Polytropes and Recording Studios

By Michael on November 5, 2006 at 2:49 pm | In Astrophysics, Blog Posts |

I’ve been an amateur astronomer for a long time but I had never heard the word “polytrope” before. It turns out it is an important concept in stellar astrophysics. It also, in a round about way, brings me back to my first job at a recording studio.

In 1988 I graduated from Berklee College of Music and got a job in Lake Geneva, Wisconsin at a recording studio called Royal Recorders. Unbeknownst to me at the time, Yerkes Observatory is also located on Lake Geneva, just a few miles from where I worked. One of the great theoretical astronomers of the 20th century, Subramanyan Chandrasekhar, aka “Chandra”, worked at Yerkes for almost 30 years.

There was a time in astronomy when we didn’t know for sure that nucleosynthesis was powering the luminosity of stars. We hadn’t figured out how to get the temperature high enough for thermonuclear reactions. Chandra, standing on the shoulders of many giants, helped figure it out and formalized a theory for stars based on an idealized fluid model — a polytropic process. Polytropic means it is a reversible process where the pressure is proportional to a power of the density.

By combining hydrostatic equilibrium with a polytropic model of stars, we could finally solve the equations to predict the temperature and density of stars. When we plugged in the numbers, using the “standard model” of stars developed by Eddington, we found central temperatures in the tens of millions of degrees — plenty hot for nucleosythnesis.

So in terms of astronomy, a polytrope is a mathematical model of a star. You plug in a few assumptions and you get out many of the physical parameters that describe a star — the temperature, density, mass, radius and pressure. We can describe much of the structure of the HR diagram, from first principles, using this model.

Chandra left Yerkes around 1965, the year I was born. I visited Yerkes for the first time just this year. I’m also learning about Chandra’s work for the first time in the astrophysics class I’m taking. It is fun to think that I walked the same streets and drove the same roads as Chandra, in a little corner of Wisconsin, a long time ago.