Yes, some. That much is a step forward from a decade ago, when a common assumption was that the Milky Way’s rotation curve remained flat at the speed at which the sun orbited. This was a good guess based on empirical experience with other galaxies, but not all galaxies have rotation curves that are completely flat, nor can we be sure the sun is located where that is the case.
A bigger question whether the Milky Way’s rotation curve is declining in a Keplerian fashion. This would indicate that the total mass has been enclosed. That would be a remarkable result. If true, it would be the first time that the total mass of an individual galaxy has been measured. There have been claims to this effect before that have not panned out when the data have been extended to larger radii, so one might be inclined to be skeptical.
There are several claims now to see a distinctly declining rotation curve based on the third data release (DR3) from Gaia. The most recent, Jiao et al., has gained some note by virtue of putting “Keplerian decline” in the title, but very similar results have also been reported by Ou et al., Wang et al. and Sylos Labini et al. They all obtain basically the same answer using the same data, with minor differences in the error assessment and other details. There are also differences in interpretation*, which is always possible even when everyone agrees about what the data say.
Jiao et al. measure a total mass for the Milky Way of about 2 x 1011 M☉. Before looking at the data, let’s take a moment to think about that number. Most mass determinations – and there are lots, see Fig. 2 of Wang et al. – for the Milky Way have been in the neighborhood of 1012 M☉. Indeed, for most of my career, it was traditionally Known to be 2 x 1012 M☉. The new measurement is an order of magnitude smaller. That’s a lot to be off by, even in extragalactic astronomy. The difference, as we’ll see, has to do with what data we use.
The mass of stars and gas in the Milky Way is about 6 x 1010 M☉, give or take ten billion. That means that nearly a third of the total mass is normal baryonic matter that we can readily see. So the ratio of dark-to-baryonic mass is only 2.3:1, well short of the cosmic ratio of about 6:1. That’s embarrassing – especially since much of the effort in galaxy formation theory has been to explain why the baryon fraction is much less than the cosmic fraction, not much more. And here our Galaxy is an outlier, having much less dark matter for its stellar mass than everything else. It is always a bad sign when the Galaxy appears to violate the Copernican Principle.
Nonetheless, this is what we find if we look at the Gaia DR3 data. Here is a model I’ve shown before, extrapolated to larger radii with some new data added. The orange circles are the Gaia DR3 rotation curve as given by Jiao et al. For radii greater than 18 kpc, they show a clear decline consistent with a Keplerian curve for a 1.95 x 1011 M☉ point mass (dotted line), as per Fig. 9 of Jiao et al.
This is the first time we’ve been able to trace the rotation curve so far out with stars in the disk of the Milky Way, and the Keplerian line is a good match. If that’s all we know, then a total mass of only 2 x 1011 M☉ is a reasonable inference. That’s not all we know.
As I alluded above, a halo mass this small makes no sense in the context of cosmology. Not only is 2 x 1011 M☉ too small, the more commonly inferred dynamical mass of 1012 M☉ is also too small. According to abundance matching, which has become an important aspect of LCDM, the Milky Way should reside in a 3 or 4 x 1012 M☉ halo. So the new mass makes a factor of 2 or 3 problem into a factor a ten problem. That is too large to attribute to scatter in the stellar mass-halo mass relation. Worse, there is no evidence that the Milky Way is an outlier from scaling relations like Tully-Fisher. We can’t have it one way and not the other.
The traditional mass estimates that obtain ~1012 M☉ rely on dwarf satellite galaxies as tracers of the gravitational potential of the Milky Way. Maybe they’re not fair tracers? We have to make assumptions about their orbits to use them to infer a mass; perhaps these assumptions are wrong? It is conceivable that many of our satellites are on first infall rather than in well-established orbits. Indeed, the consensus is that our largest satellites, the Magellanic Clouds, are on first infall, and that they cause a substantial perturbation to the halo of the Milky Way. This was an absurd thought 15 years ago – the Magellanic clouds must have been here forever, and were far too small to do damage – but now this is standard lore.
There are tracers at large radii besides dwarf satellite galaxies. The figure above shows three: globular clusters (pink triangles) and two types of stars in the halo: blue horizontal branch stars (green squares) and K giants (red squares). These are well-known parts of the Milky Way that have been with us for many billions of years, so they’ve had plenty of time to become equilibrium tracers of the gravitational potential. They clearly indicate a larger enclosed mass than predicted by the Keplerian decline traced by the Gaia rotation curve, and are consistent with traditional satellite analyses. Perhaps these data are somehow misleading, but it is hard to see how.
Gaia is great, but has its limits. It is really optimized for nearby stars (within a few kpc). Outside of that, the statistics… leave something to be desired. Is it safe to push out beyond 20 kpc? I don’t know, but I did notice this panel from Fig. 8 of Wang et al.:
The radial velocity is a minor component of disk motion, where azimuthal motion dominates. However, one does need to know it to solve the Jeans equation. Having it wrong will cause a perceptible systematic error. You notice the bifurcation in the data for R > 22 kpc? That, in technical terms, is Messed Up. I don’t know what goes awry there, but I’ve done this exercise enough times for the sight of this to scare the bejeepers out of me. No way I trust any of these data at R > 22 kpc, and I hope having seen this doesn’t give me nightmares tonight.
Perhaps the uncertainty caused by this is adequately reflected in the large error bars on the orange points above. Those with R > 22 kpc are nicely Keplerian, but also consistent with a lot of things, including the blue line that successfully predicts the halo stars and globular clusters. That’s not true for the data around R = 20 kpc where the error bars are much smaller: there the discrepancy with the blue line I take seriously. But that is a much more limited affair that might indicate the presence of a ring of mass – that’s what gives the bumps and wiggles at smaller radii – and certainly isn’t enough to imply the entire mass of the Milky Way has been enclosed.
But who knows? Perhaps fifteen years hence it will be the standard lore that all galaxies reside in dark matter halos that are only twice the mass of their luminous disks. At that mass ratio, all the galactic dark matter could be baryonic. I wouldn’t bet on it, but stranger things have happened before, and will happen again.
*A difference in interpretation is largely what the debate about dark matter and MOND boils down to. There is no doubt that there are acceleration discrepancies in extragalactic objects that require something beyond what you see is what you get with normal gravity. Whether we should blame what we can’t see or the assumption of normal gravity is open to interpretation. I would hope this is obvious, but this elementary point seems to be lost on many.
Triton Station 
Forgot to enable comments. They should be open now.
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Very interesting discussion! I agree with many points. The sample by Ou et al 2023 and Eilers et al. 2019 are substantially different from ours (even though based on Gaia). The off plane behaviors is clearly a new topic in the kinematic of the MW …
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Indeed, it is interesting that independent groups come up with very similar answers while analyzing the Gaia data in independent ways. Out of plane motions are important, as is extinction, distance determinations, the Galactic warp – all the classical astronomy issues that you have struggled with that are underappreciated by people who don’t do this kind of work.
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Dr McGaugh: I assume that the mass of stars and gas in the Milky Way of ~6×10^10 M sun is sufficient to explain the rotation curves assuming gravity in accordance with MOND; is this correct? … and the higher mass estimates include a large amount of assumed dark matter?
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Yes. The blue line is from applying the radial acceleration relation over the range 3 < R < 8 kpc – see https://tritonstation.com/2018/08/29/a-precise-milky-way/. Everything outside this radial range is a prediction. The stellar mass of the fit is 6E10 and there is another 1E10 of gas. Higher mass estimates are the Newtonian dynamical enclosed mass. This is about 5E11 at R=50 kpc for the blue line, if memory serves. But the blue line is asymptoting to flat, so the enclosed mass never converges to a finite value – it continues to grow linearly with increasing radius. This has long been a puzzle with flat rotation curves with the default assumption that this behavior cannot persist forever. There is precious little evidence that it doesn't, so any indication of a Keplerian decline is important.
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Nice to note that Chae’s and Hernandez’s studies limits its data to within 200 pc respectively 130 pc distance from the sun, which both is less than 9 kpc from the milky way’s center.
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Gaia really excels nearby, as both parallax and proper motion accuracy declines with distance, and it is also known that systematics also creep in.
Of course, where one would really like to perform the wide binary test is in the deep MOND regime, which is too far outside the solar neighborhood for Gaia to do.
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(1) “Nearly a third of the total mass is normal baryonic matter that we can readily see.”
I thought at least some of the missing mass could be explained by a halo of hot gas enveloping the Galaxy?
Nicastro, F. et al., 2016. A distant echo of Milky Way central activity closes the Galaxy’s baryon census. Astrophysical Journal Letters 828, L12.
(2) “Perhaps the uncertainty … is adequately reflected in the large error bars on the orange points. Those with R > 22 kpc are nicely Keplerian, but also consistent with a lot of things, including the blue line that successfully predicts the halo stars and globular clusters.”
I’m not convinced by this. If there were just one orange datum with a wide error bar beyond 22 kpc, yes it would pose no challenge, but with each successive orange point this becomes more difficult to argue. The orange points are consistently well below the blue line, and the dotted line of the Keplerian model consistently passes through the middle of them. The chances of throwing a six once are 1 in 6; the chances of throwing a six twice in a row are 1 in 6 x 6. There seems to be a real tension between the orange data and the squares & triangles.
(3) It may now be a commonplace that the Magellanic Clouds are on first infall, but, being less au fait, I would be glad of a reference please.
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(1) Yes, there is some evidence that there may be hot gas in the halo that is perhaps as massive as the stars. So that’d get us up to 2/3. The part of that which most scientists will take issue with is the low dark matter halo mass, not that there might be more baryons out there.
(2) Yeah, Nah. You are making the classic mistake of treating astronomical error bars as if they behave as they should statistically. The real worry are the systematic uncertainties. In this case, there is clearly a tension between these Gaia-based indications of a Keplerian downturn and every other sort of data ever taken, of which I only show a few examples. See the review by Wang for lots of others. The tension is between these data and most other data; they can’t all be correct.
(3) That the LMC is on first infall has become common wisdom largely by word of mouth sense. I’m not aware of a reference per se. The observation that drives this inference is measurement of its proper motion from HST), which is too fast for a conventional dark matter halo to contain it on a closed orbit with a period much shorter than a Hubble time (e.g https://arxiv.org/abs/1008.2210), hence the inference that it is on first infall. This inference depends on our assumptions about the potential. It is hard to avoid in NFW-like potentials with reasonable masses, but one expects more rapid speeds in a MOND-like potential to which it could easily be bound.
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Including the hot gas in broad-brush fashion would mean that the ratio of DM to baryons falls from 3:1 (Jiao et al, or 2.3:1 in your piece) to only 1.5 to 1 (1.15:1). Does not the hot gas also affect the calculation of the blue line (based on MOND, I understand)?
Also, if the data as reported by Jiao et al do support Keplerian decline, why is there a need for DM at all? But as a lay reader I get the impression that Jiao et al do in fact factor in some DM mass. Unfortunately I don’t have the ability to say whether it is factored into the arriving of the data or in some other way.
I feel none the wiser about error bars in astronomy if they are not to be understood in a classic sense – but then I am not an astronomer. If one can be cavalier about the orange dot error bars, presumably the same applies to the square and triangle error bars? Moreover, Jiao et al claim to drastically reduce uncertainties and systematics, their error bars being expressions of the systematic uncertainties that remain (caption to fig. 7).
Finally, while you have shown only a few of the examples that line up with the squares and triangles, Gaia DR3 is supposed to offer an advance in accuracy (especially on the 1989 paper that you cite to illustrate previous non-robust claims of a Keplerian decline!), and as figs. 1-2 of Jiao show, the different methodologies and star samples of three different teams (Wang, Ou, Jiao) all agree from 13 kpc out. The Zhou team curve differs somewhat, but according to Jiao agrees if their distance estimates are re-evaluated. Such agreement strikes me as rather impressive.
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Re-reading your blog, I see that the DM component assumed by Jiao et al informs the dotted-line prediction of Keplerian motion. And of course you have yourself properly noted the agreement between the different teams.
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Regarding the DM to baryon ratio, Nicastro et al. conclude: ‘Adding the hot baryon mass to the visible mass of the Milky Way, gives a total baryonic mass in the range of (0.8-4.0) x 10^11 M⊙.’
So it seems one can get to a total mass of 1.94 x 10^11 M⊙ without invoking DM at all.
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Yes, with hot gas at the upper end of that range, one can pretty much get there.
And yes, this hot gas does affect the blue line, but only at large radii where this gas is. It adds about 6 km/s at R = 100 kpc. This is the difference between Vtot and Vtotcorona in http://astroweb.case.edu/ssm/models/MW2018model.dat
One should never be cavalier with error bars, but one must always take them with a giant dose of salt in astronomy. There are LOTS of other constrains – see the Wang review, I’m not going to repeat the entirety of that here. The claims of a Keplerian decline contradict pretty much all other data in existence. They are also contradict the the LCDM at least as much as the do MOND. The contradiction with both theories makes it really important if true, but the contradiction to literally dozens of independent analyses makes it suspect.
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Very interesting results. I would just like to point out that the role of the analysis used by these authors, however, is crucial, because it allows to double the radial range up to 30 kpc. Using the trigonometric parallax of Gaia DR3 directly, good up to 20%, one cannot go beyond 15 kpc from the galactic center.
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Indeed; I am not sure how far out I trust the Gaia data. Clearly not beyond 22 kpc regardless of analysis approach.
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Dr McGaugh: new paper that doesn’t support MOND
arXiv:2309.05252 (astro-ph)
[Submitted on 11 Sep 2023]
A severe challenge to the MOND phenomenology in our Galaxy
Man Ho Chan, Ka Chung Law
Download PDF
Modified Newtonian Dynamics (MOND) is one of the most popular alternative theories of dark matter to explain the missing mass problem in galaxies. Although it remains controversial regarding MOND as a fundamental theory, MOND phenomenology has been shown to widely apply in different galaxies, which gives challenges to the standard Λ cold dark matter model. In this article, we derive analytically the galactic rotation curve gradient in the MOND framework and present a rigorous analysis to examine the MOND phenomenology in our Galaxy. By assuming a benchmark baryonic disk density profile and two popular families of MOND interpolating functions, we show for the first time that the recent discovery of the declining Galactic rotation curve in the outer region (R≈17−23 kpc) can almost rule out the MOND phenomenology at more than 5σ. This strongly supports some of the previous studies claiming that MOND is neither a fundamental theory nor a universal description of galactic properties.
Comments: Accepted in ApJ
Subjects: Astrophysics of Galaxies (astro-ph.GA)
Cite as: arXiv:2309.05252 [astro-ph.GA]
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But… From my understanding, the new results should be equally challenging for LCDM. Why they were quick to rule out just MoND?
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After rejecting MOND they did not discuss dark matter. Because dark matter always has an excuse that density and even presence of dark matter may vary from location to location. From galaxy to galaxy. But MOND pretends to be a universal law.
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Yes, that’s right. You can make the dark matter distribution whatever you need it to be. In this case, it is so far off what LCDM expects that both theories could in principle be ruled out.
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This particular paper is basically a form of pseudo-scientific trolling, inviting me to waste my time responding to its many misleading statements. They cherry pick the range of radii they discuss, for example. Looks bad if you only look at the bad parts!
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even if they cherry pick the range of radii they discuss shouldn’t MOND give the correct results, since MOND is a universal law?
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One will always find counterexamples to any given scientific law in experimental data, because experimental data is never completely correct or pristine. Sometimes those deviations indicate the universal law breaks down in certain regimes, like the precession of Mercury, but more often is due to fuzziness in the measurements or systematic or unsystematic error. If you cherry-pick data, one can ‘disprove’ literally any scientific theory.
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Exactly.
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is it the data or the calculated value ?
so is there a problem with the data declining Galactic rotation curve in the outer region (R≈17−23 kpc) ?
did the authors correctly used Modified Newtonian Dynamics (MOND) for declining Galactic rotation curve in the outer region (R≈17−23 kpc) ?
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Some of both. They use an exponential disk to describe the mass distribution of the stars, which we know to be an inadequate approximation for MOND. However, I think their laser focus on this narrow range of radii is more problematic. These data do not agree with lots of other data, irrespective of theory.
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However, I think their laser focus on this narrow range of radii is more problematic. These data do not agree with lots of other data, irrespective of theory.
just to clarify the third data release (DR3) from Gaia in the range of (R≈17−23 kpc) might be wrong as These data do not agree with lots of other data?
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And the sad part is that Ethan Siegel will cite only that paper and not also your answer and will not point that is also problematic for LCDM. And that will strengthen the public opinion about MoND = bad, LCDM = good.
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Yep. That’s how disinformation feeds cognitive dissonance.
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As pointed out in this blog post, the measurements above ~20-22 kpc are probably wrong. This seems to be ignored by some.
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But they have rejected MOND for 17-23 KPC and not for 20-22 KPC
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Looks bad if you only look at the bad parts. From 18-20 kpc or so, I can imagine this being due to a ring of mass in the outer galaxy, much like the bumps and wiggles at smaller radii are due to spiral arms. Such features are known to exist, e.g., if the Monoceros ring is an over density in the outer disk. https://en.wikipedia.org/wiki/Monoceros_Ring
If we believe this continues much further, then it is bad for both LCDM and MOND. Funny they don’t mention the LCDM part.
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sir, if they accept LCDM part also then what is your plan c?
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The paper specifically adresses the new GAIA data (all references for a declining rotation curve are from 2023). It does not look at the actual values, which (as can be seen in the graph Stacy shows) lie very close to the milky way model. It only looks at the derivative (how fast the GAIA data are going downward). This can be seen from 17 kpc and above in Stacy’s graph, the orange dots go down from that point.
Above 25 kpc it becomes clear that this decline is a systematic error compared to the triangles (globular clusters), green squares (blue horizontal branch stars) and red squares (red giants). The question is only if this systematic error begins in the derivative at 17 kpc.
Independently, if there’s one galaxy where MOND’s predicted rotation curve doesn’t match the data from a new method while it succeeds for all others, and this is the unique galaxy where this new measurement method cam be used: take your own conclusions.
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Yes. If we accept that MOND is a statistical approximation for galaxy type mass distribution and not a universal law.
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MC, in the previous post you made the claim that within a disc of uniform density, the total gravitational force is constant. I tried to reply to that comment Word Press lost my comment while I was logging in (or perhaps comments were closed while I was doing so). So this is my belated reply:
Based on geometry and symmetry, the total attraction at the center of the disc is zero; for every point in the disc pulling on the center in one direction, there is an opposite point along the same diametrical line while pulls in the opposite direction. Consider an x-y coordinate system with its origin at the disc center, and select a point with coordinate (-a, 0)–on the negative x-axis, a short way from the center (a << the disc radius, r). Draw a circle with the same radius as the disc around that point, and consider the area-intersection of this circle with the disc. That intersection is symmetrical about the point (-a/2, o), so the intersection area produces no net force at that point. The only remaining part of the disc is a crescent-moon shape on the right side, such that none of its points are left of point (-a/2,o). Therefore that point feels a positive gravitational force towards the center of the disc. (Since the crescent is symmetrical about the x-axis). Since a/2 is small, the crescent area is small, and the force is small, but not zero. Now increase a, still less than r, but farther to the left, inscreasing the size of the crescent, but with the same minimum distance from the crescent to point (-a/2,0). Therefore the force must be larger for larger a. Possibly the force will reach some maximum for a<r, but it certainly is not constant. I have done a simplified numercial analysis which indicates the maximum is in fact at a=r.
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Sorry, that should be a/2=r, not a=r, for the maximum.
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Addendum: I should have said the distance from (-a/2,0) to the crescent shape along the x-axis is r-a/2, so it decreases as a increases, also indicating that the attractive force on the point (-a/2,0) must increase as a/2 increases, at least until the points of the crescent bow inwards, and perhaps even then.
Meanwhile, I have refined my numerical model slightly and it gives a maximum at about a/2=0.95r. I don’t trust that to be an accurate result though. The model only divides the disc into 80 segments.
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In previous post I made that claim. It was a sort of disk version of Newton’s Theorem XXXIII. This theorem xxxiii says that for a uniform density sphere, the gravity is directly proportional to radius. From center to surface, the gravity increases linearly. Underlying logic is simple. For sphere of uniform density, mass is proportional to r cube. And gravity is inversely proportional to r square. So by dividing r cube with r square we get r that means gravity for such a sphere with uniform density is directly proportional to r. I also showed that MOND theory and even Poisson equation is totally devoid of the implications of theorem xxxiii. There was a definite need to work out a disk version of xxxiii. So I presented the disk version. For a disk of uniform density and width equal to the width of one unit mass, the gravity within the disk will be directed towards center and everywhere there will be same gravity throughout the disk. The underlying logic being that for such disk of uniform density, the mass is proportional to r square and gravity is inversely proportional to r square. So by dividing r square by r square, we get 1 which means that gravity is same everywhere in a disk of uniform density.
After that I thought about ring version of the theorem and concluded that test particle will settle at the middle. That means it is not like halo shell of sphere. I spherical halo shell, there is no gravity. In a 2 dimensional ring there is gravity directed towards everywhere and center is the point where all directional outward attraction is canceled and particle is settled at the center.
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So I accept that there is no analogue ring version of halo spherical shell theorem. But there is a definite version with slightly different behavior. This difference is also due to simple difference that for sphere, mass of outer shell is proportional to r cube and for ring, the mass of ring is proportional to r square. And there is a definite disk version of theorem xxxiii. For a disk of minimal width and having uniform density there are automatically flat rotation curved. In other words, flat rotations are default orbit behavior within a disk of uniform density. Greater width of the disk will make it somewhat upward linear curve. And exponential decrease of density from center to edges will maintain the curves in flat order. There is no dark matter and there is no reality in MOND.
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The poisson differential method is mathematically identical to the integration method Newton used to produce his theorems, so there is no possible contradiction between it and any of Newton’s theorems. My argument above shows that your intuitions about gravity in a disc are not sound. You have proved nothing here, just made statements, some of which are mathematically false. Such as that the poisson differential equation would not predict one of Newton’s Theorems, and that the gravity within a thin uniformly-dense disc is constant. (There are probably others, if we did the work to examine them.) I am sorry to have to tell you this, but you have much to learn, starting with the poisson equation for Newtonian gravity. (How it is derived, and how to use it.) I hope you take the time and effort to do so. I think you should, before contradicting people who have studied and worked on such matters for most of their lives.
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The Poisson-Equation differential method is mathematically identical to the integration method which Newton used to discover his theorems. There is no possible contradiction between PE results and any of Newton’s theorems.
The gravity within a thin disc of uniform density is not constant, but increases from zero at the center to a maximum at or near the outer edge.
Those are two strikes against your intuitions. I am sure more would be found if we took the time to examine more of them. Intuitions about complex mathematical problems without any knowledge of the relevant mathematics (such as integration and differential equations) are very rarely useful. Please at least learn about the Poisson Equation for Newtonian gravity (how it is derived and how to ue it) before making claims about it.
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Sorry for the double response. The first one did not appear until now so I tried again. I will make a donation to compensate for the wasted space.
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OK I try to tell in brief. For the gravitational interactions of spheres, there is section XII in Principia. There are total 13 theorems in this section. Some of these theorems are collectively known as shell theorem. Name shell theorem is not used in the Principia. However specifically this is Theorem XXX in the Principia which is about spherical halo shell. This is also the first theorem in section XII of Principia. Of the total 13 theorems in section XXII at least three theorems are fundamental. Rest of them are further derivatives of those three fundamental theorems. These fundamental theorems are XXX, XXXI and XXXIII.
Now position is that developers and promoters of Poisson Equation never realized the fundamental importance of theorem XXXIII. For them, only two theorems are fundamental which are XXX and XXXI.
In this way, till date, Poisson Equation has remained devoid of the implications of theorem XXXIII.
I refer to section 3.2 of Jo Bovy’s book titled “Dynamics and Astrophysics of Galaxies”.
In this section 3.2, Jo Bovy mentions that for spherical mass distributions, Newton had proved TWO fundamental theorems. He calls those two theorems as first shell theorem and second shell theorem.
Basically in Principia, they are theorem xxx and xxxi.
So clearly he did not mention another fundamental theorem xxxiii.
Section 3.2 starts with this sentence: For spherical mass distributions, Newton proved two fundamental theorems that significantly simplify all work with spherical mass distributions and, in particular, that of solving the Poisson Equation.
My point is that scientists failed to realize the fundamental importance of theorem xxxiii. They should have worked out the disk version of theorem xxxiii which they never did. They ended up in the faulty disk and ring versions of shell theorem because their methods did not incorporate the actual method of xxxiii.
Now using the actual method of xxxiii, I have presented a disk version of this theorem according to which gravity remains the same in a disk of minimal width and uniform distribution of mass.
And flat rotations are default behavior of such disks. For actual galactic disks, there is considerable width of the disk due to which rotation curves should be slightly upward moving. But since for actual galactic disk, density decreases exponentially that would maintain the flat rotation curve up to that point where density remains above a certain threshold. After that point, the curve will get downslope. And that is what recent observations say.
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I would be happy to accept the MOND is some sort of effective approximation. But there then needs to be a satisfactory explanation for that, which is utterly lacking in the DM lore. If such a thing could be readily explained (and it cannot: I have spend much more time trying to come up with a workable DM explanation than I have working on MOND itself, starting with https://arxiv.org/abs/astro-ph/9501102), one would not see these papers appear claiming to falsify MOND at every tiny blip, because that would also falsify whatever DM-driven reason there is for the observed phenomenology.
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Here’s a theoretical paper of Milgrom: https://arxiv.org/abs/2305.19986
It describes a non-relativistic theory TRIMOND with three potentials which reduces to AQUAL and QUMOND in 2 specific cases. Milgrom hopes a form of BIMOND (which is relativistic and in many configurations gives light-speed tensor-mode gravitational waves as required by LIGO data) is hiding in a configuration of TRIMOND.
Personally, I like the idea of three potentials and therefore of TRIMOND. I’m a fan of moving from binary analyses in science (duality) to ternary (trialities).
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Good day, I have advanced a solution that removes the mystery of LCDM and MOND and consolidates ‘mass discrepancy’ phenomena under a single classical action – the virial theorem. This solution has been around for over a century and presented a missed opportunity. I revisit the virial theorem as the motivation for a “global” solution that bridges all structure independent of mass, morphology, or means of velocity support. This work is published in arXiv as a pre-print (2210.08264) and cleanly reveals the Milky Way’s strong “Keplerian” escape velocity profile is consistent with the latest RC decline and fall-off in the outer regions. The real issue is that a conceptual break must be made from the still unsubstantiated expectations for highly extended/flat RCs rather than focusing on the veracity of the methods and results.
Recently the Galaxy’s RC has garnered much attention with much lower dynamic mass estimates than anticipated (compared to other tracer cohorts providing typically higher mass estimates). There is nothing inherently wrong with this mass differential. This is akin to one blindfolded guy feeling the elephant’s trunk (RC) while the other touching the tail (satellite galaxies). Each description is different, but both are still correct. The key is not to isolate, but to integrate. My follow-up article (2307.03975) does precisely this, providing a coherent picture for the ‘mass discrepancy’ phenomena from SPARC dwarf galaxies to massive HIFLUGCS galaxy clusters. I find this phenomenon can be made truly physical when considering and appreciating the kinetic energy content of these virialized mass-energy configurations.
I offer this proposal as a neutral party with no conflict of interest. Just because there are two popular options, it is not automatically guaranteed one is correct while the other is not. There is a third path that provides a physical solution satisfying the observational constraints that will remain elusive with the two competing theories. I thank Dr. McGaugh for offering a forum to share and discuss these new but perhaps not so surprising findings. Regards, Jeffrey M. La Fortune
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Finally, something that makes sense.
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Finally, an approach that makes sense.
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Difference between Newton and MOND.
There is a point of view that basis of Newton’s gravity were also phenomenal observations. So what if MOND is also based on phenomenology?
Well, Newton’s universal law was based on (I) simple phenomenon and (ii) geometrical proof.
MOND is based on (I) complex phenomenon and (ii) there is no geometrical proof.
Universal law could only be derived from observations of simple phenomenon. Newton built his theories on results that were taken from observations of simplest phenomenon. Robert Hook and others had recently conducted experiments on simple falling objects. Newton himself had conducted experiments on pendulums which are simple and crude systems. He had the data of Kepler’s laws and Galileo’s experiments about inclined plane motion and projectile motion. All these were simple systems and a genius combination of the results of these simple phenomena helped Newton reaching to the general or universal law.
Moreover, inverse square distance law had the basis in the geometry of spherical space as well.
But MOND was based on complex phenomenon. Universal Law should not have been derived directly from a complex system. First there was need to break down the complex system into the simplest component. Then universal law could be derived. But MOND directly derived so-called universal law from observation of complex systems. And now after 40 years is in a struggle to break down the complex system into simplest component like wide binary studies etc.
Moreover, MOND has no solid geometrical basis. Actual geometry suggests simple inverse square law.
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Newton’s simple derivation turned out to be false, though. Nature isn’t necessarily simple or elegant. We ended up with General Relativity which is more complex and derived from complex experimental results.
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MOND applies to all galaxies that we can observe. MOND applies to dwarf galaxies from about 100,000 stars to large galaxies with 10,000,000,000 stars. MOND applies to a range of 5 orders of magnitude and in this sense is universal.
The facts are very simple. One observes individual stars of a galaxy and determines distance from the center and their orbital velocity. Unfortunately, the galaxies are far away, our telescopes are comparably small, and the errors are correspondingly high.
And yes, there is so far no derivation and no suitable geometry.
Will you look for a suitable geometry and a derivation of MOND?
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Galaxy is not a simple system. When you observe single star of galaxy in relation with whole galaxy then you are observing a complex system. Complex system was already determined by density and shape/mass configuration. General law could not be derived from such a complex system. MOND promoters only unduly defend this not very sound theory. The founder of MOND seems to be a person of unsound wisdom who straight derived universal law from a complex system. Complex sytems are the ones whose behavior is shaped by density and shape profiles of the available chunk of mass. If you wanted to draw universal law then first you needed to break down the complex system into simplest system.
Perhaps Newton was only lucky that he had the data of only simple systems amd perhaps Milgrom was only unlucky that he had the data of a complex system so only he failed and only Newton succeeded.
But Newton was not really such an unwise person. If he encountered with a complex system he would have first break down the system in to its simplest components … before attempting to derive a universal law from such a system.
Galaxy was already a complex system. Behavior of Galaxy was already determined by the density and shape of interior mass.
Now after 40 years this MOND is trying to search a simple system study such a wide binary study. This step was required before deriving a universal law.
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You keep saying that galaxies are not simple systems. Why, then, do they obey a simple law?
I am extremely tolerant of contrary views but not at all tolerant of ad hominem attacks. So you’re welcome to think MOND is not a sound theory, but you are not welcome to cast aspersions on Milgrom’s wisdom in coming up with it, or that of anyone else for taking it seriously. Persistence in this behavior will get you banned from the comments.
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Sir,
I am sorry if my argument looked like an Ad Hominem fallacy. But let me somewhat contest by way of example:
Ad Hominem: Mr. X is not wise therefore his theory is wrong.
Not Ad Hominem: Since his theory is wrong at basic or simple point, Mr. X seems not a very wise person.
Sir, my point had the second structure. I am sorry anyways and will avoid bringing any personality in similar sentence structures.
About complexity:
Galaxy is a complex system yet it follows simple universal law.
Sir, that it should be. ..!
If it is flat rotation then it is by a complex way of radius square (for mass: universal law) divided by radius square (for distance from center: universal law). Radius square divided by radius square gives 1 which means that rotations have flat curves.
Rotations have flat curves NOT because universal law itself is different.
Complexity of this type is phenomenal complexity. It is not the ultimate complexity. Ultimate complexity is one where our known laws actually fail AFTER HAVING ACCOUNTED FOR THE IMPLICATIONS OF PHENOMENAL COMPLEXITY.
If scientists ignore or overlook or avoid to consider the implications of the phenomenal complexity then the actual failure of the known universal law has not actually occurred. Given that actual known universal law has not failed so far then it is undue and fallacious to modify the universal law only to get the results that match or tally with the observations.
To prove this point wrong the need is to say that r square divided by r square is not applicable to interiors of a disk having uniform density and minimal width. And to say that, first it will be needed to say that r cube divided by r square is not applicable to the interiors of a sphere having uniform density.
If the sphere has uniform density, then for the interior, r cube divided by r square is applicable. Not universal but the particular law, thus for such a sphere is DIRECT LINEAR GRAVITY WITHIN THE SPHERE. (Theorem XXXIII of Newton).
If a disk of minimal width has uniform density, then for the interiors of such a disk, r square divided by r square is applicable. Not universal but the particular law, thus for such a disk is SAME GRAVITY EVERYWHERE WITHIN THE INTERIORS AND GRAVITY DIRECTED TOWARDS CENTER. (Disk version of Theorem XXXIII).
I am thankful for your great tolerance. This shows your highness.
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Kepler’s laws were, like MOND, based on data but without geometric proof. But without Kepler, Newton would not know about the elliptical orbits to validate his reasoning and force law. They would be seen as circles.
Without MOND, some future researchers won’t be able to find the confidence and validation of a FUNDAMOND theory.
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One even wonders if some string theorist has come across a theory that gives MOND but rejected it as obviously wrong because he didn’t even know about MOND.
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To be a human for a moment and talk about emotions. I am really happy that they rejected MOND. Otherwise another sickness was ready to be imposed on us. The sickness of emergent Gravity based on Strings Theory.
Now we have only curved mentality syndrome. Then we also would have a strings mentality where everywhere there would have been mysterious strings doing charmic communications with the local and universal curvatures of spacetime.
phenominal reality is simpler. Only unltimate reality is complex. And dark matter or even expanding universe theory all are about phenomenon. They should be simple matters.
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I disagree with your depiction from the outset. The phenomena MOND successfully describes in galaxies is simple. There is one effective force law. That is very much the same as what Newton found. The phenomena he was describing must have seemed comparably complex at the time; it only seems simpler now after four centuries of familiarity.
The geometric reason for the inverse square law does not appear to have occurred to Newton for 20 years, and only then at the prompting of letters from Bentley that he struggled to answer satisfactorily. It takes time to wrap our heads around these things – even if you’re a genius like Newton.
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There are a couple of questions I would like to direct to Dr. McGaugh. As the data shows, SPARC galactic disks and HIFLUGCS clusters (hydrostatic gas) mass discrepancies rarely exceed D~12 at their observational limits. Why the upper value, and why 12? According to MOND, D can take on much larger values and one would expect to see this reflected in the observations, but we don’t (maybe Brouwer?).
Another characteristic of the RAR is a truncation at low accelerations (as pointed out by Desmond, arXiv 2301.04368, the SPARC data stops at 8.32×10-13 m/s2, but did not give an explanation). I provide an explanation in arXiv 2307.03975 Appendix A that is near identical to Desmond’s value but for physical reasons related to escape velocity. From a MOND perspective, what is the cause?
Other than the functional form of the RAR, these two major features have not been fully resolved (or I have inadvertently missed it). The data is clear, but the reasons are not. If you could entertain my inquiry, it would be greatly appreciated. Regards, Jeff
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You are correct that the mass discrepancy in rotating galaxies rarely exceeds a factor of 12. This seems to have entirely to do with where the data peter out, and nothing to do with theory. There are technical limits on how low in column density we can observe with radio interferometers, at least in the amount of observing time that is typically available. That’s what sets the limits for most of the SPARC sample.
Lower accelerations are observed in dwarf Spheroidal galaxies, which have discrepancies of dozens sometimes approaching 100. The lensing data of Brouwer that you mention extends even farther. Those data are fraught, and I hope to have more to say about them in the near future. But I think it is fair to say that they do probe the very low acceleration regime where the amplitude of the discrepancy is >> 12.
As astronomers, we are of necessity passive observers: we only get to see that part of the universe that is accessible to our remote sensing techniques.
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Dear Dr. McGaugh, thank you for your reply. I’d like to continue the discussion a bit further. We find LCDM works well for massive galaxy clusters but not for smaller disk galaxies, while MOND does well for galaxies, but not for clusters. Why? Should not a truly viable theory be able harmonize these two major structural classes, self-consistently or offer a reason why they don’t (without adding complexity)?
Both theories seem to be turtles all the way down with neither capable of reproducing observations ‘standalone.’ It appears the stack of turtles is piled higher and deeper for LCDM, but MOND has added layers too, witness the revived interest in the EFE, neutrino mass support in clusters, and potentially string theory(?) We don’t want MOND turning into the dark matter detection debacle with its constantly moving goal posts and the de rigor statement, “This failure opens up a whole new parameter space to explore!” In jest, where do we sign up for these Participation Trophies in this ‘Great Game?’
As an alternative, I invite all to take a look at arXiv 2307.03975 for a ‘solution’ that only entails global observed parameters: Mb, V, and R along with a refreshing rational interpretation for the form and function of the Mdyn-Mbar scaling relation. This relation is mature and faithfully reflects the physical dynamics (without ambiguity). There is no cherry picking, exceptions, or outliers. If dwarf spheroidal galaxies (not included in this analysis) appear to be odd ducks, perhaps they are…but they still remain within the realm of standard physics. If not, we know where that line of thinking has taken us for the past near century….materially nowhere. We are still arguing which unsubstantiated claims represent reality. It’s high time we move on.
At the end of the day, galaxies and clusters are very simple structures. Both share similar global dynamic signatures inferring a known, universal, and pervasive regulatory process. Is the virial theorem too mundane or too obvious to even consider? Reading some of the literature on the fantastic (and pseudo-magical) properties of dark matter has me wondering. I’ll entertain challenges and answer any questions. Please take my comments in the spirit of the scientific method, logic, and even philosophy as applied to this meaty problem. Thanks and best regards, Jeff
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Dr. McGaugh,
your post is about cold dark matter and Milky Way’s rotation curve
if you were to write a paper one Milky Way’s rotation curve using third data release (DR3) from Gaia, and applying MOND, what would be MOND’s prediction for Milky Way’s declining rotation curve esp in the 17-23 kpc region?
Is MOND’s prediction of Milky Way’s declining rotation curve consistent with third data release (DR3) from Gaia, within observational error?
could there be a type of dark matter that could be consistent with Milky Way and Gaia data?
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Hi Stacy,
Thank you for your post on “Is the Milky Ways’ rotation curve declining?”.
One would expect the Gaia Collaboration to know their own data and it is interesting to note that they only produce a rotation curve out to 13.5 kpc, they make no attempt to go anywhere near the 26.5 kpc of Jiao et al (Fig 17 of Gaia Data Release 3; Drimmel et al 2023; arxiv.2206.06207; as referenced by Jiao et al). Also their Fig 19 shows some data out to around 19 kpc and the large scatter is very apparent, as is the lack of any obvious decline in the rotation curve; and the amount of data beyond 19 kpc seems to be really sparse.
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