Hayashi track
Encyclopedia
The Hayashi track is a path taken by protostar
s in the Hertzsprung–Russell diagram
after the protostellar cloud has reached approximate hydrostatic equilibrium
. In 1961 Chūshirō Hayashi
showed that there is a minimum effective temperature
(equivalently, a boundary on the right-hand side of the H–R diagram) cooler than which hydrostatic equilibrium cannot be maintained; this boundary corresponds to a temperature around 4000 K
. Protostellar clouds cooler than this will contract and heat up until they reach the Hayashi boundary. Once at the boundary, a protostar will continue to contract on the Kelvin–Helmholtz timescale, but its effective temperature will no longer increase, as it will remain at the Hayashi boundary. Thus the Hayashi track is close to a vertical line on the H–R diagram. Stars at the Hayashi boundary are fully convective: this is because they are cool and highly opaque
, so that radiative energy transport is not efficient, and consequently have large internal temperature gradients. Stars with masses < 0.5 Solar mass
remain on the Hayashi track (i.e. are fully convective) throughout their pre–main sequence stage, joining the main sequence
at the bottom of the Hayashi track. For stars with masses > 0.5 Solar mass
the Hayashi track ends, and the Henyey track begins, when the internal temperature of the star rises high enough that its central opacity drops and radiative energy transport becomes more efficient than convective transport: the lowest luminosity on the Hayashi track for a star of a given mass is thus the lowest luminosity at which it is still fully convective.
The convection on the Hayashi track means that stars will reach the main sequence with a fairly homogeneous composition.
Protostar
A protostar is a large mass that forms by contraction out of the gas of a giant molecular cloud in the interstellar medium. The protostellar phase is an early stage in the process of star formation. For a one solar-mass star it lasts about 100,000 years...
s in the Hertzsprung–Russell diagram
Hertzsprung–Russell diagram
The Hertzsprung–Russell diagram is a scatter graph of stars showing the relationship between the stars' absolute magnitudes or luminosities versus their spectral types or classifications and effective temperatures. Hertzsprung–Russell diagrams are not pictures or maps of the locations of the stars...
after the protostellar cloud has reached approximate hydrostatic equilibrium
Hydrostatic equilibrium
Hydrostatic equilibrium or hydrostatic balance is the condition in fluid mechanics where a volume of a fluid is at rest or at constant velocity. This occurs when compression due to gravity is balanced by a pressure gradient force...
. In 1961 Chūshirō Hayashi
Chushiro Hayashi
was a Japanese astrophysicist. Hayashi tracks on the Hertzsprung-Russell diagram are named after him.He earned his B.Sc in physics at the Imperial University of Tokyo in 1942. He then worked as a research associate under Hideki Yukawa at Kyoto University...
showed that there is a minimum effective temperature
Effective temperature
The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation...
(equivalently, a boundary on the right-hand side of the H–R diagram) cooler than which hydrostatic equilibrium cannot be maintained; this boundary corresponds to a temperature around 4000 K
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
. Protostellar clouds cooler than this will contract and heat up until they reach the Hayashi boundary. Once at the boundary, a protostar will continue to contract on the Kelvin–Helmholtz timescale, but its effective temperature will no longer increase, as it will remain at the Hayashi boundary. Thus the Hayashi track is close to a vertical line on the H–R diagram. Stars at the Hayashi boundary are fully convective: this is because they are cool and highly opaque
Opacity (optics)
Opacity is the measure of impenetrability to electromagnetic or other kinds of radiation, especially visible light. In radiative transfer, it describes the absorption and scattering of radiation in a medium, such as a plasma, dielectric, shielding material, glass, etc...
, so that radiative energy transport is not efficient, and consequently have large internal temperature gradients. Stars with masses < 0.5 Solar mass
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
remain on the Hayashi track (i.e. are fully convective) throughout their pre–main sequence stage, joining the main sequence
Main sequence
The main sequence is a continuous and distinctive band of stars that appears on plots of stellar color versus brightness. These color-magnitude plots are known as Hertzsprung–Russell diagrams after their co-developers, Ejnar Hertzsprung and Henry Norris Russell...
at the bottom of the Hayashi track. For stars with masses > 0.5 Solar mass
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
the Hayashi track ends, and the Henyey track begins, when the internal temperature of the star rises high enough that its central opacity drops and radiative energy transport becomes more efficient than convective transport: the lowest luminosity on the Hayashi track for a star of a given mass is thus the lowest luminosity at which it is still fully convective.
The convection on the Hayashi track means that stars will reach the main sequence with a fairly homogeneous composition.