2024-01-12 00:43:04
Introduction
The Chandrasekhar mass is the maximum mass that an object’s electronic degeneracy pressure can withstand without gravitational collapse. It occurs when matter accumulates around an object (Generally speaking, the word object (from the Latin objectum, 1361 ) designates an entity defined in…) made of degenerate matter (Matter is said to be degenerate when its density is high enough to…), such as a white dwarf (A white dwarf is a gaseous celestial object resulting from the evolution of a star of…) or a star core (A star is a celestial object emitting light autonomously, similar to a…) massive (The word massive can be used as :).
History
The limit was calculated in 1930 by the Indian physicist Subrahmanyan Chandrasekhar (October 19, 1910 in Lahore, Punjab, British India – 21…) then aged 20 during a trip on a liner. passenger transport. The name comes from…) to Bombay. Chandrasekhar discovered that Eddington and Fowler had forgotten to take into account the effects of relativity in their calculations. Eddington opposed Chandrasekhar for a long time to such an extent (Graphic) that in 1939 he wrote a book concerning the structure of stars which definitively closed the question.
Applications
The Chandrasekhar mass is involved in the origin of type I and type II supernovae.
Woman blanche
A white dwarf, the remains of a star following the outer layers have been blown away, is a star formed of degenerate matter, housing a mass ( The term mass is used to designate two quantities attached to a…) of the order of that of the Sun (The Sun (Sol in Latin, Helios or Ήλιος in Greek) is the star…) in a sphere ( In mathematics, and more precisely in Euclidean geometry, a…) with a radius of the order of that of the Earth (The Earth is the third planet in the Solar System in order of distance…). Hence a very high density. For a white dwarf composed of carbon (Carbon is a chemical element of the crystallogen family, with symbol C,…) and oxygen (Oxygen is a chemical element of the chalcogen family, of… ), the mass of Chandrasekhar amounts to 1.44 times the mass of the Sun, or 2.9.10³⁰ kg. At the end of the evolution of a star, a white dwarf has a mass well below the Chandrasekhar mass (less than one solar mass), but can accumulate matter, which happens in particular if another star orbit (In celestial mechanics, an orbit is the trajectory that a body draws in space…) near it. As its mass increases, its radius decreases until, near Chandrasekhar’s mass, gravitational contraction and episodes of novae have sufficiently heated the interior of the star for fusion to begin (In physics and metallurgy , fusion is the transition of a body from the solid state to the state…) of carbon. When the reaction begins, the increase in temperature (The temperature is a physical quantity measured using a thermometer and…) inside the star is isochoric (The transformation of a system (which can be solid, liquid, gaseous,…) is called isochoric if…) because of degeneracy (independence of temperature from pressure). As the reaction is very strongly dependent on temperature, it runs out of control and the energy released exceeds the energy gravitational binding of the white dwarf. The latter becomes a supernova (A supernova is the set of phenomena resulting from the explosion of a…) of type Ia, explosion (An explosion is the rapid transformation of a matter into another matter having a… .) which sees the white dwarf completely disappear, leaving only a cloud (A cloud is a large quantity of water droplets (or crystals of ice) in…) hot expanding gas.
Heart of a massive star
Stars with a mass greater than 12 solar masses are hot enough for thermonuclear fusion reactions to lead to the formation of nickel-56 by fusion of silicon (Silicon is a chemical element of the crystallogen family, with the symbol Si.. .). When the central silicon has been completely transformed into iron and into nickel 56 there remains a core of nickel 56 (Nickel 56 , denoted 56Ni, is the isotope of nickel whose mass number is equal to…) and inert iron (Inert is the state of doing little or nothing.) surrounded by a layer of silicon always in reaction. The inert nucleus contracts until it reaches the pressure of electron degeneration, and constitutes a degenerate body whose Chandrasekhar mass is approximately 1.2 solar masses (In astrophysics, solar mass is the unit of mass conventionally used for…). The fusion of silicon continues to provide nickel (Nickel is a chemical element, symbol Ni and atomic number 28.), which is deposited on the body and becomes degenerate in turn. When the accumulated mass exceeds the Chandrasekhar mass, gravitational collapse occurs and supernova begins, leaving a neutron star with a diameter (In a circle or sphere, the diameter is a line segment passing through the center. ..) of a few tens of kilometers (The meter (symbol m, from the Greek metron, measurement) is the basic unit of length of the System…) and containing at least 1.5 times the mass of the sun.
Physique
The physics discussed below mainly concerns electronic degeneracy.
Properties of degenerate matter
Matter is said to be degenerate when its density and its “low” temperature cause the fermions (mainly electrons) to occupy levels of energy higher than what the Maxwell distribution predicts. This gives it particular properties, namely:
- very low compressibility at constant mass;
- pressure and density almost independent of temperature;
- very high thermal conductivity.
Bodies composed of degenerate matter are always very massive (of the order of 10³⁰ kg) and self-gravitating, because considerable confinement is necessary to maintain this matter. For example, the matter making up the surface of a white dwarf has a density of around a million (A million (1,000 000) is the natural number that follows nine hundred and ninety-nine…) times that of water (Water is a chemical compound ubiquitous on Earth, essential for all…) , at a temperature of several hundred thousand degrees. Extracted from the intense confinement and placed in a more familiar environment, this material would explode and dilute very quickly.
Equation of state
Mass-radius relationship of a white dwarf (red curve). We actually observe that when the radius of the star decreases, the mass tends towards a limit of 1.44 solar masses. The green and blue curves represent the cases of a polytrope γ=5/3 and γ=4/3. The points magenta, cyan (Cyan (from the Greek kuanos, namely azurite) is a pure color of light of length…) and yellow (There are (at least) five definitions of yellow which designate roughly the same…) represent the coordinates of the stars Sirius (Sirius is the main star of the constellation Canis Major. Seen from Earth, Sirius is…) B, Stein 2051 and 40 Eri B.
The equations of state are quite easy to calculate for gases assumed to be highly degenerate and either non-relativistic or ultra-relativistic. For a highly degenerate non-relativistic gas, the state equation is written as . For a massive body, solving the hydrostatic equation gives a polytrope of index 3/2 whose radius is proportional to the inverse (In mathematics, the inverse of an element x of a set provided with a law of…) of the cube (In Euclidean geometry, a cube is a prism of which all faces are square….) of the mass. For an ultra-relativistic gas (near the Chandrasekhar limit), the equation of state becomes , which corresponds to a polytrope of index 3. Solving the hydrostatic equation for such a polytrope shows that the mass of the object considered is necessarily less than a limiting mass. It is this limiting mass which is called the Chandrasekhar mass. For a complete relativistic treatment, an interpolation between the two equations must be made. The figure opposite shows the radius of a white dwarf as a function of its mass.
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