A Galaxy Without Dark Matter?

The Hubble Space telescope has observed an ultra diffuse galaxy which does not seem to have any dark matter or modified gravity effects. The abstract of the preprint states:

Studies of galaxy surveys in the context of the cold dark matter paradigm have shown that the mass of the dark matter halo and the total stellar mass are coupled through a function that varies smoothly with mass. Their average ratio M_{halo}/M_{stars} has a minimum of about 30 for galaxies with stellar masses near that of the Milky Way (approximately 5x10^{10} solar masses) and increases both towards lower masses and towards higher masses. The scatter in this relation is not well known; it is generally thought to be less than a factor of two for massive galaxies but much larger for dwarf galaxies. 

Here we report the radial velocities of ten luminous globular-cluster-like objects in the ultra-diffuse galaxy NGC1052-DF2, which has a stellar mass of approximately 2x10^8 solar masses. We infer that its velocity dispersion is less than 10.5 kilometers per second with 90 per cent confidence, and we determine from this that its total mass within a radius of 7.6 kiloparsecs is less than 3.4x10^8 solar masses. 

This implies that the ratio M_{halo}/M_{stars} is of order unity (and consistent with zero), a factor of at least 400 lower than expected. NGC1052-DF2 demonstrates that dark matter is not always coupled with baryonic matter on galactic scales.

Pieter van Dokkum, et al., "A galaxy lacking dark matter",  arXiv (March 27, 2018). A follow up paper by the same authors is here. It's abstract is as follows:

We recently found an ultra diffuse galaxy (UDG) with a half-light radius of R_e = 2.2 kpc and little or no dark matter. The total mass of NGC1052-DF2 was measured from the radial velocities of bright compact objects that are associated with the galaxy. Here we analyze these objects using a combination of HST imaging and Keck spectroscopy. Their average size is <r_h> = 6.2+-0.5 pc and their average ellipticity is <{\epsilon}> = 0.18+-0.02. From a stacked Keck spectrum we derive an age >9 Gyr and a metallicity of [Fe/H] = -1.35+-0.12. Their properties are similar to {\omega} Centauri, the brightest and largest globular cluster in the Milky Way, and our results demonstrate that the luminosity function of metal-poor globular clusters is not universal. The fraction of the total stellar mass that is in the globular cluster system is similar to that in other UDGs, and consistent with "failed galaxy" scenarios where star formation terminated shortly after the clusters were formed. However, the galaxy is a factor of ~1000 removed from the relation between globular cluster mass and total galaxy mass that has been found for other galaxies, including other UDGs. We infer that a dark matter halo is not a prerequisite for the formation of metal-poor globular cluster-like objects in high redshift galaxies.

Pieter van Dokkum, et al., "An enigmatic population of luminous globular clusters in a galaxy lacking dark matter" (March 27, 2018).

This is an extreme outlier of a result, which, if true, poses serious issues for modified gravity theories and for theories about how dark matter usually ends up tightly correlated with baryonic matter if it exists.

There are several possibilities:

1. It could be the product of MOND with an external field effect. The paper notes that the MOND prediction is off by about a factor of two (which beats the factor of 400 problem with the expectation from dark matter theory noted in the abstract handily), but the calculation, at first glance, didn't appear to have considered the external field effect, which should tweak the result in the right direction. If MOND with an external field effect makes an accurate prediction it is a huge vindication of that particular theory (which obviously still have to be generalized to the relativistic case) and very close cousins of it. But, if the reality is contrary to the MOND with external field effect prediction, it could suggest that, at a minimum, MOND is not the right way to modify gravity. Specifically, the paper states with respect to what MOND would predict that:

For a MOND acceleration scale of a0 = 3.7 × 10^3 km^2 s^−2 kpc^−1, the expected velocity dispersion of NGC1052–DF2 is σM ≈ (0.05 GMstarsa0) 1/4 ≈ 20 km s^−1 , a factor of two higher than the 90% upper limit on the observed dispersion.

The external field effect reduces velocity dispersion in dwarf galaxies when present by an amount that appears to be about right on an order of magnitude basis.

This would happen if the gravitational field was NGC1052 at a range of 20 MPc was greater than a0 or greater than the gravitational field due to the dwarf galaxy.

2. It could be a function of a unique geometry that causes gravitational effects from dark matter and/or modified gravity to cancel out (or at least appear to cancel out for a viewer from our direction). In Deur's work, this happens when a galaxy or other structure is spherically symmetric or nearly so. In other cases, some geometries can cause force vectors from gravitational pulls in opposite directions from different masses to cancel out if they are arranged just so.

3. It could be a methodology problem. The calculation of the inferred dark matter and velocity dispersion is quite involved and there are lots of instrumental issues and calculation issues that could lead to such an extreme outlier result.

All three possibilities are supported by this description of the galaxy (emphasis added):

In terms of its apparent size and surface brightness it resembles dwarf spheroidal galaxies such as those recently identified in the M101 group at 7 Mpc, but the fact that it is only marginally resolved implies that it is at a much greater distance. Using the I814 band image we derive a surface brightness fluctuation distance of DSBF = 19.0 ± 1.7 Mpc (see Methods). It is located only 14' from the luminous elliptical galaxy NGC 1052, which has distance measurements ranging from 19.4 Mpc to 21.4 Mpc. We infer that NGC1052–DF2 is associated with NGC 1052, and we adopt D ≈ 20 Mpc for the galaxy.

For the Crater II galaxy, a distance of 120 kpc from the Milky Way galaxy led to a Milky Way gravitational field eight times larger than necessary to induce a strong external field effect, and while this dwarf galaxy is about 166 times further from the NGC 1052 as Crater II is from the Milky Way, elliptical galaxies are typically much larger than spiral galaxies, so they have stronger external fields at the same distance.

The Milky Way's mass is about 5.8*10^11 solar masses. NGC1052-DF2 appears to have a mass about 200 times smaller than the Milky Way. Giant elliptical galaxies have up to about 10^13 solar masses. But, the mass of this one has been measured to be only about 1.25 to 4 times larger than the Milky Way (up to almost 6x at two sigma). The estimated mass of NGC1052 (the parent galaxy) is as follows:

Using the kinematic information from the 16 GCs, we can estimate the mass enclosed within the radius of the GC system observed. We use the projected mass estimator (Evans et al. 2003), assuming isotropy and an r−4 distribution, to derive a mass of 1.7 ± 0.9 × 10^12M⊙ within 19 kpc (∼6.5re). The mass estimate error was calculated by bootstrapping the observed velocities and errors. van Gorkom et al. (1986) used HIkinematics to measure a mass of 3.1 × 10^11M⊙ within 23 kpc.

Given the only moderately greater mass and much greater distance, whether or not the external field effect applies here is close thing. If the greater distance reduces the external field strength by less than a factor of 18-54 (284 km/s for the Milky Way external field on Crater II v. 20 km/s for this galaxy scaled by the higher mass of this galaxy; up to about 81 at two sigma for the NGC1052 mass), then the external field effect should be present. But, a distance 166 times further from the dwarf galaxy should reduce the parent galaxy's gravitational field on the dwarf galaxy by more than a factor of 54 (or even the two sigma factor of 81). So, my back of napkin estimate, which could be flawed, suggests that there should be an external field effect from NGC1052 on NGC1052-DF2, or at least, not a full fledged one, unless there is some other source of a stronger external field acting on NGC1052-DF2.

So, spherical symmetry in the Deur paradigm looks like a more likely explanation than the external field effect in MOND, at first glance.

Another possibility is that an unusually rich interstellar gas/dust medium could increase a naive estimate of the strength of local gravitational fields in this system.

Still, this bears further investigation as it is a potentially extremely important data point, which is something I don't have the time to do in depth at the moment.

UPDATE April 2, 2018: This post suggests that the correctly calculated MOND prediction is 14+/- 4 and that the measured value is 8.4 with a 90% confidence interval upper limit of 10. So, it does not disprove MOND, the paper's calculation simply failed to consider the external field effect. The limited data points used in the calculation (ten) also suggests that the measured value is likely to be an underestimate as it was in FORNAX. And, the 20 mpc was distance from Earth, not distance from the dwarf to the elliptical which is about 80 kpc, which is the main reason that my calculation was off.

UPDATE April 3, 2018 (from the comments to the previous link by its author):

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.

UPDATE April 11, 2018

One of the authors addresses a variety of concerns (of the kind that quite honestly should have been addressed at a pre-print/peer review stage rather than post-publication) (hat tip Backreaction).

In particular, he justifies at great length his velocity dispersion calculation, although the paper really fails seriously in failing to address just how problematic and assumption prone it really is and the reasoning behind the choices made. The uncertainty due to fundamental assumption issues is greatly understated.

He acknowledges that he screwed up the MOND calculation and shifts attention from that mistake to a different dwarf galaxy (Dragonfly 44) where MOND might be off without conclusively showing that this is the case. He states:  "The whole MOND / alternative gravity discussion in the paper rests on a misunderstanding on my part."

He acknowledges the need for more and better data to get a more accurate measurement, some of which can be done quite easily (and really should have been done prior to publication in Nature).

He unconvincingly argues that "lacking" and "without" have different meanings while backpedaling on the "no" dark matter claim, although this criticism isn't honestly such a big deal since other language in the abstract does clarify the point (and indeed highlights that the dark matter a priori prediction was off by a factor of 100 v. a factor of about 0.4 at most for the correctly done MOND prediction).

Bottom line: Nature printed what was really a rough draft with some serious problems as a final and definitive work.

UPDATE April 14, 2018

A rebuttal paper.