1. Questions 1 – 24: Due Wednesday, February 29, 5:00 pm.
Homework #4
Questions 1 – 24: Due Wednesday, February 29, 5:00 pm.
Questions 25 & 26: Due now

2. What are they and how do we know?
Stars
Energy output
Sizes
Masses
Colors
Temperatures
Lifetimes
What are they and how do we know?

3. How do we measure stellar temperatures?

4. Properties of Thermal (Continuous spectrum) Radiation
Hotter objects emit more light per unit area at all wavelengths.
Hotter objects have their peak emission at shorter (bluer) wavelengths.

5. Thermal spectra from stars show…
Hottest stars:
50,000 K
Coolest stars:
3,000 K
Sun’s photosphere is 5,800 K

6. Activity involved developing classification scheme for spectra1 2 3 4 5 6 7

7. Prominence of specific lines were used in initial spectra classification. Spectral types were named A, B, C, D, … A B F G K M O

8. Reordering of spectral types in order of decreasing temperature removed some spectral typesB A F G K M

9. Absorption lines in a star’s spectrum correspond to a spectral type that reveals its temperature
(Hottest) O B A F G K M (Coolest)

10. (Hottest) O B A F G K M (Coolest)
Remembering Spectral Types
(Hottest) O B A F G K M (Coolest)
Oh, Be A Fine Girl, Kiss Me
Only Boys Accepting Feminism Get Kissed Meaningfully

11. How do we measure stellar masses?

12. The orbit of a binary star system depends on the strength of gravity
I’m not sure where this came from, if it’s not on the CD, let me know.
Many stars are in binary systems, where two stars orbit about each other.
The orbit of a binary star system depends on the strength of gravity

13. Types of Binary Star Systems
Visual Binary
Eclipsing Binary
Spectroscopic Binary
About half of all stars are in binary systems

14. We can directly observe the orbital motions of these stars
Visual Binary
We can directly observe the orbital motions of these stars

15. Eclipsing Binary
We can measure periodic eclipses

16. Spectroscopic Binary
We determine the orbit by measuring Doppler shifts

17. We measure mass using gravity
Direct mass measurements are possible only for stars in binary star systems
p = period
a = average separation
4π2
G (M1 + M2)
P2 = a3

18. Need 2 out of 3 observables to measure mass:
Orbital Period (P)
Orbital Separation (a or r = radius)
Orbital Velocity (v)
For circular orbits, v = 2pr / P v r M

19. Most massive stars:
100 MSun
Least massive stars:
0.08 MSun
(MSun is the mass of the Sun)

20. We have learned that a star is a large, luminous ball of gas and plasma that is massive enough to have the central temperatures and pressures necessary for nuclear fusion to occur.

21. But stars have different colors (temperatures) and different luminosities.
How do we explain these differences?

22. “Hertzsprung-Russell Diagram”
A convenient way to gain insight into properties and life-cycles of stars is through the most famous and perhaps the most important diagram in astronomy:
“Hertzsprung-Russell Diagram”

23. Hertzsprung-Russell Diagram: A plot of the temperature, color or spectral type of stars (they are all inter-related) against their luminosity (or its equivalent, absolute magnitude)

24. An HR diagram for ~15,000 stars within 100 parsecs (326 light years) of the Sun shows that stars do not fall everywhere in the H-R Diagram, but rather fall into four areas:
Main Sequence
Giants
Supergiants
White dwarfs

25. Most stars fall somewhere on the main sequence of the H-R diagram
Luminosity (Solar Luminosities)
Surface Temperature (K)

26. Hot stars (bluer) are found at the upper left hand end of the Main Sequence while cooler (redder) stars are found to the lower right.
Luminosity (Solar Luminosities)
Surface Temperature (K)

27. Large radius
Stars with lower T (lower emissions per surface area) and higher L (greater overall brightness) than main-sequence stars must have larger radii:
giants and supergiants
Luminosity (Solar Luminosities)
Surface Temperature (K)

28. Stars with higher T (higher emissions per surface area) and lower L (lower overall brightness) than main-sequence stars must have smaller radii:
white dwarfs
Luminosity (Solar Luminosities)
Small radius
Surface Temperature (K)

29. A star’s full classification includes spectral type (spectral line identities) and luminosity class (line shapes, related to the size of the star):
I - supergiant
II - bright giant
III - giant
IV - subgiant
V - main sequence
Examples: Sun - G2 V
Sirius - A1 V
Proxima Centauri - M5.5 V
Betelgeuse - M2 I

30. H-R diagram depicts: Temperature Color Spectral Type Luminosity Radius

31. Main-sequence stars are fusing hydrogen into helium in their cores, like the Sun
Luminous main-sequence stars are hot (blue)
Less luminous ones are cooler (yellow or red)

32. 60 M
30 M
10 M
Measurements of stellar masses show that hotter (bluer) main sequence stars are much more massive than cooler (redder) main sequence stars
5 M
1 M
0.1 M
(1 M = 1 solar mass)

33. High-mass stars
The mass of
a normal, hydrogen-burning star, i.e., a main sequence star, determines its luminosity and spectral type!
Low-mass stars

34. Core pressure and temperature of a higher-mass star need to be larger in order to balance gravity
Higher core temperature boosts fusion rate, leading to larger luminosity

35. Stellar Properties Review
Luminosity: from brightness and distance
10-4 LSun LSun
Temperature: from color and spectral type
3,000 K ,000 K
Mass: from period (P) and average separation (a)
of binary-star orbit
0.08 MSun MSun

36. Mass & Lifetime Sun’s life expectancy: 10 billion years
Life expectancy of 10 MSun star:
10 times as much fuel, uses it 104 times as fast
10 million years ~ 10 billion years x 10 / 104
Life expectancy of 0.1 MSun star:
0.1 times as much fuel, uses it 0.01 times as fast
100 billion years ~ 10 billion years x 0.1 / 0.01
Until core hydrogen (10% of total) is used up

37. 107 yrs
Hotter, more massive stars have shorter main sequence lifetimes than cooler, less massive stars
108 yrs
109 yrs
1010 yrs
1011 yrs

38. Very rare
Observations show that hotter main sequence stars are much less common than cooler main sequence stars.
There are two reasons for this: 1) the former have very short lifetimes, 2) more low mass stars are born than high mass stars.
Very common

39. Main-Sequence Star Summary
High Mass Stars:
High Luminosity
Short-Lived
Rare
Large Radius
Blue
Low Mass Stars:
Low Luminosity
Long-Lived
Common
Small Radius
Red
Main-Sequence Star Summary

40. Giants, supergiants, & white dwarfs

41. Off the Main Sequence
Stellar properties depend on both mass and age: those that have finished fusing H to He in their cores are no longer on the main sequence
All stars become larger and redder after exhausting their core hydrogen: giants and supergiants
Most stars end up small and white after fusion has ceased: white dwarfs

42. We will return to a discussion of giants, supergiants and white dwarfs when we discuss the deaths of stars.