1. Binary Stars Astronomy 315 Professor Lee Carkner Lecture 9

2. Masses of Stars   How do you find mass?   Weighing means measuring how gravity affects the object   Watch how the star moves under the influence of the gravity of another star

3. Binary Stars  Many stars are in multiple systems   How do we find binary stars?   Called optical doubles  May just be a projection effect   In orbit around each other

4. Visual Binaries  The simplest type to observe are visual binaries   The periods of such stars are often very long   Most visual binaries have a relatively stationary bright star and a moving fainter star

5. Binary Motion of Castor

6. Problems with Binaries   In order to resolve the stars they have to have a large separation, but his also means a long period   The orbit is not exactly face on to you, so you see its projection onto the plane of the sky

7. Inclination Effects

8. Using Binary Stars  Orbital period (P)    Orbital radius (r A and r B )    The center of mass is the common point around which they both orbit  Need the distance to the binary from parallax first

9. Center of Mass Distances

10. Ratio of Mass  M A /M B = r B /r A  The more massive star is closer to the center of mass  Examples:   If both stars are equally distant from the center of mass, they have the same mass

11. Kepler’s 3 rd Law  a = r A + r B  We can relate this to the period via Kepler’s 3 rd Law: M total = M A + M B = a 3 /P 2  where:   a is the semi-major axis of the orbit in astronomical units (AU), 1 Earth-Sun distance  P is the period of the orbit in years (yr)

12. Orbits Star A Star B Center of Mass a x rBrB rArA

13. Finding Masses  M A = (M total )(r B ) / (r A + r B )  Where again mass is in solar masses and r is in AU   Newton “discovered” gravity by thinking about Kepler’s laws  He showed that gravitational force depends only on mass and distance

15. Spectroscopic Binaries   We have to try and find binaries in other ways   We can’t resolve two individual stars (they are too close together)  however, we see two sets of spectral lines

16. Spectroscopic Binary Motion   Can get the velocity of the orbit from the Doppler shift   Can also get the period of the star from the Doppler shift  Time for Doppler shift to go from zero to max away to zero to max towards to zero

17. Spectroscopic Binary in Action

18. Velocities of Binary Components

19. Spectroscopic Binary Masses   Velocities highest in edge-on system and go to zero in face-on system  We only see component of Doppler shift for motion towards and away from us   Assume a random distribution of inclinations

20. Masses of Stars  Compare mass to position on HR diagram  Main sequence:   Medium-bright yellow stars have solar masses (M ~ 0.8-2 M sun )   White dwarfs   Giants  Large range of masses

21. Masses on the HR Diagram

22. Mass Distribution  There is a relationship between mass and luminosity for main sequence stars: L = M 3.5   White dwarfs are very dense   Giants have low density 

23. Next Time  No homework due Monday  But there is homework due Wednesday  First quiz Monday!  Study guide on web page  Bring (real) calculator and pencil