Hayashi limit

The Hayashi track is a luminosity–temperature relationship obeyed by infant stars of less than 3 M_☉ in the pre-main-sequence phase (PMS phase) of stellar evolution. It is named after Japanese astrophysicist Chushiro Hayashi. On the Hertzsprung–Russell diagram, which plots luminosity against temperature, the track is a nearly vertical curve. After a protostar ends its phase of rapid contraction and becomes a T Tauri star, it is extremely luminous. The star continues to contract, but much more slowly. While slowly contracting, the star follows the Hayashi track downwards, becoming several times less luminous but staying at roughly the same surface temperature, until either a radiative zone develops, at which point the star starts following the Henyey track, or nuclear fusion begins, marking its entry onto the main sequence.

The shape and position of the Hayashi track on the Hertzsprung–Russell diagram depends on the star's mass and chemical composition. For solar-mass stars, the track lies at a temperature of roughly 4000 K. Stars on the track are nearly fully convective and have their opacity dominated by hydrogen ions. Stars less than 0.5 M_☉ are fully convective even on the main sequence, but their opacity begins to be dominated by Kramers' opacity law after nuclear fusion begins, thus moving them off the Hayashi track. Stars between 0.5 and 3 M_☉ develop a radiative zone prior to reaching the main sequence. Stars between 3 and 10 M_☉ are fully radiative at the beginning of the pre-main-sequence. Even heavier stars are born onto the main sequence, with no PMS evolution.

At an end of a low- or intermediate-mass star's life, the star follows an analogue of the Hayashi track, but in reverse—it increases in luminosity, expands, and stays at roughly the same temperature, eventually becoming a red giant.

In 1961, Professor Chushiro Hayashi published two papers that led to the concept of the pre-main-sequence and form the basis of the modern understanding of early stellar evolution. Hayashi realized that the existing model, in which stars are assumed to be in radiative equilibrium with no substantial convection zone, cannot explain the shape of the red giant branch. He therefore replaced the model by including the effects of thick convection zones on a star's interior.

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