The observed motions of members of a typical cluster of galaxies suggests that, in order for the galaxies to be gravitationally bound together, the cluster must have a mass of at least 1014 solar masses (i.e., a hundred trillion Suns' mass). The cluster contains 100 galaxies, each of which has roughly the same amount of visible matter as the Milky Way (which is 1011 solar masses, i.e., 0.1 trillion Suns' mass). Thus we can conclude:

Question

BlackTom AI · Accepted Answer

The problem presents the observed motions requiring a total cluster mass of at least 10^14 solar masses, while the visible (luminous) matter amounts to roughly 100 galaxies × 10^11 solar masses ≈ 10^13 solar masses. This means the majority of the cluster’s mass cannot be seen directly.
Option a: Enhanced star formation inside the cluster galaxies is not what is implied by the mass discrepancy. The statement about dark matter is about the overall mass budget, not a statement about current star formation activity in member galaxies. So this is not the direct inference from the given masses.
Option b: The Big Bang must have occurred to account for the existence of this cluster. While the Big Bang is a broad cosmological framework, the specific calculation here does not hinge on invoking the Big Bang; it hinges on the mass discrepancy between total dynamical mass and visible mass. Thus this claim overstates what the data strictly imply about the origin event.
Option c: Around 90% of the cluster's mass is dark matter. Given total mass ≥ 10^14 M☉ and visible mass ≈ 10^13 M☉, the unseen mass is about 9×10^13 M☉, which is roughly 90% of the total. This directly follows from comparing dynamical mass to luminous mass and is the standard interpretation for such clusters.
Option d: The cluster is in a process of formation. The mass discrepancy alone does not necessarily indicate that the cluster is actively forming; it could be a mature bound system whose mass is dominated by dark matter. Without additional evidence of ongoing assembly, inferring active formation is not warranted.

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