1. BINARY STARS How they help us to determine the mass of stars and the size of our galaxy.

2. How do they form?

3. Mizar A and B are visual binaries.

4. The very bright star, Sirius, is actually a visual binary, too. Sirius is the main star in the constellation Canis Major, so it is called Alpha Canis Majoris. It is actually a blue- white giant (A) with a white dwarf companion (B). The elliptical orbit has been well-plotted out. ORION SIRIUS

5. The orbit of Sirius B:

6. Revolution around the center of mass In reality both objects revolve around a common point, known as the center of mass. The center of mass is closer to the more massive object and farther from the less massive one.

7. Binary star orbits are usually double ellipses: The center of mass () is close to the massive blue star. It revolves around in a small elliptical orbit. yellowThe less massive yellow star revolves in a much larger orbit. Notice the pattern of a binary system in motion. Visual Binary Animation

8. 20 = 4 5 1 4:1 ratio in mass Ratio of the masses Star A Star B 5 AU20 AU D B = M A D A M B

9. Kepler’s Law….Modified In the Solar System, we ignore the mass of the sun and the planets (since M 1 = 1 and M 2 is very small). With binary stars, the masses must be taken in account. If we know D and P, we can determine the masses of both stars.

10. Finding the masses of binary stars with Kepler’s Law M 1 + M 2 = D 3 P 2 M A + M B = 10 3 5 2 M A + M B = 1000 ÷25 = 40 suns Star A Star B D = 10 AU P = 5 yrs M A = 32 suns M B = 8 suns

11. Eclipsing Binary Stars The stars have different luminosities, and they eclipse each other as they revolve around the center of mass.

12. The stars are too close to be seen separately. When an eclipse occurs, you can tell which star is brighter. The flat bottoms (2,4) indicate that one star is smaller than the other. When the cycle repeats, you can tell the period of revolution. Eclipsing Binary Animation

13. Spectroscopic Binaries We can’t see their orbits or see eclipses, but we can observe Doppler shifts in the spectrum. These shifts occur when stars move toward us (blue shift) or away from us (red shift).

14. Revolving Stars cause Doppler shifts only when moving away or toward the observer. The larger the shift the higher the velocity. Spectroscopic Binary Animation

15. How does this help us with non- binary stars? It can help to determine their masses, luminosities, and their distances from Earth. K3 star

16. Find luminosity from the H-R Diagram The K5 (orange star) has a luminosity of 0.1 (10 -1 ) suns.

17. Mass-Luminosity Graph Since the luminosity of this K5 star is 10 -1 (0.1) its mass is around 0.6 sun. This is a red-orange dwarf (on the main sequence). This method works only for main sequence stars.

18. Distance is found from the difference between the apparent and the absolute magnitudes by the formula: D = 10 (Mapp - Mabs + 5)/5 D = 10 (2 - 7 + 5)/5 = 10 0 = 1 parsec L = 0.1 M abs = 7 M app = 3

19. Try this yourself! You find an A0 star. Use the H-R diagram to find its luminosity. Then find its mass from this graph.

20. Now find the distance… What is its absolute magnitude? Suppose we see this star as a fifth magnitude star. Substitute into this formula: D = 10 (Mapp - Mabs + 5)/5

21. Hate Math? Try this method… Determine the difference between the apparent and absolute magnitude of this A0 star. Then read the result off of this graph.

22. CONCLUSIONS! From the study of binary stars we can determine the masses of stars. If we know the mass of a main-sequence star, we can determine its luminosity from a graph or by formula. The H-R diagram can be used to find absolute magnitude, temperature, and spectral class. We can estimate the distance of the star from the magnitude difference graph, or by using the second formula.