# Lecture 26 The Hertzsprung- Russell Diagram January 13b, 2014

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1 1 Lecture 26 The Hertzsprung- Russell Diagram January 13b, 2014

2 2 Hertzsprung-Russell Diagram Hertzsprung and Russell found a correlation between luminosity and spectral type (temperature) Hot, bright stars Luminosity (Solar units) Sun Cool, dim stars hot O B A F G K M Main Sequence cooler

3 3

4 4 Most stars (~90%) are on the main sequence The greater the temperature, the more luminous the star M type stars are the most common. O type stars are the least common.

5 5 Sizes of Stars Size of star is related to the temperature and the luminosity by: Luminosity Temperature Radius L T 4R If you know the position on HR diagram you know the size of the star.

6 6 A star is twice as luminous as the Sun and has twice the surface temperature. What is its radius relative to the Sun s radius? A. R star /R Sun = 4.0 B. R star /R Sun = 2.8 C. R star /R Sun = 0.5 D. R star /R Sun = 0.35

7 7 A star is twice as luminous as the Sun and has twice the surface temperature. What is its radius relative to the Sun s radius? star Sun L T 4 R R L 4 T 4 4 L 4T star star star Sun 4 4 Sun Sun Sun star R L T R L T L T

8 8 100 R R Supergiants Luminosity (Solar units) R White Dwarfs Sun 0.1 R Giants Cool, dim stars Main Sequence hotter 0.01 R O B A F G K M Spectral Classification cooler

9 9 Supergiants -- cool, bright, red, large stars Giants -- cool, bright red, less large stars Main Sequence -- spans range from hot, bright stars to cool, dim stars. White dwarfs -- hot, small, dim stars. These classifications will give clues to stages in the evolution of stars.

10 10 Stars come in many sizes!

11 11 Sizes of Objects in our Universe Images from webisto.com/space

12 12 Sizes of Objects in our Universe

13 13 Sizes of Objects in our Universe

14 14 Sizes of Objects in our Universe

15 15 Sizes of Objects in our Universe

16 16 Masses of Stars We cannot directly measure the mass of an isolated star. If something is orbiting the star, can use the general form of Kepler s Third Law 2 3 M M P a 1 2 Luckily, 2/3 of all stars are binary stars, two stars that orbit one another

17 17 A binary star system consists of one star that is twice as massive as the other. They are 2.0 AU apart and have an orbit period of 0.50 y. What is the mass of the smaller star in terms of solar masses? A. 11 M Sun B. 4 M Sun C M Sun D M Sun

18 18 A binary star system consists of one star that is twice as massive as the other. They are 2.0 AU apart and have an orbit period of 0.50 y. What is the mass of the smaller star in terms of solar masses? A. 11 M Sun 2 3 m 2m P a B. 4 M Sun C M Sun D M Sun 3 a 2.0 AU m 3P y 3 11M

19 19 Mass-Luminosity Relation True ONLY for Main Sequence stars As the mass increases, the luminosity increases rapidly 3 Luminosity Mass

20 20 HR Diagram: Main sequence stars labeled by mass in units of solar masses.

21 21 Question How do the following properties differ with respect to the Sun for the listed main sequence types? What properties would not change for non-main sequence stars? Temperature Mass Size Color Luminosity O G M

22 22 Question How do the following properties differ with respect to the Sun for the listed main sequence types? What properties would not change for non-main sequence stars? O G M Temperature* Higher Same Lower Mass Higher Same Lower Size Larger Same Smaller Color* Blue White Red Luminosity Higher Same Red

23 23 Apparent Brightness The brightness an object appears to have. The further away the object, the dimmer it looks Apparent Brightness Luminosity 2 4 d d = distance

24 24 Star A has a brightness of 1.0 μw/m 2 and is known to be 4.0 ly away. Star B is 9.0 ly away and has a brightness of 3.0 μw/m 2. How much more luminous is star B than star A? A. 240 B. 15 C. 6.8 D. 3.0

25 25 Star A has a brightness of 1.0 μw/m 2 and is known to be 4.0 ly away. Star B is 9.0 ly away and has a brightness of 3.0 μw/m 2. How much more luminous is star B than star A? A. 240 B. 15 C. 6.8 D. 3.0 B L L B A 4 2 B B B 2 2 A A A L L d B 4d L 4 d B ly 3.0 W/m ly 1.0 W/m 2 15

26 26 Spectroscopic Parallax If luminosity and apparent brightness are known, distance can be determined. m M 5log d 5 It can be difficult to accurately measure luminosity for one star Use spectra to get spectral type and class But, you can use a cluster of stars Distance to the cluster can be determined by comparing the HR diagram of the cluster with a template HR diagram

27 27 Spectroscopic Parallax Observations Template hot O B A F G K M cooler hot O B A F G K M cooler

28 28 Spectroscopic Parallax hot O B A F G K M cooler Now the vertical axis is on an absolute scale. We can read off the luminosities of the stars, and from that, together with the apparent brightness, we can determine the distance to the stars.

29 29 The Distance Ladder See Extending Our Reach on p. 484 First rung: parallax Second rung: spectroscopic parallax Third rung: standard candles/inverse square law

30 30 The Distance Ladder We will be discussing the longer distance rungs of the ladder in subsequent lectures. Figure 26.12, Freedman and Kaufmann, 7 th ed. Universe, 2005 W. H. Freeman & Company

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