1. Chapter 8:
The Family of Stars

2. Motivation We already know how to determine a star’s
We already know how to determine a star’s
surface temperature
chemical composition
surface density
In this chapter, we will learn how we can determine its
distance
luminosity
radius
mass
and how all the different types of stars make up the big family of stars.

3. Recent Picture from SDO
A flare erupts from the sun's surface on March 30, in one of the first images sent back by NASA's Solar Dynamics Observatory. Launched in February, SDO is the most advanced spacecraft ever designed to study the sun. SDO provides solar images with clarity 10 times better than high-definition television.

4. Solar Flare -- SDO

5. Hipparchus -- ~ 150 BC Credited with first star catalog
Introduced 360° in a circle
Introduced use of trigonometry
Using data from solar eclipse was able to calculate distance to moon.
Accurate star chart with 850 stars
Created magnitude scale of 1 to 6

6. Hipparcos High Precision Parallax Collecting Satellite
Mission – Map nearest stars to 2 milliseconds of arc
Map another stars to 10 milliseconds of arc along with color information.
Exceeded goals stars to 1milliseconds
Launched Ended 1993
Exceeded all goals. ESA European Space Agency

7. Hipparcos Satallite

8. Distances to Stars __ 1 d = p Trigonometric Parallax: 1 pc = 3.26 LY
d in parsec (pc) p in arc seconds __ 1
d = p
Trigonometric Parallax:
A star appears slightly shifted from different positions of the Earth on its orbit.
1 pc = 3.26 LY
The further away the star is (larger d), the smaller the parallax angle p.

9. The Trigonometric Parallax
Example:
Nearest star, a Centauri, has a parallax of p = 0.76 arc seconds
d = 1/p = 1.3 pc = 4.3 LY
The Limit of the Trigonometric Parallax Method:
With ground-based telescopes, we can measure parallaxes p ≥ 0.02 arc sec
=> d ≤ 50 pc
=> This method does not work for stars further away than 50 pc.

10. Intrinsic Brightness / Absolute Magnitude
The more distant a light source is, the fainter it appears.
The same amount of light falls onto a smaller area at distance 1 than at distance 2 => smaller apparent brightness
Area increases as square of distance => apparent brightness decreases as inverse of distance squared

11. Intrinsic Brightness / Absolute Magnitude
The flux received from the light is proportional to its intrinsic brightness or luminosity (L) and inversely proportional to the square of the distance (d): L __
F ~ d2
Star A
Star B
Earth
Both stars may appear equally bright, although star A is intrinsically much brighter than star B.

12. Distance and Intrinsic Brightness
Example:
Recall:
Betelgeuse
Magn. Diff.
Intensity Ratio 1
2.512 2
2.512*2.512 = (2.512)2 = 6.31 … 5
(2.512)5 = 100
App. Magn. mV = 0.41
Rigel
App. Magn. mV = 0.14
For a magnitude difference of 0.41 – 0.14 = 0.27, we find a flux ratio of (2.512)0.27 = 1.28

13. Distance and Intrinsic Brightness
Rigel appears 1.28 times brighter than Betelgeuse.
Betelgeuse
But, Rigel is 1.6 times further away than Betelgeuse.
Thus, Rigel is actually (intrinsically) 1.28*(1.6)2 = 3.3 times brighter than Betelgeuse.
Rigel

14. Absolute Magnitude
To characterize a star’s intrinsic brightness or luminosity, we define the Absolute Magnitude (MV):
Absolute Magnitude MV = Magnitude that a star would have if it were at a distance of 10 pc.

15. Absolute Magnitude Back to our example of Betelgeuse and Rigel:
Back to our example of Betelgeuse and Rigel:
Betelgeuse
Betelgeuse
Rigel mV
0.41
0.14 MV
-5.5
-6.8 d
152 pc
244 pc
Rigel
Difference in absolute magnitudes: 6.8 – 5.5 = 1.3
=> Luminosity ratio = (2.512)1.3 = 3.3

16. The Distance Modulus
If we know a star’s absolute magnitude, we can infer its distance by comparing absolute and apparent magnitudes:
Distance Modulus
= mV – MV
= log10(d [pc])
Distance in units of parsec
Equivalent:
d = 10(mV – MV + 5)/5 pc

17. The Size (Radius) of a Star
We already know: flux increases with surface temperature (~ T4); hotter stars are brighter
But brightness also increases with size:
Star B will be brighter than star A. A B
Absolute brightness is proportional to the surface area of the star, and thus its radius squared, L ~ R2.
Quantitatively: L = 4 p R2 s T4
Surface flux due to a blackbody spectrum
Surface area of the star

18. Thus, Polaris is 100 times larger than the sun.
Example:
Polaris has just about the same spectral type (and thus surface temperature) as our sun, but it is 10,000 times brighter than our sun.
Thus, Polaris is 100 times larger than the sun.
This causes its luminosity to be 1002 = 10,000 times more than our sun’s.

19. Organizing the Family of Stars: The Hertzsprung-Russell Diagram
We know:
Stars have different temperatures, different luminosities, and different sizes.
To bring some order into that zoo of different types of stars: organize them in a diagram of:
Luminosity
versus
Temperature (or spectral type)
Absolute mag.
Hertzsprung-Russell Diagram
Luminosity or
Temperature
Spectral type: O B A F G K M

20. Most stars are found along the Main Sequence
The Hertzsprung Russell Diagram
Most stars are found along the Main Sequence

21. The Hertzsprung-Russell Diagram
Same temperature, but much brighter than MS stars
→ Must be much larger
Stars spend most of their active life time on the Main Sequence.
→ Giant Stars
Same temp., but fainter → Dwarfs

22. Radii of Stars in the Hertzsprung-Russell Diagram
Rigel
Betelgeuze
10,000 times the sun’s radius
Polaris
100 times the sun’s radius
Sun
As large as the sun
100 times smaller than the sun