Chandrasekhar limit

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The Chandrasekhar limit is an upper bound on the mass of bodies made from electron-degenerate matter, a dense form of matter which consists of nuclei immersed in a gas of electrons. The limit is the maximum nonrotating mass which can be supported against gravitational collapse by electron degeneracy pressure. It is named after the Indian astrophysicist Subrahmanyan Chandrasekhar, and is commonly given as being about 1.4[1][2] solar masses. As white dwarfs are composed of electron-degenerate matter, no nonrotating white dwarf can be heavier than the Chandrasekhar limit. The Chandrasekhar limit is analogous to the Tolman–Oppenheimer–Volkoff limit for neutron stars.

Stars produce energy through nuclear fusion, producing heavier elements from lighter ones. The heat generated from these reactions prevents gravitational collapse of the star. Over time, the star builds up a central core which consists of elements which the temperature at the center of the star is not sufficient to fuse. For main-sequence stars with a mass below approximately 8 solar masses, the mass of this core will remain below the Chandrasekhar limit, and they will eventually lose mass (as planetary nebulae) until only the core, which becomes a white dwarf, remains. Stars with higher mass will develop a degenerate core whose mass will grow until it exceeds the limit. At this point the star will explode in a core-collapse supernova, leaving behind either a neutron star or a black hole.[3][4][5]

Computed values for the limit will vary depending on the approximations used, the nuclear composition of the mass, and the temperature.[6] Chandrasekhar[7], eq. (36),[8], eq. (58),[9], eq. (43) gives a value of:

Here, μe is the average molecular weight per electron, mH is the mass of the hydrogen atom, and \omega_3^0 \approx 2.018236 is a constant connected with the solution to the Lane-Emden equation. Numerically, this value is approximately (2/μe)2 · 2.85 · 1030 kg, or 1.43 (2/μe)2 M, where M=1.989·1030 kg is the standard solar mass.[10] As \sqrt{\hbar c/G} is the Planck mass, MPl≈2.176·10−8 kg, the limit is of the order of \frac{M_{Pl}^3}{m_H^2}.

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