What is the Visible Mass of the Milky Way?

[RCopernicus]

On a related question to my last post, is there any consensus on the visible mass of the Milky Way? I've seen several recent mass calculations but they all assume Dark Matter. For my model I need to know the total visible matter of both the disk and the entire galaxy. I've seen old estimates of 200-400 billion solar masses, but these references appear to be very dated.

 

[Astronuc]

On a related question to my last post, is there any consensus on the visible mass of the Milky Way? I've seen several recent mass calculations but they all assume Dark Matter. For my model I need to know the total visible matter of both the disk and the entire galaxy. I've seen old estimates of 200-400 billion solar masses, but these references appear to be very dated.

Here is an estimate, but it is not clear to me if the 2E11 is visible or is the total (dark + visible) in the visible disk.
http://hendrix2.uoregon.edu/~imamura/123cs/lecture-2/mass.html

The Caltech source (in the other thread) mentions ~2E11 stars in the Milky Way, with about 6E10 solar masses in the disk, and 2E10 solar masses in the disk. But this is visible mass, I expect.
https://www.physicsforums.com/threads/milky-way-density-profile.773564/

Here is yet another, different, estimate.
http://www.uccs.edu/~tchriste/courses/PES106/106lectures/106lecMilkyWay1.html

and a more recent discussion
http://astrobites.org/2013/01/01/the-milky-way-is-cut-back-down-to-size/

 

[Vanadium 50]

This has the same problem as the last time you asked a similar question. We don't have a good view of the galaxy because we are in the middle of it. All the estimates have to go from the perhaps 15% that we can see to the 85% we can't.

 

[RCopernicus]

@Astronuc

Thanks again, very useful stuff. I also found this which appears to be a pretty recent paper on the subject:

http://arxiv.org/pdf/1310.2659v3.pdf

 

[CKH]

@Astronuc

Thanks again, very useful stuff. I also found this which appears to be a pretty recent paper on the subject:

http://arxiv.org/pdf/1310.2659v3.pdf

The first sentence in that paper makes the following claim:

The circular velocity [V(r) = ...] of a test particle at a radial distance r from the center of a mass distribution gives a direct measure of the total gravitational mass M(r) within that radius r.

This statement is false. It is false in general and in particular it is false in the case of disk galaxies which are not uniform spherical distributions.

Here is a quick counter example to prove the statement is false in the general case. The statement is true when, for example, the distribution is a point mass at radial distance r. Now suppose you stretch that point mass into a vertical line segment of uniform mass density where the distance to the line is still r and the total mass is the same as before. It is clear that the gravitational vectors (direction of gravitational force) of the portions of the line far above and below the center will cancel in the vertical component and be weaker in the horizontal component than those same portions when concentrated in the point mass because the distance to the test particle is increased for these portions of the mass distribution and the angle of action is greater resulting in a smaller horizontal component. Thus, in this counterexample, the circular velocity will be lower than in the case of the point mass (or a uniform spherical mass).

The circular velocity of a test particle depends not only on the distance from the center of mass, it depends upon the distribution of the mass, even when the distribution is axisymmetric.

Note that the quoted statement is true if the mass distribution is spherically uniform (in each shell) and entirely within the radius of the test particle. The statement implicitly makes the assumption that any mass distribution at a radius greater than r is also a uniform spherically in each outer shell and thereby has no effect on the test particle.

This mistake appears in many papers including those that cite Kepler's laws (which apply to large, concentrated central masses) to argue how much unseen mass must exist in disk galaxies.

The fact is disk-like distributions of mass exert more force on particles at a given radius (in the plane of the disk) than spherical distributions of the same mass. The equation given in the paper is wrong and leads, in the case of a disk galaxy, to an overestimation of contained mass. To see this, imagine that the mass distribution is a uniform sphere of radius a bit less that r. Portions of the sphere above and below the plane through the test particle and center of mass are more distant from the test particle than their projections onto the plane. Now squash the sphere vertically into a disk. Notice that all of the off-plane particles are now closer to the test particle and therefore exert more force on it. Moreover the directions of forces are now all working together in the plane instead of canceling each other in the vertical direction.

Is it possible that the paper makes this statement under the implicit assumptions that the baryonic mass is negligible (5%) and that DM is distributed spherically?

In the No Dark Matter thread, I posted links to several papers that point out this common mistake and correctly derive circular velocities based on disk-like distributions. The results differ greatly and demonstrate that modest amounts of unseen mass in the outer disks can explain flat rotation curves out to large distances.

So while the mass of visible matter in the galaxy can be estimated directly, extended conclusions based on dynamics are highly dependent on the assumed distribution of unseen matter.