Galaxies That Are Too Big To Fail, But Fail Anyway

Dark matter exists, but there is still a lot we don’t know about it. Presumably it’s some kind of particle, but we don’t know how massive it is, what forces it interacts with, or how it was produced. On the other hand, there’s actually a lot we do know about the dark matter. We know how much of it there is; we know roughly where it is; we know that it’s “cold,” meaning that the average particle’s velocity is much less than the speed of light; and we know that dark matter particles don’t interact very strongly with each other. Which is quite a bit of knowledge, when you think about it.

Fortunately, astronomers are pushing forward to study how dark matter behaves as it’s scattered through the universe, and the results are interesting. We start with a very basic idea: that dark matter is cold and completely non-interacting, or at least has interactions (the strength with which dark matter particles scatter off of each other) that are too small to make any noticeable difference. This is a well-defined and predictive model: ΛCDM, which includes the cosmological constant (Λ) as well as the cold dark matter (CDM). We can compare astronomical observations to ΛCDM predictions to see if we’re on the right track.

At first blush, we are very much on the right track. Over and over again, new observations come in that match the predictions of ΛCDM. But there are still a few anomalies that bug us, especially on relatively small (galaxy-sized) scales.

One such anomaly is the “too big to fail” problem. The idea here is that we can use ΛCDM to make quantitative predictions concerning how many galaxies there should be with different masses. For example, the Milky Way is quite a big galaxy, and it has smaller satellites like the Magellanic Clouds. In ΛCDM we can predict how many such satellites there should be, and how massive they should be. For a long time we’ve known that the actual number of satellites we observe is quite a bit smaller than the number predicted — that’s the “missing satellites” problem. But this has a possible solution: we only observe satellite galaxies by seeing stars and gas in them, and maybe the halos of dark matter that would ordinarily support such galaxies get stripped of their stars and gas by interacting with the host galaxy. The too big to fail problem tries to sharpen the issue, by pointing out that some of the predicted galaxies are just so massive that there’s no way they could not have visible stars. Or, put another way: the Milky Way does have some satellites, as do other galaxies; but when we examine these smaller galaxies, they seem to have a lot less dark matter than the simulations would predict.

Still, any time you are concentrating on galaxies that are satellites of other galaxies, you rightly worry that complicated interactions between messy atoms and photons are getting in the way of the pristine elegance of the non-interacting dark matter. So we’d like to check that this purported problem exists even out “in the field,” with lonely galaxies far away from big monsters like the Milky Way.

A new paper claims that yes, there is a too-big-to-fail problem even for galaxies in the field.

Is there a “too big to fail” problem in the field?
Emmanouil Papastergis, Riccardo Giovanelli, Martha P. Haynes, Francesco Shankar

We use the Arecibo Legacy Fast ALFA (ALFALFA) 21cm survey to measure the number density of galaxies as a function of their rotational velocity, Vrot,HI (as inferred from the width of their 21cm emission line). Based on the measured velocity function we statistically connect galaxies with their host halos, via abundance matching. In a LCDM cosmology, low-velocity galaxies are expected to be hosted by halos that are significantly more massive than indicated by the measured galactic velocity; allowing lower mass halos to host ALFALFA galaxies would result in a vast overestimate of their number counts. We then seek observational verification of this predicted trend, by analyzing the kinematics of a literature sample of field dwarf galaxies. We find that galaxies with Vrot,HI<25 km/s are kinematically incompatible with their predicted LCDM host halos, in the sense that hosts are too massive to be accommodated within the measured galactic rotation curves. This issue is analogous to the "too big to fail" problem faced by the bright satellites of the Milky Way, but here it concerns extreme dwarf galaxies in the field. Consequently, solutions based on satellite-specific processes are not applicable in this context. Our result confirms the findings of previous studies based on optical survey data, and addresses a number of observational systematics present in these works. Furthermore, we point out the assumptions and uncertainties that could strongly affect our conclusions. We show that the two most important among them, namely baryonic effects on the abundances and rotation curves of halos, do not seem capable of resolving the reported discrepancy.

Here is the money plot from the paper:


The horizontal axis is the maximum circular velocity, basically telling us the mass of the halo; the vertical axis is the observed velocity of hydrogen in the galaxy. The blue line is the prediction from ΛCDM, while the dots are observed galaxies. Now, you might think that the blue line is just a very crappy fit to the data overall. But that’s okay; the points represent upper limits in the horizontal direction, so points that lie below/to the right of the curve are fine. It’s a statistical prediction: ΛCDM is predicting how many galaxies we have at each mass, even if we don’t think we can confidently measure the mass of each individual galaxy. What we see, however, is that there are a bunch of points in the bottom left corner that are above the line. ΛCDM predicts that even the smallest galaxies in this sample should still be relatively massive (have a lot of dark matter), but that’s not what we see.

If it holds up, this result is really intriguing. ΛCDM is a nice, simple starting point for a theory of dark matter, but it’s also kind of boring. From a physicist’s point of view, it would be much more fun if dark matter particles interacted noticeably with each other. We have plenty of ideas, including some of my favorites like dark photons and dark atoms. It is very tempting to think that observed deviations from the predictions of ΛCDM are due to some interesting new physics in the dark sector.

Which is why, of course, we should be especially skeptical. Always train your doubt most strongly on those ideas that you really want to be true. Fortunately there is plenty more to be done in terms of understanding the distribution of galaxies and dark matter, so this is a very solvable problem — and a great opportunity for learning something profound about most of the matter in the universe.

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22 Responses to Galaxies That Are Too Big To Fail, But Fail Anyway

  1. Jason Dick says:

    Very interesting. Could this be caused by dark matter having a small but non-zero temperature?

  2. Khalil Fazal says:

    Typo in the paragraph below the graph. You mention the horizontal axis twice.

  3. James Gallagher says:

    If BICEP2 results are supported by Planck later this year won’t it make this all a bit clearer? Or are the experimental observations of primordial behaviour independent of these observations.?

  4. Carl 'SAI' Mitchell says:

    @Jason Dick
    No. “Cold” doesn’t mean absolute zero. If it’s matter, it will have a nonzero temperature as long as the third law of thermodynamics holds.

  5. Sean Carroll says:

    Jason/Carl– Actually, “warm” dark matter is definitely one of the possibilities that is on the table. (Or perhaps a mixture of hot and cold.) The cold/warm/hot descriptor actually refers to the velocity of the dark matter in the early universe, not today.

    James– CMB observations don’t really tell us anything about this question. The CMB only tells us about relatively large length scales, while the issues are on relatively small scales.

  6. John D says:

    Maybe the presumptions are the problem. There’s a presumption that dark matter is comprised of particles. Because the cosmological constant, the value of the energy density of the vacuum of space, is presumed to be constant. Because the FLRW metric starts with the assumption of homogeneity and isotropy of space. But see and note that space expands between the galaxies but not within. Apply conservation of energy and you’re left with a halo of inhomogeneous space around every galaxy. Then see and Einstein’s Leyden Address where he described a gravitational field as inhomogeneous space, and space as a thing. It has its vacuum energy, which has a mass equivalence and a gravitational effect. The vacuum catastrophe says you don’t know how much, but what you do know is that space is dark and there’s a lot of it about.

  7. stufflike says:

    What ripples when galaxy clusters collide is what waves in a double slit experiment; the dark matter.

    Einstein’s gravitational wave is de Broglie’s wave of wave-mechanics; both are waves in the dark matter.

    Dark matter displaced by the particles of matter which exist in it and move through it relates general relativity and quantum mechanics.

  8. Lords Burgos says:

    As pathetically small and elusive as they are, neutrinos are somehow detected.
    Is there any sort of prediction on the dark matter’s mass? Or maybe a possible range of energy from QFT experiments?

  9. Reynaldo Carmona says:

    Hi Dr.Carroll,

    ΔCDM is an interesting model. Δ, as you state up top, is the cosmological constant. Some cosmologists equate the cosmological constant with dark energy. So in theory, the model is combining dark energy and dark matter. The reason I’m touching on this is because I think one of the possible problems in cosmology is that space isn’t always accounted for. It is, for example, accounted for in General Relativity. Recent findings have suggested that space is liquid-like. So I wanted to illustrate a possibility that may or may not align with ΔCDM.

    Imagine a puddle on a surface that’s roughly flat (since the universe is likely roughly flat). Now imagine that that puddle undergoes evaporation, but the process never completes because the drops are suspended in air. These drops (dark matter) are then free to interact with galaxies. The puddle (dark energy), which is more uniform, can only exert whatever influence it exerts (perhaps the fifth force that some have proposed or the repulsive effects dark energy is usually thought of as having). Thus ΔCDM may be describing the puddle of space (dark energy) and the drops that have been pulled from the puddle (dark matter). This would, in turn, explain why dark matter seems to be distributed throughout the universe. I think once we recognize that space is some kind of meta-matter, if you will, we’ll be able to account for the missing mass and energy in the universe. The fabric of space, if it behaves like a liquid, may explain dark matter and dark energy in one blow. What do you think Dr.Carroll?


  10. Theresonlywhite says:

    Hi Dr.Carroll

    There are two reasons for why Dark Matter “exists”. One is that no one was smart enough to come up with a new theory of gravity yet. The other one ( and the most important ) , is that without dark matter, the whole Big Bang cosmology collapses because according with the Big Bang theory there was not enough matter in the universe to build the structures we see.
    So, does the dark matter exists ? Probably not but we will find it one day. 🙂

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  12. John D says:

    Rey: for dark energy remember that negative pressure is tension, and think of the balloon analogy. This balloon is in a vacuum, the pressure within is balanced by the tension of the skin, and there’s two ways to make it expand. One is to blow in more air. That’s increasing the pressure and is like adding more energy, which is in breach of conservation of energy. The other way is to reduce the tensile strength of the skin. Like bubble-gum. It expands, so the tensile strength reduces, so it expands, so the tensile strength reduces. And so on.

  13. Stuart says:

    Hie Sean
    The acceleration due to gravity in the weak field limit as predicted in this paper is
    The MoND like regime in galaxies begins when
    GM( r )/r^2=Hc=v^2/r from which we obtain r=v^2/Hc such that if we substitute for r in GM(r )/r^2=v^2/r we obtain
    v^4=GM(r )Hc for galaxy rotation curves.Under these conditions the acceleration is now reduced to
    vdv/dt=Hv giving
    v=Vexp(Ht) where V^4=GM(r )Hc
    Thus for galaxies
    v^4=GM(r )Hc.exp(Ht)
    is the expression for rotation curves and galactic evolution.This expression is also valid for late time cosmic acceleration which begins when the condition GM/r^2=Hc is satisified from which we explain the coincidence problem.

  14. Stuart says:

    A typo error the final expression for galaxy rotation curve and evolution should read
    v^4=GM(r )Hc.exp(4Ht)

  15. mjf says:

    Dr. Carroll,

    Referring to the “money plot” in your post…

    You describe the thick blue line as the Lambda-CDM (“LCDM”) model prediction, and note the outliers in the lower left of the graph since if the model is correct, the points should lie below/to the right.

    However I also note that there is a dotted diagonal line in the plot, and the data seems to fit that well (falls uniformly below and to the right).

    So if I denote:
    Model A = LCDM: prediction – thick blue line
    Model B = ???: prediction – diagonal dotted line

    What are the candidates for Model B to produce the diagonal dotted line prediction? Is it the warm dark matter model or similar referred to in some of the comments here? Sorry if I didn’t pick this up from the rest of the post… It seems like if we had a Model B that wasn’t contradicted by other experiments outside this “ALFALFA” one, this would be a better model for dark matter, wouldn’t it?

  16. Stuart says:

    The dotted diagonal line is described by the equation just above your post!This is the reason why I posted it. The galaxies closer to the line are older than those far below it.That is for each epoch in the universe’s life there is a corresponding dashed diagonal line.

  17. “Always train your doubt most strongly on those ideas that you really want to be true.”

    The best known advice for humankind.

  18. Stuart says:

    Observational and experimental verification is the ultimate test of an idea not subjective opinions.

  19. Douglas McFarland says:

    “Here is the money plot from the paper”

    I love this humor from Dr. Carroll. It is evenly peppered throughout his writing. I would say subtly. He is always keenly aware of the audience he is speaking to or intending to speak to. I am halfway through “The Particle At The End Of The Universe” and already I feel that I better understand Quantum Field Theory. I think that it was Richard Feynman who once said that if you think you understand Quantum Mechanics you don’t understand Quantum Mechanics. So maybe I am deluded. However it makes more sense to me when explained as vibrations or waves in fields.

    As a lay person attempting to put together a worldview that incorporates the fundamental natures of reality I find Dr. Carroll’s writings incredibly frank and useful in that he clearly demarcates what we (humanity) are fairly certain of versus what we might reasonably expect might be true versus what are far out ideas on the edge of the possibility of ever comprehending. As Carl Sagan was to cosmology and astronomy Sean Carroll is to quantum particle physics which I will endeavor to refer to as quantum field physics from now on. I mean only to compare them as popularizers of science and not in any other way.

    I wish that biology would produce a popularizer scientist in their field as effective as Sean Carroll. I am incredibly interested in biology and have read The Selfish Gene but I just don’t find many books for lay people that seek to explain to lay people the current state of our (humanity) understanding of biology or for most of the other hard sciences. The next science book on my radar is David Deutsch’s book simply because it is mentioned in Sean Carroll’s.

    Sorry this isn’t very on topic. I was considering sending Dr. Carroll a fan email expressing this but I started commenting on my appreciation of his humor expressed in this blog post and figured he is as likely to read this as a personal email and blathered on.

  20. darrelle says:

    @ Douglas McFarland

    An excellent book about matters of biology is Your Inner Fish by Neil Shubin. It is, my opinion of course, one of the best popular science books about biology so far. Neil is a scientist and in the book he tells the story of the search, and eventual discovery, by him and his colleagues, of Tiktaalik roseae. But it includes much more about other lines of research all demonstrating how we are directly related to all other life.

    Incidently there was recently a 3 part documentary series titled Your Inner Fish, narrated by Shubin himself, that aired on PBS. I have a rather poor opinion of US made documentaries in general, but this was very good.

  21. David Brown says:
  22. Johnnie Random Walker says:

    So small galaxies can’t hold their dark matter…interesting.