1. Variable Stars Eclipsing binaries (stars do not change physically, only their relative position changes) Nova (two stars “collaborating” to produce “star eruption”) Cepheids (stars do change physically) RR Lyrae Stars (stars do change physically) Mira Stars (stars do change physically)

2. Binary Stars Some stars form binary systems – stars that orbit one another –visual binaries –spectroscopic binaries –eclipsing binaries Beware of optical doubles –stars that happen to lie along the same line of sight from Earth We can’t determine the mass of an isolated star, but of a binary star

3. Visual Binaries Members are well separated, distinguishable

4. Spectroscopic Binaries Too distant to resolve the individual stars Can be viewed indirectly by observing the back-and-forth Doppler shifts of their spectral lines

5. Eclipsing Binaries (Rare!) The orbital plane of the pair almost edge-on to our line of sight We observe periodic changes in the starlight as one member of the binary passes in front of the other

6. Cepheids Named after δ Cephei Period-Luminosity Relations Two types of Cepheids: –Type I: higher luminosity, metal-rich, Pop. 1 –Type II: lower lum., metal-poor, Population 2 Used as “standard candles” “yard-sticks” for distance measurement Cepheids in Andromeda Galaxies established the “extragalacticity” of this “nebula”

7. Cepheids Henrietta Leavitt (1908) discovers the period-luminosity relationship for Cepheid variables Period thus tells us luminosity, which then tells us the distance Since Cepheids are brighter than RR Lyrae, they can be used to measure out to further distances

8. Properties of Cepheids Period of pulsation: a few days Luminosity: 200-20000 suns Radius: 10-100 solar radii

9. Properties of RR Lyrae Stars Period of pulsation: less than a day Luminosity: 100 suns Radius: 5 solar radii

10. Mira Stars Mira (=wonderful, lat.) [o Ceti]: sometimes visible with bare eye, sometimes faint Long period variable star: 332 days period Cool red giants Sometimes periodic, sometimes irregular some eject gas into space

11. Spectroscopic Parallax Assuming distant stars are like those nearby, –from the spectrum of a main sequence star we can determine its absolute luminosity –Then, from the apparent brightness compared to absolute luminosity, we can determine the distance (B  L / d 2 again!) Good out to 1000 pc or so; accuracy of 25%

12. Distance Measurements with variable stars Extends the cosmic distance ladder out as far as we can see Cepheids – about 50 million ly In 1920 Hubble used this technique to measure the distance to Andromeda (about 2 million ly) Works best for periodic variables

13. Cepheids and RR Lyrae: Yard-Sticks Normal stars undergoing a phase of instability Cepheids are more massive and brighter than RR Lyrae Note: all RR Lyrae have the same luminosity Apparent brightness thus tells us the distance to them! –Recall: B  L/d 2

14. Studying for EXAM III On Sun and Stars Many chapters in book, which has way too many details  lecture notes Focus on the general, repeating features Emphasis on concepts and reasoning (Why are more massive stars hotter, etc.)