Astronomy 490                                  Homework #7                                      Spring 2007

 

 

Due date:   Monday, April 2  at start of class. 

Please make a copy of your assignment to refer to during the class discussion.

 

Journal paper:  

   Perlmutter et al. 1999,

   Measurements of W and Λ from 42 High-Redshift Supernovae,

   Astrophysical Journal, 517, 565

 

Supplementary article:

 

   Perlmutter 2003,

   Supernovae, Dark Energy, and the Accelerating Universe

   Physics Today

 

 

 

Assignment:

 

1.  Read the Physics Today article.

 

2.  Read the first 3 sections (pp. 1-8) of the Astrophysical Journal article.

 

3.   In Fig. 5 of the Physics Today article, draw a best fit straight line by eye through the

      blue region defined by the SN Ia measurements.  Then come up with an equation for

      WΛ as a function of Wm that represents the line you drew.  Finally, compare the

      equation you get from your eyeball fit to the equation given in the abstract of the

      Astrophysical Journal (ApJ) paper.

 

4.  Take a close look at Fig. 2a of the ApJ paper. 

 

     (i)  For each of the flat-Universe models (blue dashed lines), count how many points

           fall above vs. below the line.  Use only points for which z > 0.3.  Judging from

           your results, which of the dashed blue lines gives the best fit to the data? 

 

     (ii)  For the best-fit dashed line (or two closest ones, if one doesn’t stand out as the

           clear best), count how many of the points’ error bars touch the line that defines the

           model (i.e. have values within 1s of the model).  Then count the number of points

           that land within 2s and 3s (as best you can judge this by eye).  Do the data seem

           to be reasonably well described by Gaussian random statistics (68% of points

           within 1s, 95% within 2s, 99.7% within 3s?).  If not, what reasons can you think

           of that might explain why not?