Homework 4: Physics inside stars

This homework must be submitted on paper; you may write out your work on paper, or type it into some word processor and then print it. Either way, staple together all pages and write your name legibly at the top of each page.

1. 

   A small portion of the solar spectrum near the sodium 5889 Angstrom absorption line is shown above. You can find a datafile with wavelength (column 1) and intensity (column 2) at

   • kpno_solar_5880.dat (columns separated by spaces )
   • kpno_solar_5880.csv (2 columns, separated by commas)
   1. Estimate the intensity level of the continuum in this region of the spectrum.
   2. Using a very simple method, assume that the absorption line is a triangle. Estimate the width of the base, and the depth of the triangle. Write down these values. Then use those values to calculate a (very very approximate) equivalent width for this line.
   3. Apply numerical integration to the values in the supplied datafile in order to compute a more accurate value for the equivalent width.

2. Let's use the STATSTAR program to investigate the internal properties of a 1 solar mass star on the main sequence. You can find a datafile with the STARSTAR output here:

   • starmodl.dat for 1-solar mass star (columns separated by spaces)
   • starmodl.csv for 1-solar mass star (columns separated by commas)
   1. Make a graph showing density as a function of radius throughout the star. Be sure to label the axes properly, including units.
   2. At what radius is half the mass of the star enclosed?
   3. At what radius is half the luminosity of the star enclosed?
   4. Are these two numbers the same? If not, explain why not.

3. Use the STATSTAR program to generate 4 stellar models, using the following as input for each:

   
   
                Mass       Luminosity      Temperature    X      Y
              ------------------------------------------------------
                1.0         0.86071         5500.2      0.70   0.008
                2.0        22.61200        11218.4      0.70   0.008
                4.0       341.09980        17904.0      0.70   0.008
                8.0      3421.51978        25613.6      0.70   0.008
              ------------------------------------------------------
          

   1. Use these models to estimate the exponent of the following relationships between the total mass "M" and other properties: "L" = total luminosity, "R" = outer radius, "T" = temperature of outer layers, "T_c" = temperature of innermost region.
      
4. Bonus! Can you use STATSTAR to create a successful model which has the following properties?
   • mass = 1 solar mass
   • luminosity = 0.88 solar luminosity
   • X = 0.70
   • Z = 0.008

   If you can, write down the effective temperature of this model, and include in your homework submission a copy of the "starmodl.dat" output file.