1. Inferring Stellar Masses: Binary Systems More than 50 % of all stars are part of multiple systems. a) Visual Binaries: Both components observed directly. b) Astrometric Binaries: Only brighter member can be observed; astrometric oscillations

2. c) Eclipsing Binaries In addition to stellar masses, infer relative temperatures and radii Inclination ~ 90 o

3. d) Spectrum Binaries Approaching star: blue shifted lines; Receding star: red shifted lines Doppler shift → Measurement of radial velocities → Estimate of separation a → Estimate of masses Two superimposed, discernible spectra from the 2 stars; periodic, opposite shifts:

4. Time

5. e) Spectroscopic Binaries Periodic Doppler shifts. Only one star and one absorption line system seen; → Place limits on the mass of the unseen component { 

6. Visual Binaries The Ideal Case Basically all parameters can be determined: M2M2 M1M1 a2a2 a1a1 observer i

7. Eclipsing Binaries i ≈ 90 o sin i ≈ 1 f(M) ≈ M 2 3 /(M 1 + M 2 ) 2

8. Estimating Radii and Temperatures in Eclipsing Binaries Brightness B Time t B0B0 BsBs BpBp tata tbtb tctc tdtd

9. Masses of Stars in the Hertzsprung- Russell Diagram 0.5 18 6 3 1.7 1.0 0.8 40 Masses in units of solar masses Low masses High masses Mass The higher a star’s mass, the more luminous (brighter) it is: High-mass stars have much shorter lives than low-mass stars: Sun: ~ 10 billion yr. 10 M sun : ~ 30 million yr. 0.1 M sun : ~ 3 trillion yr. L ~ M 3.5 t life ~ M -2.5