1. BINARIES Read Your Textbook: Foundations of Astronomy
Chapter 10
Homework Problems Chapter 9
Review Questions: 1, 4, 5, 7
Review Problems: 1-5
Web Inquiries: 1
Homework Problems Chapter 10
Review Questions: 1, 2, 4, 6-8
Review Problems: 1-4, 8
Web Inquiries: 2

2. Binary Center of Mass
Balance
point

3. Binary Separation
a = rA + rB
Visual
Binary
Star

4. Spectroscopic Binary
From Doppler Shift

5. Spectroscopic Orbit
This represents the orbit of the star that is farthest
from the center of mass. Its velocity amplitude is
higher. It is the lower mass star.
Velocity
Time

6. Spectroscopic Orbit
This represents the orbit of the star that is closest
to the center of mass. Its velocity amplitude is
smaller. It is the higher mass star.
Velocity
Time

7. Spectroscopic Parameters
Center of Mass
Low Mass Star Velocity Amplitude
High Mass Star Velocity Amplitude
Velocity
Time

8. Inclination K velocity = amplitude of radial velocity (m/s)
Doppler effect is maximized for an “edge-on” system;
non-existent for a “pole-on” system.
Inclination ~ 90o
Inclination ~ 0o

9. Inclination K velocity = amplitude of radial velocities v sin(i)
v = velocity
i = 90 degrees, edge on
i = 0 degrees, pole face

10. Spectroscopic Parameters
g velocity = velocity of Center of Mass (CoM)
K velocity = amplitude of radial velocity (v sin i)
P = period
Mass ratio M2/M1 = K1/K2
Smaller star orbits farther from the CoM,
Larger star is closer from the CoM.
Smaller star has large K velocity.

11. Center of Mass Velocity?
Spectroscopic Orbit
Center of Mass Velocity?

12. Spectroscopic Orbit
Orbital Period?

13. Spectroscopic Orbit

14. Spectroscopic Orbit
K velocities?

15. Spectroscopic Orbit
K2 = = 75

16. Spectroscopic Orbit
K1 = = 25

17. One Star is 3 times more massive than the other.
K2/K1= M1/M2 = 75/25 = 3
One Star is 3 times more massive than the other.
Spectroscopic Orbit

18. Eclipsing Binary Light Intensity variations are observed
because of blocking of light by each of the
stars in the system if inclination is large enough.
Systems are edge-on or nearly edge-on as seen from
earth. (i.e. inclinations are ~ 90 degrees)

19. Algol (b Perseus)
Light Curve
Light Intensity
versus
Time

20. Eclipsing Binary Light Curve

21. Eclipsing Binary Light Curve
LA + LB
LA + LB
LB + f LA
LA Only

22. Eclipsing Binary Light Curve
LA + LB
LA + LB
LB + f LA
LA Only

23. Eclipsing Binary Light Curve
LA + LB
LA + LB
LB + f LA
LA Only

24. Eclipsing Binary Light Curve
LA + LB
LA + LB
LB + f LA
LA Only

25. Simple Eclipsing Binary

26. Unequal Temperature and Size

27. Star Spots

28. Light Curve Fit

29. Light Curve Varieties

30. Light Curve Contacts

31. Light Curve Contacts Time interval (t2 - t1) ~ size of “orange” star

32. Light Curve Contacts Time interval (t3 - t1) ~ size of “yellow” star

33. Size Determinations 2 RA = (VA+VB ) ( t2 - t1 )
2 RB = (VA+VB ) ( t3 - t1 )
Velocities obtained from spectroscopic orbit.
Contact times obtained from eclipse light curve.
The radii of the stars are then calculated to yield their
size.

34. Determining Radii

35. Intrinsic Luminosity L = 4pR2sT4
Radius obtained from spectroscopic orbit with
eclipse light curve.
Temperature obtained from observations of spectrum.

36. Fundamental Stellar Parameters
Spectra
Distance
Temperature
Chemical Composition
Luminosity (if distance is known)
Velocity
Binaries
Orbital Velocities
Sizes
Masses
Luminosity

37. Fundamental Stellar Parameters