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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? - 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)

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
- m1m2 (P/2pG)(v1rv2r)3/sin3 i
- Where we can measure both v1r and v2r

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?

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