1. Pulsating Variables

2. Cepheid Variables Discovered by J. Goodricke (1784): Prototype:  Cephei Light curve of  Cephei

3. Cepheid Variables: The Period-Luminosity Relation The variability period  of a Cepheid variable is positively correlated with its luminosity: M V = -2.80 log 10  d – 1.43

4. Cepheid Variables as Distance Indicators Measuring a Cepheid’s period  determine its absolute magnitude  Distance indicator! Cepheids are Ib supergiants, L ~ 10 3 - 4 L 0 => Identifiable out to several Mpc!

5. The Instability Strip Classical Cepheids W Virginis Stars: metal-deficient (Pop. II), Cepheid-like RR Lyrae Stars: Pop. II; horizontal-branch; nearly standard-candle luminosity!  Scuti Stars: Evolved F stars near MS Increasing Period

6. Stellar Pulsations Estimate from sound travel time through the star:  -1/2 Cepheids all have approx. the same surface temperature. => Higher L => Larger R => Smaller  => Larger 

7. Radial Pulsations

8. The Valve Mechanism Nodal zone is opaque and absorbs more radiative flux than necessary to balance the weight from higher layers. => Expansion Upon expansion, nodal zone becomes more transparent, absorbs less radiative flux => weight from higher layers pushes it back inward. => Contraction. Upon compession, nodal zone becomes more opaque again, absorbs more radiative flux than needed for equilibrium => Expansion

9. Temperature [K] log  R [cm -1 ])  R ~  T -7/2 Kramer’s Opacity Law 10 4 10 5 10 6 10 7 Gas gradually becoming ionized Gas fully ionized; opacity dominated by free-free absorption For the valve mechanism to work:  needs to increase with increasing  and T → Partial Ionization Zones!

10. Location of Partial Ionization Zones ~ 10 4 K ~ 4x10 4 K Instability strip: Walve mechanism driven by He partial ionization zones LPVs: Valve mechanism driven by H partial ionization zones

11. Non-Radial Modes of Variability: g-modes: f net = (dF/dV) net = g (  s –  b ) surrounding medium (‘s’) bubble (‘b’)