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| Star Death |
1. Because the central star is very hot, most of its light is not in the visible spectrum but instead is in the UV. Thus, much of the energy being emitted to power the nebula is not directly visible when emitted from the central star, but becomes visible when the nebula absorbs the UV and re-emits much of the energy in the visible spectrum.
2. There are two things: could there be a presupernova star relatively nearby but hidden by dust? Probably not too likely, but perhaps not completely excluded. The second is more problematic. Type I supernovae occur in binary systems with white dwarfs and don't require supergiant stars. It is conceivable that a binary system destined to become a type I supernova could lie not so far from the Earth and not have been detected yet since white dwarfs in orbit around other stars are not so easy to see. In addition, it is possible that there is an isolated (not part of a binary system) white dwarf relatively nearby that is near the Chandrasekhar mass that could collapse and produce a supernova if it were disturbed by the acquisition of mass.
3. None, for two reasons. First, the brightest magnitudes are 8 or larger, but the naked eye seeing limit is 6-7. Second, even if the magnitudes were larger, the known white dwarfs are often companions to brighter stars and thus difficult to see in the glare of the other star.
4. Two reasons: most stars are parts of multiple star systems, and the presence of a white dwarf is easier to establish if it is part of a binary system and we can deduce that it is there first by its gravitational perturbation on the companion.
5. Although the cores of these stars end up as white dwarfs, there are many fundamental differences. For one thing, the composition of the white dwarf will be different. For another, the fate of their envelopes will be completely different (since the more massive stars eject much of their mass before becoming white dwarfs but in the less massive stars there is probably little ejection of mass; the entire star becomes the white dwarf). This implies very different roles in modifying the interstellar medium for the next generation of stars. Note also that because low mass stars have such long main sequence lifetimes, none of them have had time yet to evolve to the white dwarf stage, but for the intermediate mass stars there has been time for multiple generations of stars to become white dwarfs.
6. The star is initially mostly hydrogen and some helium. Thus, fuel for advanced stages will generally be lower in abundance than for hydrogen since it must either be there initially or be produced in earlier burning stages. Because of the curve of binding energy, the heavier the fusion fuel the less energy per reaction is available. Once stars leave the main sequence they become giants or supergiants, with generally greatly increased luminosity compared with the main sequence.
9. There are no stable mass 5 and 8 isotopes of any element. This makes it very difficult to make elements above mass 4 in either the Big Bang or in stars until in the hot cores of red giants the triple-alpha reaction can produce carbon and this can be used to produce heavier elements. Thus, the elements between helium and carbon occur with low abundance in nature.
10. In the plot of Solar System abundances, the region between mass numbers 150 to 180 corresponds to the lowest range of elemental abundances on the plot.
11. A type II supernova is associated with the death of a massive young star, so it occurs in a star-forming region, which is more likely in a spiral arm of the disk than the halo.
12. Technetium is very unstable, with a half-life of less than a million years. Thus, if it is found in an old star it must have been produced there. The only plausible way to make it in a star is by a series of neutron capture reactions.
13. The half-life is the time for the original population to decrease by one half. Thus, every month half the existing population of iron-59 would beta decay to cobalt-59. In twelve months, the total reduction would be one half raised to the twelfth power, which is 0.000244, the inverse of which is a little over 4000. So iron-59 formed by the s-process in a typical red giant is several thousand times more likely to beta decay than to capture another neutron if the average capture rate is one per year.
14. Stars late in their lives tend to lose large amounts of mass because of very strong stellar winds blowing from their surface. According to our understanding of stellar evolution, Sirius B became a red giant after leaving the main sequence and lost much of its mass in a strong stellar wind that probably produced a planetary nebula. The remaining core of the star, containing only a fraction of the original stellar mass, then became the white dwarf Sirius B. Since Sirius B has evolved faster than Sirius A, this implies that the original main sequence mass of Sirius B was probably considerably larger than the present mass of Sirius A.
15. Most stars late in their lives will expand to become giant or supergiant stars because of events that take place in their interiors when then begin to exhaust their nuclear fuel. In a close binary, this can cause the star to overflow its Roche lobe, leading to accretion onto the companion.
16. The neutrinos, being massless or nearly so, travel out almost from the beginning (at least after the first second) of the collapse at near light speed. Thus, they reach the Earth a little over eight minutes after the core collapse. The shock wave takes several hours to reach the surface of the star, so it would be several hours after core collapse before the light from the supernova would reach the Earth. We would never know. Presumably the intense blast of neutrinos would kill us instantly, before we ever saw any visible signal of the supernova.
17. Take the radius of the Solar System to be 40 AU ~ 40 x 150,000,000 km. The time to expand by that radius is (40 x 150,000,000 km) / (3000 km/s) ~ 2,000,000 seconds ~ 23 days.
19. No, they are completely unrelated. The blue color of Uranus and Neptune is an absorption feature: the methane in their atmospheres absorbs red and IR wavelengths very strongly, leaving the light that we see with a blue tinge. The colors of planetary nebulae are an emission feature, resulting from emission of photons by ions that have been excited by UV radiation from the hot central star.
20. Take the radius of a typical spiral to be about 50,000 ly. The distance to the galaxy is 3 x 108 ly. Thus, forming a right triangle, the tangent of half of the angular size of the galaxy corresponds to (50,000 / 3 x 108) = 0.000167. Taking the inverse tangent, the angle is 0.0095 degrees, which is about 34 arc seconds. The angular size of the galaxy is twice this or about 70 arc seconds. A simpler solution is to note that the angle is small so the small-angle approximation can be used. An even simpler solution is to use the Small-Angle Formula Calculator.