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.


69 thoughts on “The dwarf galaxy NGC1052-DF2

  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


  2. 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.


  3. “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 ?


  4. 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

  5. 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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  6. “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.


  7. 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?



  8. 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.


  9. 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?


  10. 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.

    Liked by 2 people

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