I Question about Galactic Rotation curves in the Milky Way galaxy

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Summary
This question refers to Wikipedia article on Milky Way, section on Galactic Rotation curves. I am referring to the graph on the right showing actual speed, in km/s, to distance from center of galaxy, in kpc. The actual speeds depend on the distribution of dark matter.
The graph in Wikipedia, article Milky Way, section Galactic Rotation, shows the actual rotation speeds in blue and the calculated speeds due to observed mass in red. (The graph is to the right of the article.) At about 3 kpc the actual speed is about 205 km/s. To account for the decrease in orbital speed around the center of the Milky Way, less centripetal force is needed, that is, less gravitational force. To account for this decrease in speed, dark matter needs to be located further out, lets say at 10 to 15 kpc. At 12 kpc, the orbital speed is about 220 km/s. To account for this increase in speed, a higher centripetal force is needed. To increase gravity at this distance, more dark matter closer to the galactic center is needed at lets say 3 to 7 kpc. But dark matter closer to the center will increase the orbital speed at 3 kpc. Is there a contradiction here? I know the Wikipedia articles in science and mathematics are correct and have been reviewed. Please explain.
 

Drakkith

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To account for this decrease in speed, dark matter needs to be located further out, lets say at 10 to 15 kpc. At 12 kpc, the orbital speed is about 220 km/s. To account for this increase in speed, a higher centripetal force is needed. To increase gravity at this distance, more dark matter closer to the galactic center is needed at lets say 3 to 7 kpc. But dark matter closer to the center will increase the orbital speed at 3 kpc. Is there a contradiction here? I know the Wikipedia articles in science and mathematics are correct and have been reviewed. Please explain.
A shell of dark matter located from 3-7 kpcs would have little effect on anything inside the shell. So if the shell starts just after 3 kpcs, the matter exactly at 3 kpcs wouldn't show any increase in orbital speed. The same is true for a shell starting near 10 kpcs.
 
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Sorry, next time I will paste graph with question.

Thanks for referring me to the Newton's proof of his shell theorem. I will study it on Wikipedia.
 

ohwilleke

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I know the Wikipedia articles in science and mathematics are correct and have been reviewed.
In the long run and on average, curation of Wikipedia articles on frequently viewed topics tends to be pretty reliable in practice. But, this isn't an axiom of truth upon which you can rely, and the best practice is to review the cited sources for any important proposition.

Anyone can change most Wikipedia articles at any time (and the number of people with authority to change any Wikipedia article on ordinary subject-matter regardless of level of protection at any time is still huge). There are wikis like Scholarpedia that are restricted to people who would be qualified to engage in peer review on a topic, although they tend to be somewhat less readable for introductory level readers, and are less actively monitored and reviewed.
 
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Referring back to the graph on galaxy rotation speeds from Wikipedia: At 3 kpc, the actual observed rotation speed at about 3 kpc is shown in blue to be about 205 km/s. (Again, I do not believe that Wikipedia is incorrect. Also, I am not an astronomer, just fascinated by astronomy.) The rotation speed is determined by the centripetal acceleration towards the center of our universe. (Just as in our solar system, the higher the centripetal acceleration, the higher the orbital speed around the sun.) Less centripetal acceleration results in less stellar rotation speed. The red curve shows the predicted speeds due to observed stellar and gas mass, which is about 265 km/s. This means that the centripetal acceleration is higher. What could cause the actual centripetal acceleration to be less that produced by visible stellar mass and gases? One explanation may be dark matter. (From reading Wikipedia, dark matter was needed to explain the initial clumping of mass and is needed to explain phenomenon in cosmology at very large scales. Its existence has been accepted by physicists.) How can dark matter reduce acceleration? By placing it at 3 kpc or closer to the center, it would increase acceleration, not decrease it. By placing dark matter in a shell further out, it would have no effect, according the Newton's shell theorem. Please explain.
 

Drakkith

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By placing dark matter in a shell further out, it would have no effect, according the Newton's shell theorem. Please explain.
Explain Newton's shell theorem?
 

phyzguy

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I think the discrepancy near the center is not caused by dark matter. It is caused by the central black hole, which has a mass of 4 million solar masses, and which is not included in the "stellar mass and gas".
 

ohwilleke

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Somewhat better and more accurate data on the actual rotation curve (but without a comparison to the predicted value) from an October 2018 paper is as follows:
Screen Shot 2019-10-15 at 4.28.39 PM.png


I would also prefer a different chart from a Wikipedia source that in my view is more clear:

Rotation_curve_of_the_Milky_Way.png


This does not have the 1,000-8,000 parsec distance with a predicted value that is higher than the measured value shown in the other chart in the comment above. Given similar charts that I have seen for many dozens of galaxies, I believe that part of the other chart in the comment above is an artifact of a flowed method of measuring this speed a distances closer than Earth to the galactic center, rather than accurately representing the reality.

At a very heuristic level, either dark matter or a strengthening of the pull of gravity beyond a certain critical value of field strength, pulls matter at the fringe of the spiral galaxy in more tightly than a prediction based upon Kepler's law would imply, causing matter at the fringe of the Milky Way to rotate faster than it would be expected to.

In a dark matter explanation, the dark matter is preventing the pull of gravity from getting weaker with distance.

I know that this doesn't quite answer the question you have posed in the kind of terms that you have used, but I still think that this is helpful.

Also helpful may be this illustration which breaks the observed rotation speed with distance out by each separate source of that rotation speed that contributes the observed total (not for the Milky Way itself, but illustrating how the distribution of dark matter is inferred):

fig5_20.jpg
 
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Newton's shell theorem states: If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell. Would a halo of dark matter around our universe be considered a shell or a ball of varying density?

Maybe the chart which I was referring to was not the best. It is true that gravity around the center of our galaxy will be dominated by the massive black hole. The red line does not account for a massive black hole.

Quoting from above: "At a very heuristic level, either dark matter or a strengthening of the pull of gravity beyond a certain critical value of field strength, pulls matter at the fringe of the spiral galaxy in more tightly than a prediction based upon Kepler's law would imply, causing matter at the fringe of the Milky Way to rotate faster than it would be expected to."
Please explain above paragraph. Are you implying that at the outer reaches of our galaxy gravity decreases by about 1/distance not by 1/distance^2?
 

ohwilleke

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Please explain above paragraph. Are you implying that at the outer reaches of our galaxy gravity decreases by about 1/distance not by 1/distance^2?
The dynamics of objects at the outer reaches of our galaxy are consistent with that assumption, although the reason for that is disputed.

There is a phenomenological toy model which makes this assumption and does a very good job of describing phenomena that are observed from solar system scale to large galaxies that is called MOND invented by Mordeci Milgrom in 1983. The abstract of the original paper is as follows:

Screen Shot 2019-10-17 at 12.30.26 PM.png


MOND is absolutely and admittedly not a complete and accurate theory of gravity (in its simplest form, for example, it does not have many fully established properties of general relativity, although it can be generalized as Jacob Bekenstein did in 2004 which address some of the most superficial flaws of MOND, although not its deeper problem with galactic cluster sized systems) and Milgrom himself doesn't claim otherwise. (Sadly, Milgrom's junior and much younger colleague, Bekenstein, predeceased him in 2015.)

But, any correct solution to dark matter phenomena, be it from dark matter particles or a modification of gravity, needs to explain why this reality, also called the radial acceleration relation, holds true so generally beyond a certain threshold gravitational acceleration constant called a0, with its domain of applicability which spans many order of magnitude.

The Radial Acceleration Relation in Rotationally Supported Galaxies
Stacy McGaugh, Federico Lelli, Jim Schombert
(Submitted on 19 Sep 2016)
We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons. The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions. The correlation persists even when dark matter dominates. Consequently, the dark matter contribution is fully specified by that of the baryons. The observed scatter is small and largely dominated by observational uncertainties. This radial acceleration relation is tantamount to a natural law for rotating galaxies.
Comments:6 pages, 3 figures. Accepted for publication in Physical Review Letters
Subjects:Astrophysics of Galaxies (astro-ph.GA)
Journal reference:Phys. Rev. Lett. 117, 201101 (2016)
DOI:10.1103/PhysRevLett.117.201101
Cite as:arXiv:1609.05917 [astro-ph.GA]
(or arXiv:1609.05917v1 [astro-ph.GA] for this version)
Other more sophisticated modifications of gravity reproduce the radial acceleration relation without many of the shortcomings of toy model MOND.

What Does A Complete Dark Matter Theory Look Like?

Also, to be clear, you can explain almost any kind of galaxy dynamics in any particular galaxy, simply by putting dark matter particles in places needed to produce those dynamics. So, a proposed dark matter particle theory is really not a complete operational physics model unless it also provides some way of explaining why the dark matter particles ended up in the places that they did, and why they stay in the configuration.

Thus, for example, you could have two dark matter particle theories both of which have precisely the same particles with precisely the same properties. But, one of those theories might have dark particles of that type that are produced in thermal freeze out, and another might have them produced in some other manner that would cause the dark matter to be distributed in a different manner. One might be supported by some piece of astronomy evidence, while another might be contradicted by a piece of astronomy evidence.

One of the main distinctions between dark matter particle theories (cold, warm and hot) concerns not the intrinsic properties of the particles themselves, but the mean velocity of those particles (which is correlated tightly with dark matter particle mass in thermal freeze out scenarios).

This is important, because, for example, the theory needs to explain why the radical acceleration relation arises with the kind of dark matter particle in question, i.e. why the inferred distribution of dark matter in galaxies is so tightly correlated with the distribution of ordinary matter over so many order of magnitude of galaxy scale. This is challenging because, almost by definition, any non-gravitational interactions that dark matter has with ordinary matter are extremely feeble, and naively, it is challenging to produce such a tight correlation exclusively through gravitational interactions.

Similarly, unless dark matter interacts with itself (another property of dark matter that is often assumed to not be the case, except, of course, in self-interacting dark matter a.k.a. SIDM theories), or with ordinary matter, dark matter should have what is called a Navarro-Frenk-White (NFW) distribution (a.k.a. profile) within a galaxy. But, while the evidence isn't entirely one sided, there is considerable data to support the conclusion that the inferred distribution of dark matter in most galaxies is inconsistent with an NFW profile, and instead usually has an inferred "isothermal distribution" that is also not perfectly spherical.

As a third example, elliptical galaxies have less dark matter relative to the amount of ordinary matter in them than spiral galaxies do, which in turn tend to have less dark matter relative to the amount of ordinary matter in low surface brightness dwarf galaxies (with a handful of notable exceptions in which dwarf galaxies appear to have no dark matter). And, among elliptical galaxies, more spherical elliptical galaxies have less inferred dark matter relative to the ordinary matter content than more oval shaped galaxies. But, galactic clusters have much more inferred dark matter relative to their ordinary matter content than spiral and elliptical galaxies do, and the inferred dark matter phenomena effects in galaxy clusters are stronger than MOND would predict. So, your dark matter particle theory needs to be able to explain why that is the case.

None of those properties of dark matter distributions were predicted in advance by dark matter theories, all of them, except the excess of apparent dark matter phenomena in galaxy clusters, was predicted (in multiple cases before data was available) by MOND.

Proposing a dark matter particle with particular properties that would evade direct detection experiments is easy.

But, explaining how it came to be distributed in the manner that it must be reproduce what we see in terms of galaxy, etc. dynamics and cosmology observations is a non-trivial process of limited accuracy as both analytical approaches to doing this, and N-body simulations, are more art than science with current computational power and methods even in the abstract. And, given the considerable observational constraints regarding the inferred distribution of dark matter in galaxies, this is a particularly challenging task.
 
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Thank you for your detailed answer. I will further read up at the sources which you referenced.
Is it good science to be allowed to place dark matter at any place in a galaxy to make your hypothesis come out? How can a hypothesis then be proved wrong? In physics, I always read about constraints. Where are the constraints here?
I have read about the formation of the universe and the initial need for gravitational wells to get gaseous matter clumped into stars. Dark matter was needed to explain the formation of stars in the time frame of our universe.
Maybe galaxial rotation curves and initial clumping of matter into stars are/were caused by different physical processes.
 
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At a very heuristic level, either dark matter or a strengthening of the pull of gravity beyond a certain critical value of field strength, pulls matter at the fringe of the spiral galaxy in more tightly than a prediction based upon Kepler's law would imply, causing matter at the fringe of the Milky Way to rotate faster than it would be expected to.

In a dark matter explanation, the dark matter is preventing the pull of gravity from getting weaker with distance.

I know that this doesn't quite answer the question you have posed in the kind of terms that you have used, but I still think that this is helpful.

The above answer precisely answers my original question, although my question was not clearly stated.

Does this strengthening of gravity at the fringes of our galaxy continue towards other galaxies?
 

ohwilleke

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Does this strengthening of gravity at the fringes of our galaxy continue towards other galaxies?
I don't believe that the data is terribly clear on this point for the obvious reason that the spaces between galaxies are mostly empty and the distances between galaxies are often great enough for gravitational influences from one particular source galaxy among many distant deep space masses to be hard to isolate. Clusters of galaxies where galaxies are fairly close together have lots of inferred dark matter effects. Other cases are tricker.
 
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Thank you for your reply.
 

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