Hayashi limit
Encyclopedia
Hayashi limit is a constraint upon the maximum radius
of a star
for a given mass
. When a star is fully within hydrostatic equilibrium
—a condition where the inward force of gravity is matched by the outward pressure
of the gas—then the star can not exceed the radius defined by the Hayashi limit. This has important implications for the evolution of a star, both during the formulative contraction period and later when the star has consumed most of its hydrogen supply through nuclear fusion
.
A Hertzsprung-Russell diagram displays a plot of a star's surface temperature
against the luminosity
. On this diagram, the Hayashi limit forms a nearly vertical line at about 3,500 K. Low temperature stars are always fully convective, and models of stellar structure for fully convective stars do not provide a solution to the right of this line where a star is in equilibrium (with lower surface temperatures). Thus stars are constrained to remain to the left of this limit during all periods when they are in hydrostatic equilibrium, and the region to the right of the line forms a type of "forbidden zone". Note, however, that there are exceptions to the Hayashi limit. These include collapsing protostar
s, as well as stars with magnetic fields that interfere with the internal transport of energy through convection.
Red giant
s are stars that have expanded their outer envelope in order to support the nuclear fusion of helium. This moves them up and to the right on the H-R diagram. However, they are constrained by the Hayashi limit not to expand beyond a certain radius.
The Hayashi limit is named after Chūshirō Hayashi
, a
Japan
ese astrophysicist.
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
of a star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
for a given mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
. When a star is fully within 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...
—a condition where the inward force of gravity is matched by the outward pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
of the gas—then the star can not exceed the radius defined by the Hayashi limit. This has important implications for the evolution of a star, both during the formulative contraction period and later when the star has consumed most of its hydrogen supply through nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
.
A Hertzsprung-Russell diagram displays a plot of a star's surface temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
against the luminosity
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...
. On this diagram, the Hayashi limit forms a nearly vertical line at about 3,500 K. Low temperature stars are always fully convective, and models of stellar structure for fully convective stars do not provide a solution to the right of this line where a star is in equilibrium (with lower surface temperatures). Thus stars are constrained to remain to the left of this limit during all periods when they are in hydrostatic equilibrium, and the region to the right of the line forms a type of "forbidden zone". Note, however, that there are exceptions to the Hayashi limit. These include collapsing protostar
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, as well as stars with magnetic fields that interfere with the internal transport of energy through convection.
Red giant
Red giant
A red giant is a luminous giant star of low or intermediate mass in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius immense and the surface temperature low, somewhere from 5,000 K and lower...
s are stars that have expanded their outer envelope in order to support the nuclear fusion of helium. This moves them up and to the right on the H-R diagram. However, they are constrained by the Hayashi limit not to expand beyond a certain radius.
The Hayashi limit is named after 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...
, a
Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese astrophysicist.