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Astronomy 2 Tutorials session 2002-03 Tutorial 7 Model Answer 1.1 TOT From the notes on line emission, P21 N 2A21h 21 N 2A21hc / 21 , and by the inverse square law with TOT R=1AU, P21 4R 2F21 where F21 is the line flux (10-2 Wm-2) at the earth. Hence A21 4R 2F2121 /(N 2hc) . Now the number of H atoms in corona NH is almost exactly equal to the mass of the corona divided by the mass of a proton, 1016/1.7x10-27 . Number of Fe atoms NFe = NH x abundance by number = NH x 7 x 10-5. Number of Fe atoms with electron in upper level 2 is NFe x 10-4. Thus A21 [4 (1.5 1011) 2 102 500 109 ] /[4.1 1034 6.6 1034 3 108 ] 1.75 105s1 and so 21 1 / A21 5.7 10 6 s , which is long, and so the line is forbidden. The natural line width is NAT 221 /( 4c 21 ) (5 10 7 ) 2 /[ 4 3 108 5.7 10 6 ] 9.5 10 18 m Stars and Their Spectra Model Answer Tutorial Question for 14/03/03 What are the primary advantages and disadvantages of using a colour-magnitude diagram as an alternative to a standard H-R diagram based on spectral class? Advantages: - It relies on an objective classification – i.e. measurement-based classification - It is possible to classify every object by measuring the flux through standard filters. - Avoids ‘digitisation’ of the HR diagram, as classification not based on presence or absence of discrete features in spectrum. Disadvantages - Requires accurate calibration of filters used, and good photometry - Since classification is based on the flux in different parts of the spectrum, one must beware of the effects of wavelength-dependent absorption (i.e. interstellar reddening) which would change the position of a star in the colour magnitude diagram depending on its distance as well as spectral type [5] What is meant by the term ‘luminosity indicator’? Explain the difference between a positive and a negative luminosity indicator. A luminosity indicator is a property (e.g. width, depth) of a spectral feature (e.g. a line or a group of lines) which varies with the star’s luminosity, within a single stellar spectral class (or at a given value of Teff). A positive L.I. is an indicator which is enhanced with increasing luminosity whereas a negative L.I. is reduced with increasing luminosity. [3] Vega is an AOV star, of effective temperature T = 9520 K, and absolute bolometric magnitude Mbol = 0.3. Given that the Sun has effective temperature 5800 K and Mbol = 4.72, estimate the radius of Vega in units of the solar radius, stating clearly any assumptions that you make. Assuming that the stars radiate as (spherical) blackbodies, we can write: LBol,Vega LBol, Sun 4Rvega TVega 2 4RSun TSun 2 4 4 Then use Pogson’s equation: M Bol,Vega M Bol, Sun RVega 2TVega 4 LBol,Vega 2.5 log 10 2.5 log 10 R 2T 4 L Bol, Sun Sun Sun Putting in numbers gives RVega 4.72 0.3 2.15 2.26 , 5 log 10 R Sun so that RVega=2.84 RSun [5] total [13]