. What evidence is there for the existence of dark matter in clusters of galaxies?

Gravitational lensing serves as a spectacular astrophysical phenomenon and a critical piece of evidence for the existence of dark matter. When a massive object, such as a galaxy cluster, lies between a distant source of light and an observer, it warps the fabric of spacetime around it. This bending causes the light from the source to take a curved path, resulting in multiple, distorted, or magnified images of the same celestial object.

For instance, if we observe a quasar—a very luminous and distant celestial object—its light may appear as an arc or ring around a galaxy cluster known as an 'Einstein ring.' By analyzing the distortion and the amount of bending of light, astronomers can estimate the mass of the galaxy cluster causing the effect. The surprising discovery that this mass is greater than what we can account for with visible matter alone strongly implies the presence of dark matter.

Considering a galaxy cluster as a cosmic dance hall with galaxies whirling around, velocity dispersion is the measurement of the spread in their speeds. The more mass present within the cluster, the faster the galaxies would need to move to resist being pulled together by gravity and to avoid colliding into a single structure. Astronomers can calculate this mass by observing the galaxies' velocities.

However, when the visible mass of galaxies and gas is tallied, it falls short of the total mass required to account for the observed velocities—the galaxies are moving too fast. This discrepancy suggests an additional, unseen mass within clusters exerting gravitational force, which is attributed to dark matter. Without its gravitational glue, galaxies would simply fling out of the cluster, much like a spinning carousel falling apart if the spins become too fast.

The Cosmic Microwave Background Radiation (CMBR) is the echo of the Big Bang—radiation that has cooled and stretched to microwave wavelengths as the universe has expanded. It provides a cosmic baby picture of our universe at about 380,000 years old. Detailed maps of the CMBR show slight temperature variations that correspond to regions of varying densities in the early universe.

These fluctuations, crucial for the formation of structures such as galaxies and galaxy clusters, are consistent with cold dark matter models. They signal that dark matter had to be present, influencing the distribution of matter and energy and shaping the very fabric of the cosmos from its infancy. The CMBR is like a cosmic tape measure, allowing us to infer the total amount of matter, including dark matter, throughout our universe.

Galaxy clusters are the largest gravitationally bound systems in the universe, containing not just galaxies but also large amounts of hot gas and potentially vast quantities of dark matter. They act as cosmic laboratories for studying dark matter since the gravitational effects at such large scales are pronounced.

The hot gas within them, observable via X-ray emissions, should be bound by the cluster's gravity. But interestingly, the mass of the gas and the galaxies combined is not enough to prevent the gas from escaping the cluster's pull. This implies there must be more to the cluster's mass—enter dark matter. It is hypothesized that dark matter makes up the bulk of the mass, invisibly enveloping the clusters, and ensuring that they remain coherent, gravitationally stable structures instead of dispersing into the cosmic expanse.