The estimate of the age of the universe, currently believed to be around 13.7 billion years, is not solely determined from the intensity of light from the furthest stars. It is derived from a combination of different observations and measurements, including the cosmic microwave background radiation, the redshift of distant galaxies, and the measurements of the expansion rate of the universe.
The most important piece of evidence for the age of the universe comes from studying the cosmic microwave background (CMB) radiation. The CMB is the remnant radiation from the early stages of the universe, which was released about 380,000 years after the Big Bang. Detailed observations of the CMB, such as those made by the Planck satellite, provide valuable information about the composition and evolution of the universe. By analyzing the patterns and fluctuations in the CMB, scientists can estimate the age of the universe.
Regarding the formation of stars, black holes, and galaxies, these processes occurred over vast time scales, spanning billions of years. Shortly after the Big Bang, the universe was filled with a hot, dense soup of particles and radiation. As the universe expanded and cooled down, the first atoms formed, allowing light to travel freely. It took several hundred million years for the first stars to form within the early galaxies.
The formation of black holes is intimately tied to the evolution of massive stars. When massive stars run out of nuclear fuel, they undergo a supernova explosion, leaving behind either a neutron star or a black hole. This process generally takes millions to tens of millions of years, depending on the initial mass of the star.
Galaxies, on the other hand, formed through a combination of hierarchical growth and mergers of smaller structures over billions of years. Small structures, such as gas clouds and protogalaxies, gradually came together under the influence of gravity, forming larger galaxies. The precise timescale for galaxy formation can vary depending on the size and initial conditions of the structures involved.
While the timescales for the formation of stars, black holes, and galaxies may seem long compared to the age of the universe, it's important to remember that these processes occurred concurrently over vast cosmic timescales. The age of the universe represents the elapsed time since the Big Bang, and the formation and evolution of celestial objects within it are a result of complex astrophysical processes unfolding over billions of years.