### Homework #10

HR Diagrams
Due 5pm Monday Nov 17

1. [2 pts] Draw an HR diagram that shows the location of the Main Sequence, Giant Branch, Horizontal Branch, and White Dwarfs. Be sure that you know how stars evolve on this diagram.

2. [2 pts] Constuct an HR diagram (on graph paper or with the aid of a computer plotting program - no freehand sketches acceptable) of the 25 brightest stars in the night sky, and of the 25 nearest stars to the Sun. Each plot should range from 10-5LSUN to 105LSUN on the y-axis, and from 2500K to 30000K on the x-axis. Remember that HR diagrams are plotted in logs, with red stars on the right.

3. [1 pt] What do the differences in these two diagrams tell us about the frequency of massive, hot stars vs. low mass, cool stars? Which diagram is a better representation of the true distribution of stars in our galaxy and why?

4. [2 pts] Use the equation L = constant*R2T4, where L is the stellar luminosity and R is the stellar radius, to show that objects with the same radii fall on a line in the HR diagram. [HINTS: remember that the equation of a line is y = mx+b, where m is the slope and b is the y-intercept; what variables in the HR diagram correspond to x and y?; review properties of logs]

5. [2 pts] Draw lines of 0.01 RSUN, 1 RSUN, and 100 RSUN in an HR diagram, and show where the Sun, Wolf 359, and Betelguese lie.

6. [1 pt]If the Sun were the size of Betelguese, what would it look like from the Earth?

The Brightest 25 Stars as seen at Night from Earth
 Star Name Temperature Luminosity/LSUN Sirius 9900 24 Canopus 6700 1600 Arcturus 4100 115 Alpha Centauri 5800 1.6 Vega 10400 63 Capella 5200 180 Rigel 14000 63000 Procyon 6600 8 Betelguese 2800 10000 Achernar 16000 1260 Beta Centauri 25000 2250 Altair 7800 11 Aldebaran 3200 200 Spica 25000 1000 Antares 2900 1000 Fomalhaut 9300 16 Pollux 4400 40 Deneb 9600 63000 Beta Crucis 25000 10000 Regulus 14000 200

The Closest 25 Stars
 Star Name Temperature Luminosity/LSUN Sun 5800 1.0 Alpha Cen A 5800 1.6 Alpha Cen B 5250 0.45 Alpha Cen C 3000 6x10-5 Barnard's Star 3000 4.5x10-4 Wolf 359 2500 2x10-5 Lalande 21185 3500 5.5x10-3 Luyten 726-8A 2800 6x10-5 UV Ceti 2800 4x10-5 Sirius A 9900 24 Sirius B 20000 0.003 Ross 154 3000 4.8x10-4 Ross 248 2800 1.1x10-4 Epsilon Eridani 4900 0.3 Luyten 789-6 2700 1.4x10-4 Ross 128 3000 3.6x10-4 61 Cyg A 4400 0.083 61 Cyg B 4000 0.040 Epsilon Indus 4400 0.13 Procyon 6600 8