Exam Technique

1. Exam Technique • READ THE QUESTION!! • make sure you understand what you are being asked to do • make sure you do everything you are asked to do • make sure you do as much (or as little) as you are asked to do [implicitly, by the number of marks] • Answer the question, the whole question, and nothing but the question

2. Exam Technique • Read the whole paper through before you start • if you have a choice, choose carefully • whether or not you have a choice, do the easiest bits first • this makes sure you pick up all the “easy” marks • PHY111 • do all of section A (20 questions, 40%) • do 3 from 5 in section B (3 questions, 30%) • do 1 from 3 in section C (1 question, 30%)

3. Last Year’s Exam, Section B • Answer any 3 of 5 short questions • 5 marks each • exam is out of 50 • i.e. 120/50=2.4 minutes per mark • hence each question should take ~12 minutes to answer • do not let yourself get bogged down, but • do not write 2 sentences for 5 marks!

4. Question B1 • You have the following pieces of information about a nearby star: • the apparent position of the star on the sky, measured very accurately over a period of several years; • the star’s spectrum; • the apparent brightness of the star, measured over the whole wavelength range. • Using this information, explain how you would determine: • the surface temperature of the star; • the distance of the star; • the size (radius) of the star.

5. B1 Answer • Surface temperature: • from spectral line strengths (e.g. molecular lines in cool stars) • (“from colour” got half a mark) • Distance: • from parallax (measure star’s apparent shift in position relative to distant objects, over the course of a year or so) • Size: • Combine brightness and distance to get intrinsic luminosity • Use luminosity and temperature to get size from blackbody calculation

6. Question B2 • It is often said that “the Sun is an average star”. Discuss this statement carefully, considering properties such as brightness, age, position on the HR diagram, location in the Galaxy, etc.

7. B2 Answer • For its being average: • on main sequence, midway through its life • near middle of brightness/temperature ranges (on log scale!) • located in old disc of galaxy • Against its being average: • most stars are smaller and fainter (class M and K dwarfs) • it’s not in a binary (probably more than half of all stars are) • Not clear one way or the other: • it’s got planets (this is probably more common than not, but we don’t know yet) • Conclusion • the fact that ~90% of stars are smaller and fainter than the Sun indicates it is not really an “average” star

8. Question B3 • Draw a labelled diagram of the “Hubble tuning fork” system of galaxy classification. • Explain briefly how galaxies are classified according to this scheme.

9. En where increasing n indicates increasing ellipticity. S0: disc galaxies without spiral structure. S/SB: unbarred/barred Sa/b/c: bulge size/ brightness decreases, so does tightness with which arms are wound. Irr: amorphous or disrupted. B3 Answer

10. Question B4 • Explain why we might reasonably expect that the sky would not be dark at night, carefully listing the assumptions that lead to this incorrect conclusion. • How do we explain the darkness of the night sky in the Big Bang cosmological model?

11. B4 Answer • If we assume that the universe • is infinite in spatial extent • is infinitely old • and is not expanding (so, no redshift) • then every line of sight from any observer will eventually intercept a star. • Therefore, everywhere we look we should see a stellar surface, and the average temperature of the night sky should be the average stellar surface temperature (~3000K)

12. B4 Answer • In the Big Bang model, the universe is not infinitely old, and also it is expanding. The light from many stars has not yet had time to reach the observer, and in any case it would be redshifted down to a much lower temperature (and so would not be bright). • Note: detailed analysis indicates that finite age is much the more important factor for starlight. However, you need the expansion to prevent the CMB from producing a bright night sky.

13. Question B5 • The Drake equation is a method of estimating the number of communicating technological civilisations in the Galaxy. It consists of a number of different factors multiplied together. • The first factor in the Drake equation is “the rate of formation of suitable stars.” What is meant by a “suitable star”? Why are other kinds of stars unsuitable? • List, with a brief (one sentence) explanation, any three of the remaining factors in the Drake equation.

14. B5 Answer • Suitable star: • not O, B or A class (don’t last long enough); • probably not M class (planets likely to be tidally locked; also, often flare stars); • not close binary (unlikely to support stable orbits at the right distance); • not too low in heavy elements (unlikely to form planetary system); • not seriously variable

15. B5 Answer • Other terms include any three of: • fraction of suitable stars that have planetary systems (we assume life requires a planet!) • number of suitable planets per system • fraction of suitable planets on which life does indeed develop • fraction of life-bearing planets on which an intelligent species evolves • fraction of intelligent species which develop a technological civilisation • average lifetime of a technological civilisation (where “technological” is here defined as “capable of sending and receiving radio broadcasts”; the Roman empire does not count)

16. Last Year’s Exam, Section C • Answer any 1 of 3 long questions • 15 marks each, ~36 minutes’ work • Question C3 is on the seminars: • Write short essays on any three of the following • binary stars • the search for dark matter • neutrinos in astrophysics • prospects for extraterrestrial intelligence • Note that you know this is coming, so more detail expected in answers!

17. Question C1 • The HR diagram of an old cluster is likely to include the following four branches (working from the top down): • A. the red giant branch; • B. the horizontal branch; • C. the main sequence; • D. the white dwarfs. • Put these branches in the order in which they would be visited during the evolution of a Sun-like star. • For each branch, explain what (if anything) is being fused to generate energy, and where. • Use the above information to describe the evolution of a Sun-like star.

18. C1(a) • Order: CABD • Fusion processes: • A: hydrogen to helium, in shell outside helium core • B: helium to carbon, in core • C: hydrogen to helium, in core • D: nothing; no fusion occurring

19. C1(a) • A Sun-like star starts off on the main sequence, fusing hydrogen to helium in the core. Eventually, the core hydrogen is exhausted, and the star begins to fuse hydrogen in a shell around a the (now pure helium) core: at this point the star begins to expand and cool, moving first to the subgiant branch, then to the red giant branch. • When the star reaches the top of the red giant branch, the core is hot enough for helium fusion to begin. The resulting reorganisation of the star’s internal structure causes it to become hotter but less luminous: it moves to the horizontal branch [or the red clump, but they only know about the horizontal branch]. • When the core helium is exhausted, the star begins to fuse helium in a shell around the carbon core, moving back toward the red giant branch. At this point it is highly unstable and begins to lose mass. • Eventually the star loses its whole outer envelope, stopping fusion and revealing the very hot, but inert, carbon core. The star has become a white dwarf, surrounded by a planetary nebula.

20. C1(b) • The expanding gas cloud known as the Crab Nebula is the remnant of a supernova observed by the Chinese in 1054. • Explain how this type of supernova is produced. • The Crab Nebula also contains a pulsar. What is a pulsar, how do you detect one, and why might you expect to find a pulsar associated with a supernova remnant such as the Crab?

21. C1(b) answer • Very massive stars can continue fusing successively heavier elements until they eventually produce an iron core. • Iron is the most stable nucleus, so no further fusion is possible. Once the iron core can no longer support its own weight against gravity, it suddenly collapses, producing a neutron star (or possibly a black hole). • The outer layers of the original star, falling under gravity, encounter the extremely rigid surface of the neutron star and bounce off: the resulting shock wave causes the supernova explosion and produces the remnant gas cloud.

22. C1(b) answer • A pulsar is a rotating neutron star whose rotation axis does not coincide with its magnetic axis. • It is detected (if we lie in the appropriate line of sight) by a “lighthouse beam” of radio emission emanating from the magnetic poles of the star, and swept around by the star’s rotation, so that we see the beam as regular pulses of emission (hence name). • Most core collapse supernovae are believed to produce neutron stars (rather than black holes), and the small size of the neutron star compared to the original star “concentrates” both the spin and the magnetic field, so we expect the neutron star so produced to be a pulsar. Only question is whether we are properly lined up with the lighthouse beam – in this case we clearly are.

23. C2(a) • How does each of the following observations help to establish the correctness of the Big Bang model of the universe (as opposed to the Steady State model)? • the abundances of the light elements helium and lithium; • comparison of galaxies observed at very large distances with those observed nearby; • the existence and blackbody spectrum of the cosmic microwave background.

24. C2(a) • the abundances of the light elements helium and lithium • Lithium is not produced in stars at all, and although helium is produced, its cosmic abundance is much higher than we would expect by comparing it with elements which are made in stars. • Therefore the Steady State has no good explanation of where the helium and lithium present today were made (since they are not being made now, and the Steady State assumes that ‘now’ is typical). • In the Big Bang, the helium and lithium are made in the early universe, when the temperature is comparable to the interior of stars. The amounts made are broadly consistent with what we now observe, so this supports the Big Bang theory.

25. C2(a) • comparison of galaxies observed at very large distances with those observed nearby • Galaxies observed at very large distances look rather different from modern galaxies: there are more active galaxies, more interacting galaxies, more small blue galaxies, and fewer well-developed spirals. • Again, this is inconsistent with the Steady State, which expects ‘now’ to be typical (therefore distant galaxies should look, on average, similar to modern galaxies). In the Big Bang model, distant galaxies are seen as they were when the universe was a small fraction of its present age, and so it is not surprising that they might look different. Therefore this observation is good evidence against the Steady State.

26. C2(a) • the existence and blackbody spectrum of the cosmic microwave background • The CMB is blackbody radiation, which implies it was produced by a hot dense object; it comes from everywhere, which suggests that the ‘object’ in question is the universe. • In the Big Bang model, the early universe is hot and dense: ideal conditions in which to generate the CMB. The CMB is therefore strongly supportive of the model. • The Steady State has no good way to generate this spectrum, since there is no appropriate hot dense era in which to make it.

27. C2(b) • The basic parameters of the Big Bang model are the expansion rate H, the density Ω, the curvature k, and the cosmological constant Λ. • Briefly explain how Ω, k and the fate of the universe are related if Λ = 0. • Why do observations of distant supernovae lead us to believe that in fact Λ ≠ 0?

28. C2(b) • Ω and k: • If Ω > 1, k > 0, and the universe will recollapse (Big Crunch). • If Ω = 1, k = 0, and the universe will expand forever at an ever-decreasing rate. • If Ω < 1, k < 0, and the universe will expand forever at a rate which remains finite. • Distant Type Ia supernovae (SNe Ia): • If we use SNe Ia to construct a Hubble diagram, we find that the expansion of the universe is accelerating • This cannot be achieved by any modification of Ω, k or H. The only way to get acceleration is to introduce Λ

29. C2(c) • The Big Bang theory has been improved by the introduction of inflation. What is inflation, and what problems with the Big Bang does it solve? • Inflation is a brief period of very rapid expansion in the very early universe, powered by ultra-high-energy particle physics. The result is that the universe expands by an enormous factor. • This dilutes any pre-existing curvature, resulting in a universe which is extremely flat (solving the flatness problem). • It also ensures that the visible universe expands from an extremely tiny pre-inflation region, which has reached equilibrium (solving the horizon problem).