from 'Icons from the world of science', by S.Ananthanarayanan - home page

S. Chandrashekhar and the evolution of stars

The Black Hole - a region of space where the gravitational forces are so great that even light is not able to escape, is surely one of the most spectacular icons of modern astrophysics.

The word has become a metaphor for a fate without return, a trapdoor into another world, something final, unreasoning, inexorable…. and modern astronomy, which sights X-Rays, from above the earth’s atmosphere, has now found evidence for real black holes tucked away in distant galaxies. But what is remarkable is that long before they was detected in experiment, black holes were conceived of in pure theory, the outcome of the persistence, in the face of much opposition, of Subramanian.Chandrashekhar, then barely a post-doctoral student at Cambridge.

The evolution of stars, as understood at the beginning of the 20th century was that they arose with the gravitational drawing together of the material in vast clouds of gas, mostly hydrogen. As the cloud fell into itself, it warmed, like the air in bicycle pump heats up on being compressed. The temperatures rose to millions of degrees and nuclear reactions, mostly of hydrogen nuclei combining to form helium, were sparked off. This caused immensely greater heat, which gave rise to pressure, which began to overcome force of compression due to gravity. The cloud then expanded, under the force due to the fire in the centre, and kept expanding till the fuel began to run out. When this happened, the internal pressure began to fall and gravity took over again. In the compression that followed, more energetic nuclear reactions took place, to produce heat and heavier elements still. This again led to expansion, followed by compression, and so on.

When the star is at its largest, with the center burning but dimly, the star temperature is low and the star appears large and reddish, as a red giant. When the star is compressed with the center burning vigorously, the star is smaller and hotter, with its colour more to the blue side of the spectrum. The bulk of the stars in the heavens, like our sun, are at this stage. Our own sun too, will grow to be a red giant someday, when its dimensions will engulf the orbit of Saturn, now at a distance of 1.4 billion km from the sun.

And when, after a several such cycles, the nuclear fuel is spent, there is nothing to counter the gravitational force and the star collapses. The star gets smaller and the force of gravity at the surface gets stronger. But does the star get smaller without limit and reduce to a point? What would be the density of all the matter in the star so compressed? And yet, is this the fate of a star, ultimately to disappear?

By the time these questions were raised, fortunately, the quantum nature of energy and the wave nature of matter had been understood and a way was seen out of such ‘collapse to a point’. A consequence of the quantum theory is that there is a limit to how accurately we can measure the position and the motion of a particle at the same time. For instance, if we spot and locate an electron at rest, we are, in fact, spotting the electron with the help of a photon, or particle of light, which is bouncing off the electron. Now, in this bouncing off of the photon, the electron would recoil and be set in motion. We then have the position of the electron, but the electron is no longer at rest. One way to reduce the recoil would be to use a ‘low energy’ photon. But the laws of optics are such that with low energy photons, we do not get a sharp image, only a blurred one, which leaves the position uncertain. Thus, measurement of the position and the speed of a particle in nature is always a trade off in the accuracy of either measurement.

The implication of this ‘principle of uncertainty’, for the collapsing star, is that when the particles get squeezed closer together, nature imposes on them an extent of motion, which gives rise to a pressure. This pressure has nothing to do with the temperature or energy of the star, but serves to counterbalance the pressure of gravity, in any case.

This concept saves the collapsing star from the physically untenable reduction to a geometric point and the star survives as a highly compressed, hence very hot entity. The dying star thus shines with nearly white light, as what is called the white dwarf.

This was where the evolution of stars stood when S.Chandrashekhar finished college, from Presidency College, Chennai, in 1929. Chandrashekhar was the nephew of the celebrated C V Raman and came from academically gifted stock. He was a phenomenal student and while still an undergraduate, had taught himself subjects far beyond his teachers’ comprehension.

The subject of stars and their development had gripped him early and he had already read the classic, The Internal Constitution of the Stars, by Eddington. Sir Arthur Eddington was a great pundit of astrophysics and was known for his work on stellar evolution and for his exposition of Einstein’s General Theory of Relativity.

Even while in college, Chandrashekhar had taught himself the new mechanics applicable to the world of the very small, where quantum effects, of things changing not continuously, but in steps, became important. Chandrashekhar had learnt this subject from Atomic Structure and Spectral Lines, the book by Sommerfeld, who had applied the methods to the atom. In 1918, Chandrashekhar also had the fortune of meeting with Sommerfeld, who advised Chandrashekhar of what else to read. Chandrashekhar went on to publish two research papers while yet an undergraduate!

In 1930, Chandrashekhar set out for England to study at Cambridge. And while on the two weeks’ voyage, he did much of the work that led him to an extraordinary discovery! The pressure inside a star, one can easily imagine, is related to many of its features, like the size, the rate of nuclear reactions in the core, the brightness, the colour. Only the last two features, the brightness and colour, which suggest the temperature, can be seen from the earth. The pressure then needs to be calculated from a theoretical relationship between the parameters.

By 1930 extensive data about the colour and brightness of stars was available, plotted in different charts, in order to find patterns. The methods of mathematical physics had considered what might be the behaviour of the interior of stars, as conjectured from what could be seen, to find a relation that fit the facts. And the work was still in progress. And during the voyage to England, Chandrashekhar could not keep away from working on the problem of white dwarfs.

The atoms that make up a normal star consist of a positive nucleus, surrounded by negatively charged electrons. The atoms are thus electrically neutral and behave like billiard balls in motion, moving faster when compressed or heated, and pushing out, to expand, when moving faster. But at the fantastic pressures in white dwarfs, this picture of neutral atoms like billiard balls would not hold, as the atoms would all have split up into positive nuclei and negative electrons. What we have would then be two gases, of charged particles, with huge forces of attraction and repulsion, and new, quantum mechanical rules of how they distributed their total energy among themselves.

Chandrashekhar, in the space of the voyage, attempted a rigorous application of all this to the case of the white dwarf and came up with a solution that bristled with problems! If the equations were applied to a white dwarf of low mass, they behaved well enough and gave solutions and the solutions also fit nicely with data. But when the mass of the star increased beyond a point, the equations themselves became unsolvable! Something in the problem or in way the solution was being attempted led to features that did not make sense!

The questions raised during the two weeks on the boat stayed with Chandrashekhar for many years. At Cambridge he showed his calculations to Professor Fowler, whose work he had read while in India. Professor Fowler, in fact, was the first to have seen that quantum mechanical effects would show up in white dwarfs, but still, he did not consider the way things changed at the ‘mass limit’ to be significant. Chandrashekhar could not divine where the problem could lie, but it is clear that he could not let go the conviction that there was something remarkable hiding down there!

In 1933 Chandrashekhar received his Ph.D. and also a fellowship at Trinity College. He continued his work on white dwarfs. Chandrashekhar’s work now considered that apart from quantum effects, the results of Einstein’s Theory of Relativity would also be relevant. Einstein’s Special Theory, set out in 1905, had shown that our ideas about space and time, which work quite well in daily life, break down at speeds approaching the speed of light. At these speeds, lengths and time intervals contract, mass seems to increase and speeds add up in a way that keeps their sum always less than the speed of light. The theory shows that energy and mass are equivalent and things get more massive as they move faster, which ties up with the attainment of higher speeds being more and more difficult. Chandrashekhar saw that the at the densities in white dwarfs, the speeds involved would be nearly that of light and so he worked the implications of the Theory of Relativity into the calculations.

Chandrashekhar worked out a mathematical expression for the pressure in the star, in terms of the various parameters, after taking the quantum mechanical and the relativistic effects carefully into account. The resulting expression had important differences from the earlier ones arrived at by Fowler and Chandrashekhar himself. When solved with the density kept low, when the effects of relativity would not be significant, and the old results were successful, the new relation agreed with the old results. To get a quick look at how the relation behaved in the high-density case, Chandrashekhar tried out what happened when the density was considered to be infinitely high. He found that the relation altered the way the pressure and volume of the star were related, but the relation permitted this extreme case (of infinite density) with a finite mass, some 1.4 times the mass of our sun, for the star! This was amazing. As infinite density means zero volume, it suggests that if a star had a mass of 1.4 times the mass of the sun and should run out of fuel, then the star would shrink to a point!

Chandrashekhar worked on this result for months on end and presented his work to many of his illustrious colleagues. None of them seemed to think there was anything in it. But Chandrashekhar soon grew convinced that high mass white dwarfs could not exist. The state of the low mass white dwarf was a balance between gravitational forces and the pressure due to the charged particles being squeezed together. If the mass of the star now gradually increased, maybe by matter, like asteroids, comets, crashing in, the force of gravity also increases, with the pressure also changing in a complex way. As the mass increases, the balance between the two forces gets less stable, till, at the mass limit, now known as the Chandrashekhar limit, the balance breaks down, rather like a truck tipping over as the platform it stands on is gradually tilted!

The result could also be understood in the context of a conclusion that had been drawn from Einstein’s General Theory of Relativity. In this, Einstein regards the world to be not a series of 3-dimensional pictures that change with time, but as a 4-dimensional entity, where time is a measure that is related to length, breadth and depth just as these measures are related to each other and to time. In this view, gravity caused by objects which have mass reduces to a curvature in the 4-dimensional space-time world and things affected by gravity are seen not as falling or moving in orbits, but just going straight on in a space that has been distorted by the presence of the massive object!

In this view, it had been calculated by Schwarzschild that if an object were to shrink to be small enough, and hence dense enough, it would so distort space in its vicinity that light would not be able to escape from the object. The size at which this happened for any object was the ‘Schwarzschild radius’ for the object. Chandrashekhar’s collapsed star could be seen as a star that has shrunk to its Schwarzschild radius.

For all that, so amazing and difficult to digest was Chandrashekhar’s result that just nobody who mattered, in the 1930s, was willing to give it a second thought. The great Eddington openly lashed out at the young Chandrashekhar and many other sympathetic colleagues tried to ‘reason’ with him. But a reading of the comments and critiques of these savants reveals statements like, “I think there should be a law of nature to prevent a star from behaving in this absurd way” and “ it is clear that matter cannot behave as you predict” – hardly the kind of hard logic with which one can counter cold mathematics! Even the Russian physicist, Landau, who independently arrived at the same expression as Chandrashekhar, two years after him, could not accept matter reducing to zero dimensions and said, “stars heavier than the limit (that the theory showed) should have regions where the laws of quantum mechanics are violated”!

Rather than beat his head against the wall, Chandrashekhar put down his findings about the structure of stars in a book, and his finding then lay there in black and white, to influence, more than Eddington’s remarks could, the development of the field. This done, Chandrashekhar withdrew and went to work on a new area, stellar dynamics. After a time, he wrote a comprehensive tome on that and shifted his attention to other fields. And so he went on, leaving an indelible mark on each field he took up, in a manner that few have equaled.

Chandrashekhar’s book on the structure of stars was published in 1937 and much tracking, through painstaking calculations, of the evolution of stars was carried out in the years that followed. In some of the cases, but only a few, the stars were found to explode before they collapsed to a point. But the possibility of collapse was distinctly gaining acceptance.

In 1967 came the discovery of pulsars. Pulsars were sources of regular radio pulses that came often from the center of brilliantly lit nebulae, or clouds, the remains of stars that had violently exploded. These were first thought of as maybe signals from intelligent beings in outer space, but were soon recongnised as coming from collapsing white dwarfs whose outer portions had been blown off midway. As the star collapsed, the core was crushed so hard that electrons and protons merged to form neutrons, with release of energy. The energy blew off the outer parts of the star while the neutron core collapsed into the densest matter known. The tremendous gravity as well as magnetic fields in the vicinity of the core accelerated matter to emit light and X-Rays, which illuminated the surrounding debris of the explosion. The neutron core itself rotated, like a ballerina spins when she draws her arms inward and emitted radio waves or X-Rays, in the manner of a lighthouse, seen as pulse every time it pointed our way.

The discovery of the neutron star, albeit indirectly, was a first, exciting instance of an entity suggested by the eerie theory. But what of black holes? This was where a star many times the mass of the sun ended up when its fuel was over. Unlike smaller stars that exploded and left a core that could stay on, as white dwarves or become neutron stars. But what could be the method to find a thing a few kilometers across and which emitted no light?

It was X-Ray astronomy that made it possible. X-Ray astronomy, conducted above the atmosphere with the help of rockets and satellites revealed astonishing richness of images in X-Rays pouring in from the heavens. Because the earth’s atmosphere is opaque to X-Rays (and a good thing, too!) this whole area of astronomy was blocked from view till we learnt to launch telescopes above the atmosphere. A number of neutron stars were now detected, radiating in pulses, as before, but in the X –Ray region. Many of these were seen to have paired with a larger, regular star, with the pair spinning, like a tumbling dumbbell! This motion, in fact, was detected because the nature of the pulses alternated as the neutron star was moving away from us or towards us, in the course of whirling around with its companion.

But if the heavier partner in the pair is a black hole, then the companion feels so great a pull that the tidal forces begin to suck matter right out. And so fast does this matter move, as it rushes towards the black hole, that it heats up to millions of degrees and begins to radiate X-Rays. It is by looking for these X-Rays, in places where such pairs, known as binary stars, are expected, with the tell-tale effects of the wobbling of the source of the X-Rays, but with no pulses, that the presence of a black hole can be inferred.

X-Ray astronomy and the study of the interiors of stars are now pursued by hundreds of scientists, with huge funding. Hundreds of white dwarfs, brown dwarfs, nebulae, all kinds of X-Ray sources, have now been photographed and studied. In the 60s and 70s, hundreds of ‘candidate black holes’ were detected, and in many, many cases, now, the evidence is overwhelming that they are, in fact, authentic black holes.

Chandrashekhar received 20 honorary degrees, was elected to 21 learned societies and received numerous awards including the Nobel Prize (1982), the Gold Medal of the Royal Astronomical Society of London; the Rumford Medal of the American Academy of Arts and Sciences; the Royal Medal of the Royal Society, London; the National Medal of Science; and the Henry Draper Medal of the National Academy of Sciences.

For many years and to the end he worked in the area of stellar dynamics, and as a dedicated teacher. Many of his students, in fact, received the Nobel before him!

He died in Chicago in 1995. The most sophisticated X-Ray observatory to date, NASA’s facility launched by the Columbia in 1999, was fittingly named Chandra.

------------------------------------------------------------------------------------------