1. Star Counts

In star count lingo, N(m) is defined to be the number of stars observed with apparent magnitude brighter than m. It can be shown that if the Galaxy had a uniform density of stars, that logN(m)=0.6m +C (even if stars dont all have the same brightness).

Here is a table of integrated star counts logN(m) (again, N=number of stars brighter than apparent magnitude m) from Allen's "Astrophysical Quantities." The columns are

apparent magnitude (m)
log N(m) in a direction up out of the galactic plane
log N(m) in a direction towards the galactic center

With this data, make a plot showing log N vs m in the two different directions. Explain qualitatively why the star counts in different directions are different.

Now plot the expected log N vs m given above for a uniform distribution of stars. Again, explain in detail why there are differences between each of the observed star counts and the uniform model.

2. Distance errors

Use differential calculus to show that if you are using distance modulus (m-M) to get the distance to an object, if you have a magnitude uncertainty of dm (where dm is small), you get a fractional uncertainty in distance of approximately 0.5*dm. In other words, as an example, if your distance modulus error is 0.1 magnitudes, your distance uncertainty is about 5%.

3. Calibrating a main sequence diagram

Hipparcos was a satellite mission which obtained parallax data for a large number of stars. Using this data, we can construct a calibrated Herzprung-Russell diagram for nearby stars. Here is a table of parallax data for all stars in the Hipparcos catalog which

Use the data to make a calibrated color magnitude diagram of these stars. Note -- color magnitude diagrams must always have bright blue stars in the upper left!

Now, overplot a theoretical zero age main sequence for solar metallicity (Z=0.02) stars. Describe and explain differences between the ZAMS and your Hipparcos dataset.

4. The Distance to The Stable*

Here is a dataset for an open cluster known as "The Stable" (columns: V and B-V). The Stable has a reddening of E(B-V)=0.25 magnitudes and roughly solar metallicity. Correct the colors and magnitudes for the dust (explain how!) and the plot an observed color magnitude diagram (apparent mag vs color) for the Stable. Then compare the diagram to the solar metallicity ZAMS to derive a distance to the Stable.

Estimate the error in your distance to the Stable, and explain what the sources of error are.

What is the color of the stars at the main sequence turnoff? What is the age of this star cluster? (Use Figure 13.29 from Carroll and Ostlie to help you with this question.)

5. The Distance to Laungheer 413**

Here is photometry of Laungheer 413 , a globular cluster. Again, you have apparent V magnitude and observed B-V color. Laungheer 413 has a reddening of E(B-V)=0.1 and a metallicity of [Fe/H]=-0.76. Since it is metal-poor, you'll want to compare it to this metal-poor (Z=0.004) ZAMS. Figure out the distance (and error) and age of Laungheer 413, the same way you did for the Stable.

(Note: the Carroll and Ostlie figure is really intended for age-dating Population I objects, not really globular clusters. To do this right, you would really want to use a set of isochrones for metal-poor Pop II objects to do this. But this will get us in the right ballpark....)

6. RR Lyrae Stars

Laungheer 413 has one RR Lyrae variable star in it: V9, with a mean V apparent magnitude of 14.685 and period of 0.737 days. What is the mean absolute magnitude of V9 (remember to correct for the dust!)?

If you mistakenly thought it was a Cepheid, what would you have derived for its mean absolute magnitude given the Cepheid period-luminosity relationship? Under that (mistaken) assumption, what would you then estimate of the distance to Laungheer 413 to be?