Confusion re Laniakea Super Cluster

[Buzz Bloom]

I have been trying to understand some facts about the Laniakea supercluster. I found information at three sites which when compared with each other creates some confusion.

a. http://www.ifa.hawaii.edu/info/press-releases/Laniakea/
b. https://en.wikipedia.org/wiki/Laniakea_Supercluster
c. https://en.wikipedia.org/wiki/Gravitational_binding_energy

(a) says

The orange contour encloses the outer limits of these streams, a diameter of about 160 Mpc. This region contains the mass of about 10¹⁷ suns: 100 million billion suns.​

(b) says

The Laniakea Supercluster encompasses 100,000 galaxies stretched out over 160 megaparsecs (520 million light-years). It has the approximate binding mass of 10¹⁷ solar masses.​

(b) has a link for "binding mass" the leads to (c).

(c) says

A gravitational binding energy is the energy that must be exported from a system for the system to enter a gravitationally bound state at a negative level of energy.
. . .
For a spherical mass of uniform density, the gravitational binding energy U is given by the formula

It is clear that "mass" and "binding mass" are not the same thing. At first, it seemed likely that the news article (a) was careless and used the more common term "mass" while Wikipedia's (b) used a more accurate but less familiar term "binding mass". But, then again, maybe not.

From (b)'s link to (c), is seems that a calculated value for "binding mass" would be

M_bind = U/c².​

Then the ratio

r = M_bind / M​

would be a dimensionless ratio for the fraction of the mass M that would have to be removed from the system (in the form of kinetic energy or lost mass, or what?) if the systerm was to be gravitationally bound together. This concept seems a bit strange.

So, based on the above, I conclude that (b) was wrong, and (a) was right.

Unfortunately neither (a) nor (b) nor any of their references discusses the method used to calculate the mass of the supercluster. The method I am familiar with first calculates the total star mass from the amount of visible light (corrected for redshift). This result is then multiplied by a "standard" ratio (which takes into account baryonic dark matter, e.g, unilluminated gas and dust, to get to get a value for the total baryonic mass. This result is then multiplied by another ratio to include the non-baryonic dark matter.

Can anyone help me find a source that shows the calulation of Laniakea's mass?

 

[Buzz Bloom]

I have decided after much thought to edit the Wikipedia page about the Laniakea supercluster, changing "binding mass" to "mass". An explanation for making this change is on the Talk page.

I have also reached the conlcusion that after 61 views and no responses that no one is likely to help me find a source that shows the calculation of Laniakea's mass.

I have one further related question that I hope someone will respond to. I will soon create a new thread, "The Dark Sky Ahead", in which I will post this question.