ASTR 421
Galaxies
Homework 1
POSTPONED - now due in class Thursday 17 February 2011

  1. Betelgeuese and the magnitude system

    Sparke & Gallagher problems 1.3 & 1.8.

    Note that in 1.8 they mean to refer to table 1.6, not 1.4.
    It is a good idea to check their errata.

  2. Solar Energy

    Sparke & Gallagher problem 1.4.

    Additionally, express the luminosity of the sun in Megatons per second. For perspective on scale, the largest H-bomb ever tested had a yield of about 50 Megatons of TNT; the Hiroshima A-bomb was around 50 kilotons.

  3. Stellar Evolution

    Use the data in Sparke & Gallagher Table 1.1 to answer this question.

    As a function of mass, plot*(i) the fraction of a star's life spent in post-main sequence stages, and (ii) the fraction of a star's total energy output emitted in post-main sequence stages.

    Imagine simultaneously forming a cluster of stars of all masses. This is called an simple stellar population (SSP). Using your graph and looking through the data table, at approximately what age do red giants begin to dominate the total luminosity of the SSP?

    * For a scientist, Plotting is Life. We will do it a lot. Find a better tool than excel.
    Plotting a fraction cancels out a lot of dynamic range. Try plotting L(M) linearly and logarithmically and you will begin to understand why astronomers are so fond of log-log plots.

  4. 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.

    Plot a line for the main sequence (Table 1.4 of Sparke & Gallagher). Fit this line by eye to the data. What is the distance modulus to each cluster?
    (Ignore reddening.)

    Estimate the age of each cluster.

  5. E-resources

    Explore NED. At the very least, type in a few galaxy names (e.g., NGC 6946; UGC 2885) and try to make sense of the information provided.

    There is no written component to this "problem." Just check it out!

Useful Relations
Absolute magnitude M - M⊙ = -2.5 log(L/L⊙)
Solar absolute magnitude M⊙V = 4.83 *
Distance modulus (D in pc) m - M = 5 log(D) - 5
*See also this discussion of astronomical magnitude systems.

Data for 47 Tuc and M45 Approximate Main Sequence Lifetimes
see also S&G Table 1.1
47 Tuc       M45    
Star Number Magnitude mV Color (B-V)   Star Number Magnitude mV 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		 Lifetime
(years)
O 3 X 106
B 3 X 107
A 4 X 108
F 4 X 109
G 1 X 1010
K 6 X 1010
M >1011