Variable Stars

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 / d2 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/d2

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.)