The Man who “Dwarfed” the Stars:
“CHANDRA” (Subrahmanyan
Chandrasekhar)
_________________________________________________________________________
by
Dr. Dipanjan MITRA,
Astrophysicist,
National Centre for Radio
Astrophysics,
Tata Institute of Fundamental
Research,
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Acknowledgement: Major parts of this article are compilations made
after
reading the two sources of reference given in the notes and bibliography
section.
I would like to thank my wife Anindita Mitra for her help in compiling
the bibliography of S. Chandrasekhar, adapted
from one of the reference works [2].
{For specialised terminology used in this article, please consult the
“glossary” given at the end of this article. The next volume of The Asianists’ Asia will carry a complete bibliography of
Professor S. Chandra’s articles and books by Dr. and Mrs. Dipanjan MITRA, work
on which has already begun. Editor.}
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Professor Subrahmanyan Chandrasekhar (more popularly known as Chandra) was
undoubtedly one of the greatest scientists of the 20th Century.
Already at 18, Chandra stepped into the international scientific scene, and
ever since has pursued an impeccably illustrious scientific career until his
death at the ripe old age of 85. He was a talented scientist, endowed with outstanding
mathematical skills, and imbued with a passion for science and a distinct style
of work ethic. His works span a vast range of subjects, and in each of these areas,
he displayed total mastery.
Chandrasekhar was born into a cultured Brahmin
Tamil family. He graduated at the age of
18 from
Further, Chandra became aware of the newly discovered
Fermi Dirac statistics from Professor Arnold Sommerfeld who happened
to be visiting
In 1930, he went to
Chandra, in keeping with his particular tastes,
skills, and temperament, chose a scientific area of research which he pursued
to its depths. He liked to be precise in his work. Using his fantastic
mathematical gifts and his ability to sustain reflection for long periods at a
time, he would carefully build up the subject of his research. He published his
works at regular intervals in scientific journals, and after a few years of
having felt that he had understood the subject well enough, he would write a
book on the subject, and then he would move on to another field of research. Each
of his books is a classic today and is used as text books by most professional
astrophysicists. It is however quite impossible
to write a short essay covering Chandra's immense body of work and do justice to the genius who authored it. It would require a
whole volume. In any case, here we will first try to summarize the various
fields of Chandra's research in chronological order, and then discuss in greater
detail his work on White Dwarfs
which fetched him the Noble Prize, jointly
with Professor Fowler, in 1983.
Chandrasekhar's scientific career shows a
pattern of eight distinct periods.
He started his career in 1929 in an effort to understand the physics of stars
and continued this phase until 1939. His contribution to stellar physics during
this period is monumental. He developed
the fundamental basis for relativistic astrophysics which led to the prediction
of neutron stars and black holes. Around 1939, he summarized all his
results in a book: An Introduction to the Study of Stellar Structure.
By this time Chandra had left
One of Chandra’s favourite areas of research was radiative transfer, and he devoted the
period: 1943-1950 to investigating this domain. He used elegant techniques to
investigate difficult problems on planetary
and stellar atmospheres. These were problems of classical physics posing
extremely difficult mathematics, and only someone with Chandra's mathematical gifts
could have addressed these problems. During this period, he also contributed to
the theory of negative ion of hydrogen.
As usual he wrote a book: Radiative Transfer, in 1950.
Chandra continued to look at problems which posed
exciting challenges in astrophysics.
This led him to tackle the area of magneto hydrodynamics. He worked in the
area of turbulence, Galactic magnetic field and its generation,
and the theory of collisionless
plasma. His classic monograph, "Hydrodynamic and Hydromagnetic Stability",
published
in 1961, is a summary of his monumental
contribution to this subject.
Next, motivated by the mathematical beauty of
the subject, Chandra spent the period from
1961 to 1968 working on virial methods and classical ellipsoids. Here, he played
the role of resurrecting this subject which he
pointed out had been largely neglected.
As a responsible scientist he compiled his work
in a book, entitled: Ellipsoidal Figures of
Equilibrium, in 1969. Chandra is known to have shown some
impatience during this period.
He wanted to go back to the problem of relativistic astrophysics which he left
during the 1930s. This was quite natural as
several of his theories which promoted
reflection on neutron stars were being re-discovered.
He devoted the next years of his
life to studying another important scientific
problem, the stability of black holes.
Around 1983, Chandra wrote the classic work:
The Mathematical Theory of Black Holes.
He was over 70 years at that time, but with unabated enthusiasm, he continued
to work on the theory of colliding
gravitational waves and non-radial perturbations of relativistic stars during
the period 1983-1995.
Chandra’s last book was on Newton's Principia.
Chandra also finished the book, entitled: Newton's Principia for the Common Reader,
which was published only a few weeks before he passed away.
Professor Chandrasekhar was an extremely
eminent and responsible scientist. He was highly productive throughout his
life. From his work a pattern seems to emerge. He started his work
on relativistic
stars. He moved on to other areas of research in order to educate himself.
His standards were high, and as a result all his books remain as masterpieces
with us. He returned to the subject of stellar
black holes towards the last stage of his career. By that time, he had
perfected and equipped himself with all manner of skills to address seminal
problems in black hole physics. His
comeback coincided with a time when many more eminent young researchers were
working on the black hole problem. Chandra was thrilled to work with this highly
gifted group of youngsters.
Professor Chandrasekhar's work on Stellar Physics
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The field of Astrophysics started with the
study of stellar objects. Yet for centuries it remained a mystery as to why
stars are the way they are. The first important clue towards understanding them
came from the observation of the absorption of Fraunhoffer spectral lines from the sun which were identified from the
atomic species present in the sun. This fundamental discovery prefaced the unveiling
of the physical constituents of a star. The star was understood to be a gaseous
ball made up of atoms as well as ionized
plasma (electrons and protons) and which was able to produce its own
light. Understanding the physical
constituents of stars became an exciting research area in the early part of the
20th century. The newly
discovered science of quantum mechanics therefore found instant application on stars. Here
let us digress a bit to actually understand what one was
trying to understand about stars.
Stars are mostly observed using an optical
telescope. They are formed through gravitational collapse of a huge cloud of
material and eventually shine as they have the ability to produce their own
light. The data obtained from observing stars can be used to finding a few
basic parameters for any star, as for instance: the mass, the luminosity (total energy output per second), the radius
and the composition of the outer layer. Further stars (like our sun) are
like shining globules in the sky emitting constant light. Indirect evidence for
this comes from geologists who find fossil algae in the earth more than a
billion years old. From this they estimate that the temperature of the earth then
should have been very similar to that of what it is today in order for the algae
to survive. This indicates that the sun has been shining in a very similar way a
billion years ago. However
boring it might be to observe such constant globules of light in the sky, this constancy
of stars proved to be exceedingly important towards understanding these
objects. Such a stable
configuration present in stars demands that the forces that are acting inside a
star should be in perfect equilibrium. The question is, What are the various forces (or pressures)
that hold a star together?
Naively speaking, two contrapuntally acting
pressures need to be presumed in stars which tend to balance each other up.
Consider a very small volume element at some point in the star. The pressure acting inwardly in this
element should be exactly the same as the outward pressure, and if this were
not the case, there would be a net unbalanced pressure which would cause this
small volume element to deviate from an equilibrium state; this, as we pointed
out, cannot occur due to the fantastic equilibrium observed in stars. The inwardly acting pressure is the
gravitational pressure which acts radially inward and tries to push the volume
element towards the centre of the star.
The outward pressure, which is
the characteristic of the material in this volume, and its temperature, act in
the opposite direction (radially outward) while exactly cancelling the inward
gravitational force. For the star to
remain in equilibrium, this pressure balance usually known as "Hydrostatic equilibrium" needs
to hold good at all points in the star. Considering this simple balance in holding
good or together, one can readily show that the typical temperature in the
stellar interior is of the order of 10
million kelvin.
However, the constancy of a star requires that
another kind of equilibrium should also
hold together. This is known as thermal equilibrium, which demands that the temperature be constant at
every point in the star. This is however not quite possible, as we know
that the temperature on the surface
layer of a star is a few thousand degrees kelvin
while the stellar interior is at 10 million K. Under such conditions there will
be a net energy flow
out of the star which
we measure as the luminosity from the star. Hence the thermal equilibrium operating in a
"constant" star is of the kind where there is a constant supply of energy within the star which replenishes the
amount of energy carried away from the star maintaining a constant temperature
gradient across the star. It came as
one of the greatest revelations that nuclear fusion transmuting hydrogen into
helium in stars can sustain a constant star for billions of years.
Spectroscopic observations of stars found that stars are indeed rich in
hydrogen proving that stars produce their own light by burning hydrogen and
thereby producing helium and other heavier elements. (This process is commonly
known as nuclear fusion and can be readily found in any high school physics
text book.) The net flux which flows
outwards causes another force acting outward from the star, and this goes by
the name of radiation pressure.
To summarize then, for a star to be in constant equilibrium, the net pressure acting outward, i.e., the gas
pressure and radiation pressure should balance the inward acting gravitational
force in a star. And to maintain
this equilibrium, the star should continue to burn its nuclear fuel. This remarkable theory of stability of stars
was put forward by Sir Arthur Eddington, published in his book: The Internal
Constitution of Stars, in 1926.
The next important
question that arises is what happens to stars after they have exhausted their
nuclear fuel? It means that if the stars cannot produce their
own energy, the stars would cool down,
and both the gas pressure and radiation pressure would decrease, while the
gravitational pressure would take over causing the star to collapse. At
that time, this was a puzzling issue, as Sir Arthur Eddington himself
commented, "I do not see how a star which has once got in the compressed
state is ever going to get out of it...". And to add to the puzzle, the
discovery of white dwarfs ( a star in a compressed
state with extremely high density of 10^6 gm/cc) appeared to challenge this
successful theory.
This paradox was
resolved by Fowler.
The gas pressure in fuel efficient stars is dictated by the classical Boyles law. However, at high densities where matter is extremely
compressed, Fowler argued that quantum mechanics is important and the pressure
should be calculated according to the Fermi Dirac statistics. He argued that the material at these
densities will develop another outward
pressure, known as the degenerate
pressure, which will halt the gravitational collapse. This theory could easily explain the existence
of highly dense stars like white dwarfs.
Such was the state of stellar theory when young
Chandra began his scientific career. Following this seminal idea put forward by Fowler,
Chandra almost immediately theoretically derived the exact mass-radius relation
for a completely degenerate white dwarf. His results showed that the, the
radius of the white dwarf is proportional to the cube root of the mass; density
is proportional to the square of the mass.
At that time his theory led to the idea that all stars should end their
lives as white dwarfs.
After finishing this work in
M_limiting = 5.76 mu_e^(-2) Msun (in units of
solar mass).
This limiting mass is
rightly known as Chandrasekhar limit.
For mu_e = 2, fully degenerate helium,
M_limiting = 1.4 Msun.
It is worth mentioning that simultaneously two
other scientists,
From then on, Chandra was unstoppable. He went on to first establish in intricate
detail a complete theory of white dwarfs taking special relativity into
account. By 1936 he was able to
answer another puzzling question regarding the mass of stars. It was curious to find
that thousands of stars found in the sky seemed to
have masses which were confined to very narrow mass range, varying at the most about
ten times with respect to the mass of our sun. Chandra demonstrated that the maximum mass of a stable star is again a
combination of fundamental constants which give a mass in the ballpark limit of
30 Msun, close to what is observed.
About the same time around 1932-34 Chandra focussed
his attention on the eventuality of massive stars. He first established a very
important result: that being the
criteria of developing degeneracy in a star. To summarize his findings, a star would develop degeneracy if the
radiation pressure be less than 9.2% of the total pressure. Then he found
that stars with masses exceeding 6.65 mu_e^-2 Msun, will have radiation
pressure greater than 9.2% of the total pressure, and thus the star cannot
develop degeneracy and so degenerate pressure cannot be invoked to save the
star from collapsing. Being extremely cautious (as that was his style, not to
publish anything which did not have any suitable mathematical basis), he posited
that a star unable to develop degeneracy
will keep collapsing until perhaps when the atomic nuclei of the stellar matter
are close enough to change the expression for calculating pressure.
It was Baade
and Zwicky (1934) who went ahead to declare what Chandra had indicated,
that is, when matter is dense the
neutron will drip out of their nuclei to form a neutron star which is rich
in neutron and is supported against gravitational collapse due to neutron
degenerate pressure. Chandra appreciated their conclusions and around 1939
stated that stars more massive than
M_limiting but less massive than 6.65 mu_e^-2
Msun
would collapse into a neutron star
releasing huge amounts of gravitational
energy, perhaps
resulting in the supernova phenomenon.
By 1940, stellar physics reached an advanced
stage. Most of the issues relating to stability of stars and their energy
sources were resolved. Chandra proceeded to devote his time now to answering
detailed questions relating to end stages of stellar evolution,
particularly what happens in the core of
stars after nuclear burning is over. Another seminal result evolved in this
quest. He concluded (along with other
co-workers) that if the mass of a star is less than M_limiting, the star would
find peace as a degenerate white dwarf. For mass configuration greater than
M_limiting, the star will be in an uneasy state of inequilibrium and has to
shed its mass to eventually settle down peacefully in a completely degenerate
state. This shedding of mass is commonly
known as the Type I supernova.
Chandrasekhar’s detailed study and illuminating
results on stellar structure created waves in the scientific community. The
results relating to the fate of massive stars settling as neutron stars was
remarkable. It was Oppenheimer and
Snyder (1939) who took these significant results and conjectured upon what
could happen to sufficiently massive stars. They said that such a heavy star would collapse into a singularity only
around which "..its gravitational field will persist..". This is
known as the black hole.
Today precise measurements of neutron star
masses are almost equal to 1.4 Msun. A neutron star has been found
approximately 30 years of its prediction inside many supernova remnants, the
most prominent being the crab nebula. Indirect
evidence has shown the existence of black holes. These are remarkable
confirmations of Chandra’s theory. He came at a time when classical theory of
stars failed to explain observations of highly dense stars. Chandra played a significant role in erecting
the theory of relativistic astrophysics which continues to be a major area of
research in astrophysics today.
Personal Profile
Chandra was born in
Chandra was the first son of C. S. Ayyar and
Sitalakshmi. He had two older sisters, four younger sisters and three younger
brothers. His father worked in the railways as an assistant auditor-general and
his assignments often required a change of work place. At the age of six,
Chandra's family moved from
Chandra was a healthy and charming child and
sometimes "unbearably mischievous", according to Chandra's mother
Sitalakhsmi.
“As a child,” his sister Bala recalls, "he
used to take the
lion's share of everything. He would
break his things
first and take my elder sister's. He would keep them for himself,
because he would claim they were his. They were then given to him".
Chandra's parents began all their children’s education
at home. This was a common practice among middle-class families during that
time due to poor educational facilities available in public or municipal
schools. Amongst the English-speaking educated parents of that time significant
attention was given to educating children in English as that was a prerequisite
to getting a high profile job in
Efforts were also made to learn the mother tongue
which was Tamil in Chandra's family.
Chandra learned Tamil from his mother and
English and arithmetic from his father.
In the early years Chandra recalls, "My
father used to teach me in the mornings before
he went to office, and then after he went to
office, my mother would teach me Tamil. In
the afternoon she would supervise both the
English lessons and the Tamil lessons we had
to do." Chandra thoroughly enjoyed
learning English and arithmetic. His father used
to give him assignments and Chandra would
finish them including one or two more chapters
ahead of what he was taught. His father was
amazed by this, but soon realized that
they had an exceptionally bright child in their
midst.
Chandra went to a regular school in
his initial days in school very disappointing
as he did not find the conventional formal
education to be easy nor pleasant. Only when he
discovered that the curriculum included geometry and algebra that Chandra got
excited. He started to learn maths well ahead of the rest of the classes. He
was particularly engrossed in learning maths and finished all the
courses in the shortest possible time. He
became a freshman in
Chandra was a very sensitive and warm hearted
person. As he grew older he noticed that
his sisters experienced a certain kind of
discrimination at home. They were not given
the facilities that the boys enjoyed in the
family. His sisters had to marry at an
early age, thus putting an end to their formal education.
They were unhappy about the restrictions imposed on them. Disillusioned by such
social practices, Chandra decided to divert all his energies to studying mathematics.
He found ways to mentally withdraw himself from the immediate family and
concentrate on his studies.
At college, Chandra studied mathematics,
physics, chemistry, English and Sanskrit. He was fascinated by English and read
many classics diligently. In two years he finished his intermediate at the
Chandra wanted to take mathematics for his honours.
On the other hand, Chandra's father wanted him to study physics. Following the
trends of the moment, he wanted his son to go to
He was happy to be doing physics honours. He
already knew about two great scientists in the Indian scene, the great
physicist C. V. Raman, his uncle,
and the illustrious autodidact mathematician Srinivasa Ramanujan.
He had however to struggle with his father’s dictates.
Mr. Ayyar insisted on his son becoming
an ICS officer. Fortunately for Chandra, his
mother gave him the required moral support.
"You should do what you like. Don’t
listen to him; don’t be intimidated,"
she told her son. .
Chandra was lucky to have such a strong-willed
and devoted mother who, against all odds, stood
by Chandra till the very last day of her life.
With moral support and blessings from his
mother, Chandra was encouraged. He took up
physics honours, and he devoted much time to studying
physics and maths. Special
privileges were allowed him in college: despite
his being a physics student, he was allowed to attend all the mathematics
courses. Everyone knew that Chandra was specially gifted, and favours were bestowed
on him without any apprehension.
The year 1928 became an extraordinary time for
Chandra. He was then able to visit Raman
in
As Chandra said, " From a purely
scientific point of view, the most crucial
incident was my meeting with Sommerfeld when
he visited
By 1930,
Chandra had published several scientific papers. He sent one of his papers to
Professor Fowler in
He was young and had to travel all alone several
thousand miles away from home, and once there put up with a new place, new
culture, and new society. Chandra was probably a bit scared and confused, but
his insatiable urge to undertake scientific research, goaded him along.
.
found himself amongst a galaxy of scientists
like Sir Arthur Eddington, Dirac, Milne, and so forth. Excited as he was, he
nevertheless remained in full control of himself. He wrote to his father
"..I
have to realize more fully that I have come down 6000 miles,
not to fill away my time, but by utilizing opportunities in the proper
way, to at least compensate for the anxiety
which my coming is bound
to cause in others".
Of course Chandra did more than just compensate.
He quickly immersed himself in very vital problems in astrophysics and made
fundamental contributions to them. Soon after his Ph.D. degree which he
obtained in 1933, he wanted to continue staying in
While he made great strides in his scientific
career, he was however constantly
unhappy and lonely. This was especially so because he felt his work was not
being appreciated by some of his distinguished colleagues. In particular, Sir Arthur Eddington was unhappy about Chandra's work.
Eddington was considered to be a "king" when it came to understanding
stars as he had laid the foundation for the classical theory of stars. He eventually concluded that every star, no
matter what its mass, could reach an equilibrium state and become a white
dwarf.
But Chandra's
conclusion that massive stars cannot reach such an equilibrium state
distressed Eddington.
The controversy between Eddington and young Chandra became serious.
Eddington tried to
dismiss Chandra's findings on almost every occasion he got. Even
other scientists who otherwise agreed with
Chandra, did not criticize Eddington in public.
Chandra was shocked
and puzzled. Chandra felt that the differences were not based
on honest scientific
arguments. Chandra hence decided to finally change his area of research.
He was convinced that
his work was correct and did not want to waste energy in trying
to prove it by
fighting the “greatest scientist” in the world. While much can be said about
the controversy, what Chandra said was
"I do not think Eddington's tirade
against me was derived from any personal
motives. You may attribute it to
an elitist, aristocratic view of science and
the whole world. Eddington was so
confident of his views that as far as
he was concerned he was a Gulliver in a
in the least by what other people said or did not say."
Chandra - even against
all that was being done to him - deeply respected the great scientist
that Eddington was. That was typical of Chandra.
Chandra spent a few years in
that Chandra would return home, but Chandra did
not want to go home.
was not the place where he could do research,
and, in
get a permanent position. It was then that he was offered a position in the
Chandra got married to
D. L. Lalitha on
She said "...the main thing for Chandra
and me was to understand each other. The first
priority for him was his science. There was not
much time for other things, which I
well understood and appreciated. She willingly
gave up the idea of continuing a serious
scientific career of her own. Around this time
Chandra also got an offer to return to
and work there. But Chandra and Lalitha were
determined to stay in
And what an illustrious career it was! His prolific contributions to widely
diverse
areas in astrophysics
have made him a living legend in scientific circles. He had
authored a dozen books and bagged several
awards and prizes. He was given the
Bruce Medal
(Astronomical Society of the Pacific) Gold Medal of the Royal Astronomical Society, the Royal Medal of the Royal Society (on the formal approval of Queen
Elizabeth), the National Medal of Science
(awarded by President Johnson), Padma
Vibhusana (awarded by President of India), Srinivasa Ramanujan Medal (Indian Academy of sciences), the Noble Prize in Physics and the Copley Medal of the Royal Society. He
was an excellent teacher and had more than fifty Ph.D. students under his
guidance. He was the sole editor of the Astrophysical Journal for almost twenty
years and was chiefly responsible for making it the foremost journal, in its
specialty, in the world. Chandra however was quite modest about assessing
his contributions. In a lecture delivered by him at the
"The pursuit of science has
often been compared to the scaling of mountains,
high and not so high. But who amongst us can hope, even in imagination,
to scale the Everest and reach its summit when
the sky is blue and the air is still,
and [in] the stillness of the air
survey the entire Himalayan range in the dazzling
white of the snow stretching to
infinity? None of us can hope for a comparable
vision of nature and the universe
around us. But there is nothing mean or lowly in
standing in
the valley below and awaiting the sun to rise over Kinchinjunga.[sic]"
Chandra's pursuit of science was solely in the
spirit of experiencing the beauty of it, and he believed that it was not
restricted only to great minds. So, he said:
" This is no more than the joys of
creativity are [being] restricted
to
a fortunate few. They are, indeed, accessible to each one of us provided we are
attuned
to
the perspective of strangeness in the proportion and conformity of the parts of
one
another and to the whole. And there is satisfaction also to be gained from
harmoniously
organizing the domain of science with order, pattern and coherence.."
Bibliography: BOOKS by Chandrasekhar Subrahmanyan
Compiled by Anindita Mitra
1. An Introduction to the Study of
Stellar Structure.
2. Principles
of Stellar Dynamics.
3. Radiative
Transfer.
4. Plasma
Physics: Notes Compiled by S.K.Trehan From a Course given by S. Chandrasekhar
at the
5. Hydrodynamics
and Hydromagnetics Stability.
6. Ellipsoidal
Figures of Equilibrium.
7. The
Mathematical Theory of Black Holes.
8. Eddington:
The Most Distinguished Astrophysicist of His Time.
9. Truth
and Beauty: Aesthetics and Motivations in Science.
10. Selected
Papers ( seven volumes).
11.