Comments on Quiz 2

Part A

A1. a. Parallax angle, the angle at the top of the triangle, decreases with increasing distance.
(Seeds, Fig. 9-4).
A2. b.

A3. e. But since Pluto takes "forever" to orbit the Sun, one would operate the Plutonian telescope in conjunction with one orbiting the Earth. In other words, the baseline would be Pluto-Earth not Pluto-Sun-Pluto.

A4. A straightforward exercise in BL/d² with L the same for all stars. Relative to 10pc, the 20pc star is twice as distant. B is reduced by 2²=4 times. For the 100pc star, the reduction is 10²=100 times.

A5. c.
A6. d.
A7. e. This follows from LM⁴ and the answer c to A5.
A8. d.
A9. See Seeds, Fig 9.9.
A10. A0V.
A11. M5I.
A12. a. False b. True c. False d. False
A13. a. Hydrogen b. Helium
A14. False
A15. d.
A16. c.
A17. SNII from the 20 solar mass star, and Betelgeuse.
A18. Seeds: Mass < 0.1M. Does not burn H to He in its interior.
A19. This question gave M and L. Therefore, it is not necessary to use LM⁴. Indeed, the stars do not satisfy this relation!

Expressing this in terms of the Sun's lifetime

a.

b.

Assumptions?
- luminosity remains constant
- all of the stellar mass is burnt, or, more particularly, the same fraction of the mass consumed in the star and the Sun.
- stars including the Sun have the same composition.

A20. b.
A21. c.
A22. b.
A23. a. Gravity rules again!
A24. A WD is supported against gravity by degenerate electrons. Pressure from these electrons is independent of temperature.
A25. a.

Part B
B1.a.Seeds. In describing 'visual binary' make it clear that two stars are visible. For 'eclipsing binary', it is crucial to note that they are eclipsing to us; it is not sufficient to say simply the stars pass in front of one another.

b. The critical point is that a binary is eclipsing only if the orbits are aligned with our sightline ­ a very particular alignment. On the other hand, the binary will be seen as a spectroscopic binary at all tilts of the orbits to the sightline except the perpendicular one. Clearly, the probability is much higher that a binary will be spectroscopic than eclipsing. All eclipsing binaries are also spectroscopic binaries.

c. As b.

d. At a large distance from Earth, the angular separation of the two stars becomes very small; the two stars will be unresolved (not seen as two). But their orbital motions will still be detectable through the Doppler shifts of absorption lines. Except for the fact that the brightness of the stars decreases with increasing distance, detectability of spectroscopic binaries is in independent of distance.

B2. a.The distribution of stars in the H-R diagram should have looked like the right-hand panel of Fig. 9-16.

b. For a young cluster, the main sequence unlike that above will be complete from O-type to M-type. And there will be NO white dwarfs in the young cluster.

c. Remember L=R²T⁴. This star evolves at constant L. Therefore, as T increases from base to tip, the R must decrease.

B3. a.LM⁴

b. A simple way to show the lack of a L-M relation is to plot the evolutionary tracks.

This shows that the L of a low mass red giant changes greatly in the course of its evolution. And high mass and low mass stars tend to converge in L as red giants/supergiants. Look at Seeds Fig, 10-22 and contrast the ordered masses on the main sequence with the lack of order for the evolved stars.

c.A simple exercise in LM⁴ and

For maximum illumination, A wins because 20⁴ >> 20 x 1⁴.
For maximum time, B wins because 1/1³ >> 1/20³.

B4. and B6. are discussed on Classnotes

B5. Seeds.