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DESCRIPTION OF THE HONORS OPTION FOR ASTRONOMY 485 - NIEL BRANDT
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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
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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:
"Compact Stars for Undergraduates"
I. Sagert et al. (arXiv:astro-ph/0506417)
"White Dwarf Stars"
D. Koester (http://adsabs.harvard.edu/abs/2013pss4.book..559K)
Chapter 15 of "Modern Astrophysics" book by B.W. Carroll and
D.A. Ostlie
Chapter 15 of "Modern Stellar Astrophysics" book by D.A. Ostlie
and B.W. Carroll
Chapter 15 of "High Energy Astrophysics: Volume 2" book by
M.S. Longair
Chapter 3 of "Black Holes, White Dwarfs, and Neutron Stars" book
by S.L. Shapiro and S.A. Teukolsky
Slides from a 2017 conference on white dwarf stars:
http://www.cnls.lanl.gov/External/whitedwarf/
http://www.cvent.com/events/current-challenges-in-the-physics-of-white-dwarf-stars/event-summary-06cf2ff9feef497ebb6dba446bec9b71.aspx
* 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
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)
"Hubble Space Telescope Astrometry of the Procyon System"
H.E. Bond et al. (2015, ApJ, 813, 106)
"The Sirius System and Its Astrophysical Puzzles: Hubble Space
Telescope and Ground-based Astrometry"
H.E. Bond et al. (2017, ApJ, 840, 70)
"Relativistic Deflection of Background Starlight Measures the
Mass of a Nearby White Dwarf Star"
K.C. Sahu et al. (2017, Science, 356, 1046)
"Astrophysical Implications of a New Dynamical Mass for the
Nearby White Dwarf 40 Eridani B"
H.E. Bond et al. (2017, arXiv:1709.00478)
Howard Bond and Richard Wade in the Department are white dwarf
experts. They can provide further references if you'd like to
learn more about a specific issue.
* 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.
You will turn in your final report via email to
"wnbrandt@gmail.com". Your report should be a single PDF file
submitted as an attachment. If needed for inclusion in
your report, you should scan your handwritten solutions to
the questions and problems in the Koonin book.
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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: 514A;
Skype: nielbrandt; WWW: http://personal.psu.edu/wnb3/
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