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Top Comments: Dark Matter vs. MOND (Modified Newtonian Dynamics) [1]
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Date: 2023-11-09
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Commenters in some of my previous diaries have disparaged my enthusiasm for dark matter and my distain for MOND (modified Newtonian dynamics) as an explanation for why the rate of revolution for stars around galactic centers does not slow down appreciably as distance from the galactic center increases (as the rate of revolution for planets around a star decreases as distance from the central star decreases). So I’ve decided to present an even-handed review of each of the theories, their origins, where they succeed, and where they fail. As this is a fairly long diary, I’m placing what follows below the fold, which is where you’ll also find tonight’s comments.
Background
The problem these two hypotheses are attempting to address is the discrepancy found between the observed orbital speeds of stars in galaxies, as a function of their distance from the galactic center, and the speed of the same star calculated using Newton’s universal law of gravitation and the mass of visible matter that would exert the force of gravitational attraction. The first time I wrote about dark matter, I described the issue thusly:
One particular set of observations performed in the late 1960s by [Vera] Rubin, in collaboration with W. Kent Ford, was on the arms of the Andromeda galaxy; at a mere 2.5 million light-years away, it’s one of the closest neighbors to our own Milky Way Galaxy. At that time, technology had progressed to the point where it was possible to obtain the spectral measurements from particular regions of the galaxy, rather than having to settle for the spectrum of the entire galaxy. By focusing their observations on the arms of the Andromeda Galaxy, they were able to use the Doppler effect on known spectral features to measure the speed of rotation of the stars in those arms, at various distances away from the center of the galaxy. The expectation was that the speed of rotation would drop as distance from the center of the galaxy increased. After all, this is how it works in our solar system: Mercury, closest to the Sun, speeds around in its orbit, while the speed of planetary revolution around the Sun drops for each successive planet going out, until you get to Neptune, lumbering about its orbit at about one-tenth the speed of Mercury. But that’s not what Rubin and Ford observed for the arms of the Andromeda Galaxy. The speed of rotation of stars in the arms was pretty much the same whether it was close to or distant from the galactic center.
Comparison of the observed and expected rotation curves of the typical spiral galaxy M33 (Wikipedia)
You can see the discrepancy for yourself in the figure on the right. The predicted orbital speeds calculated using Newton’s law follow the dotted line, while the observed orbital speeds are shown as a solid line fit to the data points. This is not a small deviation. The immediate assumption made by Rubin and her colleagues was that the observed data could be explained by assuming that there was a large halo of invisible matter present in and around the galaxy, exerting greater force on the stars, and thus increasing their orbital speeds; this is the dark matter hypothesis.
However, there is another possibility. Because Newton’s universal law of gravitation is observed to explain all planetary dynamics within our Solar System, it has always been issued that the law applies universally at even larger scales, that is, at the scale of galaxies, and even galaxy clusters. However, until Rubin’s observations, no one had actually tested this hypothesis until Rubin performed her observations. Rather than assuming there is invisible matter exerting extra force to explain the higher-than-expected orbital speeds, maybe the problem is that at distances much larger than the size of the Solar System, Newton’s law no longer describes the force of gravity with sufficient accuracy. This idea was first proposed by Israeli physicist Mordehai Milgrom in 1983. It is alternatively referred to as MOND or modified gravity.
I’ve written several diaries about the virtues and faults of the dark matter hypothesis, and refer you to these. Let’s look at the nature, virtues, and faults of MOND.
What is MOND?
Again, the idea is that Newton’s law of gravitation at large separation (or more accurately, at low acceleration) is augmented by an additional force function that does not die off quite as quickly as the Newtonian force. By fitting orbital speed data to his proposed functions, he hit upon a cutoff acceleration of 1.2x10-10 m s-2. A mass subjected to an acceleration this small for one hour would move just 0.8 mm. Yet, stars sufficiently far from the center of a galaxy are subject to gravitational accelerations of this size or smaller. In Milgrom’s formulation, when the star’s acceleration is greater than this cutoff, Newton’s law alone applies; when a star’s acceleration is less than the cutoff, the additional term, whose force decreases much more slowly with distance than Newton’s, must be added.
The MOND approach is entirely empirical. As yet, there is no explanation for the origin of Milgrom’s proposed additional term in the force, but if analysis is robust and the full function is found to work universally, the theorists are sure to come up with something. Of course, in the intervening 40 years since Milgrom published his idea, many people have been playing with this approach and coming up with variations. In general, MOND works to describe orbital rotation curves, such as the one above, extremely well over a large variety of galaxy types. While Milgrom’s original formulation was strictly classical, others have formulated relativistic versions of his approach. This is necessary in order to embed the proposed gravitational force into a universe where general relativity applies.
However, there are problems. Modeling galaxy clusters using MOND reduces the mass discrepancy, but a significant discrepancy remains. Also, when MOND is applied to cosmological models, it can’t reproduce anisotropy in the the cosmic background radiation as it is observed today. Further, the analysis of the Bullet Cluster, a collision between two galaxy clusters, clearly shows that there is dark matter unhindered by the collision while the visible matter is confined and blazing x-rays (you’ll find the photo here). Lastly, there are diffuse galaxies whose orbital curves do fit with Newton’s law, suggesting no need for MOND; these can simply be interpreted as galaxies where there is little or no dark matter. Weird that the absence of dark matter confirms its existence.
I’m not smart enough to say for sure, but it may be that both MOND and dark matter are necessary components of a final explanation.
On to the comments!
Top Comments (November 9, 2023):
From thesphynx:
Tweedledee5 eloquently explained how the Republican notion that Dobbs would help increase US birth rates has utterly backfired. From Joan McCarter’s front page post on how Republicans from Ohio and Michigan are trying to find ways to undermine the voters’ will on abortion rights.
From DHfromKY:
This comment from wesmorgan1. It approaches the KY governor election as being between someone who tried to nationalize it, and someone who tried to keep it localized. From Kerry Eleveld’s post on GOP setbacks in their crusade against transgender people.
Top Mojo (November 8, 2023):
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