Subrahmanyan Chandrasekhar and His Limit By: Cody Montague

Chandra's Birth Born: October 19, 1910 in Lahore, India (now part of Pakistan). First son of C. Subrahmanyan Ayyar and Sitalakshimi Balakrishman with six brothers and three sisters. He inherited his father's name Subrahmanyan and his grand- father's name Chandrasekhar which he also shares with his uncle.

Chandrasekhar: A Birth Right Chandra was the nephew of Sir Chandrasekhara Venkata Raman who won a Nobel Prize in Physics for discovering the change in wavelength of deflected light through a transparent solid. C. V. Raman was an accountant for the Indian Government, a professor of physics at the University of Calcutta, head of physics at the Institute of Science, director of Raman Research Institute, knighted, and more. Sir Chandrasekhara Venkata Raman

Living Up to His Name from the Start Chandra was homeschooled from the age of five along with some private tutoring specifically in physics and calculus until 1921 when he enrolled in the Hindu High School in Triplicane, India. For those of you doing the math that is the age of 11. After graduating at 15 he went on to Presidency College in Madras, India and graduated with a masters in physics in 1930 after publishing one of his more well known papers, "The Compton Scattering and the New Statistics." He then went to Trinity College in Cambridge, England to get his Ph. D. in astrophysics in 1933.

Notable Awards and Research In Chandra's words, "There have been seven periods in my life: stellar structure, including the theory of white dwarfs ( ); stellar dynamics, including the theory of Brownian motion ( ); the theory of radiative transfer, including the theory of stellar atmospheres and the quantum theory of the negative ion of hydrogen and the theory of planetary atmospheres, including the theory of the illumination and the polarization of the sunlit sky ( ); hydrodynamic and hydromagnetic stability, including the theory of the Rayleigh-Bénard convection ( ); the equilibrium and the stability of ellipsoidal figures of equilibrium, partly in collaboration with Norman R. Lebovitz ( ); the general theory of relativity and relativistic astrophysics ( ); and the mathematical theory of black holes ( )." Awards: National Medal of Science(1966), Dannie Heineman Prize for Mathematical Physics(1974), and the Nobel Prize in Physics(1983)

Nobel Prize in Physics Though Chandra did not like being awarded a prize in 1983 for something he did earlier in his life, this is arguably his most notable work. Awarded for his study of stellar structure and evolution. Narrowing this down to Chandrasekhar's limit for white dwarf stars to continue.

What is Chandrasekhar's Limit? First a white dwarf star is the final stage of a star between 0.07 and 1.4 solar masses which can appear any color but are much dimmer and smaller than a main sequence star and is supported by electron degeneracy (when an electron is forced into a higher energy level because of close proximity). Chandrasekhar's limit is the maximum theoretical mass possible for a stable white dwarf.

Electron Degeneracy Electron degeneracy does not depend on temperature, thus allowing the white dwarf to live on indefinitely, but the leftover radiation will eventually die out making it a black dwarf star. How does electron degeneracy work to sustain a stars size? Recall that electrons cannot occupy the same energy state as another electron and that the mass of a star has collapsed into something about the size of Earth. The atoms are close enough to consider the atom next to it's electrons as part of it's own. Thus some electrons are forced into a higher energy state stopping the star from collapsing any further. One could almost think of a white dwarf as a giant atom...almost.

Why have Chandrasekhar's Limit? White dwarf stars are odd because the more massive they are the smaller they become. This makes sense because there is a higher gravitational force pulling the star in closer but there is no real repulsive force increase. Let's say there was a two solar mass star that stopped burning, it would start to collapse like a solar mass star. However, it will hit a point where the pressure will erupt into a supernova. At what point will this occur? That is why we have Chandrasekhar's limit.

Brief Calculation of Chandrasekhar's Limit The total kinetic energy of the electron gas, K, is proportionate to the mass of the star, M, raised to the four-thirds. Thus when M becomes really large the electrons become relativistic. K can thus be found by an integral of the energies of each electron.This gives: A =in order for the white dwarf to maintain against gravity A/B>1 or M<Mc B= or more realistically(without assuming C=constant density)

And When the Limit is Exceeded? When a star exceeds that of 1.4 solar mass gravity takes over and the star implodes. This is partially due to an iron core that continues to burn without an energy source. Thus when all the mass hits a wall of neutrons(the only thing capable of stopping this amount of mass from continuing to implode) and explodes into a supernova. Two types: 1a as described above and 1b which is where a white dwarf steals from a nearby star.

A White Dwarf is Born Chandra did a lot in his lifetime as mentioned earlier(professor at Trinity College and Chicago University, national academy of science member, and his awards). Unfortunately he passed away on August 21, He will live on as what he studied, a white dwarf, for his limit of white dwarf mass.

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