Category: MOND

Recent Developments Concerning the Gravitational Potential of the Milky Way.ย II. A Closer Look at the Data

Recent Developments Concerning the Gravitational Potential of the Milky Way.ย II. A Closer Look at the Data

Continuing from last time, let’s compare recent rotation curve determinations from Gaia DR3:

Fig. 1 from Jiao et al. comparing three different realizations of the Galactic rotation curve from Gaia DR3. The vertical lines* mark the range of the Ou et al. data considered by Chan & Chung Law (2023).

These are different analyses of the same dataset. The Gaia data release is immense, with billions of stars. There are gazillions of ways to parse these data. So it is reasonable to have multiple realizations, and we shouldn’t expect them to necessarily agree perfectly: do we look exclusively at K giants? A stars? Only stars with proper motion and/or parallax data more accurate than some limit? etc. Of course we want to understand any differences, but that’s not going to happen here.

My first observation is that the various analyses are broadly consistent. They all show a steady decline over a large range of radii. Nothing shocking there; it is fairly typical for bright, compact galaxies like the Milky Way to have somewhat declining rotation curves. The issue here, of course, is how much, and what does it mean?

Looking more closely, not all of the data agree with each other, or even with themselves. There are offsets between the three at radii around the sun (we live just outside R = 8 kpc) where you’d naively think they would agree the best. They’re very consistent from 13 < R < 17 kpc, then they start to diverge a little. The Ou data have a curious uptick right around R = 17 kpc, which I wouldn’t put much stock in; weird kinks like that sometimes happen in astronomical data. But it can’t be consistent with a continuous mass distribution, and will come up again for other reasons.

As an astronomer, I’m happy with the level of agreement I see here. It is not perfect, in the sense that there are some points from one data set whose error bars do not overlap with those of other data sets in places. That’s normal in astronomy, and one of the reasons that we can never entirely trust the stated uncertainties. Jiao et al. make a thorough and yet still incomplete assessment of the systematic uncertainties, winding up with larger error bars on the Wang et al. realization of the data.

For example, one – just one of the issues we have to contend with – is the distance to each star in the sample. Distances to individual objects are hard, and subject to systematic uncertainties. The reason to choose A stars or K giants is because you think you know their luminosity, so can estimate their distance. That works, but aren’t necessarily consistent (let alone correct) among the different groups. That by itself could be the source of the modest difference we see between data sets.

Chan & Chung Law use the Ou et al. realization of the data to make some strong claims. One is that the gradient of the rotation curve is -5 km/s/kpc, and this excludes MOND at high confidence. Here is their plot.

You will notice that, as they say, these are the data of Ou et al, being identical to the same points in the plot from Jiao et al. above – provided you only look in the range between the lines, 17 < R < 23 kpc. This is where the kink at R = 17 kpc comes in. They appear to have truncated the data right where it needs to be truncated to ignore the point with a noticeably lower velocity, which would surely affect the determination of the slope and reduce its confidence level. They also exclude the point with a really big error bar that nominally is within their radial range. That’s OK, as it has little significance: it’s large error bar means it contributes little to the constraint. That is not the case for the datum just inside of R = 17 kpc, or the rest of the data at smaller radii for that matter. These have a manifestly shallower slope. Looking at the line boundaries added to Jiao’s plot, it appears that they selected the range of the data with the steepest gradient. This is called cherry-picking.

It is a strange form of cherry-picking, as there is no physical reason to expect a linear fit to be appropriate. A Keplerian downturn has velocity decline as the inverse square root of radius (see the dotted line above.) These data, over this limited range, may be consistent with a Keplerian downturn, but certainly do not establish that it is required.

Contrast the statements of Chan & Chung Law with the more measured statement from the paper where the data analysis is actually performed:

… a low mass for the Galaxy is driven by the functional forms tested, given that it probes beyond our measurements. It is found to be in tension with mass measurements from globular clusters, dwarf satellites, and streams.

Ou et al. (2023)

What this means is that the data do not go far enough out to measure the total mass. The low mass that is inferred from the data is a result of fitting some specific choice of halo form to it. They note that the result disagrees with other data, as I discussed last time.

Rather than cherry pick the data, we should look at all of it. Let’s see, I’ve done that before. We looked at the Wang et al. (2023) data via Jiao et al. previously, and just discussed the Ou et al. data. That leaves the new Zhao et al. data, so let’s look at those:

Milky Way rotation curve with RAR model (blue line from 2018) and the Gaia DR3 data as realized by Zhou et al. (2023: purple triangles). The dashed line shows the number of stars (right axis) informing each datum.

These data were the last of the current crop that I looked at. They look… pretty good in comparison with the pre-existing RAR model. Not exactly the falsification I had been led to expect.

So – the three different realizations of the Gaia DR3 data are largely consistent, yet one is being portrayed as a falsification of MOND while another is in good agreement with its prediction.

This is why you have to take astronomical error bars with a grain of salt. Three different groups are using data from the same source to obtain very nearly the same result. It isn’t quite the same result, as some of the data disagree at the formal limits of their uncertainty. No big deal – that’s what happens in astronomy. The number of stars per bin helps illustrate one reason why: we go from thousands of stars per bin near the sun to tens of stars in wider bins at R > 20 kpc. That’s not necessarily problematic, but it is emblematic of what we’re dealing with: great gobs of data up close, but only scarce scratches of it far away where systematic effects are more pernicious.

In the meantime, one realization of these data are being portrayed as a death knell for a theory that successfully predicts another realization of the same data. Well, which is it?

*Thanks to Moti Milgrom for pointing out the restricted range of radii considered by Chan & Chung Law and adding the vertical lines to this figure.

Recent Developments Concerning the Gravitational Potential of the Milky Way. I.

Recent Developments Concerning the Gravitational Potential of the Milky Way. I.

Recent results from the third data release (DR3) from Gaia has led to a flurry of papers. Some are good, some are great, some are neither of those. It is apparent from the comments last time that while I’ve kept my pledge to never dumb it down, I have perhaps been assuming more background knowledge on the part of readers than is adequate. I can’t cram a graduate education in astronomy into one web page, but will try to provide a little relevant context.

Galactic Astronomy is an ancient field, dating back at least to the Herschels. There is a lot that is known in the field. There have also been a lot of misleading observations, going back just as far to the Herschel’s map of the Milky Way, which was severely limited by extinction from interstellar dust. That’s easy to say now, but Herschel’s map was the standard for over a century – longer than our modern map has persisted.

So a lot has changed, including a lot that seemed certain, so I try to keep an open mind. The astronomers working with the Gaia data – the ones deriving the rotation curve – are simply following where those data take them, as they should. There are others using their analyses to less credible ends. A lot of context is required to distinguish the two.

The total mass of the Milky Way

There are a lot of constraints on the mass of the Milky Way that predate Gaia; it’s not like these are the first data that address the issue. Indeed, there are lots and lots and lots of other applicable data acquired using different methods over the course of many decades. Here is a summary plot of determinations of the mass of the Milky Way compiled by Wang et al. (2019).

This is an admirable compilation, and yet no such compilation can be complete. There are just so many determinations by lots of independent authors. Still, this is nice for listing multiple results from many distinct methodologies. They all consistently give numbers around 1012 solar masses. (Cast in these terms, my own estimate is 1.4 x 1012 albeit with a substantial systematic uncertainty.) I’ve added a point for the total mass according to the alleged Keplerian downturn seen in the Gaia data, 2 x 1011 solar masses. One of these things is not like the others.

The difference from the bulk of the data has nearly every astronomer rolling our collective eyes. Most of us straight up don’t believe it. That’s not to say the Gaia data are wrong, but the interpretation of those data as indicative of such a small, finite total mass seems unlikely in the light of all other results.

As I discussed briefly last time, it is conceivable that previous results are wrong or misleading due to some systematic effect or bad assumption. For example, mass estimates based on “satellite phenomenon” require the assumption that the satellite galaxies are indeed satellites of the Milky Way on bound orbits. That seems like a really good assumption, as without it, their presence is an instantaneous coincidence particular to the most recent few percent of a Hubble time: they wouldn’t have been nearby more than a billion years ago, and won’t be around another for even a few hundred million more. That sounds like a long time to you and me, but it is not that long on a cosmic scale. Maybe they’re raining down all the time to give the appearance of a steady state? Where have I heard that before?

Even if we’re willing to dismiss satellite constraints, that doesn’t suffice. It isn’t good enough to find flaw with one set of determinations; one must question all distinct methods. I could probably do that; there’s always a systematic uncertainty that might be bigger than expected or an assumption that could go badly wrong. But it is asking a lot for all of them to conspire to be wrong at the same time by the same amount. (The assumption of Newtonian gravity is a catch-all.)

Some constraints are more difficult to dodge than others. For example, the escape velocity method merely notes that there are fast moving stars in the solar neighborhood. Those stars are many billions of years old, and wouldn’t be here if the gravitational potential couldn’t contain them. The mass implied by the Gaia quasi-Keplerian downturn doesn’t suffice.

That said, the total mass of the Milky Way as expressed above is a rather notional quantity. M200 occurs roughly 200 kpc out for the Milky Way, give or take a lot. And the “200” in the subscript has nothing to do with that radius being 200 kpc for reasons too technical and silly to delve into. So my biggest concern about the compilation above is not that the data are wrong so much as they are being extrapolated to an idealized radius that we don’t directly observe. This extrapolation is usually done by assuming the potential of an NFW halo, which makes perfect sense in terms of LCDM but none whatsoever empirically, since NFW predicts the wrong density profile at small, intermediate, and large radii: where the density profile ฯ โˆ r-ฮฑ is predicted to have ฮฑ = (1,2,3), it is persistently observed to be more like (0,1,2). While the latter profile is empirically more realistic, it also fails to converge to a finite total mass, rendering the concept meaningless.

Rather than indulge yet again in a discussion of the virtues and vices of different dark matter halo profiles, let’s look at an observationally more robust quantity: the enclosed mass. Wang et al. also provide a tabulation of this quantity from many sources, as depicted here:

Rotation curve constraints implied by the enclosed mass measurements tabulated by Wang et al. (2019) combined with the halo stars and globular clusters previously discussed. The location of the Large Magellanic Cloud is also indicated; data beyond this radius (and perhaps even within it) are subject to perturbation by the passage of the LMC. The RAR-based model is shown as the blue line; the light blue line includes a very uncertain estimate of the effect of the coronal gas. This is very diffuse and extended, and only becomes significant at very large radii. The dotted line is the Keplerian curve for a mass of 2 x 1011 Mโ˜‰.

Not all of the enclosed mass data are consistent with one another. The bulk of them are consistent with the RAR model Milky Way (blue line). None of them are consistent with the small mass indicated by recent Gaia analyses (dotted line). Hence the collective unwillingness of most astronomers to accept the low-mass interpretation.

An important thing to note when considering data at large radii, especially those beyond 50 kpc, is that 50 kpc is the current Galactocentric radius of the Large Magellanic Cloud. The LMC brings with it its own dark matter halo, which perturbs the outer regions of the Milky Way. This effect is surprisingly strong*, and leads to the inference that the mass ratio of the two is only 4 or 5:1 even though the luminosity ratio is more like 20:1. This makes the interpretation of the data beyond 50 kpc problematic. If we use that as a pretext to ignore it, then we infer that our low mass Milky Way is no more massive then the LMC – an apparently absurd situation.

There are many rabbit holes we could dig down here, but the basic message is that a small Milky Way mass violates a gazillion well-established constraints. That doesn’t mean the Gaia data are wrong, but it does call into question their interpretation. So next time we’ll look more closely at the data.

*This is not surprising in MOND. The LMC is in the right place at the right time to cause the Galactic warp. The LMC as a candidate perturber to excite the Galactic warp was recognized early, but the conventional mass was thought to be much too small to do the job. The small baryonic mass of the LMC in MOND is not a problem as the long range nature of the force law makes tidal effects more pronounced: it works out about right.

Wide Binary Results Favoring MOND

I think the time has come for another update on wide binaries. These were intensely debated at the conference in St. Andrews, with opposing camps saying they did or did not show MONDian behavior. Two papers by independent authors have recently been refereed and published: Chae (2023) in the Astrophysical Journal and Hernandez (2023) in Monthly Notices. These papers both find evidence for MONDian behavior in wide binaries.

If these new results are correct, they are the smoking gun for MOND. I’ve been trying to avoid that phrase, and think of how we would explain this with dark matter. I haven’t come up with any good ideas. This doesn’t preclude others from coming up with bad ideas, but the problem this result poses is profound.

The basic idea is that galaxies reside in dark matter halos. These are diffuse entities with a particular mass distribution that must contribute the right gravitational force to explain observations on galactic scales. On local scales, like the solar neighborhood, this leads to a very low space density of about 0.007 solar masses per cubic parsec, or 0.26 GeV/cm3. For comparison, the local density of stars and gas is about 0.11 solar masses per cubic parsec. Adding up all the dark matter in the solar system within the orbit of Pluto amounts to the equivalent mass of a one km-size asteroid. That doesn’t do anything noticeable to solar system dynamics, especially when it is spread out as expected rather than concentrated in an asteroid.

Wide binaries should encompass more dark matter than the solar system by virtue of their greater size, but the enclosed mass remains too tiny to affect the orbits of the stars. There could be the occasional lump of dark matter, but those should be few and far between: the conventional expectation for binary stars is purely Newtonian, with no hint of a mass discrepancy. In contrast, the expectation in MOND is that every system that experiences the low acceleration regime should show a discrepancy of predictable amplitude. I simply don’t see how to imitate that with any of the usual dark matter suspects.

Here is the results from Chae’s paper. There are many figures like this that explore all sorts of permutations on sample selection and other effects. The answer persistently comes up the same. There is a systematic deviation from Newtonian behavior that is consistent with MOND, and in particular with the nonlinear theory AQUAL proposed early on by Bekenstein & Milgrom.

Part of Fig. 19 from Chae (2023). As one goes to lower acceleration, the data for wide binaries agrees well with the prediction of the Aquadratic Lagrangian theory of MOND (purple line in lower panel).

This figure subsumes many astronomical details, like the distribution of orbital eccentricities and the frequency of triple systems. Chae has simulated what to expect as a result of all these effects, with the results in the top panel distinguishing between the Newtonian expectation in blue and the data in red. At high accelerations, the red histogram is right on top of the blue histogram. These distributions are indistinguishable, as they should be in both theories. As one looks to lower accelerations, the red and blue histograms begin to part. They stand clearly apart in the lowest acceleration bin. This is as expected in MOND. In contrast, the histograms should never diverge in the Newtonian case, with or without dark matter.

A similar result has been obtained by Hernandez (2023), who emphasizes the importance of obtaining a clean sample for which one is sure that the binaries are genuinely bound and have radial velocities as well as proper motions. The data follow the Newtonian line until they don’t. The deviation is consistent with MOND.

Part of Fig. A1 from Hernandez (2023). The MOND effect is apparent as the break of the red points from the purely Newtonian blue line.

Again, there are many figures like this in the paper to explore all the possible permutations. These all paint the same picture: MOND. The published result Hernandez obtains is consistent with the result obtained by Chae, relieving a small tension that was present in the preprint stage.

Still outstanding is why Chae and Hernandez get a different answer from Pittordis & Sutherland (2023), who utilize many more binaries. This is a tradeoff that frequently arises in astronomical data analysis: numbers vs. quality. The risk with numbers is that the signal you’re searching for gets drowned out in a sea of noise. The risk in defining a high quality sample is that you unintentionally introduce a selection effect that causes a signal to appear where there isn’t one. It seems unlikely that this would result in MOND-like behavior – it could do any number of crazy things – but I don’t know enough about this specific subject to judge. Note that I’m willing to say when I’m out of my expertise; I expect it won’t be hard to find faux experts who don’t acknowledge the limitations of their qualifications and are perfectly happy to find flaws with studies they dislike but don’t understand.

What I hope to see in future is some convergence between the different groups, or at least for some understanding to emerge as to why their results differ. In the meantime, I expect most of the community will duck and cover.

Is NGC 1277 a problem for MOND?

Is NGC 1277 a problem for MOND?

Alert reader Dan Baeckstrรถm recently asked about NGC 1277, as apparently some people have been making this out to be some sort of death knell for MOND.

My first reaction was NGC who? There are lots of galaxies in the New General Catalog (new in 1888, even then drawing heavily on earlier work by the Herschels). I’m well acquainted with many individual galaxies, and can recall many dozens by name, but I do not know every single thing in the NGC. So I looked it up.

NGC 1277 in the Perseus cluster. Photo credit: NASA, ESA, M. Beasley, & P. Kehusmaa

NGC 1277 is a lenticular galaxy. Early type. Lots of old stars. These types of galaxies tend to be baryon dominated in their centers. One might even describe them as having a dearth of dark matter. This is expected in MOND, as the stars are sufficiently concentrated that these objects are in the high acceleration regime near their centers. The modification only appears when the acceleration drops below a0 = 1.2 x 10-10 m/s/s; when accelerations are above this scale, everything is Newtonian – no modification, no need for dark matter.

So, is NGC 1277 special in some way? Why does this come up now?

There is a recent paper on NGC 1277 by Comerรณn et al. that seems to be the source of the claims of a death knell. The title is The massive relic galaxy NGC 1277 is dark matter deficient. That sounds normal for this type of galaxy, but I guess if you disliked MOND without understanding it, you might misinterpret that title to mean there was no mass discrepancy at all, hence a problem for MOND. I guess. I’m an expert on the subject; I don’t know where non-experts get their delusions.

The science paper by Comerรณn et al. is a nice analysis of reasonably high quality observations of the kinematics of this galaxy. Not seeing what the worry is. Here is their Fig. 19, which summarizes the enclosed mass distribution:

Three-dimensional cumulative mass profiles of NGC 1277 (Fig. 19 of Comerรณn et al.) Stars and the central black hole account for everything within the observed radius; dark matter (colored bands) is not yet needed.

The first thing I did was eyeball this plot and calculate the circular speed of a test particle at 10 kpc near the edge of the plot. Newton taught us that V2 = GM/R, and the enclosed mass there looks to be just shy of 2 x 1011 solar masses, so V = 290 km/s. That’s big, but also normal for a massive galaxy like this. The corresponding centripetal acceleration V2/R is about 2a0. As expected, this galaxy is in the high acceleration regime, so MOND predicts Newtonian behavior. That means the stars suffice to explain the dynamics; no need for dark matter over this range of radii.

The second thing I did was check to see what Comerรณn et al. said about it themselves. They specifically address the issue, saying

One might be tempted to use the fact that NGC 1277 lacks detectable dark matter to speculate about the (in)existence of Milgromian dynamics (also known as MOND;ย Milgrom 1983) or other alternatives to the ฮ›CDM paradigm. Given a centrally concentrated baryonic mass ofย Mโ‹†โ€„โ‰ˆโ€„1.6โ€…ร—โ€…1011โ€†MโŠ™ย and an acceleration constantย a0โ€„=โ€„1.24โ€…ร—โ€…10โˆ’10ย m sโˆ’2ย (McGaugh 2011), a radiusย Rโ€„=โ€„13 kpc should be explored to be able to probe the fully Milgromian regime. This is about twice the radius that we cover and therefore our data do not permit studying the Milgromian regimeย 

Comerรณn et al. (2023)

which is what I just said. These observations do not probe the MOND regime, and do not test theory. So, in order to think this work poses a problem for MOND, you have to (i) not understand MOND and (ii) not bother to read the paper.

I wish I could say this was unusual. Unfortunately, it is only a bit sub-par for the course. A lot of people seem to hate MOND. I sympathize with that; I was really angry the first time it came up in my data. But I got over it: anger is not conducive to a rational assessment of the evidence. A lot of people seem to let their knee-jerk dislike of the idea completely override their sense of objectivity. All too often, they don’t even bother to do minimal fact checking.

As Romanowsky et al. pointed out, the dearth of dark matter near the centers of early type galaxies is something of a problem for the dark matter paradigm. As always, this depends on what dark matter actually predicts. The most obvious expectation is that galaxies form in cuspy dark matter halos with a high concentration of dark matter towards the center. The infall of baryons acts to further concentrate the central dark matter. So the nominal expectation is that there should be plenty of dark matter near the centers of galaxies rather than none at all. That’s not what we see here, so nominally NGC 1277 presents more of a challenge for the dark matter paradigm than it does for MOND. It makes no sense to call foul on one theory without bothering to check if the other fares better. But we seem to be well past sense and well into hypocrisy.

The MOND at 40 conference

I’m back from the meeting in St. Andrews, and am mostly recovered from the jet lag and the hiking (it was hot and sunny, we did not pack for that!) and the driving on single-track roads like Mr. Toad. The A835 north from Ullapool provides some spectacular mountain views, but the A837 through Rosehall is more perilous carnival attraction than well-planned means of conveyance.

As expected, the most contentious issue was that of wide binaries. The divide was stark: there were two talks finding nary a hint of MONDian signal, just old Newton, and two talks claiming a clear MONDian signal. Nothing was resolved in the sense of one side convincing the other it was right, but there was progress in terms of [mostly] amicable discussion, with some sensible suggestions for how to proceed. One suggestion was that a neutral party should provide all the groups with several sets of mock data, one Newtonian, one MONDian, and one something else, to see if they all recovered the right answers. That’s a good test in principle, but it is a hassle to do in practice, as it is highly nontrivial to produce realistic mock Gaia data, so no one was leaping at the opportunity to stick their hand in this particular bear trap.

Xavier Hernandez made the excellent point that one should check that one’s method recovers Newtonian behavior for close binaries before making any claims to require/exclude such behavior for wide binaries. Neither MOND nor dark matter predicts any deviation from Newtonian behavior where stars are orbiting each other well in excess of a0, of which there are copious examples, so they provide a touchstone on which all should agree. He also convinced me that it was a Good Idea to have radial velocities as well as proper motions. This limits the sample size, but it helps immensely to insure that sample binaries are indeed bound pairs of binary stars. Doing this, he finds MOND-like behavior.

Previously, I linked to a talk by Indranil Banik, who found Newtonian behavior. This led to an exchange with Kyu-Hyun Chae, who has now posted an update to his own analysis in which he finds MONDian behavior. It is a clear signal, and if correct, could be the smoking gun for MOND. It wouldn’t be the first one; that honor probably goes to NGC 1560, and there have been plenty of other smoking guns since then. The trick seems to be finding something than cannot be explained with dark matter, and this could play that role since dark matter shouldn’t be relevant to binary stars. But dark matter is pretty much the ultimate Rube Goldberg machine of science, so we’ll see explanation people come up with, should they need to do so.

At present, the facts of the matter are still in dispute, so that’s the first thing to get straight.

Thanks to everyone I met at the conference who told me how useful this blog is. That’s good to know. Communication is inefficient at best, counterproductive at worst, and most often practically nonexistent. So it is good to hear that this does some small good.

Commentary on Wide Binaries

Wide Binary Weirdness

Last time, I commented on the developing situation with binary stars as a test of MOND. I neglected to enable comments for that post, so have done so now.

Indranil Banik has shared his perspective on wide binaries in a talk on the subject that is available on Youtube, included below.

Indranil and his collaborators are not seeing a MOND effect in wide binaries. Others have, as I discussed in the previous post. After the video posted above, Indranil comments on the work of Kyu-Hyun Chae:

Regarding the article by Chae (https://arxiv.org/abs/2305.04613), equation 7 of MNRAS 506, 2269โ€“2295 (2021) shows that the relative velocity is limited such that the v_tilde parameter (ratio of relative velocity within the sky plane to the Newtonian circular velocity at the projected separation) is at most 1 for 5 M_Sun binaries and in general is sqrt(5 M_Sun/M) for a binary of total mass M. This means v_tilde only goes up to 2 for M = 1.25 M_Sun, but more generally it goes up to a higher value at lower mass. Since the main signal in MOND is a broader v_tilde distribution at lower acceleration and a lower mass reduces the acceleration, this can lead to an artificial signal whereby lower mass systems have a larger rms v_tilde. Now a simple rms statistic is not exactly what Chae did, but this does highlight the kind of problem that can arise. Indeed, the v_tilde distribution prepared by Chae for the article in its figure 25 does show a rather sharp decline in the v_tilde distribution – there is not much of an extended tail, even less than in the model! This is obviously not due to measurement errors and contaminating effects like chance alignments, which would broaden the tail further. Rather, it is due to the upper limit to v_tilde imposed from the sample selection. This just means the underlying sample used is not well suited to the wide binary test, since it was quite clear a priori that the main signal for MOND would be in the region of v_tilde = 1-1.5 or so. One possibility is to try and restrict the analysis to a narrower range of binary total mass to try and alleviate the above concern, in which case the upper limit to v_tilde would be perhaps above 2 for the full sample used. There is however another issue in that lower accelerations generally correspond to higher separations and thus lower orbital velocities, so the fractional uncertainty in the velocity is likely to be larger. Thus, the v_tilde distribution is likely to be broader at low accelerations. This can be counteracted by having low errors across the board, but then the key quantity is the uncertainty on v_tilde. This aspect is not handled very rigorously – it is assumed that if the proper motions are accurate to better than 1%, then v_tilde will be sufficiently well known. But if the tangential velocity is about 20 km/s, a 1% error means an error of 200 m/s on the velocity of each star, so the relative velocity has an uncertainty of about 280 m/s. This is quite large compared to typical wide binary relative velocities, which are generally a few hundred m/s. Without doing a more detailed analysis, perhaps one thing to do would be to change this 1% requirement to 0.5% or 1.5% and see what happens. I am therefore not convinced that the MOND signal claimed by Chae is genuine.

I. Banik

Kyu-Hyun Chae responded to that, but apparently many people are not able to see his response on Youtube. I cannot. So I asked him about it, and he shares it here:

Since Indranil sent this concern to me in person, I’m replying here. No cut on v_tilde is used in my analysis because it is a gravity test. I did not use equation 7 of El-Badry et al. (MNRAS 506, 2269โ€“2295 (2021)) to cut out high v_tilde data, so there are some (though relatively small number of) data points above equation (7). I removed chance alignment cases by requiring R < 0.01 (El-Badry et al. convincingly show that R can be used to effectively remove chance alignment cases). This is the main reason why there is no high velocity tail. I have already considered varying proper motion (PM) relative errors: there are three cases PM rel error < 0.01 (nominal case), <0.003 (smaller case), and <0.2 (larger case). The conclusion on gravity anomaly (MOND signal) is the same in all three cases although the fitted f_multi (multiplicity fraction) varies. We can have more discussion in the st Andrews June meeting. I’m sure it will take some time but you will be convinced that my results are correct.

K.-H. Chae

He also shares this figure:

This is how the science sausage is made. As yet, there is no consensus.

Wide Binary Weirdness

My last post about the Milky Way was intended to be a brief introduction to our home galaxy in order to motivate the topic of binary stars. There’s too much interesting to say about the Milky Way as a galaxy, so I never got past that. Even now I feel the urge to say more, like with this extended rotation curve that I included in my contribution to the proceedings of IAU 379.

The RAR-based model rotation curve of the Milky Way extrapolated to large radii (note the switch to a logarithmic scale at 20 kpc!) for comparison to the halo stars of Bird et al (2022) and the globular clusters of Watkins et al (2019). The location of the solar system is noted by the red circle.

But instead I want to talk about data for binary stars from the Gaia mission. Gaia has been mapping the positions and proper motions of stars in the local neighborhood with unprecedented accuracy. These can be used to measure distances via trigonometric parallax, and speeds along the sky. The latter once seemed impossible to obtain in numbers with much precision; thanks to Gaia such data now outnumber radial (line of sight) velocities of comparable accuracy from spectra. That is a mind-boggling statement to anyone who has worked in the field; for all of my career (and that of any living astronomer), radial velocities have vastly outnumbered comparably well-measured proper motions. Gaia has flipped that forever-reality upside down in a few short years. It’s third data release was in June of 2022; this provides enough information to identify binary stars, and we’ve had enough time to start (and I do mean start) sorting through the data.

OK, why are binary stars interesting to the missing mass (really the acceleration discrepancy) problem? In principle, they allow us to distinguish between dark matter and modified gravity theories like MOND. If galactic mass discrepancies are caused by a diffuse distribution of dark matter, gravity is normal, and binary stars should orbit each other as Newton predicts, no matter their separation: the dark matter is too diffuse to have an impact on such comparatively tiny scales. If instead the force law changes at some critical scale, then the orbital speeds of widely separated binary pairs that exceed this scale should get a boost relative to the Newtonian case.

The test is easy to visualize for a single binary system. Imagine two stars orbiting one another. When they’re close, they orbits as Newton predicts. This is, after all, how we got Newtonian gravity – as an explanation for Kepler’s Laws or planetary motion. Ours is a lonely star, not a binary, but that makes no difference to gravity: Jupiter (or any other planet) is an adequate stand-in. Newton’s universal law of gravity (with tiny tweaks from Einstein) is valid as far out in the solar system as we’ve been able to probe. For scale, Pluto is about 40 AU out (where Earth, by definition, is 1 AU from the sun).

Let’s start with a pair of stars orbiting at a distance that is comfortably in the Newtonian regime, say with a separation of 40 AU. If we know the mass of the stars, we can calculate what their orbital speed will be. Now imagine gradually separating the stars so they are farther and farther apart. For any new separation s, we can predict what the new orbital speed will be. According to Newton, this will decline in a Keplerian fashion, v ~ 1/โˆšs. This will continue indefinitely if Newton remains forever the law of the land. If instead the force law changes at some critical scale sc, then we would expect to see a change when the separation exceeds that scale. Same binary pair, same mass, but relatively faster speed – a faster speed that on galaxy scales leads to the inference of dark matter. In essence, we want to check if binary stars also have flat rotation curves if we look far enough out.

We have long known that simply changing the force law at some length scale sc does not work. In MOND, the critical scale is an acceleration, a0. This will map to a different sc for binary stars of different masses. For the sun, the critical acceleration scale is reached at sc โ‰ˆ 7000 AU โ‰ˆ 0.034 parsecs (pc), about a tenth of a light-year. That’s a lot bigger than the solar system (40 AU) but rather smaller than the distance to the next star (1.3 pc = 4.25 light-years). So it is conceivable that there are wide binaries in the solar neighborhood for which this test can be made – pairs of stars with separations large enough to probe the MOND regime without being so far apart that they inevitably get broken up by random interactions with unrelated stars.

Gaia is great for identifying binaries, and space is big. There are thousands of wide binaries within 200 pc of the sun where Gaia can obtain excellent measurements. That’s not a big piece of the galaxy – it is a patch roughly the size of the red circle in the rotation curve plot above – but it is still a heck of a lot of stars. A signal should emerge, and a number of papers have now appeared that attempt this exercise. And ooooo-buddy, am I confused. Frequent readers will have noticed that it has been a long time between posts. There are lots of reasons for this, but a big one is that every time I think I understand what is going on here, another paper appears with a different result.

OK, first, what do we expect? Conventionally, binaries should show Keplerian behavior whatever their separation. Dark matter is not dense enough locally to have any perceptible impact. In MOND, one might expect an effect analogous to the flattening of rotation curves, hence higher velocities than predicted by Newton. And that’s correct, but it isn’t quite that simple.

In MOND, there is the External Field Effect (EFE) in which the acceleration from distant sources can matter to the motion of a local system. This violates the strong but not the weak Equivalence Principle. In MOND, all accelerative tugs matter, whereas conventionally only local effects matter.

This is important here, as we live in a relatively high acceleration neighborhood that is close to a0. The acceleration the sun feels towards the Galactic center is about 1.8 a0. This applies to all the stars in the solar neighborhood, so even if one finds a binary pair that is widely separated enough for the force of one star on another to be less than a0, they both feel the 1.8 a0 of the greater Galaxy. A lot of math intervenes, with the net effect being that the predicted boost over Newton is less than it would have been in the absence of this effect. There is still a boost, but its predicted amplitude is less than one might naively hope.

The location of the solar system along the radial acceleration relation is roughly (gbar, gobs) = (1.2, 1.8) a0. At this acceleration, the effects of MOND are just beginning to appear, and the external field of the Galaxy can affect local binary stars.

One of the first papers to address this is Hernandez et al (2022). They found a boost in speed that looks like MOND but is not MOND. Rather, it is consistent with the larger speed that is predicted by MOND in the absence of the EFE. This implies that the radial acceleration relation depicted above is absolute, and somehow more fundamental than MOND. This would require a new theory that is very similar to MOND but lacks the EFE, which seems necessary in other situations. Weird.

A thorough study has independently been made by Pittordis & Sutherland (2023). I heard a talk by them over Zoom that motivated the previous post to set the stage for this one. They identify a huge sample of over 73,000 wide binaries within 300 pc of the sun. Contrary to Hernandez et al., they find no boost at all. The motions of binaries appear to remain perfectly Keplerian. There is no hint of MOND-like effects. Different.

OK, so that is pretty strong evidence against MOND, as Indranil Banik was describing to me at the IAU meeting in Potsdam, which is why I knew to tune in for the talk by Pittordis. But before I could write this post, yet another paper appeared. This preprint by Kyu-Hyun Chae splits the difference. It finds a clear excess over the Newtonian expectation that is formally highly significant. It is also about right for what is expected in MOND with the EFE, in particular with the AQUAL flavor of MOND developed by Bekenstein & Milgrom (1984).

So we have one estimate that is MOND-like but too much for MOND, one estimate that is straight-laced Newton, and one estimate that is so MOND that it can start to discern flavors of MOND.

I really don’t know what to make of all this. The test is clearly a lot more complicated than I made it sound. One does not get to play God with a single binary pair; one instead has to infer from populations of binaries of different mass stars whether a statistical excess in orbital velocity occurs at wide separations. This is challenging for lots of reasons.

For example, we need to know the mass of each star in each binary. This can be gauged by the mass-luminosity relation – how bright a main sequence star is depends on its mass – but this must be calibrated by binary stars. OK, so, it should be safe to use close binaries that are nowhere near the MOND limit, but it can still be challenging to get this right for completely mundane, traditional astronomical reasons. It remains challenging to confidently infer the properties of impossibly distant physical objects that we can never hope to visit, much less subject to laboratory scrutiny.

Another complication is the orientation and eccentricity of orbits. The plane of the orbit of each binary pair will be inclined to our line of sight so that the velocity we measure is only a portion of the full velocity. We do not have any way to know what the inclination of any one wide binary is; it is hard enough to identify them and get a relative velocity on the plane of the sky. So we have to resort to statistical estimates. The same goes for the eccentricities of the orbits: not all orbits are circles; indeed, most are not. The orbital speed depends on where an object is along its elliptical orbit, as Kepler taught us. So yet again we must make some statistical inference about the distribution of eccentricities. These kinds of estimates are both doable and subject to going badly wrong.

The net effect is that we wind up looking at distributions of relative velocities, and trying to perceive whether there is an excess high-velocity tail over and above the Newtonian expectation. This is far enough from my expertise that I do not feel qualified to judge between the works cited above. It takes time to sort these things out, and hopefully we can all come to agreement on what it is that we’re seeing. Right now, we’re not all seeing eye-to-eye.

There is a whole session devoted to this topic at the upcoming meeting on MOND. The primary protagonists will be there, so hopefully some progress can be made. At least it should be entertaining.

A few words about the Milky Way

A few words about the Milky Way

I recently traveled to my first international meeting since the Covid pandemic began. It was good to be out in the world again. It also served as an excellent reminder of the importance of in-person interactions. On-line interactions are not an adequate substitute. I’d like to be able to recount all that I learned there, but it is too much. This post will touch on one of the much-discussed topics, our own Milky Way Galaxy.

When I put on a MOND hat, there are a few observations that puzzle me. The most persistent of these include the residual mass discrepancy in clusters, the cosmic microwave background, and the vertical motions of stars in the Milky Way disk. Though much hyped, the case for galaxies lacking dark matter does not concern me much: the examples I’ve seen so far appear to be part of the normal churn of early results that are likely to regress toward the norm as the data improve. I’ve seen this movie literally hundreds of times. I’m more interested in understanding the forest than a few outlying trees.

The Milky Way is a normal galaxy – it is part of the forest. It is easy to get lost in the leaves when one has access to data for millions going on billions of individual stars. These add up to a normal spiral galaxy, and we know a lot about external spirals that can help inform our picture of our own home.

For example, by assuming that the Milky Way falls along the radial acceleration relation defined by other spiral galaxies, I was able to build a mass model of its surface density profile. The resulting mass distribution is considerably more detailed than the usual approach of assuming a smooth exponential disk, which would be a straight line in the right-hand plot below. With the level of detail becoming available from missions like the Gaia satellite, it is necessary to move beyond such approximations.

Left: Spiral structure in the Milky Way traced by regions of gas ionized by young stars (HII regions, in red) and by the birthplaces of giant molecular clouds (GMCs, in blue). Right: the azimuthally-averaged surface density profile of stars inferred from the rotation curve of the Milky Way using the Radial Acceleration Relation. The features inferred kinematically correspond to the spiral arms known from star counts, providing a local example of Renzo’s Rule.

This model was built before Gaia data became available, and is not informed by it. Rather, I took the terminal velocities measured by McClure-Griffiths & Dickey, which provide the estimate of the Milky Way rotation curve that is most directly comparable to what we measure in external spirals, and worked out the surface density profile using the radial acceleration relation. The resulting model possesses bumps and wiggles like those we see corresponding to spiral arms in external galaxies. And indeed, it turns out that the locations of these features correspond with known spiral arms. Those are independent observations: one is from the kinematics of interstellar gas, the other from traditional star counts.

The model turns out to have a few further virtues. It matches the enclosed mass profile of the inner bulge/bar region of the Galaxy without any attempt at a specific fit. It reconciles the rotation curve measured with stars using Gaia data with that measured using gas in the interstellar medium – a subtle difference that was nevertheless highly significant. It successfully predicts that the rotation curve beyond the solar radius would not be perfectly flat, but rather decline at a specific rate – and exactly that rate was subsequently measured using Gaia. These are the sort of results that inclines one to believe that the underlying physics has to be MOND. Inferring maps of the mass distribution with this level of detail is simply not possible using a dark matter model.

The rotation curve of the Milky as observed in interstellar gas (light grey) and as fit to the radial acceleration relation (blue line). Only the region from 3 to 8 kpc has been fit; the rest follows. This matches well stellar observations from the inner, barred region of the Milky Way (dark grey squares: Portail et al. 2017) and the gradual decline of the outer rotation curve (black squares: Eilers et al. 2019) once corrected for the presence of bumps and wiggles due to spiral arms. These require taking numerical derivatives for use in the Jeans equation; the red squares show the conventional result obtained when neglecting this effect by assuming a smooth exponential surface density profile. See McGaugh (2008 [when the method was introduced and the bulge/bar model for the inner region was built], 2016 [the main fitting paper], 2018 [an update to the distance to the Galactic center], 2019 [including bumps & wiggles in the Gaia analysis]).

Great, right? It is. It also makes a further prediction: we can use the mass model to predict the vertical motions of stars perpendicular to the Milky Way’s disk.

Most of the kinetic energy of stars orbiting in the solar neighborhood is invested in circular motion: the vast majority of stars are orbiting in the same direction in the same plane at nearly the same speed. There is some scatter, of course, but radial motions due to orbital eccentricities represent a small portion of the kinetic energy budget. As stars go round and round, the also bob up and down, oscillating perpendicular to the plane of the disk. The energy invested in these vertical motions is also small, which is why the disk of the Milky Way is thin.

View of the Milky Way in the infrared provided by the COBE satellite. The dust lanes that afflict optical light are less severe at these wavelengths, revealing that the stellar disk of the Milky Way is thin but for the peanut-shaped bulge/bar at the center.

Knowing the surface density profile of the Milky Way disk, we can predict the vertical motions. In the context of dark matter, most of the restoring force that keeps stars near the central plane is provided by the stars themselves – the dark matter halo is quasi-spherical, and doesn’t contribute much to the restoring force of the disk. In MOND, the stars and gas are all there is. So the prediction is straightforward (if technically fraught) in both paradigms. Here is a comparison of both predictions with data from Bovy & Rix (2013).

The dynamical surface density implied by vertical motions (data from Bovy & Rix 2013). The dark blue line is the prediction of the model surface density described above – assuming Newtonian gravity. The light blue line is the naive prediction of MOND.

Looks great again, right? The dark blue line goes right through the data with zero fitting. The only exception is in the radial range 5.5 to 6.4 kpc, which turns out to be where the stars probing the vertical motion are maximally different from the gas informing the prediction: we’re looking at different Galactic longitudes, right where there is or is not a spiral arm, so perhaps we should get a different answer in this range. Theory gives us the right answer, no muss, no fuss.

Except, hang on – the line that fits is the Newtonian prediction. The prediction of MOND overshoots the data. It gets the shape right, but the naive MOND prediction is for more vertical motion than we see.

By the “naive” MOND prediction, I mean that we assume that MOND gives the same boost in the vertical direction as it does in the radial direction. This is the obvious first thing to try, but it is not necessarily what happens in all possible MOND theories. Indeed, there are some flavors of modified inertia in which it should not. However, one would expect some boost, and in these data there appears to be none. We get the right answer with just Newton and stars. There’s not even room for much dark matter.

I hope Gaia helps us sort this out. I worry that it will provide so much information that we risk missing the big picture for all the leaves.

This leaves us in a weird predicament. The radial force is extraordinarily well-described by MOND, which reveals details that we could never hope to access if all we know about is dark matter. But if we spot Newtonian gravity this non-Newtonian information from the radial motion, it predicts the correct vertical motion. It’s like we have MOND in one direction and Newton in another.

This makes no sense, so is one of the things that worries me most about MOND. It is not encouraging for dark matter either – we don’t get to spot ourselves MOND in the radial direction then pretend that dark matter did it. At present, it feels like we are up the proverbial creek without a paddle.

Ask and receive

Ask and receive

I want to start by thanking those of you who have contributed to maintaining this site. This is not a money making venture, but it does help offset the cost of operations.

The title is not related to this, but rather to a flood of papers addressing the questions posed in recent posts. I was asking last time “take it where?” because it is hard to know what cosmology under UT will look like. In particular, how does structure formation work? We need a relativistic theory to progress further than we already have.

There are some papers that partially address this question. Very recently, there have been a whole slew of them. That’s good! It is also a bit overwhelming – I cannot keep up! Here I note a few recent papers that touch on structure formation in MOND. This is an incomplete list, and I haven’t had the opportunity to absorb much of it.

First, there is a paper by Milgrom with his relativistic BIMOND theory. It shows some possibility of subtle departures from FLRW along the lines of what I was describing with UT. Intriguingly, it explicitly shows that the assumptions we made to address structure formation with plain MOND should indeed hold. This is important because a frequent excuse employed to avoid acknowledging MOND’s predictions is that they don’t count if there is no relativistic theory. This is more a form of solution aversion rather than a serious scientific complaint, but people sure lean hard into it. So go read Milgrom’s papers.

Another paper I was looking forward to but didn’t know was in the offing is a rather general treatment of structure formation in relativistic extensions of MOND. There does seem to be some promise for assessing what could work in theories like AeST, and how it relates to earlier work. As a general treatment, there are a lot of options to sort through. Doing so will take a lot of effort by a lot of people over a considerable span of time.

There is also work on gravitational waves, and a variation dubbed a khronometric theory. I, well, I know what both of them are talking about to some extent, and yet some of what they say is presently incomprehensible to me. Clearly I have a lot still to learn. That’s a good problem to have.

I have been thinking for a while now that what we need is a period of a theoretical wild west. People need to try ideas, work through their consequences, and see what works and what does not. Ultimately, most ideas will fail, as there can only be one correct depiction of reality (I sure hope). It will take a lot of work and angst and bickering before we get there: this is perhaps only the beginning of what has already been a long journey for those of us who have been paying attention.

New and stirring things are belittled because if they are not belittled, the humiliating question arises, ‘Why then are you not taking part in them?’

H. G. Wells

Take it where?

Take it where?

I had written most of the post below the line before an exchange with a senior colleague who accused me of asking us to abandon General Relativity (GR). Anyone who read the last post knows that this is the opposite of true. So how does this happen?

Much of the field is mired in bad ideas that seemed like good ideas in the 1980s. There has been some progress, but the idea that MOND is an abandonment of GR I recognize as a misconception from that time. It arose because the initial MOND hypothesis suggested modifying the law of inertia without showing a clear path to how this might be consistent with GR. GR was built on the Equivalence Principle (EP), the equivalence1 of gravitational charge with inertial mass. The original MOND hypothesis directly contradicted that, so it was a fair concern in 1983. It was not by 19842. I was still an undergraduate then, so I don’t know the sociology, but I get the impression that most of the community wrote MOND off at this point and never gave it further thought.

I guess this is why I still encounter people with this attitude, that someone is trying to rob them of GR. It’s feels like we’re always starting at square one, like there has been zero progress in forty years. I hope it isn’t that bad, but I admit my patience is wearing thin.

I’m trying to help you. Don’t waste you’re entire career chasing phantoms.

What MOND does ask us to abandon is the Strong Equivalence Principle. Not the Weak EP, nor even the Einstein EP. Just the Strong EP. That’s a much more limited ask that abandoning all of GR. Indeed, all flavors of EP are subject to experimental test. The Weak EP has been repeatedly validated, but there is nothing about MOND that implies platinum would fall differently from titanium. Experimental tests of the Strong EP are less favorable.

I understand that MOND seems impossible. It also keeps having its predictions come true. This combination is what makes it important. The history of science is chock full of ideas that were initially rejected as impossible or absurd, going all the way back to heliocentrism. The greater the cognitive dissonance, the more important the result.

Continuing the previous discussion of UT, where do we go from here? If we accept that maybe we have all these problems in cosmology because we’re piling on auxiliary hypotheses to continue to be able to approximate UT with FLRW, what now?

I don’t know.

It’s hard to accept that we don’t understand something we thought we understood. Scientists hate revisiting issues that seem settled. Feels like a waste of time. It also feels like a waste of time continuing to add epicycles to a zombie theory, be it LCDM or MOND or the phoenix universe or tired light or whatever fantasy reality you favor. So, painful as it may be, one has find a little humility to step back and take account of what we know empirically independent of the interpretive veneer of theory.

As I’ve said before, I think we do know that the universe is expanding and passed through an early hot phase that bequeathed us the primordial abundances of the light elements (BBN) and the relic radiation field that we observe as the cosmic microwave background (CMB). There’s a lot more to it than that, and I’m not going to attempt to recite it all here.

Still, to give one pertinent example, BBN only works if the expansion rate is as expected during the epoch of radiation domination. So whatever is going on has to converge to that early on. This is hardly surprising for UT since it was stipulated to contain GR in the relevant limit, but we don’t actually know how it does so until we work out what UT is – a tall order that we can’t expect to accomplish overnight, or even over the course of many decades without a critical mass of scientists thinking about it (and not being vilified by other scientists for doing so).

Another example is that the cosmological principle – that the universe is homogeneous and isotropic – is observed to be true in the CMB. The temperature is the same all over the sky to one part in 100,000. That’s isotropy. The temperature is tightly coupled to the density, so if the temperature is the same everywhere, so is the density. That’s homogeneity. So both of the assumptions made by the cosmological principle are corroborated by observations of the CMB.

The cosmological principle is extremely useful for solving the equations of GR as applied to the whole universe. If the universe has a uniform density on average, then the solution is straightforward (though it is rather tedious to work through to the Friedmann equation). If the universe is not homogeneous and isotropic, then it becomes a nightmare to solve the equations. One needs to know where everything was for all of time.

Starting from the uniform condition of the CMB, it is straightforward to show that the assumption of homogeneity and isotropy should persist on large scales up to the present day. “Small” things like galaxies go nonlinear and collapse, but huge volumes containing billions of galaxies should remain in the linear regime and these small-scale variations average out. One cubic Gigaparsec will have the same average density as the next as the next, so the cosmological principle continues to hold today.

Anyone spot the rub? I said homogeneity and isotropy should persist. This statement assumes GR. Perhaps it doesn’t hold in UT?

This aspect of cosmology is so deeply embedded in everything that we do in the field that it was only recently that I realized it might not hold absolutely – and I’ve been actively contemplating such a possibility for a long time. Shouldn’t have taken me so long. Felten (1984) realized right away that a MONDian universe would depart from isotropy by late times. I read that paper long ago but didn’t grasp the significance of that statement. I did absorb that in the absence of a cosmological constant (which no one believed in at the time), the universe would inevitably recollapse, regardless of what the density was. This seems like an elegant solution to the flatness/coincidence problem that obsessed cosmologists at the time. There is no special value of the mass density that provides an over/under line demarcating eternal expansion from eventual recollapse, so there is no coincidence problem. All naive MOND cosmologies share the same ultimate fate, so it doesn’t matter what we observe for the mass density.

MOND departs from isotropy for the same reason it forms structure fast: it is inherently non-linear. As well as predicting that big galaxies would form by z=10, Sanders (1998) correctly anticipated the size of the largest structures collapsing today (things like the local supercluster Laniakea) and the scale of homogeneity (a few hundred Mpc if there is a cosmological constant). Pretty much everyone who looked into it came to similar conclusions.

But MOND and cosmology, as we know it in the absence of UT, are incompatible. Where LCDM encompasses both cosmology and the dynamics of bound systems (dark matter halos3), MOND addresses the dynamics of low acceleration systems (the most common examples being individual galaxies) but says nothing about cosmology. So how do we proceed?

For starters, we have to admit our ignorance. From there, one has to assume some expanding background – that much is well established – and ask what happens to particles responding to a MONDian force-law in this background, starting from the very nearly uniform initial condition indicated by the CMB. From that simple starting point, it turns out one can get a long way without knowing the details of the cosmic expansion history or the metric that so obsess cosmologists. These are interesting things, to be sure, but they are aspects of UT we don’t know and can manage without to some finite extent.

For one, the thermal history of the universe is pretty much the same with or without dark matter, with or without a cosmological constant. Without dark matter, structure can’t get going until after thermal decoupling (when the matter is free to diverge thermally from the temperature of the background radiation). After that happens, around z = 200, the baryons suddenly find themselves in the low acceleration regime, newly free to respond to the nonlinear force of MOND, and structure starts forming fast, with the consequences previously elaborated.

But what about the expansion history? The geometry? The big questions of cosmology?

Again, I don’t know. MOND is a dynamical theory that extends Newton. It doesn’t address these questions. Hence the need for UT.

I’ve encountered people who refuse to acknowledge4 that MOND gets predictions like z=10 galaxies right without a proper theory for cosmology. That attitude puts the cart before the horse. One doesn’t look for UT unless well motivated. That one is able to correctly predict 25 years in advance something that comes as a huge surprise to cosmologists today is the motivation. Indeed, the degree of surprise and the longevity of the prediction amplify the motivation: if this doesn’t get your attention, what possibly could?

There is no guarantee that our first attempt at UT (or our second or third or fourth) will work out. It is possible that in the search for UT, one comes up with a theory that fails to do what was successfully predicted by the more primitive theory. That just lets you know you’ve taken a wrong turn. It does not mean that a correct UT doesn’t exist, or that the initial prediction was some impossible fluke.

One candidate theory for UT is bimetric MOND. This appears to justify the assumptions made by Sanders’s early work, and provide a basis for a relativistic theory that leads to rapid structure formation. Whether it can also fit the acoustic power spectrum of the CMB as well as LCDM and AeST has yet to be seen. These things take time and effort. What they really need is a critical mass of people working on the problem – a community that enjoys the support of other scientists and funding institutions like NSF. Until we have that5, progress will remain grudgingly slow.

1The equivalence of gravitational charge and inertial mass means that the m in F=GMm/d2 is identically the same as the m in F=ma. Modified gravity changes the former; modified inertia the latter.

2Bekenstein & Milgrom (1984) showed how a modification of Newtonian gravity could avoid the non-conservation issues suffered by the original hypothesis of modified inertia. They also outlined a path towards a generally covariant theory that Bekenstein pursued for the rest of his life. That he never managed to obtain a completely satisfactory version is often cited as evidence that it can’t be done, since he was widely acknowledged as one of the smartest people in the field. One wonders why he persisted if, as these detractors would have us believe, the smart thing to do was not even try.

3The data for galaxies do not look like the dark matter halos predicted by LCDM.

4I have entirely lost patience with this attitude. If a phenomena is correctly predicted in advance in the literature, we are obliged as scientists to take it seriously+. Pretending that it is not meaningful in the absence of UT is just an avoidance strategy: an excuse to ignore inconvenient facts.

+I’ve heard eminent scientists describe MOND’s predictive ability as “magic.” This also seems like an avoidance strategy. I, for one, do not believe in magic. That it works as well as it does – that it works at all – must be telling us something about the natural world, not the supernatural.

5There does exist a large and active community of astroparticle physicists trying to come up with theories for what the dark matter could be. That’s good: that’s what needs to happen, and we should exhaust all possibilities. We should do the same for new dynamical theories.