#### ASTR 620 Galaxies Problem Set 1Due in class Wednesday 17 September 2003

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?

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. Galaxy Morphology

Consider the five galaxies in the table.
 M 33 M 51 NGC 3109 NGC 5850 IC 3475

Use NED (nedwww.ipac.caltech.edu) to
i) obtain and print an image of each of these galaxies. Label the orientation of each image (which way are North & East?).
ii) obtain each system's recession velocity (in km/s).
iii) obtain each object's total, extinction corrected BT0 magnitude and (B-V)T0 color index, where available. Give preference to data from the Third Reference Catalog (RC3) where multiple measures are given.
iv) Use this information to compute the total luminosity of each galaxy.
v) Use the model relations between mass-to-light ratio and color of Bell & de Jong [(2001), ApJ, 550, 212] to convert luminosity to stellar mass. Briefly justify your choice of model from the range offered by Bell & de Jong, addressing the choice of star formation history, metallicity, and IMF.

4. Surface Brightness

A. How many arcseconds are in one radian?

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

sB = 27.05 - 2.5 log(IB).

Show explicitly that observable surface brightness sB is distance independent.

C. Spiral and irregular galaxies have an azimuthally averaged radial light profile which is well approximated in many cases by the "exponential disk":
I(r) = I0 e-r/h,
where I0 is the central surface brightness (in solar luminosities per square parsec) and h 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 s(a), where a is the radius in arcseconds. You will need to define appropriate replacements for I0 and h.
ii) Integrate I(r) from 0 to 2 pi and r = 0 to x scale lengths (r = xh) 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. 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.

 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.

Data for 47 Tuc and M45 Main Sequence Lifetimes
47 Tuc       M45
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