A recently discovered dwarf galaxy designated NGC1052-DF2 has been in the news lately. Apparently a satellite of the giant elliptical NGC 1052, DF2 (as I’ll call it from here on out) is remarkable for having a surprisingly low velocity dispersion for a galaxy of its type. These results were reported in Nature last week by van Dokkum et al., and have caused a bit of a stir.

It is common for giant galaxies to have some dwarf satellite galaxies. As can be seen from the image published by van Dokkum et al., there are a number of galaxies in the neighborhood of NGC 1052. Whether these are associated physically into a group of galaxies or are chance projections on the sky depends on the distance to each galaxy.

Image of field containing DF2 from van Dokkum et al.

NGC 1052 is listed by the NASA Extragalactic Database (NED) as having a recession velocity of 1510 km/s and a distance of 20.6 Mpc. The next nearest big beastie is NGC 1042, at 1371 km/s. The difference of 139 km/s is not much different from 115 km/s, which is the velocity that Andromeda is heading towards the Milky Way, so one could imagine that this is a group similar to the Local Group. Except that NED says the distance to NGC 1042 is 7.8 Mpc, so apparently it is a foreground object seen in projection.

Van Dokkum et al. assume DF2 and NGC 1052 are both about 20 Mpc distant. They offer two independent estimates of the distance, one consistent with the distance to NGC 1052 and the other more consistent with the distance to NGC 1042. Rather than wring our hands over this, I will trust their judgement and simply note, as they do, that the nearer distance would change many of their conclusions. The redshift is 1803 km/s, larger than either of the giants. It could still be a satellite of NGC 1052, as ~300 km/s is not unreasonable for an orbital velocity.

So why the big fuss? Unlike most galaxies in the universe, DF2 appears not to require dark matter. This is inferred from the measured velocity dispersion of ten globular clusters, which is 8.4 km/s. That’s fast to you and me, but rather sluggish on the scale of galaxies. Spread over a few kiloparsecs, that adds up to a dynamical mass about equal to what we expect for the stars, leaving little room for the otherwise ubiquitous dark matter.

This is important. If the universe is composed of dark matter, it should on occasion be possible to segregate the dark from the light. Tidal interactions between galaxies can in principle do this, so a galaxy devoid of dark matter would be good evidence that this happened. It would also be evidence against a modified gravity interpretation of the missing mass problem, because the force law is always on: you can’t strip it from the luminous matter the way you can dark matter. So ironically, the occasional galaxy lacking dark matter would constitute evidence that dark matter does indeed exist!

DF2 appears to be such a case. But how weird is it? Morphologically, it resembles the dwarf spheroidal satellite galaxies of the Local Group. I have a handy compilation of those (from Lelli et al.), so we can compute the mass-to-light ratio for all of these beasties in the same fashion, shown in the figure below. It is customary to refer quantities to the radius that contains half of the total light, which is 2.2 kpc for DF2.

The dynamical mass-to-light ratio for Local Group dwarf Spheroidal galaxies measured within their half-light radii, as a function of luminosity (left) and average surface brightness within the half-light radius (right). DF2 is the blue cross with low M/L. The other blue cross is Crater 2, a satellite of the Milky Way discovered after the compilation of Local Group dwarfs was made. The dotted line shows M/L = 2, which is a good guess for the stellar mass-to-light ratio. That DF2 sits on this line implies that stars are the only mass that’s there.

Perhaps the most obvious respect in which DF2 is a bit unusual relative to the dwarfs of the Local Group is that it is big and bright. Most nearby dwarfs have half light radii well below 1 kpc. After DF2, the next most luminous dwarfs is Fornax, which is a factor of 5 lower in luminosity.

DF2 is called an ultradiffuse galaxy (UDG), which is apparently newspeak for low surface brightness (LSB) galaxy. I’ve been working on LSB galaxies my entire career. While DF2 is indeed low surface brightness – the stars are spread thin – I wouldn’t call it ultra diffuse. It is actually one of the higher surface brightness objects of this type. Crater 2 and And XIX (the leftmost points in the right panel) are ultradiffuse.

Astronomers love vague terminology, and as a result often reinvent terms that already exist. Dwarf, LSB, UDG, have all been used interchangeably and with considerable slop. I was sufficiently put out by this that I tried to define some categories is the mid-90s. This didn’t catch on, but by my definition, DF2 is VLSB – very LSB, but only by a little – it is much closer to regular LSB than to extremely (ELSB). Crater 2 and And XIX, now they’re ELSB, being more diffuse than DF2 by 2 orders of magnitude.

Surface brightness categories from McGaugh (1996).

Whatever you call it, DF2 is low surface brightness, and LSB galaxies are always dark matter dominated. Always, at least among disk galaxies: here is the analogous figure for galaxies that rotate:

Dynamical mass-to-light ratios for rotationally supported disk galaxies, analogous to the plot above for pressure supported disks. The lower the surface brightness, the higher the mass discrepancy. The correlation with luminosity is secondary, as a result of the correlation between luminosity and surface brightness. From McGaugh (2014).

Pressure supported dwarfs generally evince large mass discrepancies as well. So in this regard, DF2 is indeed very unusual. So what gives?

Perhaps DF2 formed that way, without dark matter. This is anathema to everything we know about galaxy formation in ΛCDM cosmology. Dark halos have to form first, with baryons following.

Perhaps DF2 suffered one or more tidal interactions with NGC 1052. Sub-halos in simulations are often seen to be on highly radial orbits; perhaps DF2 has had its dark matter halo stripped away by repeated close passages. Since the stars reside deep in the center of the subhalo, they’re the last thing to be stripped away. So perhaps we’ve caught this one at that special time when the dark matter has been removed but the stars still remain.

This is improbable, but ought to happen once in a while. The bigger problem I see is that one cannot simply remove the dark matter halo like yanking a tablecloth and leaving the plates. The stars must respond to the change in the gravitational potential; they too must diffuse away. That might be a good way to make the galaxy diffuse, ultimately perhaps even ultradiffuse, but the observed motions are then not representative of an equilibrium situation. This is critical to the mass estimate, which must perforce assume an equilibrium in which the gravitational potential well of the galaxy is balanced against the kinetic motion of its contents. Yank away the dark matter halo, and the assumption underlying the mass estimate gets yanked with it. While such a situation may arise, it makes it very difficult to interpret the velocities: all tests are off. This is doubly true in MOND, in which dwarfs are even more susceptible to disruption.


Then there are the data themselves. Blaming the data should be avoided, but it does happen once in a while that some observation is misleading. In this case, I am made queasy by the fact that the velocity dispersion is estimated from only ten tracers. I’ve seen plenty of cases where the velocity dispersion changes in important ways when more data are obtained, even starting from more than 10 tracers. Andromeda II comes to mind as an example. Indeed, several people have pointed out that if we did the same exercise with Fornax, using its globular clusters as the velocity tracers, we’d get a similar answer to what we find in DF2. But we also have measurements of many hundreds of stars in Fornax, so we know that answer is wrong. Perhaps the same thing is happening with DF2? The fact that DF2 is an outlier from everything else we know empirically suggests caution.

Throwing caution and fact-checking to the wind, many people have been predictably eager to cite DF2 as a falsification of MOND. Van Dokkum et al. point out the the velocity dispersion predicted for this object by MOND is 20 km/s, more than a factor of two above their measured value. They make the MOND prediction for the case of an isolated object. DF2 is not isolated, so one must consider the external field effect (EFE).

The criterion by which to judge isolation in MOND is whether the acceleration due to the mutual self-gravity of the stars is less than the acceleration from an external source, in this case the host NGC 1052. Following the method outlined by McGaugh & Milgrom, and based on the stellar mass (adopting M/L=2 as both we and van Dokkum assume), I estimate an internal acceleration of DF2 to be gin = 0.15 a0. Here a0 is the critical acceleration scale in MOND, 1.2 x 10-10 m/s/s. Using this number and treating DF2 as isolated, I get the same 20 km/s van Dokkum et al. estimate.

Estimating the external field is more challenging. It depends on the mass of NGC 1052, and the separation between it and DF2. The projected separation at the assumed distance is 80 kpc. That is well within the range that the EFE is commonly observed to matter in the Local Group. It could be a bit further granted some distance along the line of sight, but if this becomes too large then the distance by association with NGC 1052 has to be questioned, and all bets are off. The mass of NGC 1052 is also rather uncertain, or at least I have heard wildly different values quoted in discussions about this object. Here I adopt 1011 M as estimated by SLUGGS. To get the acceleration, I estimate the asymptotic rotation velocity we’d expect in MOND, V4 = a0GM. This gives 200 km/s, which is conservative relative to the ~300 km/s quoted by van Dokkum et al. At a distance of 80 kpc, the corresponding external acceleration gex = 0.14 a0. This is very uncertain, but taken at face value is indistinguishable from the internal acceleration. Consequently, it cannot be ignored: the calculation published by van Dokkum et al. is not the correct prediction for MOND.

The velocity dispersion estimator in MOND differs when gex < gin and gex > gin (see equations 2 and 3 of McGaugh & Milgrom). Strictly speaking, these apply in the limits where one or the other field dominates. When they are comparable, the math gets more involved (see equation 59 of Famaey & McGaugh). The input data are too uncertain to warrant an elaborate calculation for a blog, so I note simply that the amplitude of the mass discrepancy in MOND depends on how deep in the MOND regime a system is. That is, how far below the critical acceleration scale it is. The lower the acceleration, the larger the discrepancy. This is why LSB galaxies appear to be dark matter dominated; their low surface densities result in low accelerations.

For DF2, the absolute magnitude of the acceleration is approximately doubled by the presence of the external field. It is not as deep in the MOND regime as assumed in the isolated case, so the mass discrepancy is smaller, decreasing the MOND-predicted velocity dispersion by roughly the square root of 2. For a factor of 2 range in the stellar mass-to-light ratio (as in McGaugh & Milgrom), this crude MOND prediction becomes

σ = 14 ± 4 km/s.

Like any erstwhile theorist, I reserve the right to modify this prediction granted more elaborate calculations, or new input data, especially given the uncertainties in the distance and mass of the host. Indeed, we should consider the possibility of tidal disruption, which can happen in MOND more readily than with dark matter. Indeed, at one point I came very close to declaring MOND dead because the velocity dispersions of the ultrafaint dwarf galaxies were off, only realizing late in the day that MOND actually predicts that these things should be getting tidally disrupted (as is also expected, albeit somewhat differently, in ΛCDM), so that the velocity dispersions might not reflect the equilibrium expectation.

In DF2, the external field almost certainly matters. Barring wild errors of the sort discussed or unforeseen, I find it hard to envision the MONDian velocity dispersion falling outside the range 10 – 18 km/s. This is not as high as the 20 km/s predicted by van Dokkum et al. for an isolated object, nor as small as they measure for DF2 (8.4 km/s). They quote a 90% confidence upper limit of 10 km/s, which is marginally consistent with the lower end of the prediction (corresponding to M/L = 1). So we cannot exclude MOND based on these data.

That said, the agreement is marginal. Still, 90% is not very high confidence by scientific standards. Based on experience with such data, this likely overstates how well we know the velocity dispersion of DF2. Put another way, I am 90% confident that when better data are obtained, the measured velocity dispersion will increase above the 10 km/s threshold.

More generally, experience has taught me three things:

  1. In matters of particle physics, do not bet against the Standard Model.
  2. In matters cosmological, do not bet against ΛCDM.
  3. In matters of galaxy dynamics, do not bet against MOND.

The astute reader will realize that these three assertions are mutually exclusive. The dark matter of ΛCDM is a bet that there are new particles beyond the Standard Model. MOND is a bet that what we call dark matter is really the manifestation of physics beyond General Relativity, on which cosmology is based. Which is all to say, there is still some interesting physics to be discovered.

75 thoughts on “The dwarf galaxy NGC1052-DF2

  1. Hi,
    interesting discussion. thanks.

    One question i have is this – if better measurements show velocity dispersion of NGC1052-DF2 is within 10-14 km/s of MOND plus EFE, would this be evidence in favor of MOND and against dark matter?


    1. It would be evidence for MOND as every other measured galaxy in the Universe is already. However, a velocity dispersion of 10-14 km/s would not work against dark matter, because the DM halo is a posteriori estimate. You look what is missing in mass from the kinematics of the galaxy and add the needed DM to fill the gap. If you have a gap to fill (which would happen with a higher velocity dispersion), than everything is fine for DM.


      1. if there was a galaxy observed with a sufficiently high rms, it could be too high for MOND to explain, falsifying MOND but DM can explain it by theorist a huge DM excess


  2. On closer reading, I notice in the details of their methods section that the rms velocity dispersion is 14.3 km/s. It is only after the exclusion of one outlier that the velocity dispersion becomes unusually low. As a statistical exercise rejecting outliers is often OK, but with only 10 objects to start it is worrisome to throw any away. And the outlier is then unbound, making one wonder why it is there at all.
    Consider: if they had simply reported the rms velocity dispersion, and done the MOND calculation correctly, they would have found excellent agreement. This certainly could be portrayed as a great success for MOND. Instead, tossing out just one globular cluster makes it look like a falsification. Just one datum, and a choice of how to do the statistics. Not a wrong choice necessarily, but a human choice… not some kind of statistical requirement.


    1. that calculation 14.3 km/s is pretty close to σ = 14 ± 4 km/s of your calculation.

      If we accept the 14.3 km/s value then does this also imply that there is “dark matter” filling in the gap from 8.4 km/s km/s which is baryon and newton laws to 14.3 km/s


      1. Yes… if the measured velocity dispersion is 14 km/s, not 8 km/s, then there would (conventionally) need to be dark matter, and this would not be a dwarf devoid of dark matter.


  3. Excellent short atticle
    (blog)! I found it very readable and informative. I am a particle Astrophysics experimentalist. I am always fascinated by the cosmological issues but usually involved with high-energy astrophysical accelerators.


  4. Thanks a lot for all the interesting explanations about the external field effect and it importance in the case of NGC 1052 DF2. I am wondering it the external field effect will play a role in galaxy clusters, in the center the accelearation might be signifiantly much larger than ao and as the consequence the the dynamics should fully purley Newtons law. Is that correct, are there already observations?


    1. The EFE likely does matter in clusters, though how much will depend on the details of each cluster. There are cases where the cores of the clusters are near or in the Newtonian regime. I sometimes speculate that this may be related to to morphology-radius relation, by which elliptical galaxies are more likely to be found at the centers of clusters. In MOND, spiral galaxies are stabilized by MOND; spiral galaxies cannot reside in the Newtonian regime and remain stable. Those that pass through may suffer for it; I wonder if NGC 4438 in Virgo might be an example. http://ned.ipac.caltech.edu/img/2004PASP..116..133L/NGC_4438:I:gri:lbf2004.jpg
      More generally, there is a missing baryon problem in the centers of many clusters of galaxies. There is still a discrepancy even though it is in the Newtonian regime. What that stuff may be is unknown.

      Liked by 1 person

  5. In galaxy clusters, how is EFE calculated when many galaxies are near one another? Does MOND + EFE correctly predict behavior of galaxy clusters?


  6. Generally it isn’t – the cluster environment is a mess! In the cases I’m aware of (e.g., the Ursa Major work of Verheijen & Sanders), MOND works well for individual galaxies. Where it has persistent trouble is for the clusters themselves, where the MOND correction typically falls short of explaining the excess motions. This discrepancy is about a factor of 2 in mass, or 20% in velocity.


    1. thanks – in the news is about black holes and i posted below wondering if dark matter and MOND is compatible, with dark matter simply being black holes

      btw do u plan to write a paper on this blog post?


      1. There will likely be a paper, though I weary of correcting simple mistakes. To test a theory, you need to apply that theory, not some straw-man version thereof. This form of logical fallacy is shockingly common.


  7. In the news

    “The center of the Milky Way is teeming with black holes”

    within the MOND framework, couldn’t dark matter just be black holes ? the amount of residual dark matter required under MOND is much less, so that the current bounds on black holes are based on the assumption of keeping newton/einstein intact, rather than the greatly reduced need for dark matter within MOND


  8. The residual dark matter in rich clusters could be baryonic, insofar as there are enough baryons available to do the job, according to big bang nucleosynthesis. I’ve written previously about that here. That said, I have trouble imagining what form such baryonic dark matter would take. It could be black holes – a whole lot of black holes!


    1. I was thinking of black holes, including quantum mechanical black holes, and neutrinos,
      maybe cold neutron stars?

      the amount of black holes needed within MOND could be further reduced if neutrinos have a certain mass.

      neutrinos are ruled out in standard cosmology due to being “hot” which suppresses large scale structure formation and not having enough mass, but within MOND, couldn’t a combination of neutrinos and black holes create the universe we observe?

      In the news, April 6, 2018 “Dark matter isn’t interacting with itself after all” and “Dark matter might not interact with anything other than gravity”

      if dark matter only interacts with baryonic matter via gravity, how to explain BTFR RAR and other regularities easily explained by MOND.
      it sounds like dark matter has been ruled out since recent observations suggests dark matter only interacts gravitational with baryonic matter, but that leaves unexplained the regularities that MOND predicts


      1. Yes, that is my objection to dark matter. The odds of MOND having any predictions come true are effectively nil if cold dark matter is correct. And yet it has many.
        Whether this falsifies dark matter is a philosophical issue. It is always possible to explain the observations with dark matter after the fact. But it cannot be used to make the same predictions that MOND gets right ahead of time. Can this situation be considered satisfactory?
        And yes, MOND tolerates a higher neutrino mass than CDM. The experimental limit is < 2 eV; the structure formation limit in CDM is < 0.2 eV. Structure formation in MOND is not impeded by a massive neutrino in the same way; indeed, it might even help prevent the overproduction of structure. So an experimental measurement of a mass clearly in excess of 0.2 eV would be an effective falsification of LCDM. If it comes in less than that, then it doesn't make a difference one way or the other.

        Liked by 1 person

  9. continuing,

    it’d be interesting to see how the science community reacts if neutrino masses are on order of 2 ev

    I know MOND struggles with large scale structures and BAO in CMB. Could either neutrinos, quantum mechanical black holes, or neutrons explain BAO in CMB, and either neutron stars or primordial black holes explain weak gravitational lensing and large scale structure formation within MOND cosmology?

    keep standard model intact, and posit black holes as source of “dark matter” within MOND


    1. Well, maybe 1 eV. 2 eV is the current upper limit. I am never comfortable shooting at a narrow gap; I only mention this as one of the few clear signs that structure formaiton as we know it in LCDM is wrong. Big galaxies and the cosmic web already being in place at high z would be another, which has already come to pass to some extent. This is natural in MOND, as predicted by Bob Sanders in 1998.
      Where LCDM excels is in matters of cosmic scale. LCDM became the “concordance model” in the mid-90s. In 1996, I pointed out that, if true, this required the expansion rate of the universe to be accelerating. This was famously observed in ’98 by the SN Ia teams. That in turn predicted that the first peak of the CMB would be at a certainly location, and so it proved to be. That requires a certain BAO scale, and so it is… For whatever reason, LCDM is a good description of the metric of the expanding universe. Maybe that’s because it is correct; maybe it is because it is the best approximation we can make for the assumptions that go into it.
      Similarly for MOND: it gets many predictions for galactic dynamics right either because it is in essence correct, or perhaps because it is an effective theory that describes some property of the dark matter (or whatever it is that’s going on). By and large, physicists are failing to make use of this information when they build models.

      Liked by 1 person

      1. thanks. Ethan Siegal on his blog on Forbes magazine puts a lot of stock in concordance model’s large scale prediction, and thinks the successes of MOND represent properties of dark matter. I can provide a link if you’re interested.


  10. Do not bet against the Standard Model. Do not bet against MOND.
    It’s like the Golden State Warriors vs. Puerto Rico national team. Don’t mess up with Stef Curry and Pedro of Puerto Rico LOL
    Sure, advocates of MOND can come up with all sorts of excuses. But it’s just pleading the dog ate my homework


  11. Regarding acoustic peaks in the power spectrum of the CMB which is taken to prove dark matter, with MOND is it possible the dark matter in question could be explained either as tetra-neutron bound states, neutron stars, strangelets, neutrinos or quantum mechanical black holes? in otherwords, keeping the standard model intact, and suggesting the acoustic peaks in the power spectrum of the CMB is the result of particles of the standard model, or quantum black holes, acting in unusual, but SM ways.


    1. The third peak in the acoustic power spectrum exceeds the prediction of a model with no CDM. That, to my mind, is the best evidence in favor of non-baryonic dark matter. I frequently hear it asserted that this falsifies MOND, but this is an overstatement. All the CMB falsifies is General Relativity with only baryons in the amount specified by big bang nucleosynthesis. The previous statement assumes GR is correct. Once we assume that, we must per force invoke non-baryonic dark matter. What we call CDM could be a sign of some feature of an extended theory of gravity, like a scalar field that behaves in a similar way. While this is possible, it is hard to envision!
      See http://astroweb.case.edu/ssm/mond/CMB5.html and http://astroweb.case.edu/ssm/mond/CMB6.html

      Liked by 2 people

      1. ” The third peak in the acoustic power spectrum exceeds the prediction of a model with no CDM. That, to my mind, is the best evidence in favor of non-baryonic dark matter.”

        but is it possible that something like neutrons, bound states of neutrons, neutrinos, strangelets or quantum mechanical black holes or even higgs bosons or glueballs or geons behave identically to CDM and also give rise to the third peak?


        1. The third peak “wants” an entity that can provide a net driving term in the acoustic oscillations. Particles that interact electromagnetically cause a net drag force. It seems difficult to arrange what you suggest.

          Liked by 1 person

  12. Yes, when I first read about this Dwarf galaxy I thought the problem might be EFE. I’m glad to see you confirming that.
    One thing I have wondered is: how did Milgrom come up with the EFE in the first place? I don’t understand how it is motivated by the other concepts of Mond. Obviously it appears he is correct, but, as far as I can tell, he just magically summoned it out of thin air.


    1. FWIW, MOND itself is a purely phenomenological model. In other words, its an equation derived from trying to fit data, not based upon some underlying mechanism.


      1. As are most theories, to begin with.
        What troubles me is that this equation, once written, has predictive success well beyond the scope of the original input. Both MOND and dark matter were invoked to explain flat rotation curves. Once written down, the equation of MOND is a restrictive straight jacket unlike dark matter, which can do pretty much anything. So why does MOND ever work at all?


      1. I am not claiming that it has any actual truth to me, but heuristically, I think of Newtonian gravity in the weak field limit as a first order effect, and MOND as a second order quantum gravity effect that may be present all of the time but is only significant relative to the first order effect when the field is very weak that arises because the density of gravitons is low since there are few non-graviton mass-energy sources relative to graviton self-interactions. In that purely heuristic ansatz, EFE is a function of the graviton density being high enough that the first order effects are overwhelming the second order quantum effects since the total volume of non-graviton gravitational sources is high relative to graviton self-interactions.


  13. The EFE was discussed in the first Milgrom (1983) paper, and argued using its only Figure. It is thus part of the original theory. What is absent so far from the discussion are the properties of NGC 1052 itself. It has HI emission, described in Van Gorkom et al. (1986), and globular clusters, discussed e.g. in Pierce et al. (2005), who even derive an uncertain mass estimate of 1.9 +- 0.7 10**12 M_sun within a radius of 19 kpc. They also quote the mass of 3 10**11 M_sun within 23 kpc derived by Van Gorkom et al. (1986) from their HI data. Hence the EFE could be stronger than discussed sofar. There is more to say about this (unusual) galaxy, anyway.


  14. As usual, you are correct, Albert. The EFE was present already in the original MOND papers. It is also true that the EFE could be stronger than the quick calculation I made above. However, the HI velocity quoted by van Gorkum (1986) is ~ 200 km/s, which is consistent with the estimate made here from the stellar mass. That said, the observational uncertainty in the EFE is pretty big, both in the mass of the giant host, and in the true distance between dwarf and host. A more detailed calculation will be coming to an arxiv posting Soon.


  15. I can’t hit reply to your reply, but i picked neutrons and neutrinos as a possible candidates from the SM to explain the third peak in CMB which is explains as non-SM BSM dark mater they are electrically neutral.

    here is a link to a reply


    “In any case, getting back to the question whether MOND is able to fit other galaxies than DF2, the closer MOND gets to explaining NGC1052-DF2, the harder it is to explain Dragonfly 44. This galaxy, as discussed in a 2016 paper, is even larger than DF2, has a similar stellar mass, and a velocity dispersion of 47 +- 7 km/s.”

    among the claims is that if MOND could explain NGC1052-DF2 it would not be able to explain dragon fly 44

    does MOND have anything to say about dragon fly 44? velocity dispersion of 47 +- 7 km/s seems quite high leading to a dark matter of 99.99%


  16. First of all, this is a form of misdirection. We messed up X, so look instead at Y.
    It is incorrect to say that as MOND gets closer to explaining one, it somehow gets farther from explaining the other. The predictions of MOND do not move with the data. Either it explains the data, or it doesn’t. Each and every galaxy poses a distinct test: DF2 and DF44 should each be explained separately. Working or failing for one is not contingent on the other.
    In the case of DF2, the prediction made for MOND by van Dokkum et al. for DF2 is simply wrong because it neglected the EFE. When you do it properly, there is no serious conflict with the data.
    DF44 is different, in that it has a velocity dispersion that is too high for MOND. I had looked into this when it first came out, and the discrepancy is real, but it is similarly unpersuasive. These galaxies are very challenging targets to observe. In short, I do not believe that +/-7 captures the uncertainty on the DF44 measurement any more than I believe that the 90% c.l. upper limit on the velocity dispersion of DF2 is 10.5 km/s. That’s probably closer to the actual value than an upper limit.
    If and when it is possible to obtain better data, I expect the velocity dispersion for DF44 will come down. Not so much because MOND predicts this, but because DF44 is an outlier from well established empirical relations: the BTFR and the RAR, and because that’s what my experience has been over and over and over – when a galaxy appears to deviate from these relations, it gets closer when better data are obtained.
    There are always goofy data in astronomy. There are hundreds of galaxies with better data that fall smack on the relations predicted by MOND. To focus on the occasional and inevitable outlier is to refuse to see the forest because one tree is off to the side.

    Liked by 1 person

  17. btw, Sabine Hossenfelder suggested MOND in a recent paper may cause a redshift, have you had a chance to review the idea and if so, is it sound and can you find a way to test it?

    Liked by 1 person

  18. I believe she was predicting how the empirical MONDish relation we see locally might evolve with redshift. But would have to check if we’re referring to the same thing.


  19. hi,

    I saw your paper on this

    MOND and the dynamics of NGC1052-DF2
    B. Famaey, S. McGaugh, M. Milgrom
    https://arxiv.org/abs/1804.04167 (Submitted on 11 Apr 2018)

    do you plan to also discuss dragonfly 44 within MOND?


    btw, could neutrinos explain the third acoustic peak in the CMB within MOND? neutrinos do not have electromagnetic interactions, and large scale structure formation for MOND differs from CDM.


  20. I have no plans to discuss DF44 any more than I did above. There is not much to say, really. It is an outlier. If it is correct, that falsifies MOND. At the time it was reported, Pieter made a big fuss about DF44 being an outlier from the halo mass-stellar mass relation, claiming this was a Milky Way mass halo containing a much lower luminosity galaxy. If true, this is also a big problem for LCDM. We can at least tolerate it in LCDM, but only because LCDM makes no definitive prediction the way MOND does. Most likely, it is simply misleading, in either theory, as most outliers usually are.
    Neutrinos cannot explain the third peak of the CMB. A massive neutrino may well play a role in slimming the peaks, which are a bit wider than observed in pure baryon models. A ~1 eV neutrino would also help explain the residual mass discrepancy in clusters while being impossible to reconcile with standard LCDM structure formation. Experimental measurement of the neutrino mass may thus prove interesting.


    1. thanks,

      i now understand neutrinos alone can’t do the job. since within MOND the desire is to keep the SM intact, could neutrinos in combination with primordial black holes explain the third peak of the CMB and also help explain the residual mass discrepancy in clusters ? black holes with masses of 100 GEV created during the big bang and so light they cannot decay any further via hawking radiation. it’s not clear what the lower limit on masses for black holes are, but black holes where quantum mechanics also play a role.


  21. In principle, any entity in place early enough in the universe that behaves like CDM can do the trick. Theories that attempt to mate GR and MOND usually invoke scalar fields. But the right mass fraction in “stuff with the right properties” should work. Garry Angus has shown this can be done with sterile neutrinos, for example. https://arxiv.org/abs/0805.4014
    I worry that hybrid solutions are like Tycho Brahe’s geocentric model, but at this point, who knows?


    1. The paper you cite is what i had in mind. A possible advantage of hybrid solutions is that according to Angus paper, if MOND is correct a neutral particle of mass 11 ev is “predicted” so it is a matter of identifying it.

      Have you had a chance to review Lee Smolin MOND as a regime of quantum gravity arXiv:1704.00780

      providing a physical basis for MOND


  22. I have seen Smolin’s work. I’d like to have the time to understand and comment sensibly on it, but of late I’ve been busy correcting elementary errors. It is hard to make progress in science while some fraction of the community has its foot firmly on the pedal in reverse gear.


    1. “I have seen Smolin’s work…It is hard to make progress in science while some fraction of the community has its foot firmly on the pedal in reverse gear.”

      the reason i ask is there a general relativistic version of MOND you favor? in the news, gravitational waves traveling at c discredit some versions of general relativistic generalizations of MOND like TEVS gravity and Moffat gravity.

      “In principle, any entity in place early enough in the universe that behaves like CDM can do the trick. ”

      could black holes do the trick, perhaps in combination with neutrinos and neutron stars. neutron do not feel a net electromagnetic radiation and while neutrons are unstable, bound states of neutrons by gravitational in neutron stars are stable.

      to put it another way, if MOND is correct, can MOND provide constraints on properties of dark matter ?


  23. I do not have a favored general relativistic version of MOND. TeVeS was a great example that it is at least possible to construct such a theory, but I don’t think it is correct in detail, nor am I aware of something better. Certainly I have not seen any sensible theories that predict that gravitational waves propagate at a speed different from light. Excluding those is good but unsurprising. It is also unsurprising that this has been over-interpreted to be a problem for MOND. There is nothing in MOND that suggests any such silliness.
    If you want there to be dark matter in black holes or what not, they have to be made early enough to do what you want them to do. So in principle primordial black holes could do the trick. But how did the universe make such things?
    MOND certainly provides constraints on the properties of dark matter, even if it is wrong. Whatever is going on has to produce this phenomenology. Something like Khoury’s superfluid DM or Blanchet’s dipolar DM might do the trick. But I think that answers a different question than you pose. If MOND is correct, then the excess unseen stuff has to be something real – unseen baryons or massive neutrinos, etc. Eventually those should be detectable.

    Liked by 1 person

    1. I think these topics could make good research papers for you.

      “There is nothing in MOND that suggests any such silliness.”

      the popular press released news articles that the speed of gravitational waves for colliding neutron stars is c which they state rules out many modified gravity theories that predict a different value.

      “If you want there to be dark matter in black holes or what not, they have to be made early enough to do what you want them to do. So in principle primordial black holes could do the trick. But how did the universe make such things?”

      the goal here is to try to explain the third peak in CMB without extending the standard model. Couldn’t density fluctuation at the instant of the big bang create primordial black holes which could then explain CMB third peak, without extending the standard model?

      in the “standard” picture, the universe is supersymmetric and at high energies of the big bang enough WIMPS in the form of neutralinos of 100 GEV mass to form dark matter in exactly the right amount, the WIMP miracle. if the universe is not supersymmetric, perhaps instead of neutralinos the early hot universe produced micro-black holes.

      In “Pop Goes the Universe,” by Anna Ijjas, Paul J. Steinhardt and Abraham Loe, they express deep skepticism of standard inflation theory, which if correct, shows the standard big bang paradigm is in deep trouble. their conclusion is that inflation is highly disfavored by the data and that new ideas of the origin of the universe are required. in some ways their views on the conflict between standard inflation theory predictions and actual data mirrors your research into MOND vs dark matter.

      “MOND certainly provides constraints on the properties of dark matter, even if it is wrong. Whatever is going on has to produce this phenomenology. Something like Khoury’s superfluid DM or Blanchet’s dipolar DM might do the trick. But I think that answers a different question than you pose. If MOND is correct, then the excess unseen stuff has to be something real – unseen baryons or massive neutrinos, etc. Eventually those should be detectable.”

      yes on the second, after “but I think that answers a different question than you pose” I’m wondering if gravity has to be modified to reproduce MOND, perhaps along the lines Lee Smolin suggests, what sort of dark matter would be consistent with it. since superfluid DM is actively researched with axions as a possible candidate. what I had in mind is some combination, to explain the third peak in CMB and weak gravitational lensing, black holes, neutron stars white dwarfs. certainly an interesting research paper that could then make recommendations on observations to provide support for the hypothesis.

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  24. “Something like Khoury’s superfluid DM or Blanchet’s dipolar DM might do the trick.”

    Both approaches need to add “extra stuff” to the universe, this is not a parsimonious approach IMHO. On the other hand, I think Blanchet is spot on with its dipolar medium idea, the thing is this medium could very well be the quantum vacuum, simply, if antimatter and matter repel each other though gravitational interactions. In this case the gravitational dipoles are virtual pairs from the quantum vacuum. Interestingly, the mutual interaction between virtual pions in the QCD vacuum ( pi(+)-pi(-) pairs) is of the order of MOND a0 parameter. This means that as long as the external field is greater than that, dipoles are efficiently aligned and contribute to a net radial mass density from the induced polarization field,and when it is weaker, dipoles are more difficult to align, which contributes to a decrease of the induced polarization field over distance: this mimics very well “MONDIAN” phenomenology. Plus anti-gravitational antimatter hypothesis explains the close to zero observed cosmological constant value, as the gravitational mass of the quantum vacuum is zero in this case ( the known calculated value of 10^107 J/cm^3 actually corresponds to the inertial mass of the vacuum, not its gravitational mass). So basically we should be contemplating violations of both the WEP and the SEP by the gravitational behavior of antimatter in order to solve the astrophysical and cosmological conundrums of our time, IMHO.


  25. Hello Dr. McGaugh,

    can you still clarify some issues.

    within MOND, dark matter can exist such as primordial black holes, correct?
    there is an article now
    Is dark matter made of primordial black holes?

    black holes would require no extension of the standard model.

    does MOND have anything to say about weak gravitational lensing, which is often used as evidence of dark matter? within MOND theory, is weak gravitational lensing attributed to black holes or some change in gravity that also creates weak gravitational lensing?

    has there been any computer models using both MOND and primordial black holes for structure formation and how do these models compare with actual data?

    presumably the black holes would not be needed to explain galaxy rotation curves, but perhaps they can be placed outside the galaxy so as to contribute to weak gravitational lensing and large scale structure formation?



  26. I’ve come late to this conversation, but I’ve been following Sabine Hossenfelder’s comments about this dwarf galaxy; it seems to me that her blog and this are talking about two entirely different MONDs. See: “backreaction.blogspot.com/2018/04/no-that-galaxy-without-dark-matter-has.html”

    sean s.


  27. do you have any thoughts on extended mond proposals to explain galaxy clusters?

    Generalizing MOND to explain the missing mass in galaxy clusters
    Authors: Alistair Hodson, Hongsheng Zhao

    how does extended mond compare with external field effect, to explain galaxy clusters?


  28. It makes a difference!
    I am aware of this and another, independent effort that also finds a closer distance for this object. I follow the arguments – Trujillo et al. make a compelling case – but also the counter arguments offered by Pieter on his web page (https://www.pietervandokkum.com/ngc1052-df2). I do not have a strong opinion one way or the other; it boils down to whether we’re seeing the tip of the red giant branch or not. I do not pretend to know at this juncture which way this will resolve.
    If DF2 is at the closer distance, then it is less abnormal as a dwarf galaxy. It’s luminosity and mass would be less – about 6E7 rather than 2E8 solar masses. For the lower mass estimated by Trujillo et al., the isolated MOND prediction for the velocity dispersion becomes 14.7 +/- 5.3 km/s (if I did it right on the proverbial back of the envelope. The large uncertainty is that due to the uncertainty on the stellar mass quoted by Trujillo et al.)
    This is a tad higher than the velocity dispersion for DF2 at the larger distance, where it is subject to the EFE of NGC1052. If it is also subject to the external field effect at its nearer distance, the velocity dispersion would be less. How much depends on the external field. Trujillo et al. discuss the environment and give the distinct impression that DF2 may well be in a dense enough environment that the EFE could matter. This would not be due to NGC1052, but one of the other galaxies along the line of sight. However, it isn’t entirely clear to me which of these is the most likely host, if there is one – it is a messy region of the sky. So I have not yet attempted any estimate of the EFE.
    That said, the EFE is unlikely to makes as much as a factor of 2 difference in the velocity dispersion. That means the object will remain consistent with MOND for pretty much all permutations of distance, given the current large uncertainties on the measured velocity dispersion. This might become an interesting test if both the distance accuracy and than in velocity dispersion can be substantially improved.

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  29. Hi Tritonstation,

    I’ve been reading through your recent post about MOND and galaxies – it’s interesting stuff.

    The thing I don’t understand is why everyone is not jumping on Kourey’s superfluid dark matter idea. https://kicp.uchicago.edu/depot/talks/khoury-colloquium.pdf. It seems to square the circle perfectly.

    Dark matter is a particle in the eV range, so all the large scale dark matter predictions (microwave power spectrum, evolution of large scale structure etc.) continue to work.

    But the superfluid bit gives you a MOND-like behaviour at the galaxy scale, so all your galaxy level MOND behaviour works, without the unpleasantness of having to modify gravity.

    You also get a prediction for the mass of the dark matter particle.

    So what am I missing? Why aren’t people more excited about it?

    All the best


    1. Some people are excited about this. But it takes time for new ideas to sink in. A lot of the community is still in denial about whether the problems that this proposal might solve are even problems. So the one-word answer is Attitude.


  30. As a fan of MOND I was a bit shocked to read the latest Starts With A Bang article by Ethan Siegel about the dwarf galaxy Segue 1, which reputedly has a visible mass of only 175 suns, but needs a whopping 600,000 solar masses of Dark Matter to explain internal motions. Might it be possible that external field effects are distorting the motions of this galaxy”s stars to mimic a much greater mass than is actually there?


    1. This has been known for over a decade, so kinda puzzled why it is “news” now.
      In order to estimate the dark matter mass, one assumes that a system is in dynamical equilibrium. That’s usually a good assumption. Here, it is a terrible assumption.
      Segue 1, and very nearly all of the so-called ultrafaint dwarfs, are deep in the potential of the Milky Way where they are subject to strong tidal forces. This violates the assumption of equilibrium, in any theory. There is an eternal energy source: the stars are not just responding to their own gravitational field (and that of ‘their own’ dark matter). Thus it is likely that the motions of the stars have been stirred up by the external field so that the dynamical mass is overstated.
      In the dark matter galaxy formation picture, one expects small galaxies like this to be accreted by larger galaxies like the Milky Way. In that process, they are tidally stripped. First the outer parts of their dark matter halo, then down to the stars, then ultimately they’re shredded completely. There’s no good way to tell how far along this process Segue 1 is, but it and the other ulrtafaints dwarfs are the poster children for hierarchical accretion.
      In MOND, I had initially thought this was a huge problem (see https://arxiv.org/abs/1003.3448). The external field effect, by itself, does not explain this observation. Long story short, it turns out that tidal effects are even stronger in MOND, and the assumption of dynamical equilibrium certainly does not hold. So – same problem.
      There is one difference: in MOND, there is a quantitative criterion for when an object is not in equilibrium (see https://arxiv.org/abs/astro-ph/0005194). All of the ultrafaints, including Segue 1, fail to meet this criterion. There is no chance that the measured velocity dispersion reflects the equilibrium value of an isolated system. Indeed, one can see the onset of this effect in the data (see Figs 6 and 7 of arxiv:1003.3448). From that perspective, this is another successful prediction of MOND: it not only predicts correctly the velocity of stars in equilibrium systems, it also tells you when it can’t.
      There is no equivalent criterion in dark matter. If things don’t work out, we infer that the system is out of equilibrium. The difference is that MOND tells you when this must be invoked. All the famous cases (e.g., And XIX, Crater 2, and a half dozen others whose names I don’t recall offhand) that are now considered to be out of equilibrium in dark matter were predicted in advance by MOND.


  31. Stacey, thank you for the very detailed response. I’ll check out those links you provided.


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