Introduction to "simulating" a star

The Sun is the nearest star, so it looks like the brightest and biggest star. In reality, the Sun is a typical star, in the sense that its physical parameters are very close the averaged ones for all the stars. However, the values of mass, radius and luminosity change remarkably from a star to another, while the chemical composition turns out to be fairly similar.

A star is en enormous sphere of gas in equilibrium between the force exerted by its own gravity and the force produced by a pressure varying from the center to the surface. Pressure is exerted by the gas itself and/or by radiation produced in the nuclear reactions (which are due to the very high temperature involved).

Computers are the "probes" that the astrophysicists use to explore the stellar interiors, determining how the relevant physical quantities - such as pressure, temperature, density, chemical composition, and radiation field - change going from the surface towards the innermost layers.

A computer, indeed, simulates the physical behaviour of a star by calculating a star model, where the word "model" does not mean a scale rebuilding of the star, but its theoretical description by means of suitable mathematical formulas. In practice, such a model is an extended computer code including a large number of physical processes, such as all types of chemical mixing, detailed nucleosynthesis, and hydrodynamic effects.

Since the nuclear reactions in the central region of the star change the chemical composition, and since the energy released by these reactions is finally radiated away in space at the surface, stellar models are changing not only as a function of a space coordinate, but also in time. The evolution of a star is therefore computed as a number of successive models separated by certain time steps.

The most elementary stellar models are the so-called polytropic models or polytropes, developed by well-known physicists like Lane, Kelvin and Emden, who at the beginning of this century tried to construct a simple model of the stellar interior. Polytropes are no longer used these days in professional astronomy, but they offer a good introduction to stellar structure and the construction of stellar models.

Today the explosive rise of personal computers occurred during recent years allows every amateur astronomer to perform a numerical exploration of a stellar interior. In this site we'll show you, in particular, how to use an electronic spreadsheet program and a polytropic model to compute the internal structure of a star.

There are semi-professional algorithms which, by taking into account more interdependencies, are able to reproduce some physical properties remarkably well. However, our models give a good appoximation of how the main physical parameters vary throughout a star, and they are the only stellar models that can be programmed by an inexperienced amateur.


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