In this post, I will summarise our discussion with Reza Katebi about my research on formation of supernovae, explosions of stars and use of computers to simulate them.
What are stars and why do they shine?
Stars are big hot balls of gas. One may ask why doesn’t the gas making up the stars fly away or, flow away? Well, it’s the same reason as to why we are not flying away from the Earth into space — gravity. Gravity of the different parts of the gas pull each other. You may wonder then, why don’t they just keep falling in and stop at nothing, squeezing everything to a point? The answer to this question is related to another obvious question about stars — why do they shine?
We see shining stars every day and night in the sky. They shine because they produce energy; a large fraction of which comes out in the form of light. This energy is produced by fusing elements together to form new elements near core of stars dues to high pressure. Almost all of the energy comes from fusing 4 Hydrogen (H) nuclei to form one Helium (He) nucleus. Such reactions produces energy because the mass of one He nucleus is slightly less than the mass of four H nuclei. The difference in mass gets converted into energy in accordance with Einstein’s famous formula — 
The light coming out of the star’s center not only make it shine but also prevent it to collapse under its own gravity. The produced energy in form of light i.e. photons bump into the gas and keep them from falling. They maintain what is technically called hydrostatic equilibrium (hydro: water, static: at rest).
But, stars have only so much Hydrogen to spend! Usually, these reactions proceed at a slow and constant pace. That’s why they keep producing energy for millions and millions of years. If the mass of the star is more, the reactions happen at a faster rate and it consumes its fuel in a shorter time and reaches its end state sooner than than a low mass star.
How do stars live their life?
Stars live on Hydrogen and they have only so much to spend and hence so much to live! Usually, the nuclear reactions proceed at a slow and constant pace. That’s why they keep producing energy for millions and millions of years. If the mass of the star is more, the reactions happen at faster rate and it consumes its fuel in shorter time and reaches its end state sooner than than a low mass star.
This is the reason for a famous fact that most of the shining stars — hot stars (high surface temperature) are blue, cold stars are red.
What leads the star to explode and go supernova?
Sometime towards end of their life, stars reach a stage where the stellar fuel sits there like a cracker, large amount of highly compact fuel. Just like a bomb, it burns, but fails to expand in time because of the heat produced. High concentration of fuel means higher production of heat and higher heat means faster reactions. This positive feedback can go unstable and a runaway process may result, commonly known as detonation. These are so powerful that it produces as much energy as our Sun will produce in its entire lifetime!! We use these bright events to study our universe; just like sailors use light house to guide their ships in oceans.
The first recorded supernova in history is considered to be the one recorded by Chinese astronomers as “guest star” in 1054 AD. It is also believed to be painted in the caves by native Americans. With modern analysis, we came to know that the that neutron star at the center of Crab nebula was produced by the very same supernova explosions seen by our ancestors about thousand years ago.
White Dwarfs, Subrahmanyann Chandrasekhar and Arthur Eddington
White dwarfs are peculiar stars whose white color indicates very high surface temperature. On the other hand, observations shows they are also very small. They don’t follow the trend set by most of the stars. Painstaking observations and complex arguments by several scientists unveiled that they are actually the end state of low mass stars (with masses up to 8 solar mass).
During the early twentieth century detailed theory of structure of matter were laid out by Planck, Einstein, Heisenberg, Schrödinger and others. Among them Enrico Fermi and Paul Dirac were thinking about collective properties of electrons as gas. This is how electrons behave inside metals.
Subrahmanyan Chandrasekhar (people used to call him Chandra) used these recently discovered theories to find the structure of white dwarfs. He found that as the mass of a white dwarf increases, its radius decreases going to zero at a critical mass, called Chandrasekhar mass.
Famous astrophysicist and Chandra’s advisor, Arthur Eddington was not ready to accept this conclusion. He suspected that “some” physical process has to intervene and stop the collapse when the mass of white dwarf increases. He was right too in some sense, however he failed to recognize the importance of Chandrasekhar’s result that the maximum mass limit is direct consequence of statistical properties of electrons. Neutrons have same statistical properties hence they will also have maximum mass. This general result can be taken to be inspired from Chandrasekhar’s work. In fact, later general relativity is used to establish a much general result about existence of maximum mass independent of statistical properties i.e. equation of state.
How do we simulate star explosions on a computer?
Simulations are an extension, though a very sophisticated one, of the calculation that we do using pen and paper. Simulations are a way to test our scientific understanding of nature. Our concept of scientific understanding of the world is different for two distinct types of natural phenomena. In one case, we do experiments where we can manipulate the variables that control the behavior or, output such as fluid flow, sound, light, heat etc. While we also have natural systems which do not allow us to manipulate their conditions (such as astrophysical and evolutionary phenomena). In the later case, we can only observe the multitude of conditions that are already present. We can imagine the varying conditions of the system akin to manipulating the controlling variables. In this sense, the universe itself is a laboratory presenting us myriad possibilities of the input variables. This picture also tells us that our understanding of nature in terms of science is probabilistic.
How much computation power is needed to solve the problems of astrophysics?
In principle, one can put all the governing equations in the form of computer programs and solve it for any arbitrary initial conditions but, there are several conceptual and practical difficulties in such a scheme of answering astrophysical questions. Firstly, there will this objection — Are the equations used and implementations of the computer program valid in all possible domains pertaining to the problem at hand? Even without such objections, such a simulation would be unfeasible because it would require ridiculously long amount of computational time. Hence, there is always certain amount of “art” involved in performing the computational work. This artistic freedom here is not subjective but, an objective one. The demand of computational power depends on our question of what observable we want to compare with observation and what accuracy we need. The answer to this question then determines which pieces of physics must be included which are not important. Many of such answers can be obtained using a single laptop but, the questions at the fore front of knowledge demand large scale supercomputing facilities.
Compact Binary Mergers 