Astronomy

17. Some theorists expected that observations would show that the density of matter in the universe is just equal to the critical density. Do the current observations support this hypothesis?

Every observation made to date shows that the density of matter is much less than the critical density. The amount of matter is best estimated by measuring its gravitational influence, and this has been done for galaxies (rotation curves) and clusters of galaxies. Even if dark matter is included, the density of matter is only about 30% of the critical density.

4. Briefly describe the main parts of our Galaxy.

Our Milky Way Galaxy contains a barred bulge; a thin disk of stars, gas, and dust with concentrations in spiral arms; a much less substantial thick disk of stars; and a spheroidal halo of ancient stars and globular star clusters. Deep within the central bulge dwells a supermassive black hole. In addition, there appear to be considerable amounts of unknown dark matter surrounding the Galaxy.

18. Why can we not determine distances to galaxies by the same method used to measure the parallaxes of stars?

Parallaxes can be measured accurately out to distances of 100 light-years or so (300 light-years from the Hipparcos data). The nearest galaxies are about 50,000-80,000 light-years from the Sun. Therefore, there is no perceptible change in the apparent position of any galaxy as we view it from opposite sides of Earth's orbit.

2. Describe the arguments supporting the idea that quasars are at the distances indicated by their redshifts.

Quasars have extremely large redshifts, indicating that they are receding from us at large fractions of the speed of light. Any objects moving this rapidly from a nearby galaxy would easily achieve escape speeds from even the largest host galaxies. Hubble Space Telescope observations have shown that quasars sit in the middle of host galaxies, and the host galaxies have the same redshifts as their quasars, confirming that quasars obey Hubble's law and their high redshifts are due to their distance.

8. What is dark energy and what evidence do astronomers have that it is an important component of the universe?

The notion of dark energy was suggested to help explain measurements, using Type Ia supernovae as distance indicators, that the expansion of the universe is speeding up. Such acceleration requires a source of energy. Scientists don't yet fully understand what dark energy is. It may be a new form of energy for which there is not yet a theoretical explanation. Alternately, it may be the vacuum energy associated with "empty" space itself, as predicted by quantum mechanics.

12. Describe the evidence that the expansion of the universe is accelerating.

The only direct evidence of acceleration comes from supernovae (as described in the chapter), although other evidence fits the standard model we have described in the book that includes dark energy. In order to determine whether the expansion is accelerating, it is necessary to measure the rate of expansion at different distances, which is equivalent to making measurements at different times in the history of the universe. We have only one "standard bulb" that allows us to measure large enough distances to perform this experiment—the supernovae produced when white dwarfs in binary systems acquire too much mass and explode. The observations show that distant supernovae are fainter than would be expected if the universe were expanding at a constant rate. This means that when we detect the light from supernovae, we are farther away from them than we would be if the expansion rate were constant. The only way that can happen is if the rate at which we are moving away from the supernovae has sped up since the time the light left them.

16. If the Sun could suddenly collapse to a black hole, how would the period of Earth's revolution about it differ from what it is now?

The period would not change at all. Far from the event horizon, a black hole's gravitational field is indistinguishable from that of any spherically symmetric object of the same mass.

15. Which is likely to be more common in our Galaxy: white dwarfs or black holes? Why?

White dwarfs are likely to be much more common. The number of stars decreases with increasing mass, and only the most massive stars are likely to complete their lives as black holes. There are many more stars of the masses appropriate for evolution to a white dwarf.

7. When astronomers make maps of the structure of the universe on the largest scales, how do they find the superclusters of galaxies to be arranged?

To the surprise of astronomers, they found the superclusters to be arranged in filaments and sheets surrounding emptier regions that are now called voids. The layout reminds them of good Swiss cheese, where the walls of cheese surround large empty regions.

13. What is the most useful standard bulb method for determining distances to galaxies?

Type Ia supernovae; cepheid variable stars are limited by distance (since individual stars are hard to make out once a galaxy gets too far away). Type Ia supernovae, on the other hand, are very luminous, and can be seen at much greater distances.

12. Consider the following five kinds of objects: open cluster, giant molecular cloud, globular cluster, group of O and B stars, and planetary nebulae.A. Which occur only in spiral arms? B. Which occur only in the parts of the Galaxy other than the spiral arms? C. Which are thought to be very young? D. Which are thought to be very old? E. Which have the hottest stars?

(Students may need reminding that planetary nebulae are produced by low-mass stars that are on the way to becoming white dwarfs.) A. open cluster, giant molecular cloud, group of O and B stars; B. globular cluster, many (but not all) planetary nebulae; C. some open clusters, giant molecular cloud, group of O and B stars; D. globular cluster, some planetary nebulae; E. planetary nebula central stars are the hottest stars known; the youngest open clusters, group of O and B stars, some molecular clouds contain fairly hot stars.

8. How is a nova different from a type Ia supernova? How does it differ from a type II supernova?

A nova is a smaller energy explosion on the surface of a white dwarf in a close binary system, where fresh material from a donor star is deposited on the surface of the white dwarf until it ignites. A type Ia supernova has a similar configuration, but in this case, the material deposited on the surface of the white dwarf is sufficient to push the white dwarf past the Chandresekhar limit. Once that happens, the white dwarf will collapse and then explode into a type Ia supernova. A type II supernova does not involve a white dwarf but instead requires a massive star to reach the end of its ability to generate energy in its core. This results in a collapse of the core and an explosion into a type II supernova.

4. Which formed first: hydrogen nuclei or hydrogen atoms? Explain the sequence of events that led to each.

A standard hydrogen nucleus consists of just a proton. Protons were formed by quark condensation at around 10-6 seconds after the Big Bang. Nucleosynthesis of other isotopes of hydrogen, such as deuterium (one proton and one neutron) and tritium (one proton and two neutrons), could happen when the universe was cool enough for more complex nuclei to form, at around three to four minutes. Hydrogen atoms (which also include an electron) did not form until the universe was about 380,000 years old, when its temperature dropped below about 3000 K. This was when the random motion of electrons became slow enough for them to be electromagnetically captured by protons to form hydrogen atoms.

30. How would the spectra of a type II supernova be different from a type Ia supernova? Hint: Consider the characteristics of the objects that are their source.

A type II supernova is formed from the collapse of a massive star, which, although it has made heavier elements in its core, is still mainly composed of hydrogen and helium. These should be visible in the spectrum, along with the other elements produced in the supernova. However, the amount of hydrogen and helium is still significantly larger than the other elements. A type Ia supernova is formed from a white dwarf star, which contains elements other than hydrogen, such as carbon, oxygen, neon, and magnesium. The spectrum of a type Ia supernova would show spectral features associated with elements other than hydrogen. (Even if the other star is dumping hydrogen onto the white dwarf, the tremendous compression and heating, and then the explosion, will convert that hydrogen to heavier elements.)

24. If most stars become white dwarfs at the ends of their lives and the formation of white dwarfs is accompanied by the production of a planetary nebula, why are there more white dwarfs than planetary nebulae in the Galaxy?

A white dwarf is visible for a billion years or more before it cools off and its radiation becomes so feeble as to be undetectable. After a time on the order of 10,000 years or so, the gas shell that is ejected in the planetary nebula phase expands and thins out to such an extent that it becomes unobservable. Therefore, there are many more white dwarfs than planetary nebulae.

25. If a 3 and 8 MSun star formed together in a binary system, which star would: A. Evolve off the main sequence first? B. Form a carbon- and oxygen-rich white dwarf? C. Be the location for a nova explosion?

A. 8 MSun; B. 3 MSun; C. 8 MSun.

22. If a quasar is moving away from us at v/c = 0.8, what is the measured redshift?

Answer In this case, we have If we solve for (z + 1)2, we get (z + 1)2 -1 = 0.8[(z + 1)2 + 1], or 0.2(z + 1)2 = 1.8, (z + 1)2 = 9, z + 1 = 3 and z = 2.

22. Construct a timeline for the universe and indicate when various significant events occurred, from the beginning of the expansion to the formation of the Sun to the appearance of humans on Earth.

Assuming that the age of the universe is 14 billion years, key events that might be mentioned include the Big Bang at time 0; inflation at 10-35 s; the universe becomes transparent to neutrinos at 1 s; nucleosynthesis of deuterium and helium occurs between 3 and 4 min; the universe becomes transparent to radiation at about 400,000 y; the first stars form at 200 million y; small galaxies begin to form at 400-500 million y; at 9.5 billion y, the solar system begins to form; at 13.95 billion y, mammals appear on Earth; at 14 billion y, we reach the present era.

11. What evidence do we have that the luminous central region of a quasar is small and compact?

Fluctuations in the energy output of a quasar can change over relatively short time periods (a few months to a few years at most). This means that the region from which the changing energy is coming cannot be larger than the distance that light can travel over a few month or a few years. In other words, the region that is fluctuating must be no more than a few light months to a few light years wide. Typical galaxies are tens of thousands to hundreds of thousands of light-years across. The short timescale energy fluctuations suggest that the region of greatest luminosity in a quasar must be much smaller than the size of the host galaxy.

7. Why do astronomers believe there must be dark matter that is not in the form of atoms with protons and neutrons?

Galaxies could not have formed as early as they did without dark matter gravitationally attracting ordinary matter and inducing galactic formation. The existence of dark matter is also necessary to explain the long-term stability of both spiral galaxies and galactic clusters. In both cases, we see material in their outer regions moving around their centers too fast for the gravity we deduce from ordinary matter to hold. There must be some other form of material there with gravity. Yet searches for electromagnetic radiation from this additional matter have been fruitless, leading scientists to believe that this "dark matter" does not consist of ordinary particles, such as protons and neutrons.

19. Which is redder—a spiral galaxy or an elliptical galaxy?

Hot blue stars are more massive and go through their lives more quickly. Therefore, as time goes on, blue stars tend to die first and galaxies become redder as the blue stars die out. The less "raw material" a galaxy has available, the fewer new stars (young stars) can be seen in it. An elliptical galaxy is redder than a spiral in integrated light because an elliptical galaxy contains only old stars, while a spiral contains both old and young stars. The nuclear bulge of a spiral (that is, excluding the light from the spiral arms) is redder than its spiral arms because the central regions of spirals contain mostly old stars.

24. Assume that the average galaxy contains 1011 MSun and that the average distance between galaxies is 10 million light-years. Calculate the average density of matter (mass per unit volume) in galaxies. What fraction is this of the critical density we calculated in the chapter?

If the average distance between galaxies is 10 million light-years, then we can approximate the distribution of matter by imagining that the universe is filled with bubbles 5 million light-years in radius around each galaxy and each galaxy is 10 million miles from its neighbor. Each bubble will contain only one galaxy, and nearly all of the universe will be filled by these bubbles, except where the tangent bubbles don't quite touch. With this approximation the average density of the universe is . If the critical density is 9.6 10-27, then this is 5% of the critical density—not a bad estimate of the contribution of the luminous matter in galaxies to the total mass density of the universe.

21. If a quasar has a redshift of 3.3, at what fraction of the speed of light is it moving away from us?

If the redshift is 3.3, then we have so the quasar is moving away from us at 90% the speed of light.v/c

12. Suppose you observe a star-like object in the sky. How can you determine whether it is actually a star or a quasar?

Take a spectrum of its light. The Doppler shift of the spectral lines in a star can be no more than a few hundred km/s. The lines in even the nearest quasars are redshifted by a much larger amount.

22. Galaxies are found in the "walls" of huge voids; very few galaxies are found in the voids themselves. The text says that the structure of filaments and voids has been present in the universe since shortly after the expansion began 13.8 billion years ago. In science, we always have to check to see whether some conclusion is contradicted by any other information we have. In this case, we can ask whether the voids would have filled up with galaxies in roughly 14 billion years. Observations show that in addition to the motion associated with the expansion of the universe, the galaxies in the walls of the voids are moving in random directions at typical speeds of 300 km/s. At least some of them will be moving into the voids. How far into the void will a galaxy move in 14 billion years? Is it a reasonable hypothesis that the voids have existed for 14 billion years?

In 14 billion years, an object moving at 300 km/s will move a distance d given by d = v t = 300 14 109 y 3.16 107 s/y = 1.3 1020 km, since there are 3.16 107 s/yr. There are 9.46 1012 km/light-year, so in 14 billion years the galaxy will move .The text says that the typical diameter of a void is 150 million light-years, so galaxies would move only about 10% of the way into the void in the entire lifetime of the universe, and the void would still exist.

18. Suppose no stars more massive than about 2 MSun had ever formed. Would life as we know it have been able to develop? Why or why not?

Stars with masses less than two times the mass of the Sun can produce elements only up to carbon and oxygen. More massive elements are not produced, and some of these more massive elements (phosphorus, calcium, silicon, iron) are essential for the forms of life found on Earth

9. Describe how you might use the color of a galaxy to determine something about what kinds of stars it contains.

Massive, hot blue stars have lifetimes on the main sequence of only a few million years. If we see a galaxy that is blue, it must have a significant population of stars in it that are very hot and therefore young. (Note that while white dwarfs and the central stars of planetary nebulae are also very blue and very hot, they are intrinsically so faint that they do not contribute significantly to the total luminosity emitted by a galaxy.) A red galaxy must contain mostly old stars.

6. What are the two best ways to measure the distance to a distant, isolated spiral galaxy, and how would it be measured?

Method 1: Type Ia supernovae can be used as a standard bulb. First, look for a supernova explosion, and determine what kind of supernova it was. If it is a type Ia, it will reach the same peak luminosity as other type Ia's. Compare that peak luminosity with the apparent brightness of the supernova at maximum to determine the distance. Method 2: The rotation rate of the spiral galaxy can be used to determine the distance using the Tully-Fisher relation. Take a spectrum of the galaxy. The line widths of the 21-cm line can then be used to determine the rotation rate of the galaxy.

15. If all distant galaxies are expanding away from us, does this mean we're at the center of the universe?

No, you can show that if the expansion follows a simple proportional relationship (Hubble's law), then all points in space within the expanding universe could make the same observation and claim to be the center.

21. Would you expect to observe every supernova in our own Galaxy? Why or why not?

Only some of the supernovae that occur in our Galaxy are observable. Type II supernovae (the explosions of massive stars) tend to occur in the disk of the Milky Way, and they may be hidden by intervening dust if they are located in more distant parts of the Galaxy. Type Ia supernovae, which require a white dwarf star in a binary star system, are brighter than type II supernovae, but some of them could also happen in older parts of the Galaxy that are hidden by the buildup of gas and dust in the disk.

11. Shapley used the positions of globular clusters to determine the location of the galactic center. Could he have used open clusters? Why or why not?

Shapley could not have used open clusters because they lie in the plane of the Galaxy. Dust in the plane absorbs starlight so efficiently that open clusters cannot be seen at distances of more than a few thousand light-years. Therefore, they cannot be used to map the extent of the Galaxy, which is about 100,000 light-years in diameter, nor can they be seen at the distance of the galactic center, which is about 25,000 light-years distant.

30. It is possible to derive the age of the universe given the value of the Hubble constant and the distance to a galaxy, again with the assumption that the value of the Hubble constant has not changed since the Big Bang. Consider a galaxy at a distance of 400 million light-years receding from us at a velocity, v. If the Hubble constant is 20 km/s per million light-years, what is its velocity? How long ago was that galaxy right next door to our own Galaxy if it has always been receding at its present rate? Express your answer in years. Since the universe began when all galaxies were very close together, this number is a rough estimate for the age of the universe.

Since V = H d, the velocity of a galaxy at a distance of 400 106 light-years = 8000 km/s for H = 20 km/s per million light-years. The time required to travel 4 108 light-years at 8000 km/s is given by

35. Say that a particular white dwarf has the mass of the Sun but the radius of Earth. What is the acceleration of gravity at the surface of the white dwarf? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the white dwarf (again granting us the dubious notion that you could survive there)?

Since the radius of Earth is 6.4 106 m, the acceleration of gravity at the surface of the white dwarf is: . So, gwhite dwarf = 3.26 106. If on Earth you weigh 150 lb, on the white dwarf you would weigh or 50

2. Why did it take so long for the existence of other galaxies to be established?

Spiral galaxies have a disk, spiral arms, and a central bulge. Elliptical galaxies appear as only a bulge—they do not have any disk or spiral arm structure. Irregular galaxies do not fit into either of the other categories and don't have well-defined or clear structure.

1. Explain why we see the Milky Way as a faint band of light stretching across the sky.

The Milky Way in the sky is our particular view of the inward part of the Milky Way Galaxy as seen from our location within the Galaxy's disk. Since we are part of the disk, we see a band of diffuse light that completely encircles us.

5. Describe the organization of galaxies into groupings, from the Local Group to superclusters.

The Milky Way is one of three spiral galaxies (with the Andromeda galaxy and M33) in the Local Group. The Local Group is part of the Virgo supercluster, which is centered on the massive Virgo cluster of galaxies. On even larger scales, clusters and superclusters of galaxies are distributed on sheets and filaments like beads on a string spanning hundreds of millions of light-years.

29. There is still some uncertainty in the Hubble constant. Current estimates range from about 19.9 km/s per million light-years to 23 km/s per million light-years. Assume that the Hubble constant has been constant since the Big Bang. What is the possible range in the ages of the universe? Use the equation in the text, and make sure you use consistent units. Twenty years ago, estimates for the Hubble constant ranged from 50 to 100 km/s per Mps. What are the possible ages for the universe from those values? Can you rule out some of these possibilities on the basis of other evidence?

The age of the universe is given by If H = 20 km/s/106 light-years (rounded up from 19.9 as stated in the problem, then We can calculate the other ages required by the problem by calculating the ratio of each velocity of expansion to 20 and multiplying 15 billion y by one over that ratio. Note that more rapid expansion makes for a shorter age in order to check the answer. If H = 23, then the age would be If H = 50 km/s/Mpc, this is equivalent to light-years, and the age equals If H =100 km/s/Mpc, the age is half of the value we got for part b, or 9.8 billion y. This age is not possible because the stars in globular clusters are older than this.

6. What is the evidence that a large fraction of the matter in the universe is invisible?

The existence of dark matter is supported by three main pieces of evidence. (1) Stars and clusters orbit the centers of their host galaxies faster than they would if only visible matter (stars, gas, dust, planets) made up most of the mass. (2) Galaxies in clusters likewise move much faster than can be explained by the gravity of only luminous matter. (3) Galaxy clusters emit copious X-rays best explained by fast motion of gas particles under the influence of gravity much stronger than just the luminous matter can supply.

5. Describe the evidence indicating that a black hole may be at the center of our Galaxy.

The most compelling evidence consists of recorded stellar tracks within 1 arcsecond (0.13 light-years) of the galactic center, whose orbital periods and radii indicate the presence of a central source of gravity having a mass equivalent to more than 4 million Suns, yet being concentrated within a radius less than 17 light-hours. Other evidence includes unique radio and X-ray emissions from the galactic center

6. Describe two properties of the universe that are not explained by the standard Big Bang model (without inflation). How does inflation explain these two properties?

The standard Big Bang model without inflation does not explain why the mass-energy density of the universe would be equal to the critical density, nor does it explain the amazing uniformity of the universe. However, both of these features can be explained when an inflationary stage is added to the standard Big Bang model. A Big Bang model with a rapid, early expansion stage (inflation) is identical to the standard Big Bang model after 10-30 s, but it is significantly different prior. In an inflationary model, within the first 10-30 s, the universe expanded by a factor of about 1050 times that predicted by standard Big Bang. Such an expansion over a very short time drives any initial mass-energy density to the critical density and also produces the scale of uniformity we observe.

6. A student becomes so excited by the whole idea of black holes that he decides to jump into one. It has a mass 10 times the mass of our Sun. What is the trip like for him? What is it like for the rest of the class, watching from afar?

The student passes through the event horizon easily, but even before he reaches the horizon, he starts to be stretched (spaghettified) by tidal forces until his body is ripped apart. The student appears to slow down and become redder (redshifted) as he approaches the event horizon, eventually seeming to appear frozen in spacetime at the event horizon.

13. Why don't any of the methods for establishing distances to galaxies, described in the chapter on Galaxies, (other than Hubble's law itself), work for quasars?

The techniques for establishing distances to galaxies all involve finding an object of known intrinsic luminosity, such as a Cepheid variable, in the galaxy. Since quasars appear as points of light, we cannot detect any "standard bulbs" in them. (We can use Hubble's Law, and estimate the distances of quasars from their radial velocities, but only after we have shown, through some other method of getting distances or by associating quasars with their host galaxies, that quasars actually obey the Hubble law.)

4. If a black hole itself emits no radiation, what evidence do astronomers and physicists today have that the theory of black holes is correct?

The theory behind black holes, Einstein's general theory of relativity, has been tested with a wide range of experiments, which all confirm the predictions the theory makes. Focusing on black holes themselves, while we cannot see phenomena inside the event horizon, we do observe things outside this limit. Black holes in binary star systems leave signs of their presence on neighbor stars that have been detected. These signs include X-ray emissions, accretion disks, and large orbit perturbations.