the Now-you-don’t paper… If I understood it correctly, what their data would show (if correct) is that the density of Dark Matter doesn’t vary much as a function of distance from the galactic center, near us. Not that there isn’t any. BTW, I agree about the press-release correlation… nicely said.

  20. @ Matt Srassler

    On april 21 you said and I quote: The nice thing about science is that we make collective judgments as community, and the opinions of individuals don’t matter. Unquote

    Do you really mean that?

    • Yes. Though I guess, said that way, it’s easy to misinterpret; and of course it’s more complex than that. Individuals impact how collective judgments get made, and strong willed individuals with good arguments can sway a lot of opinion. Most importantly, it can take decades for a collective judgment to emerge; the struggle to see clearly can take a long time, especially if the data is ambiguous. But in the end, it’s the data that tells us what to believe, and we come to a collective judgment as to which data is believable and what it means. Any one of us is going to be wrong a lot of the time, but the collective, historically, is rarely wrong (at least about what can be known at the time, before more data becomes available about more subtle issues).

      I always say: don’t trust individual scientists, but do trust science. Individual efforts are not reliable (see, for instance, OPERA) but the collective process that emerges from many individual efforts becomes, over time, reliable (see, for instance, the combination of ICARUS, revised-OPERA + LVD, supernova measurements, Cohen-Glashow, Giudice et al., and more experiments to come)

      • Angelina Crofton

        You say: “the collective process that emerges from many individual efforts becomes, over time, reliable”

        Sorry, but I think that’s a rather empty statement. There are many prejudices and misunderstandings in science that have persisted for years or even generations. Over the centuries our collective understanding has sometimes gone up, but it has also sometimes gone down. (How enlightened would you say Europe’s scientific community was in 800AD vs during the heyday of Pythagoras or Aristotle?) Perhaps now our collective scientific wisdom is at an historical apogee, but confusions persist, and often grow. I see no guarantee that real scientific wisdom won’t ebb away, especially if young postdocs are rewarded for soaring paper-counts rather than an actual understanding of their subjects.

        Saying something becomes “over time reliable” seems Popper-untestable. Are you saying that if it’s not reliable yet, we just haven’t waited long enough? And saying “the collective, historically, is rarely wrong” is very odd. On the eve of most decent paradigm-shifts, surely the collective was wrong?

        • I understand your way of thinking, but I completely disagree with you on all counts, beacause what you and I define as ‘science’ is completely different. In my view science is a predictive enterprise, and yes, before a paradigm shift the conventional view is not incorrect but incomplete, and it most definitely is reliable within its regime of validity. Moreover, when I say ‘over time’ I do mean decades. And yes, while I agree with Popper about falsifiability, I disagree that he has the full story, because ambiguity may persist conceptually even as predictive power is achieved, and the unfalsifiability of differing viewpoints does not inhibit the applicability of powerful equations. In my knowledge of history, I do not know of a case where predictive power has declined in a paradigm shift.

          However this requires a ten page article, and you and I should carry on this conversation more carefully at a later time. Unfortunately I do not have time this week to do this very important subject justice.

  21. I think he is referring to the peer review process. The original hypotheses are usually proposed by individuals or small groups, but science accepts or rejects things as a community.

    Here is a nice little article discussing the problems with MOND and some of the more recent DM work. Hopefully it is okay to link it here.

    http://blogs.discovermagazine.com/cosmicvariance/2011/02/26/dark-matter-just-fine-thanks/

  22. Robert Garisto

    Matt:
    I don’t understand the origin of the standard deviation values in Fig 4. This appears to be a claim of how separated a fitted data curve is from the theoretical curves. I took a quick look at the 2012 paper. They seem to use data from a 2010 paper (http://iopscience.iop.org/2041-8205/724/1/L122 Fig 2) to get that curve. I’d much prefer to see a bunch of data points vs the theoretical curve rather than a best-fit data curve vs the theory curves. Also, Fig 2 of the 2010 paper seems to go to z=6 whereas the smoothed data curve of the 2012 paper seems to go from z=1.5 to 4.5. Also, it’s not clear to me how the y-axes of the two plots are related. There is also another 2012 paper by them.

    In summary, I find their presentation of results confusing and not optimal from the standpoint of try to make a convincing case.

    Cheers, Robert

  23. @ Matt Strassler
    Thanks

    @ Harry

    He thanks you too.

  24. “… most claims of a radical new result turn out to be largely or completely wrong …” … “… nasty statistical accidents can play tricks on you…” Does dark matter in the form of particles exist? According to Witten, the 3 main predictions of M-theory are gravity, non-abelian gauge theory, and supersymmetry (in the form of particles). Consider the Milgrom Denial Hypothesis: The main problem with M-theory is that M-theorists fail to realize that Milgrom is the Kepler of contemporary cosmology. Is the preceding hypothesis wrong?
    Suppose that X% of dark matter consists of particles that are their own antiparticles and Y% of dark matter consists of particles that are not their own antiparticles, where X + Y = 100. How many different types of dark matter particles are there? According to Milgrom, Newton-Einstein gravitational theory is either really wrong or apparently wrong. If Newton-Einstein theory is only apparently wrong, then something extremely weird is happening that makes most of the dark matter particles look as if they are not obeying Einstein’s equivalence principle. If the problem is not Fermi pairing of dark matter particles across alternate universes, then something else extremely bizarre is manifested by the galactic rotation curves. There is too much empirical evidence for Milgrom to be 100% wrong.

    • Thank you for your argulemt. Perhaps Milgrom is only 99.99% wrong. In any case your defense of Milgrom is completely unnecessary; if he is right, the truth will eventually emerge. Why are you so worried about that?

  25. Does the Dark Matter hypothesis still hold if we leave the Big Bang theory i.e. CMBR does not measure the total amount of energy (including matter) in the universe?

    • Well, many of the tests for dark matter do not rely on heavily on the expanding universe (gravitational lensing, galaxy rotation curves, galaxy formation) but what do you mean by “leaving the Big Bang theory”? The expansion of the universe is an experimental fact. If what you mean is that we abandon the idea that the universe was really really really hot at early times, and we lose the standard interpretation of the cosmic microwave background radiation, then the argument for dark matter would become a bit weaker, but on the other hand a lot of other more important things would also break down — what, in this case, would be your explanation for why the cosmic microwave background radiation looks the way it does??

  26. Prof. Strassler: Thank you for letting me post my opinions – you are more open to anti-orthodoxy than most physicists I have encountered. The reason I am worried about Milgrom being correct is two-fold: (1) If Milgrom’s acceleration law is wrong, then all my ideas are refuted. (2) If someone else independently rediscovers what I call “the Rañada-Milgrom effect” then I could lose out in terms of credit for identifying the effect. I recently posted some complete rubbish online and now I am running scared.

  27. “Either Milgrom’s ideas agree with nature, or they don’t …” Yes, but the base of my pyramid scheme consists of Milgrom’s ideas. From Wikipedia:
    According to the Modified Newtonian Dynamics theory, every physical process that involves small accelerations due to gravity will have an outcome different from that predicted by the simple law “F=ma”.
    http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics
    According to both McGaugh and Kroupa for all the evidence that they have examined, whenever Milgrom’s law makes a precise prediction, then it predicts as well or better than the Lambda Cold Dark Matter theory. In my theory I replace the -1/2 in the standard form of Einstein’s field equations by -1/2 + cold-dark-matter-compensation-constant. However, the -1/2 might need to be replaced by -1/2 + cold-dark-matter-variability-range — if so, all my ideas are headed for the trash basket.

  28. From Sean Carroll’s Dark Energy FAQ i understand that CMBR minus local measures of galaxies and clusters leaves 73% unaccounted for “Dark energy”. That is the right amount to explain the acceleration of the universe.So CMBR as result of a Big Bang plays an important role in the DM/DE hypothesis. Now how does this match with Erik Verlinde’s idea on gravitation as emergent phenomenon and Lawrence Krauss’ universe from nothing? CMBR product of accelerating masses or remains from a Big Bang? Any sign of extremely slight CMBR temperature or energy increase? Sorry for asking so many questions, asking is easier than answereing.

    • No, that’s not correct. We already had the dark matter and dark energy measured before the modern precise measurements of the cosmic microwave background radiation (CMBR). You’re misinterpreting what Carroll is saying. He’s just telling you that the CMBR gives the most precise measurements. But you do pretty well even without using it. We wouldn’t claim something so important with such confidence without having multiple types of measurements.

      First of all, it isn’t true that CMBR is something that gives you just a sum of all the matter and energy in the universe — the details of the CMBR are very complex and give you a lot of different types of information. It’s not a number, it’s a whole spectrum with lots of information.

      Second, the acceleration of the universe measures the dark energy directly. There is also evidence from the distribution of galaxy clusters. See for example
      The Observational Case for a Low Density Universe with a Non-Zero Cosmological Constant
      Ostriker & Steinhardt 1995, Nature, 377, 600
      Notice the date: 1995.

      Similarly dark matter is studied from many different points of view. The CMBR confirms it but you would still have excellent arguments without the CMBR. And indeed, for many years, we did quite well without it.

      As for Verlinde’s ideas and Krauss’s ideas — they are completely irrelevant to these issues. Both of those physicists subscribe to the Big Bang and the standard interpretation of the CMBR.

      Accelerating masses will not give you the detailed structure of the CMBR. Sorry.

  29. Hi Matt

    I disagree. The OPERA experiment is not an individual effort but collective and transnational. Experiments, in my opinion, are not reliable or unreliable but realistic, consistent and tested properly. To emphasis the OPERA experiment as a wrong experiment, as you do any time you write down a post, reveals some obsession and might confuse the people that read the blog. Somebody wrote down that neutrinos are a fiasco but neutrinos are just particles that are as fast as the photons. On the contrary, OPERA and MINOS stimulate many people, scientist and laypersons, to investigate these fascinating particles. If you stress the negative aspect of OPERA you just lay down your ego but many people remain confused.

    • This is the second time in as many comments that you attribute motivations to me without understanding anything at all about what my motivations actually are. This is insulting and I am not going to respond to you.

  30. @ Matt Strassler

    Thanks for your time and patience.
    If, for argument’s sake, at a certain moment the Big Bang does not hold anymore, does that mean then that CMBR must have an other background? What could that possibly be?

    I heard Verlinde say in a radio interview the other day that he is not so sure anymore about the Big Bang.

  31. Matt you mentioned
    “In my experience, when papers are made public at the same time as a press release, the more confident the press release sounds, the less likely the paper is correct. ”
    Would you say the same is true for so many press releases over the years regarding scientists find a way to test string theory (which you can find on Woit’s website)

    • Yes. Though for theory papers the issue is a little different than for an experiment; the calculations might well be correct but the assumptions and simplifications might well be questionable.

  32. Prof. Strassler: Thank you for citing Prof. Carroll on MOND — I believe that he is correct about Bekenstein’s relativistic version of MOND. However, I think that Milgrom, McGaugh, and Kroupa are 3 of the best scientists in the world and they are being punished for attacking the prevailing paradigm of dark matter.
    “The paradigm was: crystals are ordered and periodic — no exceptions. … For a couple of years I was alone. I was ridiculed. I was treated badly by my colleagues and my peers. … The community of nonbelievers was very large in the beginning. In fact, it included everybody.“ Dan Schechtman
    http://youtube.com/watch?v=EZRTzOMHQ4s Prof. Dan Schechtman 2011 Nobel Prize Chemistry Interview with ATS, YouTube
    By carefully studying the paper by P. Kroupa, B. Famaey, K.S. de Boer, J. Dabringhausen, M. Pawlowski, C.M. Boily, H. Jerjen, D. Forbes, G. Hensler, M. Metz, called “Local-Group tests of dark-matter concordance cosmology. Towards a new paradigm for structure formation”, http://adsabs.harvard.edu/abs/2010A%26A…523A..32K A&A 523, 32 (2010), one can learn that something is seriously wrong with the standard model of cosmology.
    “There is a tremendous amount of evidence for dark matter. Yet all this evidence is based on the assumption that Newton’s theory can be safely applied to the scales of galaxies.” Stacy McGaugh
    http://www.astro.umd.edu/~ssm/mond/MOND_sub.pdf “Mond over matter”, 2002
    “I think few people appreciate that the main difficulty for DM is that the host of regularities pointed out by MOND, if taken as just a summary of how DM behaves and interacts with normal matter, suggests that these two matter components are coupled and correlated very strongly in many ways. … if MOND does turn out to have some truth to it, the fact that it has encountered so much opposition will just show how nontrivial a thought it was.” Mordehai Milgrom, interview entitled “Dark-matter heretic”, American Scientist, Jan.-Feb. 2003, Vol. 91, #1, p. 1
    http://www.americanscientist.org/issues/pub/dark-matter-heretic
    I quote Prof. Dr. Pavel Kroupa from a (Nov. 1, 2011) e-mail,
    “My criticism is not based on me not liking dark matter, but is a result of rigorous hypothesis testing such that, from a strictly logical and scientific point of view, LCDM is definitely not a viable model of cosmological reality. I do not write such statements because I do not like LCDM and its ingredients, but because every test I have been involved with falsifies LCDM. At the same time, the tests of MOND we performed were done on the same footing as the LCDM tests. The MOND tests yield consistency so far. I am not more “fond” of MOND or any other alternative, but the scientific evidence and the logical conclusions cannot be avoided. And it is true, I must concede, that MOND has an inherent beauty which must be pointing at a deeper description of space time and possibly associated quantum mechanical effects which we do not yet understand (compare with Kepler laws and the later Newtonian dynamics).”
    http://www.astro.umd.edu/~ssm/mond The MOND pages (McGaugh)
    http://www.astro.uni-bonn.de/~pavel/kroupa_cosmology.html Pavel Kroupa: Dark Matter, Cosmology and Progress

    • This is irrelevant, Mr. Brown. Please stop with this stuff. Do you realize how many scientists have been ridiculed for their beliefs over history? It’s par for the course; I’ve been ridiculed for some of my ideas too, but I don’t go around complaining about it to the world.

      And guess what – a small fraction of those who have been ridiculed turned out to be correct! but most of them were not!!! Just because some people ridicule the efforts of MOND advocates, unfairly or not, does not imply that MOND is correct. And just because some experts ridicule the efforts of MOND advocates does not mean that all experts ridicule them, even if they think (as I do) that these ideas are probably wrong.

      Only data will determine whether MOND is correct. And as Carroll points out, the data is not heading in MOND’s favor right now; dark matter has gained with recent data and MOND has been losing ground. But data gathering is not over, and if MOND turns out, somehow, despite the evidence against it, to be correct, the community will come around to it.

      For what it’s worth, the first bit of physics I ever did as a student was MOND related. It was a good idea but the data doesn’t bear it out. The same can be said of MOND as a whole. It’s a good idea but data is not making it look plausible.

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  35. MOND does not rule out huge amounts of undetected diffuse gas in the intergalactic medium and huge amounts of undetected hot dark matter in the form of 2 eV (or > eV) neutrinos. According to R. H. Sanders, on p. 9 of “Clusters of galaxies with modified Newtonian dynamics”, Mon. Not. R. Astron., 2002, “The fact remains that there exists an algorithm, MOND, which allows galaxy rotation curves to be predicted in detail from observed distribution of matter, and it is for these systems that the kinematic observations are most precise. This fact challenges the current CDM paradigm, and demands explanation lies behind the discrepancy. The factor two remaining discrepancy in clusters is less challenging for MOND, particularly given that MOND makes no claims about the full material content of the universe.” Turner at the U. of Chicago and others have attempted to explain the MOND phenomenology in terms of the CDM paradigm, but Milgrom says these attempts are easily refuted.

  36. Dear Pr Strassler,
    I am not a physicist at all, just interested in physic and astronomy, sorry if my question is naive. The existence of the dark matter was proposed to solve problem of the rotation anomaly of the galaxies, MOND theory was also proposed. I would like to know if twin universe/bimetric model, (vulgarisation for non physicist: http://www.savoir-sans-frontieres.com/download/eng/jumeaux.htm , scientific papers here: http://arxiv.org/abs/0803.1362 or here: http://arxiv.org/abs/0801.1477) can fit the latest observed data (http://arxiv.org/abs/1204.3919, http://arxiv.org/abs/1205.4033)?

    • Although dark matter was *proposed originally* to explain the rotation curves of galaxies, it is needed today to explain far more: details of gravitational lensing, shapes of galaxies, numbers of galaxies, galaxies with few stars, details of the cosmic microwave background radiation, galaxy disks, and so on. No existing variant of “MOND” (modified Newtonian gravity) is yet able to address all of these issues. So although the possibility that gravity is modified has been and remains worthy of consideration, it is running a distant second compared to the proposal of a dark form of matter, which has not run into serious problems.

      In fact, check out today’s post “Science Up, Down and Inside-Out”; the paper I described above as not seeing any sign of dark matter has been crticized by leading astrophysicists; they claim there is an error that, once corrected, actually gives *positive* evidence for dark matter.

  37. @ Matt Strassler, April 24, 2012, 02:34 PM

    “Accelerating masses will not give you the detailed structure of the CMBR”.

    There are accelerating masses moving away from each other and there are accelerating masses approaching each other. Does that make a difference?

  38. James T. Dwyer

    I probably can’t explain the fundamental issue with the discovery of galactic dark matter in the 1970s to physicists, but I think I can explain the problem to any children who might be reading this…

    [Because of its insulting and unpleasant tone, this comment has been deleted by the host.]

    • When you are ready to be a grown-up and be polite to the people you are addressing, you are welcome to repost your comment.

      In my long experience, people who dismiss the intelligence of other intelligent people usually turn out to be bad listeners, and as a result, usually turn out to be wrong.

      • James T. Dwyer

        I apologize for the objectionable tone of the opening statement in my previous comment, which you retained. It represents only my weary frustration. I am not a physicist. I have added a quotation to support what might otherwise seem to be an insult to a highly respected astrophysicist. I hope you can consider the remaining very simple and straightforward overview of how the requirement for galactic dark matter halos became established within the physics community.
        The speed at which planets orbit the Sun (which contains 99.86% of total Solar system mass) varies depending almost entirely on their distance from the Sun.

        The characteristic plot of planets’ orbital velocities as a function of radial distance is referred to as a Keplerian rotation curve. Astronomers studying the rotation curves of objects within the disks of spiral galaxies expected each to comply with Keplerian rotation curves, ‘just like planets in the Solar system’ (see Vera Rubin et al.). They didn’t. Instead, rotational velocities were relatively constant regardless of radial distance.

        To make a Solar system whose planets’ rotational velocities remained flat or nearly constant like spiral galaxies’, astronomers thought that an enormous undetected peripheral mass must be present, extending the mass distribution to enormous radial distances. Their models confirmed this expectation, and compelling evidence of dark matter halos was convincingly conceived.

        The problem was that, as Newton had explained in his Principia, Kepler’s laws of planetary motion provided reasonable approximations only for orbital bodies of relatively negligible mass, like planets in the Solar system.

        For vast distributions of billions of massive objects, like galactic disks, discrete objects do not independently orbit any central massive object. Each massive object most strongly interacts with its neighboring masses. As a result, galactic disk objects generally rotate around their collective center of mass as loosely bound clumps of massive objects, not individual, independently orbiting objects.

        Galactic dark matter was only necessary to correct astronomers’ misconception that stars in the disks of spiral galaxies should orbit just like planets in our Solar system! Please see: Rubin, et al., (1980), “Rotational properties of 21 SC galaxies with a large range of luminosities and radii, from NGC 4605 /R = 4kpc/ to UGC 2885 /R = 122 kpc/”, http://dx.doi.org/10.1086/158003 http://adsabs.harvard.edu/abs/1980ApJ…238..471R
        As stated in section VIII. “DISCUSSION AND CONCLUSIONS”:

        “1. Most galaxies exhibit rising rotational velocities at the last measured velocity; only for the very largest galaxies are the rotation curves flat. Thus the smallest Sc’s (i.e., lowest luminosity) exhibit the same lack of a Keplerian velocity decrease at large R as do the high-luminosity spirals. This form for the rotation curves implies that the mass is not centrally condensed, but that significant mass is located at large R. The integral mass is increasing at least as fast as R. The mass is not converging to a limiting mass at the edge of the optical image. The conclusion is inescapable that non-luminous matter exists beyond the optical galaxy.”

        While astronomers very precisely detailed their kinematic observations of galactic rotation, it was never formally established that there was any basis for the expectation that galaxy rotation should comply with Keplerian rotation curves or the laws of planetary motion, which is actually invalid.

        In more recent years it has been demonstrated that the rotational characteristics of spiral galaxies can be described using Newtonian dynamics and universal law of gravitation, without dark matter or modified gravity. Please see:
        Feng & Gallo, (2011), Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies, doi:10.1088/1674-4527/11/12/005 arXiv:1104.3236v4

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