As a schoolboy in India, one couldn't help knowing of the Chandrasekhar mass limit. I distinctly remember being challenge-quizzed by fellow schoolmates about it - as early as the sixth grade. That an Indian-born astrophysicist had discovered a fundamental limit - the stellar mass, that, if exceeded in a white dwarf, could lead to gravitational collapse - was something every Indian schoolboy in the 1970s seemed to know (at least in the schools I went to!). Later, in high school, I remember doing an elementary calculation, and later still, at college and university, more detailed calculations were done. Chandrasekhar himself became an idol of sorts, and his benign gaze, from a picture portrait framed on the wall above my desk, was deeply inspiring in the last two years of my university career. In the very last year - 1983-84, he was also awarded the Nobel Prize in Physics, for, it turned out, the very work he had done, as a nineteen-year old, in calculating his Mass Limit. [This seemed to ignore his work of a lifetime since, which did not sit at all well with him - but be that as it may for now, it can be the subject of several blog posts.]
That, apart from Subrahmanyan Chandrasekhar, there were other Indian physicists named Chandrasekhar as well, I also knew. One of them, who also shared his first initial, was Sivaramakrishna Chandrasekhar, a liquid crystals specialist, who was at the Raman Research Institute in Bangalore (which I visited often as an undergraduate, since my family happened to live near by). [The two were actually first cousins, both also being nephews of C.V. Raman.]
But it was Professor B.S. Chandrasekhar, (Bellur Sivaramiah Chandrasekhar) formerly of Case Western Reserve University and now at the Walther Meissner Institut at Munich – like me, a Delhi University alumnus (M.Sc. 1949) and a Rhodes Scholar as well - passing through some 35 years before me - for whom another Chandrasekhar limit is named. In 1962 (the year of my birth) he wrote a paper in the very first issue of the journal Applied Physics Letters: A Note on the Maximum Critical Field of High-field Superconductors. This paper defined a natural upper limit on the ambient Magnetic Field which, if exceeded, causes a complete loss of superconductivity. Independently, the idea was also suggested by A.M. Clogston, and has ever since then been known as the Chandrasekhar-Clogston (Field) Limit.
For reasons I cannot fathom, this limit on the upper critical field of superconductors has not received the type of (er ahem) critical acclaim that the first Chandrasekhar Limit received - not even noticed in the Delhi University Physics Department, of which Prof. B.S. Chandrasekhar, is a distinguished alumnus! He was felicitated for a lifetime of work in superconductivity and condensed matter physics, with a special award at the American Physical Society March Meeting in Indianapolis in 1992 (where I was fortunate to be present). I remember seeing him from afar but being too intimidated to approach him directly and introduce myself!
Professor B.S. Chandrasekhar has continued to work on superconductivity, and still does, at the Walther Meissner Institut (the Institute is of course named for the discoverer of the famous Meissner Effect - which describes the exclusion of magnetic flux from the interior of a superconductor below its critical temperature). He has worked on the critical field of Niobium, and on magnetic fields created by superconducting solenoids. As it happens, the magnetic fields required by the ITER tokamak - both the central solenoid and the toroidal field - are created by superconducting Niobium-Tin alloy - of which some 750 tons (seven hundred fifty tons) of wire, 200 km (two hundred kilometers) long will be required. Thus, considerations following from the Chandrasekhar-Clogston Limit are relevant to ITER design and operation. What is really interesting is that the other Chandrasekhar - Subrahmanyan Chandrasekhar - worked on the theory of fusion - especially laser fusion (or inertial fusion) - using the pressure of light to push two hydrogen atoms close enough that they fuse. (This is not the approach at ITER, which is a magnetic fusion reactor). Prof. B.S. Chandrasekhar has also written a popular book, Why Things Are The Way They Are.
Today, the Chandrasekhar-Clogston limit occurs most often in the physics literature in descriptions of work relating to spin-polarized fermionic atomic fluids - which display both superfluidity through a BCS-like pairing, as well as a Bose-Einstein Condensation (BEC) after dimerization (which makes them bosons) at ultra-low temperatures. A group at the University of Trento (Italy) and, appropriately, the Walther Meissner Institut (where Prof. Dr. B.S. Chandrasekhar is a 'Permanent Guest') is active in the field. The Chandrasekhar-Clogston limit appears in that context as a critical value of the ratio of up-and-down spin polarizations in a dilute fermionic atom gas, and determines phase separation of the dilute gas into a superfluid phase and a 'normal phase'.
Whether and how the two Chandrasekhar limits, in speaking of different aspects of a gas of fermions (dilute in one case, and degenerate in another) are actually (or at all) related are interesting questions I might explore in a subsequent blog post.
