================================================================ DESCRIPTION OF THE HONORS OPTION FOR ASTRONOMY 485 - NIEL BRANDT ================================================================ ---------------------------------------------------------------- The honors option for this course will involve a computational investigation of the structure of white dwarf stars. You will learn about the following: * Observations of white dwarf stars * The equation of state for degenerate white dwarf matter * The differential equations describing white dwarf stars * Polytropes and solutions to the Lane-Emden equation * The mass-radius relation for white dwarf stars * The Chandrasekhar mass limit * The effects of chemical composition on white dwarf properties * Efficient numerical integration of ordinary differential equations ---------------------------------------------------------------- The basic work that will be done for the honors option (roughly in order) is the following: * Review the basic facts about white dwarfs. For example, you could read the following: Chapter 15 of _Modern Astrophysics_ by B.W. Carroll and D.A. Ostlie Chapter 15 of _Modern Stellar Astrophysics_ by D.A. Ostlie and B.W. Carroll Chapter 15 of _High Energy Astrophysics: Volume 2_ by M.S. Longair Chapter 3 of _Black Holes, White Dwarfs, and Neutron Stars_ by S.L. Shapiro and S.A. Teukolsky * Learn about observations of white dwarf masses and radii. Here you will read a few relevant papers from the scientific literature and talk with white dwarf experts in the Department. Relevant papers will include the following: "The Mass and Radius of 40 Eridani B from Hipparcos: An Accurate Test of Stellar Interior Theory" H.L. Shipman et al. (1997, The Astrophysical Journal, 488, L43) "Testing the White Dwarf Mass-Radius Relation with Hipparcos" J.L. Provencal et al. (1998, The Astrophysical Journal, 494, 759) "PG 2131+066: A Test of Pre-White Dwarf Asteroseismology" M.D. Reed et al. (2000, The Astrophysical Journal, 545, 429) "A Redetermination of the Mass of Procyon" T.M. Girard et al. (2000, The Astronomical Journal, 119, 2428) "Procyon B: Outside the Iron Box" J.L. Provencal et al. (2002, The Astrophysical Journal, 568, 324) Richard Wade in the Department is a white dwarf expert. * Learn about efficient numerical integration of ordinary differential equations, especially the Runge-Kutta method. Solve some simple differential equations with this method, and understand the concept of coupled differential equations. You will work through Chapter 16 of the book _Numerical Recipes in C_ by W.H. Press et al. See http://www.nr.com/ for details. * Derive and appropriately scale the differential equations describing white dwarf stars. Here you will follow Chapter 2 (pages 42-48) of the book _Computational Physics_ by S.E. Koonin. You will also learn about polytropes and solutions to the Lane-Emden equation. * Write a computer program that numerically integrates the differential equations describing white dwarf stars. This program should be as elegant and generalizable as possible. * Verify the correctness of your computer program by comparisons with observations of white dwarf masses and radii. You will also recover the Chandrasekhar mass limit. * Use your computer program to investigate the dependence of white dwarf properties upon factors such as chemical composition. * Examine how the accuracy of your numerical solutions depends upon computational method and program parameters (for example, integration step size). How can you solve the white dwarf problem accurately with the best computational efficiency? * Investigate other selected issues, as time allows. * Write a final report describing the results of your investigations. This report should be typed and well written. This report should include at least the following: + A brief review of white dwarfs and observations of their masses and radii. + A review of the equations describing white dwarf structure, demonstrating that you understand these equations physically. + A description of the code you have written to solve the white dwarf problem numerically. The clearly commented code itself should be included as an appendix to the report. + A justification of the initial conditions used to start the numerical integration. + Basic tests of your code that demonstrate that it works correctly. For example, you should recover the Chandrasekhar mass and the white dwarf mass-radius relation. You should show that your mass-radius relation agrees with observations of white dwarfs. You should illustrate your test results with appropriate plots. + Examinations of the dependence of white dwarf structure upon chemical composition. You should illustrate your results with appropriate plots. + An investigation of computational efficiency in solving the white dwarf problem. + A summary of your main findings. + Suggestions for future avenues of investigation. Suggestions of how this honors project might be improved in the future for other students. + A bibliography giving proper reference information for the references used. + Written solutions to the questions and problems on pages 46-48 of the Koonin book. These do not need to be typed but should be written clearly. Your final report will be due at the start of the final exam, so please plan ahead over the semester to avoid a last-minute crisis. Last-minute extensions will not be given. ---------------------------------------------------------------- --------------------------------------------------------------------------- Niel Brandt; Department of Astronomy and Astrophysics; The Pennsylvania State University; 525 Davey Lab; University Park, PA 16802 USA Phone: (814) 865-3509; FAX: (814) 863-3399; Office room number: 507; WWW: http://www.astro.psu.edu/users/niel/index.html ---------------------------------------------------------------------------