Chandra’s Limit

A white dwarf accreting matter from a nearby companion star explodes as a Type Ia supernova when its mass reaches the Chandrasekhar Limit (credit: NASA)

A white dwarf accreting matter from a nearby companion star explodes as a Type Ia supernova when its mass reaches the Chandrasekhar Limit (credit: NASA)

Somehow in my younger days, in my haste to get out into the ‘real world’, I ended up spending five years in graduate school. Part of that time, in the summers, I studied and conducted research at the University of Chicago where I helped use laser systems to measure properties of molecules found in planetary atmospheres and the interstellar medium.

Chicago is one of the world’s great universities. Nearly 100 of its students and professors have won Nobel Prizes. But it’s not a particularly big place, so a chance sighting of a famous professor is not unusual. Still, I stopped in my tracks during my first week on campus when, on the way back to the lab from lunch, I passed on the sidewalk an older, slight man of Indian descent with thinning grey hair and alert eyes wearing a crisp white shirt and tie. I instantly recognized him as Subrahmanyan Chandrasekhar, more commonly known as Chandra, the discoverer of the Chandrasekhar Limit, winner of the 1983 Nobel Prize in Physics, and one of the most revered astrophysicists in the world.

Chandra discovered his eponymous limit when he was 19 years old while traveling on a ship from his native India to Cambridge to attend graduate school. The physics is a little hairy, but the basic idea of the Chandrasekhar Limit is not hard to understand. It’s simply a hard physical limit on the mass of a white dwarf star. A white dwarf is the end-stage of a mid-sized star, a dense, Earth-sized cinder left over after a star sheds its outer layers as a planetary nebula. A white dwarf is held up against the force of gravity by the pressure of electrons, charged particles which have an inherent resistance against being squeezed together.

But Chandra discovered this electron resistance has a limit. If the mass of a white dwarf exceeds 1.4 times the mass of our Sun, then the star will collapse into a smaller remnant called a neutron star, or possibly into to a single massive point with no dimensions and infinite density. We now call this a black hole.

A star collapsing to a single point was a radical idea in the 1930s. So Chandra’s ideas were challenged by some, including the great Arthur Eddington, who knew about the possibility of black holes but refused to believe they could exist. In 1935, Eddington publicly ridiculed Chandrasekhar’s work. The encounter rattled the young Chandra. He suspected a racial motivation to Eddington’s tirade, and began to seek a position outside the United Kingdom.

Subrahmanyan Chandrasekhar (1910-1995)

Subrahmanyan Chandrasekhar (1910-1995)

In 1937, Chandrasekhar was recruited by the upstart University of Chicago and its associated Yerkes Observatory. He remained there for the rest of his life. He worked in several fields of mathematical physics in a methodical manner that few have the patience for anymore. He focused on each field for a decade or more, developing the mathematical framework for theories of stellar structure, stellar dynamics, black holes, and radiative transfer, among others. When he felt he mastered a subject, he compiled his work into a treatise, and moved on to the next subject. His work was marked by rigorous and systematic thought and elegant solutions to complex mathematical equations.

He was also an attentive teacher and mentor to more than 50 Ph.D. students, many who became well known themselves. Carl Sagan, who was a student at the University of Chicago in the late 1950s, said “I discovered what true mathematical elegance is from Subrahmanyan Chandrasekhar.”

The Chandrasekhar Limit has important consequences in understanding the nature of the universe. Many white dwarfs are in binary star systems where they can take on additional mass from a close companion. When the mass of the white dwarf reaches the limit of 1.4 solar masses, it collapses and explodes as a Type Ia supernova, an enormously energetic event visible across million of light years. Because each white dwarf collapses at the same mass predicted by Chandrasekhar, it has approximately the same brightness. So it acts as a ‘standard candle’ that astronomers can use to measure distances to other galaxies. In the late 1990s, astronomers Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess used observations of these collapsing and exploding white dwarf stars to discover that the expansion of the universe is accelerating. They won the Nobel Prize in 2011.

The theoretical relationship for the Chandrasekhar Limit (credit: Wikipedia)

The theoretical relationship for the Chandrasekhar Limit (credit: Wikipedia)

Chandra continued his research and kept an office at the university until his final days. He died suddenly in 1995 at the age of 84. So great was Chandra’s contribution to astrophysics, NASA named one of its great space-based observatories after him. The Chandra X-ray Observatory continues to make discoveries related to very hot regions of the universe such as exploded stars, clusters of galaxies, and matter spiraling into black holes.

In the last days of my first summer in Chicago, I gathered up my courage to knock on Chandra’s office door to speak with him and ask for an autograph of a new volume of his collected scientific papers. He was kind enough to ask me about my research, which he understood right away, and discuss other matters of laboratory astrophysics. He was a close colleague of the professor with whom I worked, so I met him a few more times over the years. These sorts of encounters stay with a young student for a long time.

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