Dynamics of Local Group galaxies: Evidence for a past Milky Way–Andromeda Flyby?

Indranil_BanikThe following is a guest post by Indranil Banik. Indranil is a PHD student at the University of Saint Andrews, part of the Scottish Universities’ Physics Alliance. He was born in Kolkata, India and moved to the UK with his parents a few years later. Indranil works on conducting tests to try and distinguish between standard and modified gravity, especially by considering the Local Group. Before starting his PhD in autumn 2014, he obtained an undergraduate and a Masters degree from the University of Cambridge with top grades. There, he worked on understanding the dynamics of ice shelves, and on a Masters project on the thick disk of the Milky Way, as well as on a few other problems.

Figure_1I recently won the Duncombe Prize from the American Astronomical Society’s Division on Dynamical Astronomy for a detailed investigation into the Local Group timing argument. This was to present a recently accepted scientific publication of mine (link at bottom of article) at their annual conference in Nashville, Tennessee.

The timing argument takes advantage of the fact that the Universe has a finite age of just under 14 billion years. Thus, everything we see must have started at a single point at that time, which we call the Big Bang. Due to the finite speed of light, by looking very far away, we are able to look back in time. In this way, we observe that, shortly after the Big Bang, the Universe was uniform to about one part in 100,000. Thus, we know that the expansion of the Universe was very nearly homogeneous at early times. This means that any two objects were moving away from each other with a speed almost proportional to the distance between them. This is called the Hubble law.Figure_2new

The Hubble law also works today, but only on large scales. On small scales, the expansion of the Universe is no longer homogeneous because gravity has had a long time to change the velocities of objects. As a result, our galaxy (the Milky Way, MW for short) and its nearest major galaxy, Andromeda (or M31) are currently approaching each other. This implies that there must have been a certain amount of gravitational pull between the MW and M31.

Although this has been quantified carefully for nearly 60 years, my contribution involves analysing the effects of the MW and M31 on the rest of the Local Group (LG), the region of the Universe where gravity from these objects dominates (out to about 10 million light years from Earth). Recently, a large number of LG dwarf galaxies have been discovered or had their velocity measured for the first time (McConnachie, 2012). We took advantage of this using a careful analysis.

We treated the MW and M31 as two separate masses and found a trajectory for them consistent with their presently observed separation. We treated the other LG dwarf galaxies as massless, which should be valid as they are much fainter than the MW or M31. For each LG dwarf, we obtained a test particle trajectory whose final position (i.e. at the present time) matches the observed position of the dwarf. The velocity of this test particle is the model prediction for the velocity of that galaxy.

Figure_3The basic feature of the model is that the expansion of the Universe has been slowed down locally by gravity from the MW and M31. At long range (beyond 3 Mpc or about 10 million light years), this effect is very small and so objects at those distances should essentially just be following the Hubble law. But closer to home, the results of this model are clear: the MW and M31 are holding back the expansion of the Universe, and objects within about 1.5 Mpc should be approaching us rather than moving away (see figure above). By comparing the detailed predictions of our model with observations, we were able to show that, for all plausible MW and M31 masses, a significant discrepancy remains. This is because a number of LG galaxies are flying away from us much faster than expected in the model.

An important aspect of these models is that the MW and M31 have never approached each other closely. Although one can in principle get them to have a past close flyby in Newtonian gravity if they are assigned very high masses, there are several problems with this. Such high masses are unreasonable given other evidence. More importantly, if there had been such a flyby, the dark matter halos of the MW and M31 would have overlapped, leading to a substantial amount of friction (of a type called dynamical friction, which is reliant only on gravity). This would have caused the galaxies to merge, contradicting the fact that they are now 2.5 million light years apart.

I was aware of an alternative model for galaxies called Modified Newtonian Dynamics (MOND – Milgrom, 1983). This is designed to address the fact that galaxies rotate much faster than one would expect if applying Newtonian dynamics to their distributions of visible mass. The conventional explanation is that galaxies are held together by the extra gravitational force provided by a vast amount of invisible dark matter. Many galaxies need much more dark matter than the amount of actually observed matter. But, so far, this dark matter has not been detected directly. What MOND does is to increase the gravitational effect of the visible matter so that it is enough to explain the observed fast rates of rotation. In this model, there is no longer any need for dark matter, at least in halos around individual galaxies. You can find out more about MOND here on McGaugh’s MOND pages and here on Scholarpedia.

Figure_4In MOND, the MW and M31 must have undergone a past close flyby (Zhao et al, 2013). In this model, the absence of dark matter halos around galaxies means that there need not have been any dynamical friction during the flyby (remember that the disks of the MW and M31 are much smaller than their hypothetical dark matter halos, which are only needed if we apply Newton’s law of gravity).

The high relative speed of the MW and M31 at this time (about 9 billion years ago) would probably go a long way towards explaining these puzzling observations. This is because of a mechanism called gravitational slingshots, similar to how NASA was able to get the Voyager probes to gain a substantial amount of energy each time they visited one of the giant planets in our Solar System. The idea in this case would be for the MW/M31 to play the role of the planet and of a passing LG dwarf galaxy to play the role of the spacecraft.


This mechanism is illustrated in the figure above. In the left panel, there is a small galaxy moving at 1 km/s while a much heavier galaxy moving at 5 km/s catches up with it. The massive galaxy sees the dwarf approaching at 4 km/s (right panel). The trajectory of the dwarf is then deviated strongly, so it ends up receding at 4 km/s back in the direction it approached from. Combined with the velocity of the massive galaxy (which is almost unchanged), we see that the velocity of the dwarf has been increased to 5 + 4 = 9 km/s.

We do in fact observe many LG dwarf galaxies moving away from us much faster than in the best-fitting dark matter-based model (see figure below, observed radial velocities are on the y-axis while model-predicted ones are on the x-axis). Moreover, based on the distances and velocities of these objects, we can estimate roughly when they would have been flung out by the MW/M31. This suggests a time approximately 9 billion years ago, which is also when one expects the MW and M31 to have been moving very fast relative to each other in MOND as they were close together.


These high-velocity LG dwarfs would have been flung out most efficiently in a direction parallel to the velocity of whichever heavy galaxy they interacted with. Naturally, the MW and M31 have not always been moving in the same direction. But it is very likely that they were always moving within much the same plane. Thus, one test of this scenario (suggested by Marcel Pawlowski) is that these high-velocity dwarfs should preferentially lie within the same plane.

There is some evidence that this is indeed the case. Moreover, the particular plane preferred by these objects is almost the same as what would be required to explain the distribution of satellite galaxies around the MW and M31. This is described in more detail towards the end of this lecture I gave recently about my work.

Even without this evidence, there is a strong case for MOND. One of the astronomers heavily involved in making this case is Professor Stacy McGaugh. I was very pleased to meet him at this conference. We discussed a little about his current work, which focuses on using rotation curves of galaxies to estimate forces within them. For a modified gravity theory which does away with the need for dark matter, it is important that these forces can be produced by the visible matter alone. Stacy was doing a more careful investigation into estimating the masses of galaxies from their observed luminosities and colours (which give an idea of the mix of different types of star in each galaxy, each of which has its own ratio between mass and luminosity, old stars being red and young ones blue). The success enjoyed by MOND in explaining dozens of rotation curves is one of the major reasons the theory enjoys as much support as it does.

This brought us on to discussing how we came to favour the theory over the conventional cosmological model (ΛCDM) involving Newtonian gravity and its consequent dark matter. Stacy explained how it was particularly his work on low surface brightness galaxies which convinced him. This is because such galaxies were not known about when the equations governing MOND were written down (in the early 1980s). Despite this, they seemed able to predict future observations very well. This was somewhat surprising given that the theory predicted very large deviations from Newtonian gravity. In the ΛCDM context, the presence of large amounts of invisible mass makes it difficult to know what to expect. As a result, it is difficult for the theory to explain observations indicating a very tight coupling between forces in galaxies and the distribution of their visible mass – even when most of the mass is supposedly invisible (a feature called Renzo’s Rule). A broader overview of what the observations seem to be telling us is available here (Famaey & McGaugh 2012) and here (Kroupa 2015).

I then explained my own thinking on the issue. I was aware of some of the observations which persuaded Stacy to favour MOND and I was aware of the theory, but I did not favour it over ΛCDM. Personally, what got me interested in seriously considering alternatives to ΛCDM was its missing satellites problem. The theory predicts a large number of satellite galaxies around the MW, much larger than the observed number. Although it is unclear if MOND would help with this problem, that does seem likely because structure formation should proceed more efficiently under the modified gravity law. This should lead to more concentration of matter into objects like the MW with less being left over for its satellites.

Although this suggested MOND might be better than ΛCDM, my initial reaction was to consider warm dark matter models. Essentially, if the dark matter particles were much less massive than previously thought (but the total mass in the particles was the same), then they would behave slightly differently. These differences would lead to less efficient structure formation at low masses, reducing the frequency of low-mass halos and thus making for less satellite galaxies. I hoped this would explain a related problem, the cusp-core challenge which pertains to the inner structure of satellite galaxies.

What finally convinced me against such minor alterations to ΛCDM and in favour of MOND was the spatial arrangement and internal properties of the MW and M31 satellite galaxies. Much has been written in previous posts to this blog about this issue (for example, here), with this 2005 paper by Kroupa, Theis & Boily pointing out the discrepancy between observations and models for the first time.

Figure_7I have summarised the results in a flowchart (left). Essentially, the hypothetical dark matter halos around the MW and M31 need to be distributed in a roughly spherical way. This is unlike the disks of normal (baryonic) matter in these galaxies. The reason is that baryons can radiate and cool, allowing them to settle into disks. As a result, in an interaction between two galaxies, the baryons with their ordered circular motions in a disk can get drawn out into a long dense tidal tail that then collapses into small tidal dwarf galaxies. But these would be free of dark matter, and they would also be mostly located close to a plane: the common orbital plane of the interacting galaxies. You can see more about this scenario here.

The argument goes that it is difficult to form such planes of satellites in any other way (for example, see Pawlowski et al, 2014). Just such satellite planes are in fact observed around both the MW and M31. Supposedly free of dark matter, they should have quite weak self-gravity and thus low internal velocity dispersions/rotate very slowly. Yet, their observed velocity dispersions are quite high, signalling the need for some extra force to stop them flying apart.

Because the spatial arrangement of these satellites suggests a violent origin, it is unlikely that they have much dark matter. Thus, I became convinced of the need to modify our understanding of gravity. It turns out that exactly the same modification that can help explain galaxy rotation curves without dark matter could also help address this problem (McGaugh & Milgrom, 2013). Although the dark matter plus Newtonian gravity worldview might just about be able to explain galaxy rotation curves (although detailed tests are showing this not to have succeeded: Wu & Kroupa 2015), I do not think it can explain the satellite plane problem. This eventually convinced me to investigate this issue further. I explain some of the more compelling reasons for favouring MOND over ΛCDM in this lecture I gave recently.

The paper for which I won the Duncombe Prize is available here: http://arxiv.org/abs/1506.07569

The peer-reviewed version has appeared in the Monthly Notices of the Royal Astronomical Society, volume 459, issue 2, pages 2237 to 2261.

Dark Matter in the innermost regions of the Milky Way?

Spiral galaxies rotate too fast. If they would only consist of the visible (baryonic) mass we observe in them and Newton’s Law of gravity is correct, then they would not be stable and should quickly fly apart. That they don’t has been one of the first indications that the galaxies (and the Universe as a whole) either contains large amounts of additional but invisible “dark matter”, or that the laws of gravity don’t hold on the scales of galaxies. One possibility for the latter, Modified Newtonian Dynamics (MOND), proposes that gravity needs to be stronger in the low acceleration regime present in galaxies (for more details see the extensive review by Famaey & McGaugh 2012 and Milgrom’s Scholarpedia article). That the rotation curve (i.e. the function of circular velocity of the galactic disc with radius) of our Milky Way galaxy follows the same trend as the rotation curves of other spiral galaxies has been known for a long time, too. So it appears to be a bit surprising that the Nature Physics study “Evidence for dark matter in the inner Milky Way” by Fabio Iocco, Miguel Pato and Gianfranco Bertone makes such a splash in the international press. That the MW should contain dark matter is not news, but nevertheless the paper got a huge amount of press coverage.

Rotation curves of two spiral galaxies (images in the background). The black line illustrates the Newtonian expectation for the rotation curve based on the observed baryons (stars and gas), the blue line is the MOND fit.
Rotation curves of two spiral galaxies (images in the background). The black line illustrates the Newtonian expectation for the rotation curve based on the observed baryons (stars and gas), they are clearly not high enough to explain the data points (small circles). The blue line is the MOND fit for which the mass-to-light ratio is the only free parameter. Credit: Stacy S. McGaugh, private communication

One thing emphasized a lot by the press articles (and press releases) is that the authors claim to have found proof for the presence of dark matter in the ‘core‘, ‘innermost region‘, or even ‘heart of our Galaxy1, not just in the intermediate and outer regions. This might be worrisome for modified gravity theories like MOND, which predict that regions very close to the center of the Milky Way should be in the classical Newtonian regime, i.e. the rotation curve should be consistent with that predicted by applying Newton’s law to the observed mass distribution. The underlying reason is that due to the higher density of baryonic matter in the center of the Milky Way the gravitational acceleration of the baryons there already exceeds the low-acceleration limit. But only once the acceleration drops below a certain threshold the non-Newtonian gravity effect kicks in. Interpreted naively (i.e. assuming Newtonian dynamics), this would mimic dark matter appearing only beyond a certain radial distance from the Galactic Center.

Without even going into the details of checking their assumed Milky Way models, the way the observational data is combined and whether there are systematic effects, a simple look at figure 2 in Iocco et al. already reveals that their strong claim unfortunately is not as well substantiated as I would wish.

Credit: Fig. 2 of Ioco et al. (2015).

The plot’s upper panel is what is of interest here. It shows the angular circular velocity in the Milky Way disk versus the Galactocentric radius. The red points with error bars are observed data for different tracers. The grey band is the range of velocities allowed for the range of baryonic mass distributions in the Milky Way considered by Iocco et al. (that are all consistent with observations). If there would be only baryonic matter and Newtonian Dynamics, the rotation curve of the Milky Way should lie somewhere in this area.

First of all, the figure shows that they did not consider any data in the region within 2.5 kpc. That makes sense because that region will be dominated by the bar and bulge of the Milky Way. Stars in the bulge don’t follow circular orbits, so one can’t measure circular velocities there.

So, what is the core, heart or ‘innermost region’ of the Milky Way? Lets try to come up with something motivated by the structure of our Galaxy. The Galactic disk is often modeled by an exponential profile, with a scale length of about 2.2 kpc. What if we say the core of the MW is everything within one scale length? Immediately there’s a problem with the claim by Iocco: They are not even testing data on this scale.

Lets ignore the phrase ‘core’ or ‘heart’ of the Milky Way and focus on the more general formulation they also use in their paper’s title: “Evidence for dark matter in the inner Milky Way”. Looking at their Figure again, we can see that the data start to leave the grey band at a distance of about 6 kpc from the MW center. Thus, within 6 kpc (almost three scale radii of the Milky Way disk!) the purely baryonic models encompass the data. Consequently, here is no need to postulate that dark matter contributes significantly to the dynamics. The figure clearly shows that there is no need, and therefore no evidence for dark matter within 6 kpc of the Galactic Center, which is as generous a definition of ‘inner Milky Way’ as it gets in my opinion. The authors themselves even write that ‘The discrepancy between observations and the expected contribution from baryons is evident above Galactocentric radii of 6-7 kpc’. In this regard it doesn’t matter whether the majority of the possible baryonic models predict a lower rotation curve: as long as the data agree with at least one baryonic model that is consistent with the observed distribution of mass in the Milky Way, there can not be evidence for dark matter.

I really don’t understand why they then claim to have found proof of dark matter in the innermost regions of the Milky Way. My suspicion is that the authors and their press releases seem to have a (literally) quite broad interpretation of the term ‘innermost region’. Judging from the context, they seem to subsume everything within the solar circle of ~ 8 kpc (the distance of the Sun from the Galactic Center) as ‘innermost’. I don’t think it is an appropriate definition, after all it makes the vast majority of the baryonic mass of the Milky Way part of the innermost region. Half the light of an exponential disk is already contained within less than 1.7 scale length (1.7 x 2.2 kpc = 3.7 kpc for the Milky Way), and all of the bulge/bar is in there, too. But if we nevertheless roll with it for the moment we can see that yes, between 7 and 8 kpc there seems to be need for dark matter … or for a MOND-like effect.

Rotation curve of the Milky Way: Observed velocities (squares), baryons + Newtonian Dynamics (black line) and MOND rotation curve (magenta line). Note the excellent prediction of the observed rotation curve given the observed distribution of baryons only which is achieved in MOND; the Galaxy appears entirely Newtonian within the innermost 2 kpc.
Rotation curve of the Milky Way: Observed velocities (squares), baryons + Newtonian Dynamics (black line) and MOND rotation curve (magenta line). Note the excellent prediction of the observed rotation curve given the observed distribution of baryons only which is achieved in MOND; the Galaxy appears entirely Newtonian within the innermost 2 kpc. Credit: McGaugh (2008)

So, lets have a look at one MOND rotation curve constructed for the Milky Way (from McGaugh 2008) to see where we expect to find a difference in Newtonian and MONDian circular velocities. The expected Newtonian rotation curve is shown as a black line in the plot, equivalent to the purely baryonic rotation curves making up the grey band in the figure of Iocco et al.. The rotation curve predicted by MOND is shown as a magenta line and the observed circular velocities are the small squares.

The plot immediately reveals that a discrepancy between the Newtonian and the MONDian rotation curves is expected already at small radii, well within 6 kpc. The findings of Iocco et al. that there appears to be some mass missing within the solar circle therefore do not disagree with the MONDian expectation, in contrast to what one of the authors is quoted saying in a Spektrum article. Furthermore, the plot demonstrates that the need for dark matter (or MOND) in the region inside the solar circle was already well known before this new study.

So, in summary, the study doesn’t show all that much new or surprising, the claimed ‘evidence’ for dark matter in the innermost Milky Way is not present in their data (unless you define ‘innermost’ very generously) and some apparent dark matter contribution within the solar circle is not even unexpected based on MOND predictions.


1: The press releases of the TU Munich and Stockholm University even call it a ‘direct observational proof of the presence of dark matter in the innermost part our Galaxy’ (which is clearly wrong, there is obviously nothing direct about it and the innermost part would imply the very center of the Milky Way).


See the overview of topics in The Dark Matter Crisis.