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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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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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