Editing Hadean Eon (section)

==== Gravitational Collapse ====
The accumulation of gas, dust, and plasma in the ISM can reach a threshold where gravitational forces overcome internal pressure, leading to collapse and the formation of new stars; this is called '''gravitational collapse'''. This process is influenced by the density and temperature of the cloud, as well as external factors such as shock waves from nearby supernovas; it relates to the '''Jeans instability criterion''', which describes the conditions under which a cloud will begin to collapse under its own gravity.

* <u>Jeans Mass</u>: The minimum mass that a cloud must have for gravitational forces to overcome internal pressure and initiate collapse. If a cloud's mass is greater, it is considered gravitationally unstable and likely to collapse to form stars. The internal '''thermal energy''' of a cloud provides the outward pressure needed to resist gravitational collapse. When a cloud's mass increases (holding temperature constant), its gravitational attraction becomes stronger, making it more difficult for the thermal pressure to resist collapse. Conversely, if the cloud can lose thermal energy (cool down), the reduced     pressure makes it easier for gravity to dominate, leading to collapse. During the collapse, gravitational potential energy is converted into kinetic energy (heat) as particles accelerate toward the cloud's center. This heat must be radiated away for the collapse to proceed; otherwise, it would increase the internal pressure and add resistance to further collapse.
* <u>Jeans Radius</u> (or Jeans Length): The critical radius of a cloud at which it becomes gravitationally unstable, and prone to collapse. It essentially marks     the minimum size that a cloud must have, given its mass and temperature, for gravity to overcome the internal gas pressure and initiate collapse. Efficient cooling mechanisms (such as radiation from dust and stable molecules) lower the temperature, thereby decreasing the Jeans radius. During collapse, a cloud can fragment into smaller pieces, each potentially with its own Jeans radius based on its local conditions (mass, temperature, density). This '''fragmentation''' can lead to the formation of multiple stars or a star system, rather than a single monolithic star. This also enhances the cloud's instability by making it easier for any portions that exceed this reduced Jeans radius to collapse into star formation.

When a molecular cloud reaches the Jeans instability criterion, several key processes unfold, leading to star formation. The specific timeframe for these processes can vary widely depending on the initial conditions of the cloud, such as its mass, temperature, and composition. During the <u>Free-fall Phase</u>, the cloud contracts, and the density increases, particularly at the center. For a '''solar-mass''' star, the initial collapse from a diffuse cloud to a denser core might take about 100,000 years; a relatively short period compared to the total lifetime of a star.

As the cloud collapses, it may fragment into smaller clumps due to variations in density. Each clump, containing a few solar masses of material, can potentially form a star or a star system; this fragmentation is critical in determining the initial mass function of stars (the distribution of stellar masses at birth). The collapsing material forms a '''protostar''' at the center of each clump; the material from the surrounding cloud continues to '''accrete''' onto it, increasing its mass and temperature. For a solar-mass star, the <u>Accretion Phase</u> might last around 100,000 to several million years.

Protostars often exhibit powerful outflows and '''jets''', which help to remove '''angular momentum''' and allow accretion to continue. These outflows can impact the surrounding cloud, influencing further star formation. As the core of the protostar becomes increasingly dense and hot (reaching about 10 million Kelvin for a star like Sol), hydrogen nuclei begin to fuse into helium''',''' releasing energy through nuclear fusion. This marks the birth of a star and its entry into the '''main sequence''' phase of its life. The outward pressure from nuclear fusion balances the inward pull of gravity, stabilizing the star; it will remain in the main sequence phase for the majority of its lifetime, converting hydrogen to helium in its core. For the <u>Sun</u>, this phase will last about 10 billion years (which gives it something close to 6 billion years of life left).