Physics 110: Homework #6 Solutions

6.1

The equation of state of a normal gas depends on both temperature and density, while that of a degenerate gas does not depend on temperature. Electron degeneracy plays an important role in (1) determining the minimum mass of main sequence stars, (2) the helium flash in solar mass stars, (3) white dwarfs, (4) the onset of core collapse in type II supernovae, and (5) neutron stars.

6.2

The mass of this stellar core is larger than the Chandrasekhar limit (1.4 ), which is the maximum mass of a white dwarf. Figure 20-5 shows that main sequence stars with masses greater than 8 are too heavy to produce white dwarfs (they must collapse to neutron stars or black holes), so the star must be more massive than 8 .

6.3

Type II supernovae show hydrogen lines in their optical spectra, while type I do not. Since hydrogen is the most abundant element in the Universe, it's absence in type I supernovae is remarkable. Because of this, the stars that explode as type I supernovae must have lost their hydrogen rich envelopes. There are believed to be at least two situations where this has happened: (1) very massive stars that have blown off their outer layers entirely leaving only the metal-rich core of the star to undergo collapse and explode, and (2) older white dwarfs that are composed almost entirely of carbon, oxygen, neon, and magnesium. In the second case, something triggers the white dwarf to grow in mass beyond the Chandrasekhar limit to cause the spectacular explosion. Because of their hydrogen content, type II supernovae are well established as the core collapse of massive stars that have retained their hydrogen rich outer layers.

6.4

The magnetic poles, from which the beams of radiation are emitted, would always point in the same directions and couldn't sweep past the direction to the Earth. The pulse-producing mechanism turns off when the pulsar reaches a few seconds. The minimum possible period of a pulsar is somewhat less than 1 millisecond. If a neutron star rotated faster than this rate it would disintegrate (its equatorial rotation speed would be faster than the escape velocity).

6.5

We would see the motion of the object slow as it approaches the event horizon. It would appear to hover just above the event horizon, but would quickly become redder and dimmer and disappear. The length of the year would remain the same and the distance from the Sun would be unchanged if the Sun were replaced by a black hole of the same mass. Far from a black hole, gravity is normal. Think of it in the following way. There is the same amount of mass within one solar radius from the center of a solar mass black hole as there is within one solar radius of the Sun. So beyond this radius, gravity would be very nearly the same regardless of whether the Sun was a normal star, a white dwarf, neutron star, or black hole. Once you got closer than one solar radius, then gravity will become stronger for the white dwarf, neutron star, and black hole cases. Gravity would be strongest of all at the event horizon of a black hole, which is merely 3 km for a solar mass one. Basically one needs to get very close to a compact object for the effects of strong gravity to become important.

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