Astronomy 201
Assignment #1: - SOLUTION
Please answer the following from the practice sections of the on-line course notes. Each question is worth 3 marks so write a brief paragraph (but not longer) explaining as concisely and completely as you can. If mathematical calculations are required be sure to show your work and explain what you are doing.
- How does an H-R diagram make it clear that giant stars are larger than main-sequence stars of the same temperature? (Fall lecture 8.3)
- Main sequence and Giants of the same spectral type have essentially the same temperature
- Giants are located above the main sequence and hence brighter
- Star brightness determined by temp and area (size)
- Why do we think halo stars and globular clusters formed much earlier than stars found nearby - the Pleiades for example? (Lecture 12.2)
- Halo stars travel on highly elliptical orbits not confined o galactic plane and exhibit high velocity
- Halo and GC stars are pop II
- Population II stars still have some metal content. Why is this problematic and suggests the possibility of an even older population of stars?(Lecture 12.2)
- Pop II stars still have metal content and hence must have formed in the presence of metals
- Metals were not formed in the big bang hence the metals in popII stars must have come via nucleosynthesis from an earlier generation (pop III)
- Explain why the presence of hot young stars on the edges of spiral arms supports the density wave theory for spiral structure.(Lecture 12.3)
- The spiral density wave is a compression wave travelling slowly around the galaxy. The galaxy rotates faster than the spiral wave and matter enters the density wave where it is compressed
- Differential rotation (different speeds at different locations) helps create the spiral pattern
- Compression triggers star formation which then delineates the spiral arm
- Why is the discovery of rapidly varying x-ray emission from Sagittarius A consistent with idea that there is a super massive black hole at the center of the galaxy? (Lecture 12.4)
- x-ray emission requires a very energetic source - compact objects like neutron stars and black holes are candidates
- the rapid variation suggests that the source must be very small - argues for a BH
Problems (6 marks each):
- Complete the following table:
| Star |
m |
M |
Distance Modulus |
d (pcs) |
| Vega |
0.03 |
0.60 |
-0.57 |
7.68 |
| Rigel |
0.13 |
-7.84 |
7.97 |
392.6 |
| Algol |
2.12 |
-0.07 |
2.19 |
27.4 |
| Maia |
3.87 |
-1.53 |
5.4 |
120 |
- Shown below is the spectrum of a star for which m = 6.8. Explain why you think this is an A0 star. If we assume that it is a main-sequence star calculate its distance from us. What if the star was not a main-sequence star but was instead a supergiant - how would the distance that you found change?
- The prominent pattern of dark lines is due to Hydrogen atoms (the Balmer lines). These are strongest for A-type stars. If you consult the HR diagram you see that the absolute Mag M is 0 for an A-type main sequence star. From this you can determine the distance modulus (m-M = 6.8 - 0 = 6.8) and then determine the distance (d= 10(m-M+5/5)) = 200 pcs. If the star is a supergiant then M = -6 and now the distance modulus is much bigger (12.8) and the distance becomes 3600 pcs. There will be a similar range in your answer.
- The Hubble Space Telescope (HST)image shown below is a series of images of a cepheid variable in the galaxy M100. You may assume that this is a population I Cepheid and the Hubble data indicates that the apparent magnitude varies between 24.5 to 25.3 with a period of 51.3 days. Use this to estimate the distance to M100. If there was (unknown to you) obscuring dust between us and M100, how would this affect your distance determination?
The average apparent magnitude is (24.5+25.3)/2 = 24.9. From the P-L relationship and period of 51.3 days corresponds to an absolute magnitude of M = -6.2. This means that the distance modulus is 24.9 - (-6.2) = 31.1 and the Cepheid is (d= 10(m-M+5/5)) = 16.6 Mpc. If there was obscuring dust then the cepheid would be dimmed and you would over estimate its distance - ie the galaxy is closer to you than 16.6 Mpc.