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star clusters L13.docx

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Department
Science
Course
SCI 238
Professor
Mike Fich
Semester
Winter

Description
13 - Star Clusters How do we measure stellar masses? (binary stars) - Newton’s version of Kepler’s third law o applied only when we can observe one object orbiting another, and it requires that we measure both the orbital period and the average orbital distance of the orbiting object. - binary star systems—systems in which two stars continually orbit one another. o - detected visually, spectroscopically, and via eclipses Types: 1. visual binary: pair of stars we can see distinctly as the stars orbit each other 2. eclipsing binary a. one star passes in front of the other, blocking some of the light reaching us and causing a change in the systems brightness b. When neither star is eclipsed, we see the combined light of both stars. c. A light curve, or graph of apparent brightness against time, reveals the pattern of the eclipses. d. Algol’s brightness drops to only a third of its usual level for a few hours about every three days as the brighter of its two stars is eclipsed by its dimmer companion. 3. spectroscopic binary a. detect by observing Doppler shifts in its spectral lines b. only one star is visible; it shows no visible motion, but from its spectrum one can see a regular periodic motion from doppler shifts; sometimes only brighter stars spectrum is seen, sometimes both c. Sometimes we see two sets of lines shifting back and forth— one set from each of the two stars in the system (a double- lined spectroscopic binary). Other times we see a set of shifting lines from only one star because its companion is too dim to be detected (a single-lined spectroscopic binary). d. Blueshifted: star approaching us 13 - Star Clusters Measuring Masses in Binary Systems a. apply Newton’s version of Kepler’s third law only if we can measure both the orbital period and the separation of the two stars. Orbital period: observe how long each orbit takes 1. Visual binaries: period determined form motion of one star about the other o eclipsing binary: we measure the time between eclipses  in an eclipsing binary we observe periodic changes brightness: eclipses  timescale => orbital period  eclipse timing => ratio of radii  eclipse depth + radius => temperature and luminosity ratios  if also spectroscopic => true radii; +mass -> densities   o spectroscopic binary: we measure the time it takes the spectral lines to shift back and forth.  in a spectroscopic binary we observe periodic changes in spectral line wavelengths  timescale => orbital period
  amplitude => orbital scale amplitude ratio => mass ratio Average separation of the stars in binary system: 1. can measure the separation directly; 2. know the actual orbital speeds of the stars from their Doppler shifts. o Doppler shift tells us only the portion of a star’s velocity that is directed toward us or away from us o But, orbiting stars generally do not move directly along our line of sight, their actual velocities can be significantly greater than those we measure through the Doppler effect. 3. exceptions are eclipsing binary stars. Because these stars orbit in the plane of our line of sight, their Doppler shifts can tell us their true orbital velocities. = important to find stellar masses  we can determine their radii by timing how long each eclipse lasts.  The overall range extends from as little as 0.08 times 13 - Star Clusters the mass of the Sun (0.08MSun) to about 150 times the mass of the Sun (150MSun). Center of mass •location of center of mass depends on relative masses
 •in an equal mass system, CM is midway between •in SS MSun >> Mplanet and CM is inside the Sun more general form of KIII (1 +m2)P = a = (a 1a 23 Relative orbital size: m 1m =a2/a 2v /1 2 1 example: Spectroscopic Binary star example:  The separation between two stars in a binary system is 0.5AU and the orbital period is 0.1 y 2 3 3  (m1+m2)P = a = (a1+a2)  What is the sum of their masses? m1+m2 = (0.5AU) /(0.1y) = 12.5MSun  Assume we know one star is moving in orbit twice as fast as the other; what are the individual masses of the two stars??  v2/v 12=m /m 1here2ore m =2m 
and 1 2 m 1m =32 =12.2MSun  m =4.2MSun, m =8.3MSun 2 1  v=2pi a/P  3.5 L proportional to M  the lifetimes of stars depend on  1) the amount of fuel (mass) and  2) the rate at which the star uses up that fuel (luminosity)  Stella radii can be as small as a planet or as big as Mars’ orbit 90% of stars have mass smaller than Msun 13 - Star Clusters Star clusters These groups are known as star cl
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