I Question about Galactic Rotation curves in the Milky Way galaxy

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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?
 

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