{"id":1168,"date":"2017-12-20T00:02:04","date_gmt":"2017-12-20T05:02:04","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/?post_type=chapter&p=1168"},"modified":"2020-03-29T14:51:38","modified_gmt":"2020-03-29T18:51:38","slug":"27-4-collaborative-group-activities-questions-and-exercises","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/27-4-collaborative-group-activities-questions-and-exercises\/","title":{"raw":"27.5 Collaborative Group Activities, Questions and Exercises","rendered":"27.5 Collaborative Group Activities, Questions and Exercises"},"content":{"raw":"
\r\n

Collaborative Group Activities<\/h1>\r\n
    \r\n \t
  1. When quasars were first discovered and the source of their great energy was unknown, some astronomers searched for evidence that quasars are much nearer to us than their redshifts imply. (That way, they would not have to produce so much energy to look as bright as they do.) One way was to find a \u201cmismatched pair\u201d\u2014a quasar and a galaxy with different redshifts that lie in very nearly the same direction in the sky. Suppose you do find one and only one galaxy with a quasar very close by, and the redshift of the quasar is six times larger than that of the galaxy. Have your group discuss whether you could then conclude that the two objects are at the same distance and that redshift is not<\/em> a reliable indicator of distance. Why? Suppose you found three such pairs, each with different mismatched redshifts? Suppose every<\/em> galaxy has a nearby quasar with a different redshift. How would your answer change and why?<\/li>\r\n \t
  2. Large ground-based telescopes typically can grant time to only one out of every four astronomers who apply for observing time. One prominent astronomer tried for several years to establish that the redshifts of quasars do not indicate their distances. At first, he was given time on the world\u2019s largest telescope, but eventually it became clearer that quasars were just the centres of active galaxies and that their redshifts really did indicate distance. At that point, he was denied observing time by the committee of astronomers who reviewed such proposals. Suppose your group had been the committee. What decision would you have made? Why? (In general, what criteria should astronomers have for allowing astronomers whose views completely disagree with the prevailing opinion to be able to pursue their research?)<\/li>\r\n \t
  3. Based on the information in this chapter and in Black Holes and Curved Spacetime<\/a>, have your group discuss what it would be like near the event horizon of a supermassive black hole in a quasar or active galaxy. Make a list of all the reasons a trip to that region would not be good for your health. Be specific.<\/li>\r\n \t
  4. Before we understood that the energy of quasars comes from supermassive black holes, astronomers were baffled by how such small regions could give off so much energy. A variety of models were suggested, some involving new physics or pretty \u201cfar out\u201d ideas from current physics. Can your group come up with some areas of astronomy that you have studied in this course where we don\u2019t yet have an explanation for something happening in the cosmos?<\/li>\r\n<\/ol>\r\n<\/section>
    \r\n

    Review Questions<\/h1>\r\n
    \r\n
    \r\n\r\n1:<\/strong> Describe some differences between quasars and normal galaxies.\u00a0 [latexpage]\r\n\r\n<\/div>\r\n<\/div>\r\n
    \r\n
    \r\n

    2:<\/strong> Describe the arguments supporting the idea that quasars are at the distances indicated by their redshifts.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    3:<\/strong> In what ways are active galaxies like quasars but different from normal galaxies?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    4:<\/strong> Why could the concentration of matter at the centre of an active galaxy like M87 not be made of stars?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    5:<\/strong> Describe the process by which the action of a black hole can explain the energy radiated by quasars.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    6:<\/strong> Describe the observations that convinced astronomers that M87 is an active galaxy.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    7:<\/strong> Why do astronomers believe that quasars represent an early stage in the evolution of galaxies?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    8:<\/strong> Why were quasars and active galaxies not initially recognized as being \u201cspecial\u201d in some way?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    9:<\/strong> What do we now understand to be the primary difference between normal galaxies and active galaxies?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n\r\n10:<\/strong> What is the typical structure we observe in a quasar at radio frequencies?\r\n\r\n<\/div>\r\n<\/div>\r\n
    \r\n
    \r\n

    11:<\/strong> What evidence do we have that the luminous central region of a quasar is small and compact?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section>

    \r\n

    Thought Questions<\/h1>\r\n
    \r\n
    \r\n

    12:<\/strong> Suppose you observe a star-like object in the sky. How can you determine whether it is actually a star or a quasar?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    13:<\/strong> Why don\u2019t any of the methods for establishing distances to galaxies, described in Galaxies<\/a> (other than Hubble\u2019s law itself), work for quasars?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    14:<\/strong> 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.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    15:<\/strong> A friend of yours who has watched many Star<\/em> Trek<\/em> episodes and movies says, \u201cI thought that black holes pulled everything into them. Why then do astronomers think that black holes can explain the great outpouring<\/em> of energy from quasars?\u201d How would you respond?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    16:<\/strong> Could the Milky Way ever become an active galaxy? Is it likely to ever be as luminous as a quasar?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    17:<\/strong> Why are quasars generally so much more luminous (why do they put out so much more energy) than active galaxies?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    18:<\/strong> 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?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    19:<\/strong> A friend tries to convince you that she can easily see a quasar in her backyard telescope. Would you believe her claim?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section>

    \r\n

    Figuring for Yourself<\/h1>\r\n
    \r\n
    \r\n

    20:<\/strong> Show that no matter how big a redshift (z<\/em>) we measure, v\/c<\/em> will never be greater than 1. (In other words, no galaxy we observe can be moving away faster than the speed of light.)<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    21:<\/strong> If a quasar has a redshift of 3.3, at what fraction of the speed of light is it moving away from us?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    22:<\/strong> If a quasar is moving away from us at v\/c<\/em> = 0.8, what is the measured redshift?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    23:<\/strong> 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?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    24:<\/strong> 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.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    25:<\/strong> 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 $$\\frac{\\Delta\\lambda}{\\lambda}=4.1.$$ 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 $$\\frac{\\Delta\\lambda}{\\lambda}=4.1?$$<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    26:<\/strong> Once again in this chapter, we see the use of Kepler\u2019s 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\u2019s third law around and use the information given in this chapter about the galaxy NGC 4261\u2014the mass of the black hole at its center and the diameter of the surrounding ring of dust and gas\u2014to 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.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    27:<\/strong> In the Check Your Learning section 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 analyzed the 410 nm line. Show that you will obtain the same redshift regardless of which absorption line you measure.\u00a0 In other words, prove that the SHIFT is the same no matter what the original rest wavelength is.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    28:<\/strong> In the Check Your Learning section, the author commented that even at z<\/em> = 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<\/em> = 0.1? What is it for z<\/em> = 0.5? What is it for z<\/em> = 1?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n

    29:<\/strong> The quasar that appears the brightest in our sky, 3C 273, is located at a distance of 2.4 billion light-years. 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.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section>","rendered":"

    \n

    Collaborative Group Activities<\/h1>\n
      \n
    1. When quasars were first discovered and the source of their great energy was unknown, some astronomers searched for evidence that quasars are much nearer to us than their redshifts imply. (That way, they would not have to produce so much energy to look as bright as they do.) One way was to find a \u201cmismatched pair\u201d\u2014a quasar and a galaxy with different redshifts that lie in very nearly the same direction in the sky. Suppose you do find one and only one galaxy with a quasar very close by, and the redshift of the quasar is six times larger than that of the galaxy. Have your group discuss whether you could then conclude that the two objects are at the same distance and that redshift is not<\/em> a reliable indicator of distance. Why? Suppose you found three such pairs, each with different mismatched redshifts? Suppose every<\/em> galaxy has a nearby quasar with a different redshift. How would your answer change and why?<\/li>\n
    2. Large ground-based telescopes typically can grant time to only one out of every four astronomers who apply for observing time. One prominent astronomer tried for several years to establish that the redshifts of quasars do not indicate their distances. At first, he was given time on the world\u2019s largest telescope, but eventually it became clearer that quasars were just the centres of active galaxies and that their redshifts really did indicate distance. At that point, he was denied observing time by the committee of astronomers who reviewed such proposals. Suppose your group had been the committee. What decision would you have made? Why? (In general, what criteria should astronomers have for allowing astronomers whose views completely disagree with the prevailing opinion to be able to pursue their research?)<\/li>\n
    3. Based on the information in this chapter and in Black Holes and Curved Spacetime<\/a>, have your group discuss what it would be like near the event horizon of a supermassive black hole in a quasar or active galaxy. Make a list of all the reasons a trip to that region would not be good for your health. Be specific.<\/li>\n
    4. Before we understood that the energy of quasars comes from supermassive black holes, astronomers were baffled by how such small regions could give off so much energy. A variety of models were suggested, some involving new physics or pretty \u201cfar out\u201d ideas from current physics. Can your group come up with some areas of astronomy that you have studied in this course where we don\u2019t yet have an explanation for something happening in the cosmos?<\/li>\n<\/ol>\n<\/section>\n
      \n

      Review Questions<\/h1>\n
      \n
      \n

      1:<\/strong> Describe some differences between quasars and normal galaxies.\u00a0 <\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      2:<\/strong> Describe the arguments supporting the idea that quasars are at the distances indicated by their redshifts.<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      3:<\/strong> In what ways are active galaxies like quasars but different from normal galaxies?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      4:<\/strong> Why could the concentration of matter at the centre of an active galaxy like M87 not be made of stars?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      5:<\/strong> Describe the process by which the action of a black hole can explain the energy radiated by quasars.<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      6:<\/strong> Describe the observations that convinced astronomers that M87 is an active galaxy.<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      7:<\/strong> Why do astronomers believe that quasars represent an early stage in the evolution of galaxies?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      8:<\/strong> Why were quasars and active galaxies not initially recognized as being \u201cspecial\u201d in some way?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      9:<\/strong> What do we now understand to be the primary difference between normal galaxies and active galaxies?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      10:<\/strong> What is the typical structure we observe in a quasar at radio frequencies?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      11:<\/strong> What evidence do we have that the luminous central region of a quasar is small and compact?<\/p>\n<\/div>\n<\/div>\n<\/section>\n

      \n

      Thought Questions<\/h1>\n
      \n
      \n

      12:<\/strong> Suppose you observe a star-like object in the sky. How can you determine whether it is actually a star or a quasar?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      13:<\/strong> Why don\u2019t any of the methods for establishing distances to galaxies, described in Galaxies<\/a> (other than Hubble\u2019s law itself), work for quasars?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      14:<\/strong> 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.<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      15:<\/strong> A friend of yours who has watched many Star<\/em> Trek<\/em> episodes and movies says, \u201cI thought that black holes pulled everything into them. Why then do astronomers think that black holes can explain the great outpouring<\/em> of energy from quasars?\u201d How would you respond?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      16:<\/strong> Could the Milky Way ever become an active galaxy? Is it likely to ever be as luminous as a quasar?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      17:<\/strong> Why are quasars generally so much more luminous (why do they put out so much more energy) than active galaxies?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      18:<\/strong> 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?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      19:<\/strong> A friend tries to convince you that she can easily see a quasar in her backyard telescope. Would you believe her claim?<\/p>\n<\/div>\n<\/div>\n<\/section>\n

      \n

      Figuring for Yourself<\/h1>\n
      \n
      \n

      20:<\/strong> Show that no matter how big a redshift (z<\/em>) we measure, v\/c<\/em> will never be greater than 1. (In other words, no galaxy we observe can be moving away faster than the speed of light.)<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      21:<\/strong> If a quasar has a redshift of 3.3, at what fraction of the speed of light is it moving away from us?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      22:<\/strong> If a quasar is moving away from us at v\/c<\/em> = 0.8, what is the measured redshift?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      23:<\/strong> 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?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      24:<\/strong> 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.<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      25:<\/strong> 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 <\/p>\n

        <\/span>   <\/span>\"\[\frac{\Delta\lambda}{\lambda}=4.1.\]\"<\/p>\n

      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 <\/p>\n

        <\/span>   <\/span>\"\[\frac{\Delta\lambda}{\lambda}=4.1?\]\"<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      26:<\/strong> Once again in this chapter, we see the use of Kepler\u2019s 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\u2019s third law around and use the information given in this chapter about the galaxy NGC 4261\u2014the mass of the black hole at its center and the diameter of the surrounding ring of dust and gas\u2014to 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.<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      27:<\/strong> In the Check Your Learning section 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 analyzed the 410 nm line. Show that you will obtain the same redshift regardless of which absorption line you measure.\u00a0 In other words, prove that the SHIFT is the same no matter what the original rest wavelength is.<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      28:<\/strong> In the Check Your Learning section, the author commented that even at z<\/em> = 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<\/em> = 0.1? What is it for z<\/em> = 0.5? What is it for z<\/em> = 1?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      29:<\/strong> The quasar that appears the brightest in our sky, 3C 273, is located at a distance of 2.4 billion light-years. 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.<\/p>\n<\/div>\n<\/div>\n<\/section>\n","protected":false},"author":9,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1168","chapter","type-chapter","status-publish","hentry"],"part":794,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/1168","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/users\/9"}],"version-history":[{"count":7,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/1168\/revisions"}],"predecessor-version":[{"id":2660,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/1168\/revisions\/2660"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/parts\/794"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/1168\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/media?parent=1168"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapter-type?post=1168"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/contributor?post=1168"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/license?post=1168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}