Hayashi track

Lore & Background

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. A few years prior, Osterbrock proposed deep convection zones with efficient convection, analyzing them using the opacity of H− ions (the dominant opacity source in cool atmospheres) in temperatures below 5000 K. However, the earliest numerical models of Sun-like stars did not follow up on this work and continued to assume radiative equilibrium. In his 1961 papers, Hayashi showed that the convective envelope of a star is determined by a parameter, and modelling stars as polytropes with index 3/2, he found that this parameter defines a curve on the HR diagram, to the right of which the star cannot exist. He then computed the evolutionary tracks and isochrones for a variety of stellar masses and noted that NGC2264, a very young star cluster, fits the isochrones well. In 1962, Hayashi published a 183-page review of stellar evolution, discussing the evolution of stars born in the forbidden region. In 1965, numerical models by Iben and Ezer & Cameron realistically simulated pre-main-sequence evolution, including the Henyey track that stars follow after leaving the Hayashi track.

Reader's Guide

The Hayashi track is a nearly vertical curve on the Hertzsprung–Russell diagram. Low-mass stars have nearly vertical evolution tracks until they arrive on the main sequence. For more-massive stars, the Hayashi track bends to the left into the Henyey track. Even more-massive stars are born directly onto the Henyey track. 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 H− ions. Stars less than 0.5 solar masses 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 solar masses develop a radiative zone prior to reaching the main sequence. Stars between 3 and 8 solar masses are fully radiative at the beginning of the pre-main-sequence. Even heavier stars appear to be born onto the main sequence, with limited observable PMS evolution. At the 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.

Did You Know?

• The Hayashi track is named after Japanese astrophysicist Chushiro Hayashi (1920-2010).
• The forbidden zone is the region on the HR diagram to the right of the Hayashi track where no star can be in hydrostatic equilibrium.
• Newborn protostars start out in the forbidden zone and rapidly move towards the Hayashi track.
• Stars on the Hayashi track are nearly fully convective and have their opacity dominated by H− ions.