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Binary Stars PHYS390 (Astrophysics) Professor Lee Carkner Lecture 6 Questions 1) If m1 is much larger than m2, what are m and M approximately equal to? Since m = m1m2/(m1+m2) and M = m1+m2, M ~ m1 , m ~ m 2 2) If m1 is much larger than m2, what is the total kinetic energy of the system and which mass has all the kinetic energy? Since K = ½mv2 and m ~ m2, K = ½m2v2 and the smaller mass has all the kinetic energy (it is the only thing moving) Spectroscopic Binaries For spectroscopic binaries we cannot find a or a The radial velocity vr is related to the actual orbital velocity v by vr = v sin i For circular, edge-on orbits, vmax is the true orbital velocity Mass and Velocity m1/m2 = v2r/v1r m1+m2 = (P/2pG)[(v1r+v2r)3/sin3 i] Where we can measure both v1r and v2r Inclination and Statistics Often we can’t find i We can’t find mass for one star, but we can find an average mass for a class of stars Gives mass-luminosity relationship How does mass produce luminosity? Eclipsing Binaries Light will dim when hotter star goes behind cooler From Doppler shift we can get the velocity of each star Smaller = vs Relative velocity v = vs + vl Eclipsing Binaries and Radius rs = (v/2)(tb-ta) Time for smaller to emerge from behind larger is just tc-ta, so radius is rl = (v/2)(tc-ta) Eclipse Flux Variations B0 Bs Bp Maximum light = B0 Primary minimum = Bp Secondary minimum = Bs Larger star completely behind smaller Temperature B0-Bp = B0-Bs = Since flux is proportional to temperature to the 4th power, (B0-Bp)/(B0-Bs) = [1-(Bp/B0)]/[1-(Bs/B0)]= (Ts/Tl)4 Next Time Test #1 For Friday: Read: 8.1 Homework: 8.1, 8.6a