**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 **

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

W_{Λ
}as a function of W_{m} 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?