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- 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.

Best,

Richard

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.

Best,

Richard