Astronomy 421 Winter 2005 Quiz 5
Due: February 15, 2005
<Worth 10 points, or two quizzes; answer on separate sheet of paper or through email>
1. State the equations [P(r), M(r), L(r), T(r)] for
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
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condition of hydrostatic equilibrium
mass conservation equation
energy generation equation
equation of energy transport
o radiative transport
o adiabatic convective transport
identifying the terms in each equation. How does the stellar structure code treat each of the
equations?
2. What is meant by the phrase “Standard Solar Model”? A web site that you may wish to use as
your reference is linked from our homepage:
http://www.ap.stmarys.ca/~guenther/solar/what_is_ssm.html
Read through the information given there, and summarize in a paragraph here.
3. Define mean molecular weight in your own words. How would we figure out, with the fewest
number of approximations, the mean molecular weight of a system of particles (atoms and ions)?
4. Someone asks you to explain, in easily understood language, the conditions necessary for
convection to dominate radiative transport in a star [see pp. 352-364]. Do so.
5. The stellar interior code uses a method called Runge-Kutta to integrate the 4 differential
equations of stellar structure.
a. Review the information on either of the following 2 sites, and summarize briefly how this
numerical program works
 http://astron.berkeley.edu/~eros/ay160A/runga/runga.html
 http://lib-www.lanl.gov/numerical/bookcpdf.html
(look under Integration of Ordinary Differential Equations)
b. The Fortran program uses a subroutine called RUNGE to do this. It then calls another
subroutine, that then calls the appropriate functions. Try to follow the logic used in the
program based upon your reading from part a just above. Write down one question you
have on the Runge-Kutta method, either on how it works or how the program uses it or a
combination of both.
INSTRUCTIONS FOR STATSTAR
Initial steps in preparing to run the stellar interior code:
1. Create a directory within your working directory that will be explicitly used for this
project.
2. “cd” to that directory
3. Copy the Fortran programs into that directory. (Note the space and period following
statstar.f)
4. Before you can run the program, you must compile it within Linux; “runstatstar” is an
example of a name to use. This file will be in binary format.
5. You need to tell the computer that this file is executable.
6. Test out the program by typing “runstatstar,” putting in reasonable values at the prompts.
Examples:
yourtopdirectory(1)% mkdir StatStar
yourtopdirectory(2)% cd StatStar
StatStar(3)% cp /net/projects/Astro_421/FORTRAN/statstar.f .
StatStar(4)% g77 –o runstatstar statstar.f
StatStar(5)% chmod +x runstatstar
StatStar(6)% runstatstar
I’m having you all copy and run the program in your directories so that you will feel free to
modify the Fortran program. I will be explaining the various features of the program in class,
and pointing out simple modifications that you may wish to make. There are ways to streamline
the process so that with a few “do loops” and handling of file names, you could have the entire
run of stellar models done within seconds. Any time you make changes in the Fortran code, you
would need to recompile it via Step 4 above. All of the programs the model uses are contained in
one file – the main routine, the subroutines, and the functions – so that you need compile only the
one program. I would like each of you to think about what you want the program to do, and then
we can figure out how to do it together. I do not expect you to learn Fortran, although you will
most likely find out that it is not that much different from IDL.
Caution: The program as written will overwrite the files created. Thus, you may go along
happily running dozens of stellar models to find out, in the end, all you’ve got left is the last one.
The reverse side of this sheet contains the problems you are to work through from Chapter 10 of
Carroll and Ostlie, slightly modified for this project. After you run your models, you will need to
plot the data in various ways for your analysis and write up. We will be using a plotting program
called Super Mongo (SM for short), that is fairly straightforward and simple. Instructions on
using SM are linked from our homepage:
http://www.astro.washington.edu/astro497d/SM/tutorial.html
The files containing the initial parameters for the models are also linked from our home page:
◦ X=0.7, Y=0.29, Z=0.01
◦ X=0.7, Y=0.292, Z=0.008
Problem 10.18, P. 378 – follow the directions given in the book (a warm-up to the program).
Problem 10.19, P. 378
Use the stellar structure code statstar.f and calculate the models for the following stellar masses:
Mass (Msun) Luminosity (Lsun) Effective Temperature
0.5
0.02150
2331.45
1.0
0.86071
5500.20
2.0
22.61200
11218.40
3.0
116.57999
15007.30
4.0
341.09998
17904.00
5.0
747.92000
20302.00
6.0
1375.34998
22310.00
7.0
2260.19995
24074.00
8.0
3421.51978
25613.60
9.0
4880.79980
27061.20
10.0
6641.59961
28263.60
for X = 0.7, Y = 0.292, and Z = 0.008
(a) After obtaining satisfactory models, overplot these masses on a P vs. r graph; these masses in
an Mr vs r graph, these masses in an Lr vs r graph, and these masses in aT vs r graph.
(b) For each of these stellar masses, at what temperature has Lr reached 99% of its surface value?
50% of its surface value? Is the temperature associated with 50% of the total luminosity
consistent with the rough estimate found in Eq. (10.33)? Comment on your results for each mass,
explaining “why or why not” to the questions posed here.
(c) For each of the stellar masses modeled, what are the values of Mr/M* for the two temperatures
(99% and 50% of the surface value) found in part (b)? M* is the total mass of the stellar model.
(d) This part is done automatically when you overplot the results for each comparison as a
function of stellar mass. Comment, however, on your results as if you were providing the
explanatory caption for those figures.
(e) Follow the directions given in the text since you have all of the information you need.
Problem 10.20, P. 379
Repeat the above steps for the different composition: X = 0.7, Y = 0.29, and Z=0.01, and answer
the questions given in the text. Note that the luminosities and effective temperatures for these
masses are different for this different composition. Read off the values for the masses above from
the file linked from our home page.