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Binary Stars

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Binary Stars PHYS390 (Astrophysics) Professor Lee Carkner Lecture 6 Questions If m1 is much larger than m2, what are m and M approximately equal to? – PowerPoint PPT presentation

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Date added: 5 September 2019
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Title: Binary Stars


1
Binary Stars
  • PHYS390 (Astrophysics)
  • Professor Lee Carkner
  • Lecture 6

2
Questions
  • If m1 is much larger than m2, what are m and M
    approximately equal to?
  • Since m m1m2/(m1m2) and M m1m2, M m1, m
    m2
  • 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)

3
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

4
Mass and Velocity
  • m1/m2 v2r/v1r
  • m1m2 (P/2pG)(v1rv2r)3/sin3 i
  • Where we can measure both v1r and v2r

5
Inclination and Statistics
  • Often we cant find i
  • We cant 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?

6
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

7
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)

8
Eclipse Flux Variations
B0
Bs
Bp
  • Maximum light B0
  • Primary minimum Bp
  • Secondary minimum Bs
  • Larger star completely behind smaller

9
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

10
Next Time
  • Test 1
  • For Friday
  • Read 8.1
  • Homework 8.1, 8.6a
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