# Orbital Velocities and Mass Distribution in Galaxies

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• cosmologyscience
In summary: Because the stars are so far from the center, they only have a small impact on the overall mass distribution.In summary, there is evidence for a dark matter-free galaxy, but it is unclear how much visible mass is required to maintain a stable orbit.
cosmologyscience
TL;DR Summary
The necessary visible mass density distributions to obtain static observed orbital speeds in the Milky Way.
Has anyone looked into the details of stellar orbital speeds and required (visible) mass distribution in the Milky Way?

Doing some math here - if the local mass density is significantly higher in the inner 10-15% of the galaxy, and then lower and gradually thinning outwards in the disk, we will get a linear relation between mass and radius in the galaxy. (2x more radius, 2x more mass. While 2x more radius, 8x more volume).

If the mass is adjusted so we have a linear radius to mass relation, you get a constant orbital speed v at every point in the disk (which is roughly what is observed).

The local densities in the milky way would then be (given orbital speeds c. 220km/s):
0-1 kly from the center: 1.728 E-18 kg/m^3
9-10 kly from the center: 6.378 E-21 kg/m^3
49-50kly from the center: 2.351 E-22 kg/m^3

Meaning the local density at radius 0-1 kly is about 270x more dense than at 9-10kly. And then out in the disk, 49-50 kly is just 27x more dense than at 9-10 kly radius.

Given that the bulge is a dense ball, and the "shells" outwards mostly only have (visible) mass in a thin sliver with the disk, this might still maintain the requirement that each "shell" needs to have the same amount of mass.

Wonder if anyone has done any work on this, or what the calculations are that imply up to 90% mass deficiency to obtain the observed orbital speeds.Richard

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Most of the matter is dark matter, seriously affecting orbits, etc.

vanhees71
cosmologyscience said:
Wonder if anyone has done any work on this, or what the calculations are that imply up to 90% mass deficiency to obtain the observed orbital speeds.
I imagine there are hundreds of studies of galactic visible mass densities. There's a summary of the methods here:

Here's one for a specific spiral galaxy:

https://iopscience.iop.org/article/10.3847/1538-4357/aaf57b

vanhees71 and cosmologyscience
cosmologyscience said:
Has anyone looked into the details of stellar orbital speeds and required (visible) mass distribution in the Milky Way?

If the mass is adjusted so we have a linear radius to mass relation, you get a constant orbital speed v at every point in the disk (which is roughly what is observed).
For a fun time, see this recent thread.

vanhees71 and cosmologyscience
strangerep said:
For a fun time, see this recent thread.
That's a collection of great references. Thank you!

vanhees71
vanhees71 said:
Note that there's evidence for dark-matter-free galaxies:

https://www.nature.com/articles/s41586-022-04665-6 (open access!)
Very interesting, thank you.
And I'm still struggling to see the jump from density profile calculations to estimations of percentages visible matter/invisible matter in spiral galaxies. In the linked paper in an earlier comment (https://iopscience.iop.org/article/10.3847/1538-4357/aaf57b) - they seem to do everything right including estimating the mass density profile, which indicates that about 80-85% of the mass is in the disk.

But then it jumps to: "The outer halo mass is significant and it is four times more than the mass of the inner (more dense) regions, which confirm the existence of a massive halo and giving evidence as to the existence of dark matter." But looking at the galaxy NGC 3198 (attached), estimating the visible mass in the disk accounting for 80-85% of the total mass of the galaxy looks quite reasonable. And even if the star density "thins out" further out from the center, that is what Kepler's law predicts given a stable velocity - the density has to fall by 1/r^2 to maintain a constant amount of mass added pr. increment.

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vanhees71

## 1. What is orbital velocity?

Orbital velocity is the speed at which an object moves in its orbit around a central body. In the context of galaxies, it refers to the speed at which stars and other objects move around the center of the galaxy due to the gravitational pull of the galaxy's mass.

## 2. How is orbital velocity related to mass distribution in galaxies?

The orbital velocity of objects in a galaxy is directly related to the mass distribution within the galaxy. The greater the mass of the galaxy, the stronger its gravitational pull, and the faster objects will orbit around its center. This relationship is described by Newton's law of gravitation.

## 3. What factors influence the orbital velocities of objects in galaxies?

The primary factor that influences orbital velocities in galaxies is the distribution of mass within the galaxy. Other factors, such as the presence of dark matter, can also have an impact on orbital velocities. Additionally, the distance of an object from the center of the galaxy and the shape of the galaxy can also affect orbital velocities.

## 4. How do scientists measure orbital velocities in galaxies?

Scientists use various methods to measure orbital velocities in galaxies, including spectroscopy and observations of the Doppler shift in the light emitted by objects in the galaxy. These measurements can provide valuable insights into the mass distribution and dynamics of galaxies.

## 5. What can we learn from studying orbital velocities and mass distribution in galaxies?

Studying orbital velocities and mass distribution in galaxies can provide valuable information about the structure and evolution of galaxies. It can also help us understand the role of dark matter in the universe and provide insights into the formation of galaxies and the larger structures of the universe.

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