#### Transcript mass-luminosity relationship

```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

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: