ASTR 100 (McGaugh)
Homework #7 solutions

Chapter 15, Problem # 1

Lets take a rough approximation on the length of recorded history to be 10,000 years. The first convincing evidence that some nebulae are in fact remote galaxies similar to our own (and thus that we live in an isolated galaxy which is just one of many such systems) was Hubble's measurement of the distance to the Andromeda galaxy, which was published in 1925. Thus, people have known about distant galaxies for about 75 years. So, the length of time they have not known about them is 10,000 - 75 = 9,925 years or 9,925/10,000 = .99 = 99 % of recorded human history.

During most of recorded history, people thought that the universe was far smaller than we now know it to be. Although we often do not know exactly how large people thought the universe was, we know that they generally thought that the Earth, planets, and stars they could see were the entire extent of the universe. Also, they often believed that the stars and planets were relatively small objects, and thus that they were rather close to the Earth. Therefore, they viewed the "total universe" made up of the Earth, planets, and stars to be probably smaller than what we have more recently calculated to be the size of our solar system. And we now know that our solar system in only a very small piece of our galaxy which is only one among the many galaxies that are spread throughout the vastness of the universe.

Chapter 15, Problem # 5

The present constellations will not be recognizable in Earth's sky 100 million years from now, because the differential rotation of the galaxy, combined with the random motions of the stars, causes the stars in our galaxy to continually (but very slowly) change their positions relative to each other. 100 million years is a sufficiently long time for these slow changes in the relative positions of the stars to disrupt the patterns of stars which we call the constellations. (Note that the time for the Sun to make one complete rotation about the center of the galaxy is 240 million years, so 100 million years is a substantial fraction of that time.)

(a) If our solar system was very close to the galactic center, the night sky would be full of very bright stars, since there is an extremely high density of young, bright stars near the galactic center. Also, we would see dark clouds of dust and glowing clouds of gas lying along the plane of the galactic disk. We might also see the brightly glowing accretion disk which would surround the black hole which may lie at the center of the galaxy.

(b) If our solar system was moved far above the galactic disk to a location in the halo, the night sky would have very few bright stars, since the halo contains a low density of stars and most of the stars which are there are old, low luminosity stars. However, if you looked toward the center of the galaxy, you would see an amazing view of the galaxy's disk and bulge. You could see the disk's spiral arms, young star clusters, and gas and dust clouds. At the center of the disk, you would see the bright bulge made up of older red stars.

(c) If our solar system was at the center of a globular cluster, the night sky would contain a large number of reddish main sequence stars distributed uniformly across the sky, and producing combined starlight that was ten times brighter than the full moon. Behind those stars, in the direction of the galactic center, you would see a view of the galactic disk and bulge as described in part (b).

(d) If our solar system was located near the center of the Orion star-forming region, the night sky would be dominated by glowing ionized gas which would be visible in all directions. You would also see some darker regions of dust. Also, you might see some young bright stars which were just beginning to emerge from their "cocoons" of dust and debris.

(e) If our solar system was moved to the edge of the milky way disk, most of the night sky would be relatively dark, containing only a few stars. However, in the direction of the galactic center, you would see a band of stars, gas, and dust, since you would be looking at the galactic disk edge-on. This band would extend only partway around the sky.

It would be unlikely to find a Sun-like star in the Orion Nebula, because the stars there are younger than the Sun. If a star with the Sun's mass formed in the Orion Nebula at the same time as the other stars present there, it would not yet have had time to evolve onto the main sequence. It would also be unlikely to find a Sun-like star in the halo, since most of the halo stars are older than the main sequence lifetime of the Sun.

Chapter 15, Problem # 10

(a) If spectra showed that a faint distant galaxy was reddish with a spectrum of K-type stars, you would expect it to be an elliptical galaxy. If spectra showed that the galaxy was bluish with B- and A-type stars, you would expect it to be an irregular galaxy.

(b)The dominance of young stellar features in irregular galaxies does not prove that the galaxies themselves formed recently. It simply means that so much star formation is occurring in these galaxies at the present time that the light from the young stars being created dominates over the light of whatever population of older stars might also exist within the galaxy.

The prominent light from star-forming regions comes from massive, hot, blue stars, because these stars are far brighter that the less massive stars which are forming in these regions at the same time.

Massive, hot, blue stars are not see outside the star-forming regions, because their lifetimes are so short that they die before they have moved very far from their birthplaces.

Chapter 16, Problem # 4

(a) If galaxies showed equal numbers of redshifts and blueshifts (uniformly mixed in all directions), this would imply that the universe was static and that the observed redshifts and blueshifts were due to the random motions of the galaxies within the universe.

(b) If all the galaxies showed blueshifts with the size of the blueshift increasing in proportion to the distance to the galaxy, this would imply that the universe was collapsing.

(c) If all the galaxies on one half of the sky showed redshifts while all the galaxies on the other half of the sky showed blueshifts, this would imply that our galaxy is moving through a static universe (at a speed greater than that of the random motions of the galaxies). This would cause all the galaxies in front of us (in the direction our galaxy is moving toward) to appear blueshifted, while all the galaxies behind us (in the direction our galaxy is moving away from) would appear redshifted. This configuration of blueshifted and redshifted galaxies could also occur if our galaxy was sitting still while the rest of the universe was flowing past it.

Chapter 16, Problem # 10

The current theory of the power source of quasars is that there is a supermassive black hole at the center of a quasar. This rotating black hole is surrounded by an accretion disk made of material which is rotating around the black hole and falling toward it. The acceleration of this material causes it to emit huge amounts of radiation.

The evidence for supermassive black holes in quasars includes the observation that quasars' emission regions are very small, only about 10 times the diameter of the solar system, yet they have very high luminosities of about 1012 to 1015 times the luminosity of the Sun. Thus, normal stellar processes cannot be responsible for producing the quasar's emission. Also, scientists have used the width of emission lines from the hot gas near the quasars' cores to determine the velocity of this gas, which then can be used to estimate the mass of the central portion of the quasars. Comparing this mass to the energy output of the quasars, scientists find that the energy source of the quasar is so efficient that it releases 10-30 percent of the mass-energy in the matter in the central region of the quasar. Stellar fusion is again ruled out by these observations, since it is not efficient enough. However, a rotating black hole can convert 20-30 percent of the mass it accretes into energy. Thus, the evidence points to a massive black hole as the likely candidate for the energy source of a quasar.

The evidence for massive black holes in some nearby galaxies includes the observed central light peaks in these galaxies which could be caused by either a black hole or by a very dense star cluster. More convincing is the fact that spectroscopic measurements have shown sharp increases in stellar velocities near the galactic nuclei, indicating a very large mass concentrated within that small region. Combining these two measurements, scientists find that the mass to light ratio within the nuclei of these galaxies is higher than the ratio for ordinary stellar material, indicating that the concentration of mass at the center of these galaxies is not emitting light as stars do. Thus, a massive black hole is the best candidate for what lies at the center of these galaxies.