I Orbital Velocities and Mass Distribution in Galaxies

[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

 

[mathman]

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

 

[PeroK]

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:

https://link.springer.com/referenceworkentry/10.1007/978-94-007-5612-0_19

Here's one for a specific spiral galaxy:

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

 

[cosmologyscience]

I imagine there are hundreds of studies of galactic visible mass densities. There's a summary of the methods here:

https://link.springer.com/referenceworkentry/10.1007/978-94-007-5612-0_19

Here's one for a specific spiral galaxy:

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

Thank you, that was exactly what I was looking for. Very helpful.

 

[strangerep]

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.

 

[cosmologyscience]

For a fun time, see this recent thread.

That's a collection of great references. Thank you!

 

[vanhees71]

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

https://www.nature.com/articles/s41586-022-04665-6 (open access!)

 

[cosmologyscience]

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.