#### ASTR 620 Galaxies Problem Set 1Due in class Wednesday 26 September 2007

1. Color Magnitude Diagrams

Use the data for M45 and 47 Tuc tabulated below to answer this question.

Plot color magnitude diagrams for M45 and 47 Tuc.

i. Plot a line for the Zero Age Main Sequence (Table 3.9 of Binney & Merrifield). Fit this line by eye to the data. What is the distance modulus to each cluster?
(Ignore reddening.)

ii. Estimate the age of each cluster.

2. Milky Way Clusters

Use the Dias Open Cluster Catalog and the Harris Globular Cluster Catalog to answer this question.

A. Plot the RA & Dec of the open clusters.
i. What does this tell you about the structure of the Milky Way?
ii. What does this tell you about the orientation of the solar system within the Milky Way?
iii. What quantitative measure about the orientation can you extract from this plot?

B. Add the globular clusters to your plot.
i. What qualitatively new information does this add?
ii. What does the distribution of open and globular clusters suggest about the location of star formation in the Milky Way at different epochs?
iii. Estimate the RA & Dec of the center of the Milky Way.

3. E-resources

A. Explore some of the many wondrous electronic resources available to you:
NED | DSS | 2Mass | Lambda | SDSS.
Tell me about any good ones I've omitted.

B. UGC 303 and UGC 4663.
i) Use the Digital Sky Survey to find and examine the galaxies UGC 303 and UGC 4663.
Print the DSS image and give a brief description of the morphology of each.
ii) Find the same galaxies on the prints of the POSS plates in the reading room (in the cabinet immediately on your right as you enter CSS 1255). How do the POSS prints compare to the DSS? Do you perceive anthing extra on one or the other?

C. Successfully extract your choice of any interesting data from the Sloan Digital Sky Survey. Show me what you got and why you thought it interesting.

4. Surface Brightness

A. How many arcseconds are in one radian?

B. If ΣB is the B-band surface brightness is solar luminosities per square parsec, show that the surface brightness μB in magnitudes per square arcsecond is

μB = 27.05 - 2.5 log(ΣB).

Show explicitly that observable surface brightness μB is distance independent.

C. Spiral and irregular galaxies have an azimuthally averaged radial light profile that is well approximated in many cases by the "exponential disk":
Σ(r) = Σ0 e-r/rd,
where Σ0 is the central surface brightness (in solar luminosities per square parsec) and rd is the scale length (in kpc) of a galaxy fit by this description.

i) Derive what this relation looks like in units of magnitudes per square arcsecond μ(θ), where θ is the radius in arcseconds. You will need to define appropriate substitutes for Σ0 and rd, e.g., μ0 and α.
ii) Integrate Σ(r) from 0 to 2π and r = 0 to x scale lengths (r = xrd) to obtain an expression for the luminosity enclosed by x scale lengths.
• Is the total luminosity finite as x ⇒ ∞ infinity? If not, what is it?
• How many scale lengths contain half the total light? (This is known as the half-light radius, re.)
• Plot the cumulative enclosed luminosity L(< x).

5. Plummer Potential

A simple spherically symmetric potential commonly used to approximate star clusters is the Plummer Potential:

Φ(r) = -GM/(r2+b2)1/2.

A. Derive the density distribution ρ(r) that corresponds to this potential.

B. Integrate the result from (A) along the z axis to obtain the projected surface density Σ(R).
[Hint: r2 = x2+y2+z2 and R2 = x2+y2; so R2+z2 appears in the integrand.]

C. It is common to refer to the core radius of this distribution as the location where Σ drops to half its central value: Σ(Rc) = Σ(0)/2.
What is Rc in terms of b?

Plot ρ(r) and Σ(R) and mark the location of Rc.

 Absolute magnitude M - Mo = -2.5 log(L/Lo) Solar absolute magnitude MoB = 5.48 * Distance modulus m - M = 5 log(d) - 5
*See Binney & Merrifield Table 2.1 for this and other filter information.
See also this discussion of astronomical magnitude systems.

Data for 47 Tuc and M45 Main Sequence Lifetimes
M45       47 Tuc
Star Number Magnitude Color (B-V)   Star Number Magnitude Color (B-V)
10012 19.6 0.76   133 14.4 1.28
10170 20.6 0.98   165 7.6 0.12
10200 21.0 1.05   345 11.6 0.84
10206 21.0 0.96   522 11.9 0.90
10278 21.6 1.23   697 8.6 0.35
10335 22.0 1.31   804 7.9 0.20
10359 22.2 1.23   950 4.2 -0.10
10489 22.6 1.33   1040 15.8 1.44
10610 23.0 1.45   1103 14.8 1.47
20028 17.6 0.53   1234 6.8 0.02
20034 17.7 0.58   1266 8.3 0.36
20049 18.0 0.57   1305 13.5 1.18
20070 18.4 0.60   1309 9.5 0.47
20104 18.8 0.65   1355 14.0 1.23
20130 19.1 0.69   1432 2.9 -0.09
20185 19.8 0.83   1454 12.8 1.16
20210 20.1 0.88   1516 14.0 1.31
20239 20.4 0.93   1766 9.1 0.47
20335 21.4 1.10   1797 10.1 0.56
20364 21.6 1.20   1924 10.3 0.62
30014 13.5 1.10   2168 3.6 -0.08
30103 15.5 0.82   2181 5.1 -0.08
40002 12.0 1.45   2209 14.4 1.47
40022 12.6 1.25   2406 11.1 0.76
40043 12.9 1.14   2425 6.2 -0.05
40130 14.0 0.99   2588 13.1 1.22
40135 14.0 0.69   2601 15.0 1.55
40144 14.0 0.79   2655 15.5 1.36
40164 14.0 0.59   2870 12.5 1.07
40351 14.9 0.85   2881 11.8 0.86
40628 16.2 0.73
40821 16.6 0.73
41051 16.9 0.70
41107 17.0 0.58
41456 17.2 0.51
Spectral
Type