Meghnad Saha's Ionization Equation (1920) And India's Entry Into Astrophysics

In 1920 Meghnad Saha, a young lecturer at the University College of Science, Calcutta, published a theory of thermal ionisation that explained the sequence of stellar spectra as a sequence of temperatures. The Saha equation became a foundation of astrophysics and later of plasma physics, and it marked the entry of Indian science into theoretical astrophysics. This paper revisits the equation in its historical and physical context. It sets out the thermodynamic argument by which Saha obtained it, shows that the numerical form he published is consistent with the modern statistical-mechanical expression, and reproduces with the Saha and Boltzmann equations the calculations that made the theory persuasive: the degree of ionisation of hydrogen as a function of temperature and pressure, the maximum strength of the Balmer lines near 10 000 K, the successive ionisation of calcium, and the progression of line-forming populations of calcium, hydrogen and helium that underlies the spectral sequence from M to O stars. The pressure dependence of ionisation, which explains the differences between giant and dwarf stars, is also quantified. The paper then discusses how the theory was taken up by Fowler, Milne and Payne, how it relates to the earlier work of Eggert, and what it meant for science in India, where it was produced without access to a telescope.