Subrahmanyan chandrasekhar

project on s. chandrashekar

1. INDIAN SCHOOL DARSAIT Submitted to :- Jayalakshmi Submitted by :- Sonu.S.S Class :-11.B Physics Project Topic:- Famous Scientist and his major contributions

2. INDEX Sl. No Topic Page no 1 Pertaining to the scientist 1 2 Chandrasekhar’s works 2 3 Chandrasekhar’s most notable work 3 4 Chandrasekhar’s Legacy 4 5 List of notable awards 5 6 The Chandrasekhar Limit 6 7 According to the limit 7

3. INDEX Sl. No Topic Page no 8 Limit according to Physics 8 9 Calculated values for the limit 9 10 Limit value calculation formula 10 11 Application of limit 12 12 Super Chandrasekhar mass supernovae 14 13 Tolman-Oppenheimer-Volkoff limit 15 14 Conclusions 16 15 Bibliography 17

4. Subrahmanyan Chandrasekhar 1910 –1995 Indian-American  astrophysicist Nobel Prize Winner

5. Pertaining to the scientist Subrahmanyan Chandrasekhar (October 19, 1910 – August 21, 1995) was an Indian-American astrophysicist who, with William A. Fowler, was awarded the 1983 Nobel Prize for Physics for his mathematical theory of black holes, which was a key discovery that led to the currently accepted theory on the later evolutionary stages of massive stars. Chandrasekhar was the nephew of Sir Chandrasekhara Venkata Raman, who was awarded the Nobel Prize for Physics in 1930. 1

6. Chandrasekhar’s works Chandrasekhar worked in various areas, including stellar structure, theory of white dwarfs, stellar dynamics, theory of radiative transfer, quantum theory of the negative ion of Hydrogen, hydrodynamic and hydro magnetic stability, equilibrium and the stability of ellipsoidal figures of equilibrium, general relativity, mathematical theory of black holes and theory of colliding gravitational waves. 2

7. Chandrasekhar's most notable work Chandrasekhar's most notable work was the astrophysical Chandrasekhar limit. The limit describes the maximum mass of a white dwarf star, ~1.44 solar masses, or equivalently, the minimum mass which must be exceeded for a star to ultimately collapse into a neutron star or black hole . The limit was first calculated by Chandrasekhar in 1930 during his maiden voyage from India to Cambridge, England for his graduate studies.  3

8. Chandrasekhar’s Legacy  In 1999, NASA named the third of its four "Great Observatories" after Chandrasekhar. The Chandra X-ray Observatory was launched and deployed by Space Shuttle  Columbia  on July 23, 1999. The Chandrasekhar number, an important dimensionless number of magneto hydrodynamics, is named after him. The asteroid 1958 Chandra is also named after Chandrasekhar. American astronomer Carl Sagan, who studied Mathematics under Chandrasekhar, at the University of Chicago, praised him in the book  The Demon-Haunted World : "I discovered what true mathematical elegance is from Subrahmanyan Chandrasekhar." 4

9. Award Year Fellow of the Royal Society 1944 Henry Norris Russell Lectureship 1949 Bruce Medal  1952 Gold Medal of the Royal Astronomical Society 1953 Rumford Prize of the American Academy of Arts and Sciences 1957 National Medal of Science, USA 1966 Award Year Padma Vibhushan 1968 Henry Draper Medal of the National Academy of Sciences 1971 Nobel Prize in Physics 1983 Copley Medal of the Royal Society 1984 Honorary Fellow of the International Academy of Science  1988 Gordon J. Laing Award  1989 List of notable awards 5

10. The Chandrasekhar limit  The  Chandrasekhar limit  is the maximum mass of a stable white dwarf star. The limit was first published by Wilhelm Anderson and E. C. Stoner, and was named after Subrahmanyan Chandrasekhar, the Indian-American astrophysicist who improved upon the accuracy of the calculation in 1930, at the age of 19. This limit was initially ignored by the community of scientists because such a limit would logically require the existence of black holes, which were considered a scientific impossibility at the time. The currently accepted value of the limit is about 1.39 M  ( 2.765 × 10 30  kg). 6

11. According to the limit White dwarfs, unlike main sequence stars, resist gravitational collapse primarily through electron degeneracy pressure, rather than thermal pressure. The Chandrasekhar limit is the mass above which electron degeneracy pressure in the star's core is insufficient to balance the star's own gravitational self-attraction. Consequently, white dwarfs with masses greater than the limit undergo further gravitational collapse, evolving into a different type of stellar remnant, such as a neutron star or black hole. Those with masses under the limit remain stable as white dwarfs 7

12. Limit according to physics Electron degeneracy pressure is a quantum-mechanical effect arising from the Pauli exclusion principle. Since electrons are fermions, no two electrons can be in the same state, so not all electrons can be in the minimum-energy level. Rather, electrons must occupy a band of energy levels. Compression of the electron gas increases the number of electrons in a given volume and raises the maximum energy level in the occupied band. Therefore, the energy of the electrons will increase upon compression, so pressure must be exerted on the electron gas to compress it, producing electron degeneracy pressure. With sufficient compression, electrons are forced into nuclei in the process of electron capture, relieving the pressure. 8

13. Calculated values for the limit Calculated values for the limit will vary depending on the nuclear composition of the mass. Chandrasekhar gives the limit’s expression, based on the equation of state for an ideal Fermi gas. 9

14. Limit value calculation formula 10

15. Limit value calculation formula where; w i s the reduced Planck constant c  is the speed of light G  is the gravitational constant  e   is the average molecular weight per electron, which depends upon the chemical composition of the star. m H is the mass of the hydrogen atom.  3 y 2.018236is a constant connected with the solution to the Lane-Emden equation. 11

16. Applications of the limit The core of a star is kept from collapsing by the heat generated by the fusion of nuclei of lighter elements into heavier ones. At various stages of stellar evolution, the nuclei required for this process will be exhausted, and the core will collapse, causing it to become denser and hotter. A critical situation arises when iron accumulates in the core, since iron nuclei are incapable of generating further energy through fusion. If the core becomes sufficiently dense, electron degeneracy pressure will play a significant part in stabilizing it against gravitational collapse. 12

17. Applications of the limit If a main-sequence star is not too massive less than approximately 8 solar masses, it will eventually shed enough mass to form a white dwarf having mass below the Chandrasekhar limit, which will consist of the former core of the star. For more massive stars, electron degeneracy pressure will not keep the iron core from collapsing to very great density, leading to formation of a neutron star, black hole, or, speculatively, a quark star.  During the collapse, neutrons are formed by the capture of electrons by protons in the process of electron capture, leading to the emission of neutrinos. The decrease in gravitational potential energy of the collapsing core releases a large amount of energy which is on the order of 10 46  joules (100 foes). Most of this energy is carried away by the emitted neutrinos. This process is believed to be responsible for supernovae of types Ib, Ic, and II. 13

18. Super-Chandrasekhar mass Supernovae In April 2003, the Supernova Legacy Survey observed a type Ia supernova, designated SNLS-03D3bb, in a galaxy approximately 4 billion light years away. According to a group of astronomers at the University of Toronto and elsewhere, the observations of this supernova are best explained by assuming that it arose from a white dwarf which grew to twice the mass of the Sun before exploding. They believe that the star, dubbed the "Champagne Supernova" by University of Oklahoma astronomer David R. Branch, may have been spinning so fast that centrifugal force allowed it to exceed the limit. Alternatively, the supernova may have resulted from the merger of two white dwarfs, so that the limit was only violated momentarily. Nevertheless, they point out that this observation poses a challenge to the use of type Ia supernovae as standard candles. 14

19. Tolman–Oppenheimer–Volkoff limit After a supernova explosion, a neutron star may be left behind. Like white dwarfs these objects are extremely compact and are supported by degeneracy pressure, but a neutron star is so massive and compressed that electrons and protons have combined to form neutrons, and the star is thus supported by neutron degeneracy pressure instead of electron degeneracy pressure. The limit of neutron degeneracy pressure, analogous to the Chandrasekhar limit, is known as the Tolman–Oppenheimer–Volkoff limit. 15

20. Conclusion Subrahmanyan Chandrasekhar was an Indian-American astrophysicist, best known for his work on the theoretical structure and evolution of stars, and particularly on the later evolutionary stages of massive stars and the calculation of the Chandrasekhar limit. He won the Nobel Prize in Physics shared with William Fowler in 1983 largely for this early work, although his research also covered many other areas within theoretical physics and astrophysics. he calculated the maximum non-rotating mass which can be supported against gravitational collapse by electron degeneracy pressure. This limit describes the maximum mass of a white dwarf star, or, alternatively, the minimum mass above which a star will ultimately collapse into a neutron star or a black hole, following a supernova event, rather than remaining as a white dwarf. His calculations revealed that this was approximately 1.44 solar masses. 16

21. Bibliography 17 scienceworld.wolfram.com en.wikipedia.org www.physicsoftheuniverse.com farside.ph.utexas.edu