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: where E is unitless, and not the energy. Modelling stars as polytropes with index 3/2—in other words, assuming they follow a pressure-density relationship of —he found that E=45 is the maximum for a quasistatic star. If a star is not contracting rapidly, E=45 defines a curve on the HR diagram, to the right of which the star cannot exist. He then computed the evolutionary tracks and isochrones (luminosity-temperature distributions of stars at a given age) for a variety of stellar masses and noted that NGC2264, a very young star cluster, fits the isochrones well. In particular, he calculated much lower ages for solar-type stars in NGC2264 and predicted that these stars were rapidly contracting T Tauri stars. In 1962, Hayashi published a 183-page review of stellar evolution. Here, he discussed the evolution of stars born in the forbidden region. These stars rapidly contract due to gravity before settling to a quasistatic, fully convective state on the Hayashi tracks. 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. These standard PMS tracks can still be found in textbooks on stellar evolution. Forbidden zone 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, even those that are partially or fully radiative. Newborn protostars start out in this zone, but are not in hydrostatic equilibrium and will rapidly move towards the Hayashi track. Because stars emit light via black-body radiation, the power per unit surface area they emit is given by the Stefan–Boltzmann law: The star's luminosity is therefore given by: For a given L, a lower temperature implies a larger radius, and vice versa. Thus, the Hayashi track separates the HR diagram into two regions: the allowed region to the left, with high temperatures and smaller radii for each luminosity, and the forbidden region to the right, with lower temperatures and correspondingly higher radii. The Hayashi limit can refer to either the lower bound in temperature or the upper bound on radius defined by the Hayashi track. The region to the right is forbidden because it can be shown that a