Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Astronomy
Describe the arguments supporting the idea that quasars are at the distances indicated by their redshifts.In what ways are active galaxies like quasars but different from normal galaxies?Why could the concentration of matter at the center of an active galaxy like M87 not be made of stars?Describe the process by which the action of a black hole can explain the energy radiated by quasars.Describe the observations that convinced astronomers that M87 is an active galaxy.Why do astronomers believe that quasars represent an early stage in the evolution of galaxies?Why were quasars and active galaxies not initially recognized as being “special” in some way?What do we now understand to be the primary difference between normal galaxies and active galaxies?What is the typical structure we observe in a quasar at radio frequencies?What evidence do we have that the luminous central region of a quasar is small and compact?Suppose you observe a star-like object in the sky. How can you determine whether it is actually a star or a quasar?Why don’t any of the methods for establishing distances to galaxies, described in Galaxies (other than Hubble’s law itself), work for quasars?One of the early hypotheses to explain the high redshifts of quasars was that these objects had been ejected at very high speeds from other galaxies. This idea was rejected, because no quasars with large blueshifts have been found. Explain why we would expect to see quasars with both blueshifted and redshifted lines if they were ejected from nearby galaxies.A friend of yours who has watched many Star Trek episodes and movies says, “I thought that black holes pulled everything into them. Why then do astronomers think that black holes can explain the great outpouring of energy from quasars?” How would you respond?Could the Milky Way ever become an active galaxy? Is it likely to ever be as luminous as a quasar?Why are quasars generally so much more luminous (why do they put out so much more energy) than active galaxies?Suppose we detect a powerful radio source with a radio telescope. How could we determine whether or not this was a newly discovered quasar and not some nearby radio transmission?A friend tries to convince you that she can easily see a quasar in her backyard telescope. Would you believe her claim?Show that no matter how big a redshift (z) we measure, v/c will never be greater than 1. (In other words, no galaxy we observe can be moving away faster than the speed of light.)If a quasar has a redshift of 3.3, at what fraction of the speed of light is it moving away from us?If a quasar is moving away from us at v/c=0.8 , what is the measured redshift?In the chapter, we discussed that the largest redshifts found so far are greater than 6. Suppose we find a quasar with a redshift of 6.1. With what fraction of the speed of light is it moving away from us?Rapid variability in quasars indicates that the region in which the energy is generated must be small. You can show why this is true. Suppose, for example, that the region in which the energy is generated is a transparent sphere 1 light-year in diameter. Suppose that in 1 s this region brightens by a factor of 10 and remains bright for two years, after which it returns to its original luminosity. Draw its light curve (a graph of its brightness over time) as viewed from Earth.Large redshifts move the positions of spectral lines to longer wavelengths and change what can be observed from the ground. For example, suppose a quasar has a redshift of =4.1 . At what wavelength would you make observations in order to detect its Lyman line of hydrogen, which has a laboratory or rest wavelength of 121.6 nm? Would this line be observable with a ground-based telescope in a quasar with zero redshift? Would it be observable from the ground in a quasar with a redshift of =4.1 ?Once again in this chapter, we see the use of Kepler’s third law to estimate the mass of supermassive black holes. In the case of NGC 4261, this chapter supplied the result of the calculation of the mass of the black hole in NGC 4261. In order to get this answer, astronomers had to measure the velocity of particles in the ring of dust and gas that surrounds the black hole. How high were these velocities? Turn Kepler’s third law around and use the information given in this chapter about the galaxy NGC 4261-the mass of the black hole at its center and the diameter of the surrounding ring of dust and gas-to calculate how long it would take a dust particle in the ring to complete a single orbit around the black hole. Assume that the only force acting on the dust particle is the gravitational force exerted by the black hole. Calculate the velocity of the dust particle in km/s.In the Check Your Learning section of Example 27.1, you were told that several lines of hydrogen absorption in the visible spectrum have rest wavelengths of 410 nm, 434 nm, 486 nm, and 656 nm. In a spectrum of a distant galaxy, these same lines are observed to have wavelengths of 492 nm, 521 nm, 583 nm, and 787 nm, respectively. The example demonstrated that z=0.20 for the 410 nm line. Show that you will obtain the same redshift regardless of which absorption line you measure.In the Check Your Learning section of Example 27.1, the author commented that even at z=0.2 , there is already an 11% deviation between the relativistic and the classical solution. What is the percentage difference between the classical and relativistic results at z=0.1 ? What is it for z=0.5 ? What is it for z=1 ?The quasar that appears the brightest in our sky, 3C 273, is located at a distance of 2.4 billion lightyears. The Sun would have to be viewed from a distance of 1300 light-years to have the same apparent magnitude as 3C 273. Using the inverse square law for light, estimate the luminosity of 3C 273 in solar units.How are distant (young) galaxies different from the galaxies that we see in the universe today?What is the evidence that star formation began when the universe was only a few hundred million years old?Describe the evolution of an elliptical galaxy. How does the evolution of a spiral galaxy differ from that of an elliptical?Explain what we mean when we call the universe homogeneous and isotropic. Would you say that the distribution of elephants on Earth is homogeneous and isotropic? Why?Describe the organization of galaxies into groupings, from the Local Group to superclusters.What is the evidence that a large fraction of the matter in the universe is invisible?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?How does the presence of an active galactic nucleus in a starburst galaxy affect the starburst process?Describe how you might use the color of a galaxy to determine something about what kinds of stars it contains.Suppose a galaxy formed stars for a few million years and then stopped (and no other galaxy merged or collided with it). What would be the most massive stars on the main sequence after 500 million years? After 10 billion years? How would the color of the galaxy change over this time span? (Refer to Evolution from the Main Sequence to Red Giants.)Given the ideas presented here about how galaxies form, would you expect to find a giant elliptical galaxy in the Local Group? Why or why not? Is there in fact a giant elliptical in the Local Group?Can an elliptical galaxy evolve into a spiral? Explain your answer. Can a spiral turn into an elliptical? How?If we see a double image of a quasar produced by a gravitational lens and can obtain a spectrum of the galaxy that is acting as the gravitational lens, we can then put limits on the distance to the quasar. Explain how.The left panel of Figure 27.1 shows a cluster of yellow galaxies that produces several images of blue galaxies through gravitational lensing. Which are more distant-the blue galaxies or the yellow galaxies? The light in the galaxies comes from stars. How do the temperatures of the stars that dominate the light of the cluster galaxies differ from the temperatures of the stars that dominate the light of the blue-lensed galaxy? Which galaxy’s light is dominated by young stars? Figure 27.1 Hubble Ultra-Deep Field. The deepest picture of the sky in visible light (left) shows huge numbers of galaxies in a tiny patch of sky, only 1/100 the area of the full Moon. In contrast, the deepest picture of the sky taken in X-rays (right) shows large numbers of point-like quasars, which astronomers have shown are supermassive black holes at the very centers of galaxies. (credit left: modification of work by NASA, ESA, H. Teplitz and M. Rafelski (IPAC/Caltech), A. Koekemoer (STScI), R. Windhorst (Arizona State University), and Z. Levay (STScI); credit right: modification of work by ESO/Mario Nonino, Piero Rosati, ESO GOODS Team)Suppose you are standing in the center of a large, densely populated city that is exactly circular, surrounded by a ring of suburbs with lower-density population, surrounded in turn by a ring of farmland. From this specific location, would you say the population distribution is isotropic? Homogeneous?Astronomers have been making maps by observing a slice of the universe and seeing where the galaxies lie within that slice. If the universe is isotropic and homogeneous, why do they need more than one slice? Suppose they now want to make each slice extend farther into the universe. What do they need to do?Human civilization is about 10,000 years old as measured by the development of agriculture. If your telescope collects starlight tonight that has been traveling for 10,000 years, is that star inside or outside our Milky Way Galaxy? Is it likely that the star has changed much during that time?Given that only about 5% of the galaxies visible in the Hubble Deep Field are bright enough for astronomers to study spectroscopically, they need to make the most of the other 95%. One technique is to use their colors and apparent brightnesses to try to roughly estimate their redshift. How do you think the inaccuracy of this redshift estimation technique (compared to actually measuring the redshift from a spectrum) might affect our ability to make maps of large-scale structures such as the filaments and voids shown in Figure 28.21? Figure 28.21 Sloan Digital Sky Survey Map of the Large-Scale Structure of the Universe. This image shows slices from the SDSS map. The point at the center corresponds to the Milky Way and might say “You Are Here!” Points on the map moving outward from the center are farther away. The distance to the galaxies is indicated by their redshifts (following Hubble’s law), shown on the horizontal line going right from the center. The redshift z=/ , where is the difference between the observed wavelength and the wavelength emitted by a nonmoving source in the laboratory. Hour angle on the sky is shown around the circumference of the circular graph. The colors of the galaxies indicate the ages of their stars, with the redder color showing galaxies that are made of older stars. The outer circle is at a distance of two billion light-years from us. Note that red (older stars) galaxies are more strongly clustered than blue galaxies (young stars). The unmapped areas are where our view of the universe is obstructed by dust in our own Galaxy. (credit: modification of work by M. Blanton and the Sloan Digital Sky Survey)Using the information from Example 28.1, how much fainter an object will you have to be able to measure in order to include the same kinds of galaxies in your second survey? Remember that the brightness of an object varies as the inverse square of the distance.Using the information from Example 28.1, if galaxies are distributed homogeneously, how many times more of them would you expect to count on your second survey?Using the information from Example 28.1, how much longer will it take you to do your second survey?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?Calculate the velocity, the distance, and the look-back time of the most distant galaxies in Figure 28.21 using the Hubble constant given in this text and the redshift given in the diagram. Remember the Doppler formula for velocity (v=c) and the Hubble law ( v=Hd , where d is the distance to a galaxy). For these low velocities, you can neglect relativistic effects. Figure 28.21 Sloan Digital Sky Survey Map of the Large-Scale Structure of the Universe. This image shows slices from the SDSS map. The point at the center corresponds to the Milky Way and might say “You Are Here!” Points on the map moving outward from the center are farther away. The distance to the galaxies is indicated by their redshifts (following Hubble’s law), shown on the horizontal line going right from the center. The redshift z=/ , where is the difference between the observed wavelength and the wavelength emitted by a nonmoving source in the laboratory. Hour angle on the sky is shown around the circumference of the circular graph. The colors of the galaxies indicate the ages of their stars, with the redder color showing galaxies that are made of older stars. The outer circle is at a distance of two billion light-years from us. Note that red (older stars) galaxies are more strongly clustered than blue galaxies (young stars). The unmapped areas are where our view of the universe is obstructed by dust in our own Galaxy. (credit: modification of work by M. Blanton and the Sloan Digital Sky Survey)Assume that dark matter is uniformly distributed throughout the Milky Way, not just in the outer halo but also throughout the bulge and in the disk, where the solar system lives. How much dark matter would you expect there to be inside the solar system? Would you expect that to be easily detectable? Hint: For the radius of the Milky Way’s dark matter halo, use R=300,000 light-years; for the solar system’s radius, use 100 AU; and start by calculating the ratio of the two volumes.The simulated box of galaxy filaments and superclusters shown in Figure 28.29 stretches across 1 billion light-years. If you were to make a scale model where that box covered the core of a university campus, say 1 km, then how big would the Milky Way Galaxy be? How far away would the Andromeda galaxy be in the scale model? Figure 28.29 Growth of Large-Scale Structure as Calculated by Supercomputers. The boxes show how filaments and superclusters of galaxies grow over time, from a relatively smooth distribution of dark matter and gas, with few galaxies formed in the first 2 billion years after the Big Bang, to the very clumpy strings of galaxies with large voids today. Compare the last image in this sequence with the actual distribution of nearby galaxies shown in Figure 28.21. (credit: modification of work by CXC/MPE/V.Springel)The first objects to collapse gravitationally after the Big Bang might have been globular cluster-size galaxy pieces, with masses around 106 solar masses. Suppose you merge two of those together, then merge two larger pieces together, and so on, Lego-style, until you reach a Milky Way mass, about 1012 solar masses. How many merger generations would that take, and how many original pieces? (Hint: Think in powers of 2.)What are the basic observations about the universe that any theory of cosmology must explain?Describe some possible futures for the universe that scientists have come up with. What property of the universe determines which of these possibilities is the correct one?What does the term Hubble time mean in cosmology, and what is the current best calculation for the Hubble time?Which formed first: hydrogen nuclei or hydrogen atoms? Explain the sequence of events that led to each.Describe at least two characteristics of the universe that are explained by the standard Big Bang model.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?Why do astronomers believe there must be dark matter that is not in the form of atoms with protons and neutrons?What is dark energy and what evidence do astronomers have that it is an important component of the universe?Thinking about the ideas of space and time in Einstein’s general theory of relativity, how do we explain the fact that all galaxies outside our Local Group show a redshift?Astronomers have found that there is more helium in the universe than stars could have made in the 13.8 billion years that the universe has been in existence. How does the Big Bang scenario solve this problem?Describe the anthropic principle. What are some properties of the universe that make it “ready” to have life forms like you in it?Describe the evidence that the expansion of the universe is accelerating.What is the most useful probe of the early evolution of the universe: a giant elliptical galaxy or an irregular galaxy such as the Large Magellanic Cloud? Why?What are the advantages and disadvantages of using quasars to probe the early history of the universe?Would acceleration of the universe occur if it were composed entirely of matter (that is, if there were no dark energy)?Suppose the universe expands forever. Describe what will become of the radiation from the primeval fireball. What will the future evolution of galaxies be like? Could life as we know it survive forever in such a universe? Why?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?There are a variety of ways of estimating the ages of various objects in the universe. Describe two of these ways, and indicate how well they agree with one another and with the age of the universe itself as estimated by its expansion.Since the time of Copernicus, each revolution in astronomy has moved humans farther from the center of the universe. Now it appears that we may not even be made of the most common form of matter. Trace the changes in scientific thought about the central nature of Earth, the Sun, and our Galaxy on a cosmic scale. Explain how the notion that most of the universe is made of dark matter continues this “Copernican tradition.”The anthropic principle suggests that in some sense we are observing a special kind of universe; if the universe were different, we could never have come to exist. Comment on how this fits with the Copernican tradition described in Exercise 29.19.Penzias and Wilson’s discovery of the Cosmic Microwave Background (CMB) is a nice example of scientific serendipity-something that is found by chance but turns out to have a positive outcome. What were they looking for and what did they discover?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.Suppose the Hubble constant were not 22 but 33 km/s per million light-years. Then what would the critical density be?Assume that the average galaxy contains 1011MSunand 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?The CMB contains roughly 400 million photons per m3. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien’s law, the peak wave length in nanometers is given by max=3106T . Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters.Following up on Exercise 29.27 calculate the energy of a typical photon. Assume for this approximate calculation that each photon has the wavelength calculated in Exercise 29.25. The energy of a photon is given by E=hc , where h is Planck’s constant and is equal to 6.6261034Js , c is the speed of light in m/s, and ? is the wavelength in m.Continuing the thinking in Exercise 29.27 and Exercise 29.28, calculate the energy in a cubic meter of space, multiply the energy per photon calculated in Exercise 29.26 by the number of photons per cubic meter given above.Continuing the thinking in the last three exercises, convert this energy to an equivalent in mass, use Einstein’s equation E=mc2 . Hint: Divide the energy per m3 calculated in Exercise 29.27 by the speed of light squared. Check your units; you should have an answer in kg/m3. Now compare this answer with the critical density. Your answer should be several powers of 10 smaller than the critical density. In other words, you have found for yourself that the contribution of the CMB photons to the overall density of the universe is much, much smaller than the contribution made by stars and galaxies.There is still some uncertainty in the Hubble constant. (a) 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, T0=1H , and make sure you use consistent units. (b) 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?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.What is the Copernican principle? Make a list of scientific discoveries that confirm it.Where in the solar system (and beyond) have scientists found evidence of organic molecules?Give a short history of the atoms that are now in your little finger, going back to the beginning of the universe.What is a biomarker? Give some possible examples of biomarkers we might look for beyond the solar system.Why are Mars and Europa the top targets for the study of astrobiology?Why is traveling between the stars (by creatures like us) difficult?What are the advantages to using radio waves for communication between civilizations that live around different stars? List as many as you can.What is the “cosmic haystack problem”? List as many of its components as you can think of.What is a habitable zone?Why is the simultaneous detection of methane and oxygen in an atmosphere a good indication of the existence of a biosphere on that planet?What are two characteristic properties of life that distinguish it from nonliving things?What are the three requirements that scientists believe an environment needs to supply life with in order to be considered habitable?Can you name five environmental conditions that, in their extremes, microbial life has been challenged by and has learned to survive on Earth?Would a human have been possible during the first generation of stars that formed right after the Big Bang? Why or why not?If we do find life on Mars, what might be some ways to check whether it formed separately from Earth life, or whether exchanges of material between the two planets meant that the two forms of life have a common origin?What kind of evidence do you think would convince astronomers that an extraterrestrial spacecraft has landed on Earth?What are some reasons that more advanced civilizations might want to send out messages to other star systems?What are some answers to the Fermi paradox? Can you think of some that are not discussed in this chapter?Why is there so little evidence of Earth’s earliest history and therefore the period when life first began on our planet?Why was the development of photosynthesis a major milestone in the evolution of life?Does all life on Earth require sunshine?Why is life unlikely to be found on the surface of Mars today?In this chapter, we identify these characteristic properties of life: life extracts energy from its environment, and has a means of encoding and replicating information in order to make faithful copies of itself. Does this definition fully capture what we think of as “life”? How might our definition be biased by our terrestrial environment?Given that no sunlight can penetrate Europa’s ice shell, what would be the type of energy that could make some form of europan life possible?Why is Saturn’s moon Enceladus such an exciting place to send a mission?In addition to an atmosphere dominated by nitrogen, how else is Saturn’s moon Titan similar to Earth?How can a planet’s atmosphere affect the width of the habitable zone in its planetary system?Why are we limited to finding life on planets orbiting other stars to situations where the biosphere has created planet-scale changes?Suppose astronomers discover a radio message from a civilization whose planet orbits a star 35 lightyears away. Their message encourages us to send a radio answer, which we decide to do. Suppose our governing bodies take 2 years to decide whether and how to answer. When our answer arrives there, their governing bodies also take two of our years to frame an answer to us. How long after we get their first message can we hope to get their reply to ours? (A question for further thinking: Once communication gets going, should we continue to wait for a reply before we send the next message?)The light a planet receives from the Sun (per square meter of planet surface) decreases with the square of the distance from the Sun. So a planet that is twice as far from the Sun as Earth receives (1/2)2=0.25 times (25%) as much light and a planet that is three times as far from the Sun receives (1/3)2=0.11 times (11%) as much light. How much light is received by the moons of Jupiter and Saturn (compared to Earth), worlds which orbit 5.2 and 9.5 times farther from the Sun than Earth?Think of our Milky Way Galaxy as a flat disk of diameter 100,000 light-years. Suppose we are one of 1000 civilizations, randomly distributed through the disk, interested in communicating via radio waves. How far away would the nearest such civilization be from us (on average)?