| What can you find more of in the universe: stars with 1 solar mass or stars with 2 solar masses? Solution: 1 solar mass, because the number of stars is inversely proportional to mass. What is the Pauli exclusion principle? Solution: A principle in quantum mechanics, which says that two fermions of the same type cannot be in the same quantum state at the same time. Fermions are particles with half-integer spin, like electrons or neutrons; this principle only applies to the fermions of the same type (e.g. two electrons, but not an electron and a neutron) and does not apply to bosons (particles with integer spin, like photons or Higgs bosons). What causes degeneracy pressure? Solution: When the core contracts, more and more fermions (electrons in the case of a white dwarf, neutrons in the case of neutron stars) become packed together in the same place. The quantum states of the fermions includes both their position and their speed. According to the Pauli exclusion principle, two fermions cannot be in the same state, so they can only be in the same place if they move at different speeds. As we pack more and more fermions together, they will have to move at faster and faster speeds, and these fast-moving fermions cause pressure that can resist gravitational collapse. What is the Chandrasekhar limit? Solution: It's the maximum mass that a white dwarf can have, approximately 1.4 solar masses. Beyond this limit, electron degeneracy pressure cannot resist gravitational collapse anymore, and the core collapses into a neutron star or a black hole. What is a black dwarf? Have any been observed? Solution: The theoretical remnant of a white dwarf that has radiated away all its heat. This is estimated to take much longer than the current age of the universe, so we have not observed any black dwarfs. What is a compact object? Solution: A very small and dense stellar remnant: white dwarf, neutron star, or black hole. Consider a star that is massive enough to fuse iron. At the end of its life, just before nuclear fusion stops, where would you expect to find this iron? What about hydrogen? And other elements? Solution: Iron will be found in the innermost layer (the iron core). Hydrogen will be in the outermost layer. In general, the heavier an element is (i.e. the higher its atomic number), the lower the layer. What is electron capture? Solution: The reaction where a proton "captures" an electron and turns into a neutron, releasing a neutrino in the process. Compared to white dwarfs, are neutron stars typically larger or smaller? Solution: Neutron stars are are much smaller than white dwarfs - and thus also much denser. I have 10 cubic centimeters of neutron star material in my pocket. How much do my pants weigh? Solution: Approximately 4 trillion kg. What is the TOV limit? Solution: The Tolman-Oppenheimer-Volkoff (TOV) limit is the upper limit for the mass of a neutron star, approximately 2 solar masses. If the star is more massive than this, the combined forces of neutron degeneracy pressure and the repulsion due to the strong nuclear force will not be enough to oppose gravitational collapse, and the star will collapse to a black hole. Tungsten, an element with atomic number 74 (meaning it has 74 protons), is the heaviest element known to have a biological role, as it is used in some bacteria and archaea. Where did that tungsten come from? Solution: Since it has more protons than iron (atomic number 26), it must have been created not inside a star but due to a supernova explosion which enriched lighter elements with more protons. Consider a star with an initial mass of 0.15 solar masses. What will be this star's final state? Solution: A white dwarf made mostly of helium. What are the nova and supernova types we learned about? Solution: Nova: a white dwarf whose surface explodes due to accumulating new matter. Type Ia supernova: similar to a nova, but matter accumulates much faster, and the white dwarf explodes and gets completely destroyed. Type II supernova: a massive star that collapses and explodes, leaving behind a neutron star or black hole. Why do neutron stars spin so fast? Solution: Because of conservation of angular momentum. Angular momentum is proportional to the product of radius and rotation speed, so if the radius decreases, then rotation speed must increase in order to preserve the total angular momentum. Therefore, when a star collapses into a neutron star and its size decreases by a significant amount, its rotation speed must increase accordingly. Can we see all the pulsars in the galaxy? Solution: No, we can only see pulsars when their beams shine directly at us, like the light of a lighthouse, and there are many pulsars who are aligned such that we never see their beams. Aliens on another planet will see a different set of pulsars than the one we see. What happens to pulsars over time? Solution: They gradually lose rotational energy, which causes them to slow down. Eventually, after a few million years, they will rotate so slowly that they will not be observable to us anymore. What are magnetars? Solution: A rare type of pulsars with extremely strong magnetic fields. How will aliens who find the Pioneer plaques be able to locate Earth? Solution: They will recognize at least some of the 14 pulsars drawn on the plaques via their periods, and using the indicated distances to each pulsar, they will be able to triangulate our position. John Wheeler said: "Matter tells spacetime how to curve; spacetime tells matter how to move." Explain what each part means. Solution: "Matter tells spacetime how to curve" refers to the fact that the curvature of spacetime depends on the matter within it. The more mass the matter has, the more curvature it will create. "spacetime tells matter how to move" refers to the fact that the curvature of spacetime dictates the motion of the matter within it. In a flat spacetime, objects will move in a straight line, but in a curved spacetime, they will move in a curved line (which we interpret as the influence of gravity). What is a geodesic? Solution: It's the path that a particle takes in spacetime, which is influenced by the curvature of spacetime. Why is there no type of stellar remnant between neutron stars and black holes? Solution: Neutron stars are held together against collapse using neutron degeneracy pressure. However, if the gravitational force is stronger than neutron degeneracy pressure, there is no known mechanism to stop the collapse, so the collapse simply continues until the entire mass of the star is concentrated at a single point (at least according to classical general relativity). If there was a force stronger than neutron degeneracy pressure, then there could have been an intermediate stage between neutron stars and black holes (there are some hypotheses about such forces, but none are proven). Why is it impossible to escape a black hole? Solution: The spacetime curvature of the black hole is such that all the possible geodesic that an object can follow necessarily lead toward the center of the black hole. In other words, it is physically impossible to move in the opposite direction. Let's say I have a spaceship that can reach half the speed of light. Of course, I cannot escape a black hole with my spaceship - since nothing can escape a black hole. But is it possible that there's an object that is NOT a black hole, and yet I cannot escape it either? Solution: Yes: any object (such as a neutron star) that is massive enough to have an escape velocity larger than half the speed of light. If the escape velocity is larger than the maximum velocity my spaceship can achieve, then I can never escape. The difference is that in a black hole, it doesn't matter how fast my spaceship is, I can never escape it, because even light can't escape it, and light moves faster than any spaceship. The Schwarzschild radius of a black hole with 10 solar masses is around 30 km. What is the Schwarzschild radius of a black hole with 20 solar masses? Solution: The relation between the radius and the mass is linear: R is proportional to M. Therefore, if we multiply R by 2, M will also be multiplied by 2. Thus the answer is 60 km. If the Sun was suddenly compressed into a black hole (keeping its mass the same), what would be the radius of the event horizon? What do you think would happen to Earth's orbit? Solution: The radius of the event horizon would be ~3 km, the Sun's Schwarzschild radius. As for Earth's orbit, nothing would really happen, since the planet's orbit is determined only by the mass of the star and not by its size. So Earth will actually continue orbiting the black hole as if nothing happened. (However, the Earth will slowly freeze and all life will eventually cease, since the planet will no longer receive any energy from the Sun - a black hole does not emit any light.) |