Subrahmanyan Chandrasekhar Worked Out the Mass Limit for White Dwarf Stars at 19 on a 1930 Voyage From Bombay, Shared the 1983 Nobel Prize in Physics, and Has a NASA X-ray Observatory Named for Him

Subrahmanyan Chandrasekhar left Bombay on 31 July 1930, aged 19, on a Government of India scholarship to study at Cambridge, and finished a calculation during the voyage that set a maximum mass for white dwarf stars. That ceiling is now the Chandrasekhar limit, about 1.4 times the mass of the Sun. A share of the 1983 Nobel Prize in Physics went to him, and NASA’s flagship X-ray telescope, launched in 1999, is called the Chandra X-ray Observatory in his honour.

A Madras student who read Sommerfeld

Born in 1910 in Lahore, then part of British India, he was the third of ten children and the eldest son. Chandrasekhara Subrahmanya Ayyar, his father, worked in the Indian Audits and Accounts Department, and Sita, his mother, translated Ibsen’s A Doll House into Tamil. The family settled in Madras in 1918.

At Presidency College from 1925, he took a physics honours degree in June 1930. Eugene Parker, a University of Chicago colleague, writes in the National Academy of Sciences memoir that Chandrasekhar chose physics as a compromise with a father who wanted him in the Civil Service, and that Ramanujan inspired him. Meanwhile his uncle CV Raman won the Nobel Prize in Physics in 1930, the year Chandrasekhar left.

When Arnold Sommerfeld lectured at the college in the autumn of 1928, the student learned from him that new quantum statistics had replaced the old ones. A paper on Compton scattering followed, sent to R H Fowler at Cambridge in January 1929 and passed by Fowler to the Royal Society. Meghnad Saha invited the young author to Allahabad to discuss it, Parker says. Early in 1930 the Government of India offered a scholarship for three years in England, and Chandrasekhar asked to work under Fowler.

The calculation on the ship

According to Parker, the ship left Bombay on 31 July 1930 for Venice, and Chandrasekhar went on by rail to reach London on 19 August. Freeman Dyson names the vessel as the Pilsna, a Lloyd Triestino steamer.

In 1926 Fowler had used the new statistics to explain white dwarfs, the dense, fading remnants of stars like the Sun, each packing about a Sun’s mass into a ball the size of the Earth. Inside one, the electrons are squeezed so closely that quantum rules stop them being packed any tighter, and that resistance holds the star up against its own gravity. Slow-moving electrons were Fowler’s assumption. Chandrasekhar redid the sum with the electrons obeying Einstein’s special relativity, since at such densities they move at close to the speed of light.

That alters how the pressure responds when the star shrinks. In Parker’s explanation, the relativistic gas follows an exponent of 4/3 where Fowler’s gas had 5/3, and with 4/3 the pressure supporting the star grows no faster than gravity as the star contracts. Above a certain mass nothing stops the collapse. Dyson writes that the student finished the calculation before reaching England and never doubted the conclusion.

The resulting note in the Astrophysical Journal is signed from Trinity College, Cambridge, on 12 November 1930 and appeared in volume 74 in 1931. There it gave 0.91 of the Sun’s mass as the maximum for an ideal white dwarf, using a molecular weight of 2.5 for fully ionised material, and compared it with an earlier estimate by E C Stoner that assumed a star of uniform density. The Nobel Foundation lists a second paper, “The highly collapsed configurations of a stellar mass”, in the Monthly Notices of the Royal Astronomical Society in 1931. Dyson writes that Fowler was friendly but unconvinced, so Chandrasekhar sent the short version to the American journal without waiting for his approval.

Cambridge, January 1935

A PhD followed in the summer of 1933, along with a Prize Fellowship at Trinity College from that October to 1937. After a month in the Soviet Union in 1934, where the astronomer Viktor Ambartsumian urged him to work the problem out exactly, he built a full numerical solution on a hand calculator and finished it by the end of 1934, according to Parker.

The Royal Astronomical Society’s January 1935 meeting in London was where he presented it. Eddington, who had been dropping by his room through the autumn, asked the society’s secretary to give the paper double the usual time and arranged to speak straight after it, under the title “Relativistic degeneracy”. Parker, citing William McCrea’s obituary of Chandrasekhar, says Eddington began by agreeing that the calculation was correct for a relativistic electron gas, then argued that stars do not behave that way and that the result showed the theory itself to be wrong. MacTutor quotes him saying there should be “a law of Nature to prevent a star from behaving in this absurd way”.

Pauli, Dirac and other physicists of Chandrasekhar’s generation thought Eddington’s claims nonsense, Parker writes. MacTutor adds that Niels Bohr’s circle and Pauli agreed with Chandrasekhar’s papers but declined to join the argument, saying they were too busy. At the International Astronomical Union meeting in Paris in July 1935 Eddington spoke for an hour on the subject. Chandrasekhar recalled in a 1977 interview that he asked the chair, Henry Norris Russell, for a chance to reply and was told no.

Acceptance came gradually. In 1939 J Robert Oppenheimer and Hartland Snyder accepted that a cold star above the limit has no stable state and worked out what general relativity says happens next: the star falls inward without end, which Dyson identifies as a black hole. According to the University of Chicago Library’s finding aid, the limit was not fully accepted until more than 20 years after the opposition it drew. Chandrasekhar set out his theory in a textbook in 1939 and moved to other subjects. In one of his last interviews, the University of Chicago Magazine reports, he said that early fame from Eddington’s praise could have cost him the motivation to keep doing science.

Chicago, and seven fields in turn

On a visit to Harvard in early 1936, Chandrasekhar was offered a post by Otto Struve and the University of Chicago’s president, Robert Maynard Hutchins. He joined the faculty in January 1937. In September 1936 he had married Lalitha Doraiswamy, a Presidency College classmate, in India. The couple became United States citizens in 1953.

Seven periods make up his career in the Nobel Foundation’s biography, each ending in a book: stellar structure including white dwarfs (1929 to 1939), stellar dynamics (1938 to 1943), radiative transfer (1943 to 1950), hydrodynamic and hydromagnetic stability (1952 to 1961), ellipsoidal figures of equilibrium (1961 to 1968), general relativity (1962 to 1971) and the mathematical theory of black holes (1974 to 1983). From 1952 to 1971 he edited the Astrophysical Journal, and he supervised at least 46 doctoral students.

One episode from 1938 appears in Parker’s memoir. The dean of physical sciences vetoed Chandrasekhar’s part in a campus astronomy course, evidently on grounds of skin colour. Hutchins overruled him: “By all means have Mr. Chandrasekhar teach.”

The 1983 Nobel Prize

The Royal Swedish Academy of Sciences announced the 1983 physics prize on 19 October 1983. One half went to Chandrasekhar “for his theoretical studies of the physical processes of importance to the structure and evolution of the stars”. The other half went to William A Fowler of Caltech, a different physicist from Chandrasekhar’s Cambridge supervisor R H Fowler, for work on the nuclear reactions that form the chemical elements. Its press release calls his study of white dwarf structure, done in his twenties, possibly his best-known achievement.

His Nobel Lecture followed on 8 December 1983. Parker notes that the prize honoured work done fifty years earlier, and that Chandrasekhar’s later work on radiative transfer, stellar dynamics, plasmas, fluid stability and gravitation together made a larger contribution than the mass limit.

Other honours include election to the Royal Society in 1944, the Bruce Medal in 1952, the Royal Astronomical Society’s Gold Medal in 1953 and the United States National Medal of Science. The University of Chicago Library’s finding aid lists the Padma Vibhushan of India among them, and the University of Chicago Magazine counts 20 honorary degrees and membership of 21 learned societies. Newton’s Principia for the Common Reader, his last book, came out in 1995. Chandrasekhar died in Chicago on 21 August 1995.

What the limit explains now

In the Nobel Lecture, Chandrasekhar noted that the pulsars with reliable mass estimates were consistently close to 1.4 solar masses. The same number appears in the exploding stars called Type Ia supernovae, which NASA’s HEASARC describes as the death of a white dwarf pushed over the limit. That would make them dependable standard candles, bulbs of known brightness for judging distance.

In 2011 the Nobel Prize in Physics went to Saul Perlmutter, Brian Schmidt and Adam Riess for discovering from distant supernovae that the expansion of the universe is accelerating, and the Nobel Foundation says the two teams used Type Ia supernovae. A 2014 analysis, described by Lawrence Berkeley National Laboratory, found that most such white dwarfs sit near or slightly below the limit, with about one percent above it, so how each one reaches the explosion is still being worked out.

Black holes, the subject of his 1983 book The Mathematical Theory of Black Holes, are now detected and imaged. The University of Chicago Magazine points to the 2015 gravitational-wave detection by LIGO (how detectors hear collisions) and to the pictures released by the Event Horizon Telescope (the first black hole image).

A telescope named Chandra

NASA renamed its Advanced X-ray Astrophysics Facility the Chandra X-ray Observatory on 21 December 1998. A public contest with more than 6,000 entries from 50 US states and 61 countries produced the name. NASA’s release says he was known to the world as Chandra, and gives the Sanskrit meaning of the word as “moon” or “luminous”. Martin Rees, Britain’s Astronomer Royal, said Chandrasekhar had “probably thought longer and deeper about our universe than anyone since Einstein”.

Columbia, a Space Shuttle, carried the observatory into orbit on 23 July 1999. Four nested mirrors focus X-rays onto detectors at the end of a 9.2-metre optical bench, and the orbit takes it as far as 139,000 kilometres from Earth, above the atmosphere that blocks X-rays. Operations run from the Smithsonian Astrophysical Observatory in Cambridge, Massachusetts.

Where the sources and historians differ

Birth date first: the Nobel Foundation and the University of Chicago Library give 19 October 1910, and Parker’s memoir says 13 October.

What the star is made of sets the limit’s value. The 1931 paper gave 0.91 solar masses on a molecular weight of 2.5. MacTutor says that after the weight was revised to 2.0 the figure became 1.44. Dyson gives about 1.5 for stars that have burned all their hydrogen, and the Nobel Lecture and NASA both use about 1.4.

Historians also read the aftermath of 1935 differently. Arthur Miller, in his 2005 book Empire of the Stars, argues that Chandrasekhar never recovered from the encounter. Kameshwar Wali, who wrote the 1991 biography, replied in Physics Today in 2006 that Miller’s account of the discovery was overblown and inaccurate, and that Chandrasekhar did not have to fight for recognition that his physics was right. In the same issue D C V Mallik of the Indian Institute of Astrophysics quoted a letter Chandrasekhar wrote on 20 March 1935, two months after the meeting, saying that in Cambridge he got “the utmost sympathy and encouragement” for his work.

NASA’s 1998 release says Chandrasekhar and his wife immigrated to the United States in 1935. Parker and the Nobel Foundation put their arrival in Chicago at the end of 1936 or January 1937.