{"id":4250,"date":"2018-01-11T23:00:56","date_gmt":"2018-01-11T19:00:56","guid":{"rendered":"http:\/\/sites.williams.edu\/kkwitter\/?page_id=4250"},"modified":"2018-04-26T19:27:37","modified_gmt":"2018-04-26T15:27:37","slug":"a402t-tutorial-week-9-non-optical-nebular-studies","status":"publish","type":"page","link":"https:\/\/sites.williams.edu\/kkwitter\/astronomy-402-between-the-stars\/a402t-tutorial-week-9-non-optical-nebular-studies\/","title":{"rendered":"A402T Tutorial Week #9: Non-optical Nebular Studies"},"content":{"rendered":"

ASTRONOMY 402T \u2013 Spring 2018
\nProblems for Tutorial Week #9<\/strong><\/p>\n

1.<\/strong> The Einstein A-value for the H I spin-flip transition is 2.85 x 10-15<\/sup> sec-1<\/sup>. How long (in seconds and in years) would you have to wait, on average, for an H I atom whose proton and electron have aligned spins to spontaneously emit a 21-cm photon? Given this result, how do you explain the ubiquity and strength of 21-cm radiation in the Galaxy?<\/p>\n

2.<\/strong>\u00a0 a) Go through the argument\u00a0that, even though the time between collisions in a cold H I\u00a0cloud (T=150 K, nH<\/sub>=1 cm-3<\/sup>) \u00a0is ~103<\/sup> years, the electron distribution in the two levels involved in the 21-cm transition should be that predicted by LTE; i.e., the distribution given by the Boltzmann equation. Roughly what is the ratio between the spontaneous radiation time and the collision time?<\/p>\n

b) In the case of deuterium, the analogous hyperfine transition has an A-value of 4.69x 10-17<\/sup> sec-1<\/sup>. What is the corresponding lifetime of the upper level, in seconds and in years?<\/p>\n

c) Under the same cloud conditions as in part a, calculate the approximate ratio between the spontaneous radiation time and the collision time. Do you expect an LTE distribution?<\/p>\n

3. <\/strong>Draw the spectrum produced by a blackbody in the radio region of the spectrum on a log-log scale. For comparison, draw on the same graph a synchrotron emission spectrum. Now you should be able to describe how, spectrally, one is able to distinguish between the two. How else might one distinguish?<\/p>\n

4.\u00a0<\/strong>Think about why it is advantageous to locate ground-based infrared observatories at high altitude, or even in space: What are the main issues? Be as specific as you can, and include graphs and numbers that back up your argument.<\/p>\n

5.\u00a0<\/strong>In the Rydberg expression for hydrogen, the wavelength, \u03bb, of Lyman \u03b1 (in Angstroms) is given by:<\/p>\n

1\/\u03bb = (1\/911.8) x (1 – 1\/4).<\/p>\n

For heavier atoms that are fully ionized, the right side of the expression must be multiplied by Z2<\/sup>, where Z is the atomic number of the atom.<\/p>\n

a) Calculate the Lyman \u03b1 transition in fully ionized Fe. What region of the spectrum does this fall in?<\/p>\n

b) Do the same for Si, S, Ar, and Ca.<\/p>\n

Compare your wavelength results with those in the plotted spectrum below.<\/p>\n

\"\"<\/a>

The red, green, and blue regions in this Chandra X-ray image of the supernova remnant Cassiopeia A show where the intensity of low, medium, and high energy X rays, respectively, is greatest.<\/p><\/div>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

ASTRONOMY 402T \u2013 Spring 2018 Problems for Tutorial Week #9 1. The Einstein A-value for the H I spin-flip transition is 2.85 x 10-15 sec-1. How long (in seconds and in years) would you have to wait, on average, for an H I atom whose proton and electron have aligned spins to spontaneously emit a […]<\/p>\n","protected":false},"author":198,"featured_media":0,"parent":793,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-4250","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/kkwitter\/wp-json\/wp\/v2\/pages\/4250","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.williams.edu\/kkwitter\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.williams.edu\/kkwitter\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/kkwitter\/wp-json\/wp\/v2\/users\/198"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/kkwitter\/wp-json\/wp\/v2\/comments?post=4250"}],"version-history":[{"count":29,"href":"https:\/\/sites.williams.edu\/kkwitter\/wp-json\/wp\/v2\/pages\/4250\/revisions"}],"predecessor-version":[{"id":4452,"href":"https:\/\/sites.williams.edu\/kkwitter\/wp-json\/wp\/v2\/pages\/4250\/revisions\/4452"}],"up":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/kkwitter\/wp-json\/wp\/v2\/pages\/793"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/kkwitter\/wp-json\/wp\/v2\/media?parent=4250"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}