Write a computer program (or spreadsheet) to solve the Lane-Emden
equation for a range of polytropic indices (n = 0, 1, 2, 3, 4
and 5). Show your results in the form of a (computer generated) plot
of dimensionless density,
, on the
y-axis versus dimensionless radius,
, on the x-axis.
For each solution obtained in part 1, use the results of your program/spreadsheet in conjunction with linear interpolation to determine the value of when = 0 to an accuracy of three decimal places.
Determine which of the six polytropes you have calculated best describes
the structure of the Sun. You should do this by plotting graphs of log density
(in units of kg/m3), mass (in units of solar masses), log
pressure (in units of N/m2) and log temperature (in units of K)
versus radius (in units of solar radii) for both your polytropes and the
Standard Solar Model (SSM).
How do your calculated values of density, pressure and temperature compare with the SSM at the core and surface of the Sun, respectively? Comment on the likely source of any discrepancy.
It is imperative that you include with your final report a fully commented printout of the computer code you used to perform the above calculations. If you use a spreadsheet, you must describe the equations used to calculate the data in each column and show some example pages. It is not necessary, however, to attach all the pages of the spreadsheet.