Autumn Semester 2013-2014                  Laboratory Exercise


This lab exercise is to be completed during the four lab sessions in E36 (the astro lab) on Fridays at 14:00-17:00 during weeks 8, 9, 10 and 11. Please note that you are expected to complete this lab exercise on your own - working in groups is not permitted.

On completion of the tasks set out below, you will be required to hand in a full lab report to the Departmental Office (Hicks Building, room G12) at the end of week 12 (Friday, December 20th, 2013).

This lab is worth 20% of the total marks available for the PHY213 module.

The breakdown on the right-hand side is meant as a guide to the marks that can be obtained from each part. 75% of the marks from each part will be awarded for content, with the remaining 25% awarded for presentation.

1 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.
2 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.


  1. The relevant pages of the PHY213 notes that you will need to refer to are polytropes ( and solving the lane-emden equation (

  2. A very clear description of linear interpolation is given at this url:

  3. The Standard Solar Model is available at this url: It is recommended that you download the latest model - BS2005. You should make clear in your report exactly which model you eventually decide to use.

  4. A list of fundamental physical constants and astronomical quantities can be found by clicking on the c symbol in the top right-hand corner of this web page:

  5. A guide on how to write a laboratory report is given at this url: Some of the details given in the guide are obviously irrelevant, e.g. this laboratory exercise is a theoretical one and does not really have errors (although the starting point and step size of your integration will introduce errors in your model, which you might like to investigate). Also, the assessment breakdown given in the guide is slightly different to the one adopted for this laboratory, which will be 75% for content and 25% for data presentation, language and style. On the whole, however, I expect you to adopt the good practice outlined in the guide when you come to write your report.

Vik Dhillon, 21 November 2013