The size and mass of a star are primarily determined by the conditions during its formation and the balance between gravitational forces trying to collapse the star and internal pressure forces resisting the collapse. Several factors contribute to the size and mass of a star:
1) Mass of the Proto stellar Cloud: Stars form from large, dense regions of interstellar gas and dust called molecular clouds. The mass of the initial cloud determines the mass of the star that forms within it. Larger clouds can give rise to more massive stars.
2) Angular Momentum: The conservation of angular momentum during the collapse of a proto stellar cloud can influence the size of the resulting star. As the cloud collapses, it begins to rotate faster due to the conservation of angular momentum. The rotation can lead to the formation of a proto stellar disk, and the star forms from the material within this disk.
3) Density of the Molecular Cloud: The density of the molecular cloud affects the rate at which material collapses to form a star. Higher density regions may collapse more rapidly, leading to the formation of more massive stars.
4) Temperature of the Molecular Cloud: The temperature of the molecular cloud determines the thermal pressure resisting gravitational collapse. Colder clouds may collapse more readily, leading to the formation of smaller stars, while warmer clouds might resist collapse, allowing for the formation of larger stars.
5) Competing Forces: The gravitational force pulls material inward, attempting to collapse the proto stellar cloud, while pressure forces (such as thermal pressure and radiation pressure from nuclear reactions in the core) push outward, resisting collapse. The balance between these forces determines the equilibrium state and size of the star.
6) Nuclear Fusion in the Core: The onset of nuclear fusion in the star's core also influences its size and mass. The core temperature and pressure need to reach a critical point for nuclear fusion to begin. The mass of the star determines the internal pressure, and more massive stars can sustain higher core temperatures and pressures.
As a general trend, more massive stars tend to be larger, hotter, and have shorter lifetimes compared to less massive stars. The relationship between mass, size, temperature, and lifetime is described by the stellar mass-luminosity relationship and the Hertzsprung-Russell diagram. Stars with masses similar to the Sun, for example, fall into the category of main-sequence stars and have a well-defined relationship between their mass and other characteristics.
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