1. Binary Stars Astronomy 315 Professor Lee Carkner Lecture 9

2. Masses of Stars  While we can find the radius of a star from the Stefan-Boltzmann Law, we still do not know the mass  How do you find mass?  On Earth we weigh things  Weighing means measuring how gravity affects the object  How can we weigh things in space?  Watch how the star moves under the influence of the gravity of another star

3. Binary Stars  Most stars are in multiple systems  Our own sun is an exception  How do we find binary stars?  Some stars appear to be very close together on the sky  Called optical doubles  May just be a projection effect  We want stars that are gravitationally bound  In orbit around each other

4. Visual Binaries  The simplest type to observe are visual binaries  You can see one star orbit around another  The periods of such stars are often very long  Have to observe for decades to plot the orbit  Most visual binaries have a relatively stationary bright star and a moving fainter star

5. Binary Motion of Castor

6. Problems with Binaries  Period and Separation  In order to resolve the stars they have to have a large separation, but his also means a long period  Inclination  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  What can we measure?  Orbital period  The time for one complete orbit  Orbital radius  The distance from each star to the center of mass  Need the distance to the binary from parallax first  What do we do with this information?  Need to understand gravity

9. Kepler’s Laws  In the early 1600’s Johannes Kepler published his laws of planetary motion  His first laws states that planetary orbits are elliptical  The longest axis of the ellipse is called the major axis (1/2 of it is called the semi-major axis a)  His third law states that the period (P) of the planet’s orbit (in years) squared is equal to the semi-major axis in astronomical units (AU) cubed (1 AU is the Earth-Sun distance) P 2 = a 3

10. Kepler’s Laws

11. Kepler and Newton  Kepler did not know why his laws worked  In the late 1600’s Isaac Newton used Kepler’s laws to develop his theory of gravity  The orbits of planets obey the Law of Universal gravitation  Gravitational force depends on mass  We can use Newton and Kepler’s laws together to find the mass of binary stars

12. Finding Masses  We can write a version of Kepler’s third law for binary stars: M A + M B = a 3 /P 2  where:  M A + M B is the combined mass of both stars in solar masses (M sun )  a is the semi-major axis of the orbit in astronomical units (AU)  P is the period of the orbit in years (yr)

13. Problems with Mass Determination  Our formula only gives us the sum of the masses  However, we can find the ratio of the masses by finding the distance to the center of mass for each star  Examples:  If one star is basically stationary, it has all the mass (like the sun and earth)  If both stars are equally distant from the center of mass they have the same mass  Ratio of mass is inverse ratio of distance to center of mass

14. Center of Mass Distances

15. Spectroscopic Binaries  There are very few visible binaries in the sky, so we have very few mass measurements  We have to try and find binaries in other ways  Easier to find double line spectroscopic binaries  We can’t resolve two individual stars (they are too close together)  however, we see two sets of spectral lines

16. Spectroscopic Binary Motion  What information can we get about the orbit if we can’t see it?  Can get the velocity of the orbit from the Doppler shift  More shifted the lines the faster the star is moving in its orbit  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  The big problem with spectroscopic binaries is we do not know the inclination  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  We can get masses of stars statistically  Assume a random distribution of inclinations

20. Masses of Stars  Compare mass to position on HR diagram  Main sequence:  Cool, dim stars (red dwarfs) have low mass (M ~ 0.3-0.8 M sun )  Medium-bright yellow stars have solar masses (M ~ 0.8-2 M sun )  Hot, bright stars have high mass (M ~ 2-40 M sun )  White dwarfs  Mass about equal to sun  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  Large mass. Large luminosity  White dwarfs are very dense  Solar mass in object the size of the Earth  Giants have low density  Generally much larger than main sequence stars of the same mass

23. Next Time  No homework Monday  First quiz on Monday  Covers all material since start of course through today  Multiple choice and short essay  Short essay include both written and problems  Be able to solve problems like the exercises and be able to write a paragraph explanation of key concepts  Study notes, exercises and readings  Study hard